20 ms·

Why are D-sharp and E-flat considered to be two different notes?

368 points by tobr 4y ago

iainctduncan 4y ago
Because one is a raised D and the other a lowered E. Shit hunny... (flippant, but also accurate! of course explaining why that matters is a whole different beast. Lots and lots of good books available though...)
wizofaus 4y ago
Try sight reading something in D# major and that should tell you the difference!
petewailes 4y ago
Obviously Ethan knows this and just isn't going into it because this is more a history lesson than a theory lesson, but the same applies to white keys. So B♯ and F♭ are perfectly valid notes. C♯ major for example contains B♯, despite that there's no black key between B and C.
- chrismorgan 4y ago
  For that matter, F𝄪 (F double sharp) and A𝄫 (A double flat) are both legitimate alternatives/equivalents to G in some situations, by extrapolating the sequences. (And if you extrapolate far enough, any note has multiple possible alternatives—for example, you could get a G♮ that’s kinda more G♯♭ or G♭♯ than just straight G, to use super fuzzy terminology.)
seanhunter 4y ago
Short answer: they aren't. This is the musical equivalent of the fact that English has "guarantee" and "warranty" and they mean the same thing. Long answer: they aren't. They are enharmonic equivalents in the vast majority of music that uses any of the conventional Western systems of tuning (as the author sort of goes out of their way to demonstrate in the article), and if you use or invent a different system then what you call the notes is kind of up to you since it's your system.
- midenginedcoupe 4y ago
  Correct answer: they are. Not on a piano, but for all the other instruments with variable pitch (e.g. fretless strings, voice, trombones) they are. The enharmonic is useful information and we'll know whether to place that note just a little under or above its usual pitch to make the chord more in tune. We don't need to invent a new system to do this, we do it every day within the 12-tet system we already have.
  - seanhunter 4y ago
    Theoretically yes but actually not really. Most of the time, even if you're playing a variable pitch instrument you're going to be tuning to fixed pitch because you'll have at least one fixed pitch instrument (eg a piano) and if you don't you'll just sound out of tune. In cases (eg a consort group or string quartet or something) where you're all variable pitch, you'll be tuning to each other and to the scale/key as appropriate to the music and whatever sounds good. You may well sweeten the thirds or widen the fifths a bit etc but that doesn't apply to this question here because you're really not going to see the enharmonic equivalents in the same piece the absolute vast majority of the time for stylistic reasons and if you ever did you would just be tuning to each other to make the vertical incidences sound good rather than thinking consciously of tuning a d-sharp one way and an e-flat another way. Source: Have a degree and postgrad in music, used to be a professional double bass player[1], spouse has a degree and postgrad in music and teaches at 2 conservatoires in London as well as performing professionally, mostly early music in small consort groups where this sort of tuning thing comes up a lot. [1] So yeah you can make the standard joke about what do double bass players know about tuning.
    - midenginedcoupe 4y ago
      Sometimes yes, sometimes no. Even if playing with a fixed-pitch instrument, it only really sounds out of tune if they're playing the same notes. Which in the styles I play isn't an issue. So I guess how often this happens in practice varies between styles and eras of music, which would make sense to me. I haven't ever done early music and know nothing about it (other than trombones used to be designed terribly and we now know how to make better ones ;) Source: Also have a postgrad in music, probably from one of the conservatories your spouse teaches at, and still play trombone professionally.
im3w1l 4y ago
> The usual answer is that you are only supposed to use each letter name once in any given scale. And why is that important? Answer: This lets you write the key signature once, and then not have to bother with accidentals in front of notes.
- thaumasiotes 4y ago
  Well, no, that would only work if you were committed to never using notes that weren't in the key signature. That would be an unusual choice.
  - im3w1l 4y ago
    Not having to use accidentals for in-key notes still reduces the needed number substantially.
  - iainmerrick 4y ago
    Right, but if your tune mostly uses conventional major and minor scales (which most do!) you mostly won’t need accidentals. Also, you’ll be able to transpose to any other key just by shifting the letter names up or down and changing the key signature. That’s a really interesting and useful property. Also also, the notes with accidentals won’t change when you transpose (although the accidentals themselves will need rewriting). Transposing music would be hellish without this system!
  - PeterisP 4y ago
    Depends on the music genre probably, there are oh so many song arrangements that never use notes outside of the key signature.
- dahart 4y ago
  Perhaps more succinctly, you always write any two consecutive notes of a diatonic scale on two different lines of the staff. It would be bad if your in-key scale looked like it had two notes on the same line and then a jump of a third. Note this is true even when you have accidentals! It’s a way to keep the intention or semantics of notes more clear, and more easily readable, regardless of the pitch interval. Like how the article talks about the distinction between an augmented 2nd and a diminished 3d, the notation is designed to help clarify that distinction.
powersnail 4y ago
The explanation of enharmonic equivalent (though the author didn't use this term) is right, but I do take problem with this sentence: > but what musical difference does it make? In the present day, the answer is, none whatsoever. This is not quite right. On all fretless instruments, including most bowed strings and the human voice, enharmonic equivalent notes still have different pitches. The subtle differences in intonation is incredibly important and noticeable on the violin, for example.
- VBprogrammer 4y ago
  Out of interest, is this still the same when a violin is playing alongside fretted instruments? Wouldn't they sound out of tune in that case?
  - wumpus 4y ago
    Some players of fretted instruments move the frets to match individual pieces of music. In modern rock music, some musicians will change guitars every song to have sweeter chords depending on the particular chords in that song.
    - coldtea 4y ago
      Which "modern rock musicians" do that? It surely is not widespread in rock. Rock musicians change guitars (in a live or even studio situation) mostly to get a different sound or a different tuning (like going from "standard" to an open tuning). Not for microtuning adjustments, or because they have moved the frets to match an individual piece. Some prog musicians might do it, but it surely is not a "rock" custom. In arabic music, on the other hand, or renaissance music, and other genres, it is, and instruments there often have movable frets.
      - gromgull 4y ago
        Not moving the frets, but changing guitar: https://youtu.be/Daw93bRHe4Y https://youtu.be/Daw93bRHe4Y
ur-whale 4y ago
Are they the same frequency? Can most humans hear a difference? Do we need more than the two questions above?
- midenginedcoupe 4y ago
  Are two competing programming languages Turing-complete? Can end-users of the program tell which one was used? Do we need more than the two questions above? If programmers thought like this HN would be empty!
- swores 4y ago
  It would be possible for most humans to notice something but feel indifferent, or for a sizeable minority to really hate something. So just abstractly I'd say that yes you do need more than those two questions.
- PeterisP 4y ago
  No, and yes. The difference is obvious even those who don't distinguish pitches much (can you hear the difference in the video linked in the article - https://www.youtube.com/watch?v=7GhAuZH6phs&t=21s https://www.youtube.com/watch?v=7GhAuZH6phs&t=21s ) because the 'wrong' one played in a scale or a chord sounds really, really horrible; that's why we have all the work done on 'tempered' tuning to reduce the gap so that everything is just slightly off.
- vnorilo 4y ago
  The relationship between pitch and frequency is not simple. The physical frequency for a pitch can be derived in several ways. One example is the Pythagorean system where the interval of fifth is set as a frequency ratio of 3/2. This system yields clearly distinct frequencies for D# and Eb. In 12 tone equal temperament, a semitone is set as a frequency ratio of 2^(1/12). In this system you get the same frequency. You can also derive frequencies from simple fractions of the scale root. In this instance you would generally obtain D# and Eb from unrelated roots.
rawling 4y ago
Can't D# and D# be two different notes too, depending on what key you're in? Hell, doesn't this apply to the white keys too?
- tgv 4y ago
  By that kind of logic, D# in the key of G# should indeed sound different than D# in the key of C# or B, depending on the temperament.
- TheOtherHobbes 4y ago
  Yes, depending on the temperament. Not in 12-TET because the ratio between every semitone is the same. In other temperaments the frequency of every note can be different in every key.
MikeBattaglia 4y ago
There is some basic information that is very wrong in this article. For example: "My track is tuned in a system called five-limit just intonation via the magic of MTS-ESP. It’s the basis for all the tuning systems used in Western Europe between about 1500 and 1900." No - at no point in the last 500 years was 5-limit just intonation ever the predominant tuning system used anywhere in Western Europe. The real predominant tuning system was called "meantone temperament," to which this article sadly devotes only about 3 words - and those words are only about 12 tone meantone keyboard layouts, not about the bigger, abstract idea of meantone temperament in general as it was understood and taught by practitioners of the day. There is a very important difference between meantone and just intonation. The goal of meantone was to have four tempered perfect fifths (approximately a 3/2 frequency ratio) add together to approximate the fifth harmonic (or a 5/1 frequency ratio). Thus, the major third from the circle of fifths would approximate a 5/4 ratio with the tonic, and the major chord would approximate a very crunchy sounding 4:5:6 ratio. In order to do this, fifths are all flattened slightly to make the tradeoff - flattening the fifths by 1/4 of a "syntonic comma" was typical, or "quarter-comma meantone". Even though keyboard instruments evolved in a more well-tempered direction, meantone was the way that teachers of the common practice era (such as Leopold Mozart) still taught and thought about this stuff. Meantone sounds noticeably different from just intonation, where the major third from the circle of fifths is a syntonic comma sharp of a 5/4 ratio (about 22 cents). In just intonation, if you want your major chords to be 4:5:6, you need to bring in this other, different, independent 5/4 major third that is not on the circle of fifths. As a result, certain chord progressions that are common in Western music will tend to exhibit strange sounding "comma drifts" if you play them in just intonation. Adam Neely has a good video on "Benedetti's Puzzle" about this for those who are interested. Of course, there is nothing wrong with just intonation, and comma shifts can sound interesting if you want to deliberately use them in some kind of modern microtonal setting, but it simply isn't the tuning historically used in common practice Western music. Anyway, though, if you go through the article with a marker and replace all instances of "just intonation" with "meantone," the general idea is mostly correct.
- ethanhein 4y ago
  Hi, I'm the author of the blog post. I said that 5-limit is the basis for systems like meantone, which is true. Meantone systems take 5-limit as their starting point and then modify it. I deliberately skated over the specifics of how meantone works on purpose, because I have too much experience watching my students' eyes glaze over when I talk about this kind of thing. I'm trying to strike a balance between giving correct information and not turning people away.
tobbob 4y ago
It's the same note, but musicians are anoraks. I know because I used to be one.
- klodolph 4y ago
  Kind of like saying that “cell” and “sell” are different words. Obviously they’re different words, even though you can’t hear the difference. Just like it’s obvious that Ab and G# are different notes, even though they may sound the same. Ask an English speaker to interpret a text about a sails man who sales around the world and cells sell phones, at have price for any guessed who sends him a facts to his office in grease. It’s harder to read when you use the wrong words, just like how a score is harder to read if you use the wrong notes.
  - tobbob 4y ago
    No
alex_smart 4y ago
The distinctions between D-sharp and E-flat only make sense in the context of a key. For instance, you construct a major key in E-flat and not D-sharp for the practical need to represent the scale nicely on the staff - so each tone in the scale should have a unique place in the staff. You can construct the E-flat major scale with just three flat tones (Eb F G Ab Bb C D), whereas you would need four sharp and two double-sharp(!) tones if you started with D# (D# E# F## G# A# B# C##). And having to use F## and C## to refer to G and D tones is just ugly. (I had made a mistake in the earlier version of this comment.)
- tuukkah 4y ago
  > Also, having to call the G tone F# is just ugly. I presume you mean having to call the F tone E#.
  - alex_smart 4y ago
    Sorry, I had made a mistake. Wanting to create a major key starting with D# would end up looking like D# E# F## G# A# B# C##. The ugliness is even more stark. - two double sharp keys - F## to refer to G, C## to refer to D, B# to refer to C Yikes.
    - klodolph 4y ago
      D# would be extremely rare. I’ve only ever seen G#, and that was a temporary modulation within something larger. Most people write “x” for double-sharp, instead of ##, in order to match how it looks on a score.
- klodolph 4y ago
  Sometimes you call a G as F double-sharp. I don’t think of it as ugly. It’s just what happens sometimes. Like if you start in G# minor and then use the leading tone. It’s way better to see F-double sharp than to see two different Gs fighting each other on the page. And it’s even worse to have to decipher those awful chromatic systems that are all painful to read.
cmur 4y ago
As a former jazz musician, I always find the classical perspective on theory interesting. This article touches on Pythagorean tuning techniques, which if you ever find yourself in front of a good a cappella choir, they’ll be tuning to the true temperament tuning scheme described here. A fun comparison to make in the jazz world is enharmonic usage for the purpose of readability. Jazz chords are very dense and short lived compared to the very clean and predictable counterpoint found in classical music, so “correctness” doesn’t really matter as much. Most charts are sight read, so even though the band is sounding some flavor of a B chord, if you’re playing the 3rd, there’s a chance there may be a written E flat instead of a D sharp simply because E flat is a more commonly written note for horn players.
- klodolph 4y ago
  Pythagorean tuning is somewhat different from what’s described. In Pythagorean tuning, your E would be 81/64 above C, or equal to four fifths minus two octaves. This is slightly higher than E in the article, and the difference (81/80) is called the syntonic comma. Different tuning systems were invented in order to resolve this discrepancy, and without these advances, jazz would be radically different. One of the things about jazz is that you see distant movements that only really make sense as enharmonics—like how Coltrane’s “Countdown” uses the familiar ii-V-I, but modulates in major thirds, which only makes sense when you allow the final modulation te be the same as the first—something that only works enharmonically.
  - cmur 4y ago
    For sure, the broad similarity I’m trying to touch on is the focus on mathematical resonance and context of a key. Equal temperament removed a lot of that context, but definitely opened the door for further harmonic experimentation. Giant Steps is also a good example of what you’re talking about too.
  - ethanhein 4y ago
    I'm the guy who wrote the blog post, and I want to offer some clarity. Usually when people say "Pythagorean" tuning they are talking about three-limit just intonation, not five-limit. In three-limit, the major third is indeed tuned to 81/64, which sounds pretty terrible. That might explain why medieval people thought thirds were a dissonant interval. Five-limit just intonation tunes major thirds to 5/4.
userbinator 4y ago
I went to the Wikipedia link in the article to https://en.wikipedia.org/wiki/Five-limit_tuning https://en.wikipedia.org/wiki/Five-limit_tuning and saw that the first example there shows two very slightly different frequencies, which is a good way of setting the stage for reading the rest of the article.
perihelions 4y ago
The paradox is that you can't create a theory of music whose notes are both (a) evenly spaced and (b) contain the integer ratios. You want (a) because it you gives you nice algebraic properties (the music structure is invariant under frequency shifts). You want (b) because small-integer ratios are pleasant sounding -- partly culturally-acquired taste, partly because physics gives musical instruments acoustic spectra in integral multiples of a fundamental frequency: f, 2f, 3f ... nf. Small-integer ratios are naturally occurring and very recognizable. Modern tuning (C-f "12-TET" in the article) almost, approximately satisfies (a) and (b) simultaneously. "12" means there's twelve tones between f and 2f; the ratio between adjacent tones is defined to be 2^{1/12}. This tuning can't contain both f and 3f (so it fails (b)), but it *can* contain f and 2^{19/12}f ~ 2.9966f, which is actually close enough to 3f to be indistinguishable. (Almost works!) But as you build ratios out of larger integers, it audibly falls apart. The closest you can get to (5/3)f is 2^{9/12}f = ~1.6818f, which is already 10% of the way to the next note. And it rapidly gets worse. This is why two on-paper-identical notes can end up audibly different, depending on what key you're starting with (and hence how they are approached). There's tension internal to music theory itself.
- deleted 4y ago
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- noncovalence 4y ago
  In the context of the difference between D# and Eb, 19-TET is very interesting to play around with. It adds an extra black key between every pair of white keys, and most songs intended for 12-TET still work fine, as long as you play sharps and flats as written. If you play a D# instead of an Eb, you suddenly get a very different sounding interval.
  - bonzini 4y ago
    Also as long as sharps and flats are written in a very pedantic manner. For example a diminished C chord only sounds "right" if it's notated as C-E♭-G♭-B♭♭ rather than C-E♭-G♭-A. On top of this, harmony may or may not work the same in 19-TET and 12-TET. With the same example of diminished chords, the diminished chord does not divide the octave in four equal parts in 19-TET. Adim and Cdim are enharmonic in 12-TET, but Adim in 19-TET is A-C-E♭-G♭♭; that is, only C and E♭ are the same.
fxtentacle 4y ago
Because for most instruments, it is. A violin player won't move up for a full half tone for a D sharp, so there'll remain a small pitch difference between them. It's only for the small subset of keyed instruments like pianos that pitch is quantized into 12 subtones. But even there, organs use a different pitch to key mapping than keyboards. For a very interesting rabbit hole, search for "Wolfsquinte", which is a chord that sounds nice on keyboard but horrible on organ.
- wumpus 4y ago
  I am not aware of any manuscript having different tuning of organs vs other keyboards in the Renaissance or Baroque eras... can you cite one? The Wikipedia article for Wolfsquinte makes it clear that it has nothing to do with keyboards or organs: it's a feature of your choice of tuning. Perhaps you're used to organs and keyboards with different tuning choices?
  - CHY872 4y ago
    I don't think that's quite GP's claim. They're not necessarily saying that organs and keyboards of the same heritage had different tuning (though it's well documented that instruments had different tuning according to region even through the 1700s and 1800s), rather that historic organs which retain their original temperament sound very different to modern keyboards. Here's an article supporting this. It refers to different rates of beating in different tuning regimes, comparing equal temperament to 'cornet-ton' type things. Because it's common for organs to be hundreds of years old, and it's common for people to want historic organs to sound as close to how they did when they were made as possible because it's uncommon for them to play in non-vocal ensemble, this leads to a relatively common situation where an organ played today may well be tuned very differently to a piano played today. Depending on the organ. https://www.eunomios.org/contrib/francis2/francis2.pdf https://www.eunomios.org/contrib/francis2/francis2.pdf Here is a second article on organs by one manufacturer tuned in 'meantone' https://www.bach-cantatas.com/Topics/Meantone.htm https://www.bach-cantatas.com/Topics/Meantone.htm. It's also the case that harpsichords were commonly tuned in meantone https://www.harpsichord.org.uk/wp-content/uploads/2015/04/temperament.pdf https://www.harpsichord.org.uk/wp-content/uploads/2015/04/te... which might actually support the claim that historic non-organ keyboards sounded different from organ keyboards (specifically, if Bach didn't like the mean-tone organs he played and it was common to tune harpsichords in meantone, that would seem to provide some evidence for both temperaments existing and sounding different on the different types of instrument in the same historic period).
jimnotgym 4y ago
I play blues guitar by ear. I don't read music. The people replying to this thread, the person who wrote this blog are so far away from me it is hard to say we inhabit the same field called 'music'. I play a lot of improvised lead lines. I know my pentatonic scale shapes on the fretboard, but I also play lots of notes not in those shapes...because I like the way they sound. I also play a lot of 1/4 tone bends (notes between the piano keys) which don't even fit in the traditional system, but sound good. I say this as it is an interesting case of 'more than one way to skin a cat'
- beardyw 4y ago
  A lot of those in-between notes hark back to times before the scales were rationalised into the "well tempered" system we mostly use today. Often they are harmonics like the 5th harmonic which lives between the minor and major 3rd on the scale.
- fassssst 4y ago
  Same here, I know how to read music and tabs but gave up on it and now just play by ear, it’s way more satisfying. Western music theory is so baroque. The book Brainjo basically killed my interest in it.
- nemo44x 4y ago
  Music is kind of great like that. Much of music theory is over my head but I have spent time to understand a good bit too and I’ve gained a lot of respect for it. Everything you’re doing as a blues guitarist can be explained well by a music theorist who really know their stuff. I read an interesting article by a music theorist breaking down the song “Smells Like Teen Spirit” and remarking on the genius and uniqueness of the chord progression and how it violates a lot of what theory says would “sound good” and hence why it’s genius. It can be presumed Kurt Cobain was not too interested in music theory and if he would have been he may have never even considered the progression and other interesting aspects of that song.
  - PaulDavisThe1st 4y ago
    I've said it before, I'll say it again. It's more productive to think of "music theory" as a way for musicians and composers to talk about what they just did, or what they are just going to do, than as a way to generate those things.
elihu 4y ago
What's weirder is that if you're using just intonation in, say, the key of C major, there's two different D's. One is 9/8, and the other is 10/9. The note we call D in equal temperament is about half-way between the two. If you want to play these chords in C major: Cmaj, Fmaj, Gmaj, Dmin, Emin, and Amin, you'll need to use both of those D's: 9/8 for the 5th of Gmaj, and 10/9 for the root of Dmin. If you try to play Dmin with the 9/8 instead, it sounds absolutely awful. In other words, if you want to play those six chords that are regarded as belonging to C major, you'll need two different D's. Which means the C major scale should really have 8 notes instead of seven. But we don't have a symbol to distinguish between 9/8 and 10/9 in standard notation, they're both just plain D. Some 12-EDO music makes use of the ambiguity between these two notes (or any two notes with the same relation to each other) to string together chord progressions that don't actually make sense mathematically. If you used those progressions in just intonation, you'd find you don't return to the chord you started on, you actually shifted up or down by a small interval of 81/80. It's sort of the musical equivalent of some formula that only works if you assume that pi is equal to exactly three.
psyc 4y ago
I started asking my father, a concert pianist, composer, and teacher - this question when I was 4. He explained. In my head I said, “Bullshit.” I continued to press him on it periodically until I was a teenager. I still shook my head and thought, “What is wrong with these people.” Now, I can read sheet music just fine, but I still feel like … never mind. I’ve done a ton of composing without once taking any notice of what key any of it was in. And it all sounds fucking great. I prefer to do as much as possible “by ear”. I’m unbelievably stubborn. tl;dr - Somebody really should have picked up on the autism when I was 4, and MIDI rolls don’t give a shit about keys and accidentals.
- PaulDavisThe1st 4y ago
  MIDI rolls don't, by themselves, make any noise or even inherently define any note frequencies at all. The frequency of the sound produced by a given synthesizer when it receives any particular MIDI note number is up to the synthesizer. This is part of the point of the MIDI tuning system. The synthesizer and/or the tuning system may very much care about keys and accidentals.
  - deleted 4y ago
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- Nemrod67 4y ago
  do share! I'm a "MIDI composer" myself and love to hear what others do :) obligatory self-promotion, https://www.youtube.com/channel/UCUmdU7WpuhAv3imtVqkGpIA https://www.youtube.com/channel/UCUmdU7WpuhAv3imtVqkGpIA
  - psyc 4y ago
    That's good stuff! Reminds me very, very vaguely of: https://www.youtube.com/watch?v=vapZZdog0NI https://www.youtube.com/watch?v=vapZZdog0NI Here's a small sampler. I include one that's maybe a bit similar, the one called 'crsh' https://soundcloud.com/w37hlwyq0a/sets https://soundcloud.com/w37hlwyq0a/sets
moogly 4y ago
It would be remiss of me not to mention the archicembalo[0], which was a keyed instrument that allowed a musician to experiment with this distinction to a degree. [0]: https://en.wikipedia.org/wiki/Archicembalo https://en.wikipedia.org/wiki/Archicembalo
bazhova 4y ago
Instruments without frets don't have this problem. I played violin for many years. When you play a double stop (two strings at the same time), since there are no frets, you can play true 3rds, 6ths etc. The harmony is so "pure" that it causes a third harmonic to ring (which is how you know you're doing it right). My violin teacher always insisted that e-flat and d-sharp are not the same. When you're playing in different keys you have to put your finger in a slightly different place.
- tadhgpearson 4y ago
  Right. I had this too, but because I never got the explanation this post provides, I had to live with "because it's a different key" - but could never quite understand why it made me out of tune with an accompanying pianist. Now I know... this is awesome!
tomxor 4y ago
I'm struggling to fully understand this tbh, but was recently exposed to these subtle differences when writing a mini organ synth. When implementing the draw bars (dictating the harmonics comprising each key) I realised the true harmonics of a note and neighbouring notes calculated in the 2^n/12 way are sometimes the same and sometimes slightly off... organs just kinda ignore this fact and use the closest neighbouring notes for the draw bars anyway so that they don't need a million different oscillators, so technically the draw bars are just chords on the keyboard using the same oscillators and not harmonics (well some of them happen to be exactly the same as harmonics, others not).
Ninn 4y ago
I recon this Feakonomics podcast includes the answer amongst other interesting related topics: https://freakonomics.com/podcast/mathematician-sarah-hart-on-why-numbers-are-music-to-our-ears/ https://freakonomics.com/podcast/mathematician-sarah-hart-on... It might be worth a listen for anyone who finds the topic interesting, but the answer is obviously already found in the top response too.
daviddever23box 4y ago
tl;dr: The notation system predates the modern, commonly-used 12-Tone Equal Temperament, for which there are (at least two) ways to describe any note within the (12-Tone) octave, either by sharps (D sharp) or by flats (E flat). In 12-TET, there are exactly twelve notes in the octave, and sharps and flats can be said to "overlap". In earlier temperament systems, these notes may have been distinct (or in some cases unavailable), as the relationships between notes were based on non-equal, if not more mathematically perfect, ratios.
coldtea 4y ago
For a similar reason that "upslope" and "downslope" describe walking upon the same stretch of road on a hill: context.
mabbo 4y ago
Given that integer ratios tend to sound better, are there songs edited to use notes that maximize the number of integer ratios rather than the standard tuning? It would seem an easy hack to make people like your new pop track better. But then, I'm no musician, so maybe I'm oversimplifying.
tzs 4y ago
Guitarist might find three videos recently posted to classical guitarist and lutist Brandon Acker's YouTube channel interesting. Lutes and early guitars (before around 1800) did not have metal frets. Instead they used pieces of string tied around the neck. They did this because the strings were very expensive, with a set of strings for a lute often costing more than the rest of the lute, and strings were not as robust as more modern strings. With metal frets strings would wear out faster. You could easily end up spending more per year on strings than you had initially spent on your instrument. By making the frets of the same material as the strings they didn't need to change strings as often. Acker and luthier M.E. Brune took a classical guitar Brune was building but had not yet put frets on and played around with putting on tied gut frets and gut strings. In the first video [1] they just go over the history of tied on frets, and do some comparisons with metal frets. With tied on frets it is relatively easy to try tunings other than 12-TET. You can change the position of a fret, or you can add extra frets. You can also add partial frets. Renaissance lutists would often glue on small pieces of string behind or in front of a fret. The fret would give them some particular note from a sharp/flat pair, and the little mini fret, called a tastino, would give them the other note from that pair. The second video [2] explores the tuning possibilities of tied on frets and tastinos. Acker plays a bunch of things in 12-TET and in other tunings more suitable for the particular piece, and also gives some examples of how bad other tunings can sound when you are playing a piece in a key that doesn't fit the key your instrument was tuned for. The third video [3] is just playing around after the tied on fret experiment is over but the guitar has not yet had its metal frets installed. Acker tries to play it without frets. That turns out the be quite a mixed bag. [1] https://www.youtube.com/watch?v=--y_vf-Kg-w https://www.youtube.com/watch?v=--y_vf-Kg-w [2] https://www.youtube.com/watch?v=tiKCORN-6m8 https://www.youtube.com/watch?v=tiKCORN-6m8 [3] https://www.youtube.com/watch?v=RIQaRqr5T5U https://www.youtube.com/watch?v=RIQaRqr5T5U
analog31 4y ago
My thought is, if you peel back the first layer of music theory, you discover a chaotic, lawless world. The main thing I've noticed is that this is extremely unnerving to engineers, who want to learn it as a precise hierarchical structure. Regular people are more focused on the fact that somebody is somehow making it all sound good, and want to learn how to do that. On the other hand, most musicians are completely ambivalent to it, or even thrive in the chaos. Yet the "rules" are useful because they provide a common ground for forming ensembles, or connecting composer and performer. We've watched musicians go down the rabbit hole of nonstandard scales, innovative notation systems, etc., only to discover that nobody can play their material. I'm a double bassist. I'm happy just to be able to coordinate my ears, brain, and hands, well enough to play the same note the same way twice if I want to. Claiming that I have conscious control over temperament would be laughable. I've got too much other stuff to think about: The notes on the page, the non-notated passages (many jazz bass parts are expected to be improvised), tempo and rhythm, connecting with the rest of the band and the audience, who's coming in the front door, and so forth. This stuff is all happening in real time.
- stoeckley 4y ago
  > My thought is, if you peel back the first layer of music theory, you discover a chaotic, lawless world. That's because some people think the theory comes first, and the music is based on it. But music is just art, like any other art. The rules are soft and broken and hardly gospel. And music theory is an attempt to have some way to communicate about music using ordinary language. It isn't math, it isn't science, it's just some basic terminology and observations, none of which have much to do with the actual artistic act of making music.
  - byproxy 4y ago
    Absolutely. Music theory is descriptive, not prescriptive. It just so happens that some things that sounded pleasant to people in the past still sound pleasant to modern ears, so you sometimes get into a bit of “tail wagging the dog” when people use those descriptive academic terms and concepts when creating music today, e.g. saying “I’m gonna write a 16-bar AABA tune that’s based on a I-vi-ii-V progression and modulates to the mediant in the B section”, and therefore think these are “rules” to abide. One of the more unfortunate misconceptions when it comes to the study of music theory.
Aidevah 4y ago
>The next level of explanation is to say: “Yes, I recognize that D-sharp and E-flat sound the same, but they function differently, and the spelling communicates this functional difference.” This explanation always bothered me, because if the “function” is limited to the page and isn’t audible, then is it even a real thing? A feature of notated music (which is what most of us mean when we say "[western] classical music") is that there can be things notated and not heard. Similarly, there are also different notations which correspond to the same sound. Notation is ambiguous, and this can be a source of both frustration (for the students) and invention (for the composers). Charles Rosen opens his book The Romantic Generation with a fascinating discussion about music which is seen and not heard which deals with this philosophical issue. Of course this practice goes back much further. Composers have been playing with notation for a long time and it reached a peak of sophistication in the 15th century, as Emily Zazulia demonstrated in her PhD thesis and book[1]. This quality is obviously absent in musical cultures which do not rely on notation. I imagine to the outsider it appears as if the notation itself has taken on a life of its own to the detriment of the sounding music. Of course there is a certain elitism involved as well since explaining subtleties in notation is also a sure way of ostentatiously demonstrating one's erudition, which may explain why these kind of discussions are perennially popular here ;). [1] https://global.oup.com/academic/product/where-sight-meets-sound-9780197551912 https://global.oup.com/academic/product/where-sight-meets-so...
- vcxy 4y ago
  I would argue the difference is heard in music that broadly follows tonal harmony. Sure, the note it self sounds the same, but the difference is context. That context is there regardless of whether it is heard or seen. Edit: just to add some detail: you can definitely hear if something sounds Lydian. If it sounds Lydian, you know that's a sharp 4, not a flat 5. Put it in C e.g., then it's an F# and not a Gb, and you can hear that.
  - Aidevah 4y ago
    Yes, exactly. A note is rarely found by itself, and looking at the context surrounding the note usually clears up the function of a note pretty quickly. Now that I think about it, the notation actually reduces ambiguity in this case since it specifies the function of notes which have the same sound.
kortex 4y ago
Anyone who is interested in going down the beyond-12-equal-temperment rabbit hole: - xeharmonic wiki: https://en.xen.wiki/w/Main_Page https://en.xen.wiki/w/Main_Page - xenharmonic playlist: https://open.spotify.com/playlist/1OcPPq0ohnUarvDCERaxaR?si=lIAZAVOFSb-Eczl2v7Re5Q&utm_source=copy-link https://open.spotify.com/playlist/1OcPPq0ohnUarvDCERaxaR?si=... - Tolgahan Çoğulu and his awesome microtonal guitar creations: https://youtu.be/iRsSjh5TTqI https://youtu.be/iRsSjh5TTqI Some bands with more "approachable" sounds (vs the xenharmonic playlist, which gets spicy) known for microtonal work: Psychedelic rock: - King Gizzard and the Lizard Wizard (namely albums Flying Microtonal Banana, KG, LW) - Altin Gün - Gaye su Akyol Classic blues rock (Led Zeppelin and the like, but also OG blues like Robert Johnson, that's another rabbit hole) also has a surprising amount of off-12Tet notes, because of the blues scale In the electronic realm, Aphex Twin does some interesting stuff with microtones - Jacob Collier - musical prodigy, mostly a capella/vocal arranging, but is a genre polymath, does some incredible stuff with just harmony If anyone has anything to add, please do! I can't get enough of this stuff
exabrial 4y ago
With TTET, we really need to drop note names just use scale degrees (aka ‘Nashville Number System’). This would remove a ton of confusion when texting music theory.
rdtennent 4y ago
>Bach wrote The Well-Tempered Clavier to show off how one well temperament system (no one knows which one) sounds okay in every major and minor key. The keys closer to C sound sweeter and more euphonious, while the more distant keys sound darker and edgier. Fairly recent research has shown that Bach may have been very explicit in specifying a temperament system. A series of what appear to be decorative swirls at the top of the title page of the WTC has been conjectured to actually be instructions for tuning to the temperament system he favoured.
- ethanhein 4y ago
  I wrote a blog post summarizing this research. The idea is that the swirls specify turns of the tuning pegs to modify meantone temperament. It's more or less pure speculation, but it does produce a very nice-sounding tuning, almost equal temperament but not uniform across the keys. https://www.ethanhein.com/wp/2020/what-does-the-well-tempered-clavier-sound-like-in-actual-well-temperament/ https://www.ethanhein.com/wp/2020/what-does-the-well-tempere...
AlbertCory 4y ago
There's a ton of good information here, but it seems to assume a guitar or piano, where there's only one key or fretted space for each note. For a fretless stringed instrument, they are indeed different notes, and the same note within a single piece can sound different depending on whether the line is moving up or down. If that sounds heretical: I got this from the Alexander String Quartet, in the Q&A session after their performance. They have a measurement of microtones (I think they're called "clicks" but I forget), and all four of them have to agree on how many clicks up or down from the center of the note they're using.
- palimpsests 4y ago
  the unit of measurement is called a “cent”. there are 100 cents between each 1/2 step in 12-tone equal temperament.
  - AlbertCory 4y ago
    Thanks. I thought "clicks" didn't sound right.
- deleted 4y ago
  [deleted]
- wizofaus 4y ago
  I find that a little odd when vibrato can be as wide as 70 cents (70% of a semitone) further up the fingerboard. It makes sense for certain chords in highly tonal music though.
  - AlbertCory 4y ago
    They coordinate that, too. I asked about the movie A Late Quartet (a great movie, btw, with the immortal Phillip Seymour Hoffman), and they said, "in the movie, they say 'our vibratos aren't lining up' and that's something I actually would say in a rehearsal."
AlbertCory 4y ago
I searched the whole thread for "Autotune" and didn't find it, so let me start: I'm assuming, but I want to check with you all: does Autotune always "correct" to the exact center of the note? I assume the answer is probably Yes. If so, that's a bug, is it not?
- MikeBattaglia 4y ago
  You are correct. For instance, traditionally, in barbershop vocal music, singers are trained to deliberately deviate from 12 equal, towards an ever-shifting kind of just intonation, in order to maximize the extent to which the voices blend. Auto tune, on the other hand, just tunes things straight to 12 equal. Melodyne fares a little bit better in that it lets you tune to custom microtonal scales, or fudge things a little bit here and there, etc. Interestingly, Logic Pro X has a "Hermode Tuning algorithm" that will basically do the dynamic adjustment toward just intonation for you, but it only works for MIDI instruments and not auto tune as far as I know.
- filoeleven 4y ago
  Autotune software has different parameters available to it. These include pitch correction speed, how close a singer has to be to the note in order to start/stop pitch-correction, which pitches to correct for. The T-Pain effect, which is the autotune sound you’re probably thinking of, cranks most of those parameters all the way up in order to get to that robot voice: “instantly lock the vocals to one of these set pitches, if the singer goes lower than X, immediately switch to the next lower pitch in the set.” More subtle usage makes for a performance that is more in tune overall but keeps much more of the vocalist’s expression and pitch variation intact. Its goal usually is to not be noticed. I don’t think I understand your question (edit: about it being a bug), so I won’t attempt to answer it directly, but maybe the above info is helpful in thinking about it.
  - AlbertCory 4y ago
    > about it being a bug The comment was asserting (or questioning) the T-Pain effect. I honestly didn't know if that was what everyone was using in Autotune or not.
willnonya 4y ago
"This confusion applies to all of the black keys" Music theory must be racist!!! /sarc
lloydatkinson 4y ago
You can tell they are different because of the way they are
tzs 4y ago
Suppose we start with 12-TET and ask what simple integer ratios each note is close to. To do that we need some notion of what it means for a simple integer ratio to be a good approximation to some arbitrary given number. Consider trying to approximate some number x with an integer ratio n/m. For a given m all we can guarantee is that we can find some m so to |x-n/m| <= 1/2m. One way to define good approximation is if for a given m, we can get a lot closer than 1/2m to x then that is close. For example if we want to approximate pi with m = 6, 7, or 8, the closest we can get is 19/6, 22/7, and 25/8. The absolute errors are about 1/40, 1/790, and 1/60, respectively. They are all doing better than 1/2m, but 6 and 7 are only about 3.5 times better 1/2m, but 7 is 56 times better than 1/2m. So we say that 22/7 is a good approximation to Pi. That doesn't mean it is particular close--just that it is way closer than other approximations with similar sized denominators. For a given number x there is a way to find such good approximations. You figure out the continued fraction for x. For Pi that is 3 + 1/(7 + 1/(15 + 1/(1 + 1/(292 + 1/(1 + ..., then even though that goes on forever you type ")))))" so that the unbalanced parens don't drive you crazy, and take the sequence you get by taking finite sections from the left side of that continued fraction. So for Pi we get 3, 1 + 1/7, 3 + 1/(7 + 1/15), ..., which when simplified give 3, 22/7, 333/106, 355/113, 103993/33102, .... Note that 22/7 is in there, which is the good approximation from early. All of those numbers from taking the left parts of the continued fraction, which are called convergents of the continued fraction, are good approximation in the sense above: they are way closer to Pi than anything else with similar denominators. What we can do then to find good integer ratios that are close to the notes of 12-TET is for each 12-TET note, take its frequency divided by C's frequency, compute the continued fraction of that, and compute the first few convergents. Here are the results. I've omitted convergents with a denominator of 1 or with a denominator > 500. C#/Db: {17/16, 18/17, 89/84, 196/185} D: { 9/8, 55/49} D#/Eb: { 6/5, 19/16, 25/21, 44/37} E: { 4/3, 5/4, 29/23 34/27, 63/50, 286/227, 349/277} F: { 3/2, 4/3, 295/221} F#/Gb: { 3/2, 7/5, 17/12, 41/29, 99/70, 239/169, 577/408} G: { 3/2, 442/295} G#/Ab: { 3/2, 8/5, 19/12, 27/17, 100/63, 227/143, 781/492} A: { 5/3, 37/22} A#/Bb: { 7/4, 9/5, 16/9, 41/23, 57/32, 98/55} B: {15/8, 17/9, 168/89, 185/98}
beefman 4y ago
Great question but some unfortunate errors here. > Before the advent of temperament systems, D-sharp and E-flat were two different notes. D# and Eb were defined as elements of a temperament system, namely meantone temperament. > My track is tuned in a system called five-limit just intonation ... It's the basis for all the tuning systems used in Western Europe between about 1500 and 1900. The basis for tuning systems in Western Europe between 1400 and 1800 was meantone temperament. 5-limit JI has never been the basis of a common practice music culture anywhere or at any time in world history. > We can do this because Western people consider octaves to be equivalent. All people experience octave equivalence. > Ultimately, split black keys did not catch on. Split keys were fairly common on keyboard instruments for about a century. > Bach wrote The Well-Tempered Clavier to show off how one well temperament system (no one knows which one) sounds okay in every major and minor key. Bach was a proponent of well temperaments in general, not any specific one.
- ethanhein 4y ago
  Meantone is a modification of three-limit just intonation to try to better approximate the thirds from five-limit just intonation. I know that it is historically inaccurate to say that meantone follows from five-limit, but in order to understand the point of meantone's existence, you have to know about five-limit as the standard that meantone is aiming for. I should probably rephrase my post to say that meantone follows logically from five-limit, not that it follows historically. All humans (and some monkeys) can detect octaves, but that does not mean that all humans consider octaves to be equivalent. That's a culturally specific convention. It's a very widespread convention thanks to Europe's wide cultural reach, but it's very much not a universal one. Split keys may have been common for a while, but I think we can agree that in the long term, they did not catch on.
bewaretheirs 4y ago
Related in a distant way: https://news.ycombinator.com/item?id=31476078 https://news.ycombinator.com/item?id=31476078 my TL;DR, as a western classically-trained amateur musician largely unfamiliar with Indian music: Harmonium (a small reed organ) is widely used in Indian classical music but its use is controversial because it doesn't allow for the fine adjustments in pitch (roughly analogous to the D#/Eb distinction discussed here) that is seen as central to most/all Indian styles.
wforfang 4y ago
D-sharp and E-flat are two different notes used to describe the same physical vibration for the same reason "father" and "son" are two different words that could describe the same person. It's just a way to communicate contextual relation.
- marton78 4y ago
  This is false. D-sharp and E-flat have (slightly) different frequencies. Read the article!
  - dehrmann 4y ago
    ...in certain temperaments, but not the ubiquitous 12-TET.
    - noslenwerdna 4y ago
      ... as thoroughly explained in the article.
      - P_I_Staker 4y ago
        Well I haven't read the article, so IDK
deleted 4y ago
[deleted]
vram22 4y ago
Sort of related, and may be interesting, for the comments in this post about a Python piano app I had done some years ago: Play the piano on your computer with Python: https://jugad2.blogspot.com/2013/04/play-piano-on-your-computer-with-python.html?m=0 https://jugad2.blogspot.com/2013/04/play-piano-on-your-compu... Some of the comments gave some interesting music theory info.
d1sxeyes 4y ago
The author asks an interesting question which I didn’t see the answer to in his reply: what DO you call this note in the A minor blues scale? He says you’re only supposed to use each letter once, so am I supposed to call this an E flat and then refer to the following note as an F flat? I struggle a bit with considering the ‘blue note’ a variation of the fifth - it feels more to me like a variation of the fourth, so is it in fact a D sharp? But then the fourth would be C double-sharp, and the (flat) third would be B sharp… right? All of that just sounds mad.
JIMS_Music_Sys 4y ago
Ethan, You wrote, "your choices were these: you could limit your harpsichord playing to certain keys, or you could have a bewilderingly complex instrument that you would spend half your life tuning." May I respectfully suggest that an alternative option exist now, which did not exist then? First, please note that the tunings that you are describing are all extended meantone tunings (more or less), derived from stacking perfect fifths (P5's) that have been more-or-less tempered away from their just ratio (702 cents). If you widen the P5 to 720 cents, you get 5-tone equal temperament (5-tet). If you narrow the P5 to 686 cents, you get 7-tet. In between, you get the historical meantone tunings and today's 12-tet (P5=700). They are all defined by the same three elements: 1. Their period of repetition, the perfect octave (P8) which maps the 2nd partial to the P8. 2. Their generator, the tempered P5, which maps the 3rd partial to the P5. 3. Their comma sequence, which starts with the syntonic comma, which maps the 5th partial to the M3.(If the first comma in the sequence were the schisma, then the 5th partial would be mapped to the d4, defining the schismatic temperament.) This combination of a P8 period, P5 generator, and comma sequence that starts with the syntonic comma, is called the "syntonic temperament" in "Dynamic Tonality" (see Wikipedia for both quoted terms). An "isomorphic keyboard" is a keyboard that is generated by the same period, generator, and comma sequence as the temperament with which it is said to be isomorphic. Isomorphic keyboards had not yet been discovered before the West standardized on 12-tet. Had they been known then, then the course of musical history might have been quite different. With brings me back to your quote. A keyboard that is isomorphic with the syntonic temperament is brain-dead simple. It has the same fingering in every octave of every key of every tuning of the syntonic temperament. 12-tet, 1/4 meantone, 32-tet, 53-tet, infinity-tet -- same fingering. One can even bias the mapping of pitches to notes to support irregular tunings such as well-temperaments. Therefore, IF ISOMORPHIC KEYBOARDS HAD EXISTED during the period that you describe, then they would have had a shot at becoming the de facto standard keyboard instrument subsequently. Today, isomorphic keyboards DO exist. Anyone who is serious about exploring the frontiers of tonality should check them out (and Dynamic Tonality, which requires an isomorphic keyboard). Respectfully, Jim Plamondon

368 points by tobr 4y ago

Because one is a raised D and the other a lowered E. Shit hunny... (flippant, but also accurate! of course explaining why that matters is a whole different beast. Lots and lots of good books available though...)

wizofaus 4y ago

Try sight reading something in D# major and that should tell you the difference!

petewailes 4y ago

Obviously Ethan knows this and just isn't going into it because this is more a history lesson than a theory lesson, but the same applies to white keys. So B♯ and F♭ are perfectly valid notes. C♯ major for example contains B♯, despite that there's no black key between B and C.

chrismorgan 4y ago
For that matter, F𝄪 (F double sharp) and A𝄫 (A double flat) are both legitimate alternatives/equivalents to G in some situations, by extrapolating the sequences. (And if you extrapolate far enough, any note has multiple possible alternatives—for example, you could get a G♮ that’s kinda more G♯♭ or G♭♯ than just straight G, to use super fuzzy terminology.)

seanhunter 4y ago

Short answer: they aren't. This is the musical equivalent of the fact that English has "guarantee" and "warranty" and they mean the same thing. Long answer: they aren't. They are enharmonic equivalents in the vast majority of music that uses any of the conventional Western systems of tuning (as the author sort of goes out of their way to demonstrate in the article), and if you use or invent a different system then what you call the notes is kind of up to you since it's your system.

midenginedcoupe 4y ago
Correct answer: they are. Not on a piano, but for all the other instruments with variable pitch (e.g. fretless strings, voice, trombones) they are. The enharmonic is useful information and we'll know whether to place that note just a little under or above its usual pitch to make the chord more in tune. We don't need to invent a new system to do this, we do it every day within the 12-tet system we already have.
- seanhunter 4y ago
  Theoretically yes but actually not really. Most of the time, even if you're playing a variable pitch instrument you're going to be tuning to fixed pitch because you'll have at least one fixed pitch instrument (eg a piano) and if you don't you'll just sound out of tune. In cases (eg a consort group or string quartet or something) where you're all variable pitch, you'll be tuning to each other and to the scale/key as appropriate to the music and whatever sounds good. You may well sweeten the thirds or widen the fifths a bit etc but that doesn't apply to this question here because you're really not going to see the enharmonic equivalents in the same piece the absolute vast majority of the time for stylistic reasons and if you ever did you would just be tuning to each other to make the vertical incidences sound good rather than thinking consciously of tuning a d-sharp one way and an e-flat another way. Source: Have a degree and postgrad in music, used to be a professional double bass player[1], spouse has a degree and postgrad in music and teaches at 2 conservatoires in London as well as performing professionally, mostly early music in small consort groups where this sort of tuning thing comes up a lot. [1] So yeah you can make the standard joke about what do double bass players know about tuning.
  - midenginedcoupe 4y ago
    Sometimes yes, sometimes no. Even if playing with a fixed-pitch instrument, it only really sounds out of tune if they're playing the same notes. Which in the styles I play isn't an issue. So I guess how often this happens in practice varies between styles and eras of music, which would make sense to me. I haven't ever done early music and know nothing about it (other than trombones used to be designed terribly and we now know how to make better ones ;) Source: Also have a postgrad in music, probably from one of the conservatories your spouse teaches at, and still play trombone professionally.

im3w1l 4y ago

> The usual answer is that you are only supposed to use each letter name once in any given scale. And why is that important? Answer: This lets you write the key signature once, and then not have to bother with accidentals in front of notes.

thaumasiotes 4y ago
Well, no, that would only work if you were committed to never using notes that weren't in the key signature. That would be an unusual choice.
- im3w1l 4y ago
  Not having to use accidentals for in-key notes still reduces the needed number substantially.
- iainmerrick 4y ago
  Right, but if your tune mostly uses conventional major and minor scales (which most do!) you mostly won’t need accidentals. Also, you’ll be able to transpose to any other key just by shifting the letter names up or down and changing the key signature. That’s a really interesting and useful property. Also also, the notes with accidentals won’t change when you transpose (although the accidentals themselves will need rewriting). Transposing music would be hellish without this system!
- PeterisP 4y ago
  Depends on the music genre probably, there are oh so many song arrangements that never use notes outside of the key signature.
dahart 4y ago
Perhaps more succinctly, you always write any two consecutive notes of a diatonic scale on two different lines of the staff. It would be bad if your in-key scale looked like it had two notes on the same line and then a jump of a third. Note this is true even when you have accidentals! It’s a way to keep the intention or semantics of notes more clear, and more easily readable, regardless of the pitch interval. Like how the article talks about the distinction between an augmented 2nd and a diminished 3d, the notation is designed to help clarify that distinction.

powersnail 4y ago

The explanation of enharmonic equivalent (though the author didn't use this term) is right, but I do take problem with this sentence: > but what musical difference does it make? In the present day, the answer is, none whatsoever. This is not quite right. On all fretless instruments, including most bowed strings and the human voice, enharmonic equivalent notes still have different pitches. The subtle differences in intonation is incredibly important and noticeable on the violin, for example.

VBprogrammer 4y ago
Out of interest, is this still the same when a violin is playing alongside fretted instruments? Wouldn't they sound out of tune in that case?
- wumpus 4y ago
  Some players of fretted instruments move the frets to match individual pieces of music. In modern rock music, some musicians will change guitars every song to have sweeter chords depending on the particular chords in that song.
  - coldtea 4y ago
    Which "modern rock musicians" do that? It surely is not widespread in rock. Rock musicians change guitars (in a live or even studio situation) mostly to get a different sound or a different tuning (like going from "standard" to an open tuning). Not for microtuning adjustments, or because they have moved the frets to match an individual piece. Some prog musicians might do it, but it surely is not a "rock" custom. In arabic music, on the other hand, or renaissance music, and other genres, it is, and instruments there often have movable frets.
    - gromgull 4y ago
      Not moving the frets, but changing guitar: https://youtu.be/Daw93bRHe4Y https://youtu.be/Daw93bRHe4Y

ur-whale 4y ago

Are they the same frequency? Can most humans hear a difference? Do we need more than the two questions above?

midenginedcoupe 4y ago
Are two competing programming languages Turing-complete? Can end-users of the program tell which one was used? Do we need more than the two questions above? If programmers thought like this HN would be empty!
swores 4y ago
It would be possible for most humans to notice something but feel indifferent, or for a sizeable minority to really hate something. So just abstractly I'd say that yes you do need more than those two questions.
PeterisP 4y ago
No, and yes. The difference is obvious even those who don't distinguish pitches much (can you hear the difference in the video linked in the article - https://www.youtube.com/watch?v=7GhAuZH6phs&t=21s https://www.youtube.com/watch?v=7GhAuZH6phs&t=21s ) because the 'wrong' one played in a scale or a chord sounds really, really horrible; that's why we have all the work done on 'tempered' tuning to reduce the gap so that everything is just slightly off.
vnorilo 4y ago
The relationship between pitch and frequency is not simple. The physical frequency for a pitch can be derived in several ways. One example is the Pythagorean system where the interval of fifth is set as a frequency ratio of 3/2. This system yields clearly distinct frequencies for D# and Eb. In 12 tone equal temperament, a semitone is set as a frequency ratio of 2^(1/12). In this system you get the same frequency. You can also derive frequencies from simple fractions of the scale root. In this instance you would generally obtain D# and Eb from unrelated roots.

rawling 4y ago

Can't D# and D# be two different notes too, depending on what key you're in? Hell, doesn't this apply to the white keys too?

tgv 4y ago
By that kind of logic, D# in the key of G# should indeed sound different than D# in the key of C# or B, depending on the temperament.
TheOtherHobbes 4y ago
Yes, depending on the temperament. Not in 12-TET because the ratio between every semitone is the same. In other temperaments the frequency of every note can be different in every key.

MikeBattaglia 4y ago

There is some basic information that is very wrong in this article. For example: "My track is tuned in a system called five-limit just intonation via the magic of MTS-ESP. It’s the basis for all the tuning systems used in Western Europe between about 1500 and 1900." No - at no point in the last 500 years was 5-limit just intonation ever the predominant tuning system used anywhere in Western Europe. The real predominant tuning system was called "meantone temperament," to which this article sadly devotes only about 3 words - and those words are only about 12 tone meantone keyboard layouts, not about the bigger, abstract idea of meantone temperament in general as it was understood and taught by practitioners of the day. There is a very important difference between meantone and just intonation. The goal of meantone was to have four tempered perfect fifths (approximately a 3/2 frequency ratio) add together to approximate the fifth harmonic (or a 5/1 frequency ratio). Thus, the major third from the circle of fifths would approximate a 5/4 ratio with the tonic, and the major chord would approximate a very crunchy sounding 4:5:6 ratio. In order to do this, fifths are all flattened slightly to make the tradeoff - flattening the fifths by 1/4 of a "syntonic comma" was typical, or "quarter-comma meantone". Even though keyboard instruments evolved in a more well-tempered direction, meantone was the way that teachers of the common practice era (such as Leopold Mozart) still taught and thought about this stuff. Meantone sounds noticeably different from just intonation, where the major third from the circle of fifths is a syntonic comma sharp of a 5/4 ratio (about 22 cents). In just intonation, if you want your major chords to be 4:5:6, you need to bring in this other, different, independent 5/4 major third that is not on the circle of fifths. As a result, certain chord progressions that are common in Western music will tend to exhibit strange sounding "comma drifts" if you play them in just intonation. Adam Neely has a good video on "Benedetti's Puzzle" about this for those who are interested. Of course, there is nothing wrong with just intonation, and comma shifts can sound interesting if you want to deliberately use them in some kind of modern microtonal setting, but it simply isn't the tuning historically used in common practice Western music. Anyway, though, if you go through the article with a marker and replace all instances of "just intonation" with "meantone," the general idea is mostly correct.

ethanhein 4y ago
Hi, I'm the author of the blog post. I said that 5-limit is the basis for systems like meantone, which is true. Meantone systems take 5-limit as their starting point and then modify it. I deliberately skated over the specifics of how meantone works on purpose, because I have too much experience watching my students' eyes glaze over when I talk about this kind of thing. I'm trying to strike a balance between giving correct information and not turning people away.

tobbob 4y ago

It's the same note, but musicians are anoraks. I know because I used to be one.

klodolph 4y ago
Kind of like saying that “cell” and “sell” are different words. Obviously they’re different words, even though you can’t hear the difference. Just like it’s obvious that Ab and G# are different notes, even though they may sound the same. Ask an English speaker to interpret a text about a sails man who sales around the world and cells sell phones, at have price for any guessed who sends him a facts to his office in grease. It’s harder to read when you use the wrong words, just like how a score is harder to read if you use the wrong notes.
- tobbob 4y ago
  No

alex_smart 4y ago

The distinctions between D-sharp and E-flat only make sense in the context of a key. For instance, you construct a major key in E-flat and not D-sharp for the practical need to represent the scale nicely on the staff - so each tone in the scale should have a unique place in the staff. You can construct the E-flat major scale with just three flat tones (Eb F G Ab Bb C D), whereas you would need four sharp and two double-sharp(!) tones if you started with D# (D# E# F## G# A# B# C##). And having to use F## and C## to refer to G and D tones is just ugly. (I had made a mistake in the earlier version of this comment.)

tuukkah 4y ago
> Also, having to call the G tone F# is just ugly. I presume you mean having to call the F tone E#.
- alex_smart 4y ago
  Sorry, I had made a mistake. Wanting to create a major key starting with D# would end up looking like D# E# F## G# A# B# C##. The ugliness is even more stark. - two double sharp keys - F## to refer to G, C## to refer to D, B# to refer to C Yikes.
  - klodolph 4y ago
    D# would be extremely rare. I’ve only ever seen G#, and that was a temporary modulation within something larger. Most people write “x” for double-sharp, instead of ##, in order to match how it looks on a score.
klodolph 4y ago
Sometimes you call a G as F double-sharp. I don’t think of it as ugly. It’s just what happens sometimes. Like if you start in G# minor and then use the leading tone. It’s way better to see F-double sharp than to see two different Gs fighting each other on the page. And it’s even worse to have to decipher those awful chromatic systems that are all painful to read.

cmur 4y ago

As a former jazz musician, I always find the classical perspective on theory interesting. This article touches on Pythagorean tuning techniques, which if you ever find yourself in front of a good a cappella choir, they’ll be tuning to the true temperament tuning scheme described here. A fun comparison to make in the jazz world is enharmonic usage for the purpose of readability. Jazz chords are very dense and short lived compared to the very clean and predictable counterpoint found in classical music, so “correctness” doesn’t really matter as much. Most charts are sight read, so even though the band is sounding some flavor of a B chord, if you’re playing the 3rd, there’s a chance there may be a written E flat instead of a D sharp simply because E flat is a more commonly written note for horn players.

klodolph 4y ago
Pythagorean tuning is somewhat different from what’s described. In Pythagorean tuning, your E would be 81/64 above C, or equal to four fifths minus two octaves. This is slightly higher than E in the article, and the difference (81/80) is called the syntonic comma. Different tuning systems were invented in order to resolve this discrepancy, and without these advances, jazz would be radically different. One of the things about jazz is that you see distant movements that only really make sense as enharmonics—like how Coltrane’s “Countdown” uses the familiar ii-V-I, but modulates in major thirds, which only makes sense when you allow the final modulation te be the same as the first—something that only works enharmonically.
- cmur 4y ago
  For sure, the broad similarity I’m trying to touch on is the focus on mathematical resonance and context of a key. Equal temperament removed a lot of that context, but definitely opened the door for further harmonic experimentation. Giant Steps is also a good example of what you’re talking about too.
- ethanhein 4y ago
  I'm the guy who wrote the blog post, and I want to offer some clarity. Usually when people say "Pythagorean" tuning they are talking about three-limit just intonation, not five-limit. In three-limit, the major third is indeed tuned to 81/64, which sounds pretty terrible. That might explain why medieval people thought thirds were a dissonant interval. Five-limit just intonation tunes major thirds to 5/4.

userbinator 4y ago

I went to the Wikipedia link in the article to https://en.wikipedia.org/wiki/Five-limit_tuning https://en.wikipedia.org/wiki/Five-limit_tuning and saw that the first example there shows two very slightly different frequencies, which is a good way of setting the stage for reading the rest of the article.

perihelions 4y ago

The paradox is that you can't create a theory of music whose notes are both (a) evenly spaced and (b) contain the integer ratios. You want (a) because it you gives you nice algebraic properties (the music structure is invariant under frequency shifts). You want (b) because small-integer ratios are pleasant sounding -- partly culturally-acquired taste, partly because physics gives musical instruments acoustic spectra in integral multiples of a fundamental frequency: f, 2f, 3f ... nf. Small-integer ratios are naturally occurring and very recognizable. Modern tuning (C-f "12-TET" in the article) almost, approximately satisfies (a) and (b) simultaneously. "12" means there's twelve tones between f and 2f; the ratio between adjacent tones is defined to be 2^{1/12}. This tuning can't contain both f and 3f (so it fails (b)), but it *can* contain f and 2^{19/12}f ~ 2.9966f, which is actually close enough to 3f to be indistinguishable. (Almost works!) But as you build ratios out of larger integers, it audibly falls apart. The closest you can get to (5/3)f is 2^{9/12}f = ~1.6818f, which is already 10% of the way to the next note. And it rapidly gets worse. This is why two on-paper-identical notes can end up audibly different, depending on what key you're starting with (and hence how they are approached). There's tension internal to music theory itself.

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noncovalence 4y ago
In the context of the difference between D# and Eb, 19-TET is very interesting to play around with. It adds an extra black key between every pair of white keys, and most songs intended for 12-TET still work fine, as long as you play sharps and flats as written. If you play a D# instead of an Eb, you suddenly get a very different sounding interval.
- bonzini 4y ago
  Also as long as sharps and flats are written in a very pedantic manner. For example a diminished C chord only sounds "right" if it's notated as C-E♭-G♭-B♭♭ rather than C-E♭-G♭-A. On top of this, harmony may or may not work the same in 19-TET and 12-TET. With the same example of diminished chords, the diminished chord does not divide the octave in four equal parts in 19-TET. Adim and Cdim are enharmonic in 12-TET, but Adim in 19-TET is A-C-E♭-G♭♭; that is, only C and E♭ are the same.

fxtentacle 4y ago

Because for most instruments, it is. A violin player won't move up for a full half tone for a D sharp, so there'll remain a small pitch difference between them. It's only for the small subset of keyed instruments like pianos that pitch is quantized into 12 subtones. But even there, organs use a different pitch to key mapping than keyboards. For a very interesting rabbit hole, search for "Wolfsquinte", which is a chord that sounds nice on keyboard but horrible on organ.

wumpus 4y ago
I am not aware of any manuscript having different tuning of organs vs other keyboards in the Renaissance or Baroque eras... can you cite one? The Wikipedia article for Wolfsquinte makes it clear that it has nothing to do with keyboards or organs: it's a feature of your choice of tuning. Perhaps you're used to organs and keyboards with different tuning choices?
- CHY872 4y ago
  I don't think that's quite GP's claim. They're not necessarily saying that organs and keyboards of the same heritage had different tuning (though it's well documented that instruments had different tuning according to region even through the 1700s and 1800s), rather that historic organs which retain their original temperament sound very different to modern keyboards. Here's an article supporting this. It refers to different rates of beating in different tuning regimes, comparing equal temperament to 'cornet-ton' type things. Because it's common for organs to be hundreds of years old, and it's common for people to want historic organs to sound as close to how they did when they were made as possible because it's uncommon for them to play in non-vocal ensemble, this leads to a relatively common situation where an organ played today may well be tuned very differently to a piano played today. Depending on the organ. https://www.eunomios.org/contrib/francis2/francis2.pdf https://www.eunomios.org/contrib/francis2/francis2.pdf Here is a second article on organs by one manufacturer tuned in 'meantone' https://www.bach-cantatas.com/Topics/Meantone.htm https://www.bach-cantatas.com/Topics/Meantone.htm. It's also the case that harpsichords were commonly tuned in meantone https://www.harpsichord.org.uk/wp-content/uploads/2015/04/temperament.pdf https://www.harpsichord.org.uk/wp-content/uploads/2015/04/te... which might actually support the claim that historic non-organ keyboards sounded different from organ keyboards (specifically, if Bach didn't like the mean-tone organs he played and it was common to tune harpsichords in meantone, that would seem to provide some evidence for both temperaments existing and sounding different on the different types of instrument in the same historic period).

jimnotgym 4y ago

I play blues guitar by ear. I don't read music. The people replying to this thread, the person who wrote this blog are so far away from me it is hard to say we inhabit the same field called 'music'. I play a lot of improvised lead lines. I know my pentatonic scale shapes on the fretboard, but I also play lots of notes not in those shapes...because I like the way they sound. I also play a lot of 1/4 tone bends (notes between the piano keys) which don't even fit in the traditional system, but sound good. I say this as it is an interesting case of 'more than one way to skin a cat'

beardyw 4y ago
A lot of those in-between notes hark back to times before the scales were rationalised into the "well tempered" system we mostly use today. Often they are harmonics like the 5th harmonic which lives between the minor and major 3rd on the scale.
fassssst 4y ago
Same here, I know how to read music and tabs but gave up on it and now just play by ear, it’s way more satisfying. Western music theory is so baroque. The book Brainjo basically killed my interest in it.
nemo44x 4y ago
Music is kind of great like that. Much of music theory is over my head but I have spent time to understand a good bit too and I’ve gained a lot of respect for it. Everything you’re doing as a blues guitarist can be explained well by a music theorist who really know their stuff. I read an interesting article by a music theorist breaking down the song “Smells Like Teen Spirit” and remarking on the genius and uniqueness of the chord progression and how it violates a lot of what theory says would “sound good” and hence why it’s genius. It can be presumed Kurt Cobain was not too interested in music theory and if he would have been he may have never even considered the progression and other interesting aspects of that song.
- PaulDavisThe1st 4y ago
  I've said it before, I'll say it again. It's more productive to think of "music theory" as a way for musicians and composers to talk about what they just did, or what they are just going to do, than as a way to generate those things.

elihu 4y ago

What's weirder is that if you're using just intonation in, say, the key of C major, there's two different D's. One is 9/8, and the other is 10/9. The note we call D in equal temperament is about half-way between the two. If you want to play these chords in C major: Cmaj, Fmaj, Gmaj, Dmin, Emin, and Amin, you'll need to use both of those D's: 9/8 for the 5th of Gmaj, and 10/9 for the root of Dmin. If you try to play Dmin with the 9/8 instead, it sounds absolutely awful. In other words, if you want to play those six chords that are regarded as belonging to C major, you'll need two different D's. Which means the C major scale should really have 8 notes instead of seven. But we don't have a symbol to distinguish between 9/8 and 10/9 in standard notation, they're both just plain D. Some 12-EDO music makes use of the ambiguity between these two notes (or any two notes with the same relation to each other) to string together chord progressions that don't actually make sense mathematically. If you used those progressions in just intonation, you'd find you don't return to the chord you started on, you actually shifted up or down by a small interval of 81/80. It's sort of the musical equivalent of some formula that only works if you assume that pi is equal to exactly three.

psyc 4y ago

I started asking my father, a concert pianist, composer, and teacher - this question when I was 4. He explained. In my head I said, “Bullshit.” I continued to press him on it periodically until I was a teenager. I still shook my head and thought, “What is wrong with these people.” Now, I can read sheet music just fine, but I still feel like … never mind. I’ve done a ton of composing without once taking any notice of what key any of it was in. And it all sounds fucking great. I prefer to do as much as possible “by ear”. I’m unbelievably stubborn. tl;dr - Somebody really should have picked up on the autism when I was 4, and MIDI rolls don’t give a shit about keys and accidentals.

PaulDavisThe1st 4y ago
MIDI rolls don't, by themselves, make any noise or even inherently define any note frequencies at all. The frequency of the sound produced by a given synthesizer when it receives any particular MIDI note number is up to the synthesizer. This is part of the point of the MIDI tuning system. The synthesizer and/or the tuning system may very much care about keys and accidentals.
- deleted 4y ago
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Nemrod67 4y ago
do share! I'm a "MIDI composer" myself and love to hear what others do :) obligatory self-promotion, https://www.youtube.com/channel/UCUmdU7WpuhAv3imtVqkGpIA https://www.youtube.com/channel/UCUmdU7WpuhAv3imtVqkGpIA
- psyc 4y ago
  That's good stuff! Reminds me very, very vaguely of: https://www.youtube.com/watch?v=vapZZdog0NI https://www.youtube.com/watch?v=vapZZdog0NI Here's a small sampler. I include one that's maybe a bit similar, the one called 'crsh' https://soundcloud.com/w37hlwyq0a/sets https://soundcloud.com/w37hlwyq0a/sets

moogly 4y ago

It would be remiss of me not to mention the archicembalo[0], which was a keyed instrument that allowed a musician to experiment with this distinction to a degree. [0]: https://en.wikipedia.org/wiki/Archicembalo https://en.wikipedia.org/wiki/Archicembalo

bazhova 4y ago

Instruments without frets don't have this problem. I played violin for many years. When you play a double stop (two strings at the same time), since there are no frets, you can play true 3rds, 6ths etc. The harmony is so "pure" that it causes a third harmonic to ring (which is how you know you're doing it right). My violin teacher always insisted that e-flat and d-sharp are not the same. When you're playing in different keys you have to put your finger in a slightly different place.

tadhgpearson 4y ago
Right. I had this too, but because I never got the explanation this post provides, I had to live with "because it's a different key" - but could never quite understand why it made me out of tune with an accompanying pianist. Now I know... this is awesome!

tomxor 4y ago

I'm struggling to fully understand this tbh, but was recently exposed to these subtle differences when writing a mini organ synth. When implementing the draw bars (dictating the harmonics comprising each key) I realised the true harmonics of a note and neighbouring notes calculated in the 2^n/12 way are sometimes the same and sometimes slightly off... organs just kinda ignore this fact and use the closest neighbouring notes for the draw bars anyway so that they don't need a million different oscillators, so technically the draw bars are just chords on the keyboard using the same oscillators and not harmonics (well some of them happen to be exactly the same as harmonics, others not).

Ninn 4y ago

I recon this Feakonomics podcast includes the answer amongst other interesting related topics: https://freakonomics.com/podcast/mathematician-sarah-hart-on-why-numbers-are-music-to-our-ears/ https://freakonomics.com/podcast/mathematician-sarah-hart-on... It might be worth a listen for anyone who finds the topic interesting, but the answer is obviously already found in the top response too.

daviddever23box 4y ago

tl;dr: The notation system predates the modern, commonly-used 12-Tone Equal Temperament, for which there are (at least two) ways to describe any note within the (12-Tone) octave, either by sharps (D sharp) or by flats (E flat). In 12-TET, there are exactly twelve notes in the octave, and sharps and flats can be said to "overlap". In earlier temperament systems, these notes may have been distinct (or in some cases unavailable), as the relationships between notes were based on non-equal, if not more mathematically perfect, ratios.

coldtea 4y ago

For a similar reason that "upslope" and "downslope" describe walking upon the same stretch of road on a hill: context.

mabbo 4y ago

Given that integer ratios tend to sound better, are there songs edited to use notes that maximize the number of integer ratios rather than the standard tuning? It would seem an easy hack to make people like your new pop track better. But then, I'm no musician, so maybe I'm oversimplifying.

tzs 4y ago

Guitarist might find three videos recently posted to classical guitarist and lutist Brandon Acker's YouTube channel interesting. Lutes and early guitars (before around 1800) did not have metal frets. Instead they used pieces of string tied around the neck. They did this because the strings were very expensive, with a set of strings for a lute often costing more than the rest of the lute, and strings were not as robust as more modern strings. With metal frets strings would wear out faster. You could easily end up spending more per year on strings than you had initially spent on your instrument. By making the frets of the same material as the strings they didn't need to change strings as often. Acker and luthier M.E. Brune took a classical guitar Brune was building but had not yet put frets on and played around with putting on tied gut frets and gut strings. In the first video [1] they just go over the history of tied on frets, and do some comparisons with metal frets. With tied on frets it is relatively easy to try tunings other than 12-TET. You can change the position of a fret, or you can add extra frets. You can also add partial frets. Renaissance lutists would often glue on small pieces of string behind or in front of a fret. The fret would give them some particular note from a sharp/flat pair, and the little mini fret, called a tastino, would give them the other note from that pair. The second video [2] explores the tuning possibilities of tied on frets and tastinos. Acker plays a bunch of things in 12-TET and in other tunings more suitable for the particular piece, and also gives some examples of how bad other tunings can sound when you are playing a piece in a key that doesn't fit the key your instrument was tuned for. The third video [3] is just playing around after the tied on fret experiment is over but the guitar has not yet had its metal frets installed. Acker tries to play it without frets. That turns out the be quite a mixed bag. [1] https://www.youtube.com/watch?v=--y_vf-Kg-w https://www.youtube.com/watch?v=--y_vf-Kg-w [2] https://www.youtube.com/watch?v=tiKCORN-6m8 https://www.youtube.com/watch?v=tiKCORN-6m8 [3] https://www.youtube.com/watch?v=RIQaRqr5T5U https://www.youtube.com/watch?v=RIQaRqr5T5U

analog31 4y ago

My thought is, if you peel back the first layer of music theory, you discover a chaotic, lawless world. The main thing I've noticed is that this is extremely unnerving to engineers, who want to learn it as a precise hierarchical structure. Regular people are more focused on the fact that somebody is somehow making it all sound good, and want to learn how to do that. On the other hand, most musicians are completely ambivalent to it, or even thrive in the chaos. Yet the "rules" are useful because they provide a common ground for forming ensembles, or connecting composer and performer. We've watched musicians go down the rabbit hole of nonstandard scales, innovative notation systems, etc., only to discover that nobody can play their material. I'm a double bassist. I'm happy just to be able to coordinate my ears, brain, and hands, well enough to play the same note the same way twice if I want to. Claiming that I have conscious control over temperament would be laughable. I've got too much other stuff to think about: The notes on the page, the non-notated passages (many jazz bass parts are expected to be improvised), tempo and rhythm, connecting with the rest of the band and the audience, who's coming in the front door, and so forth. This stuff is all happening in real time.

stoeckley 4y ago
> My thought is, if you peel back the first layer of music theory, you discover a chaotic, lawless world. That's because some people think the theory comes first, and the music is based on it. But music is just art, like any other art. The rules are soft and broken and hardly gospel. And music theory is an attempt to have some way to communicate about music using ordinary language. It isn't math, it isn't science, it's just some basic terminology and observations, none of which have much to do with the actual artistic act of making music.
- byproxy 4y ago
  Absolutely. Music theory is descriptive, not prescriptive. It just so happens that some things that sounded pleasant to people in the past still sound pleasant to modern ears, so you sometimes get into a bit of “tail wagging the dog” when people use those descriptive academic terms and concepts when creating music today, e.g. saying “I’m gonna write a 16-bar AABA tune that’s based on a I-vi-ii-V progression and modulates to the mediant in the B section”, and therefore think these are “rules” to abide. One of the more unfortunate misconceptions when it comes to the study of music theory.

Aidevah 4y ago

>The next level of explanation is to say: “Yes, I recognize that D-sharp and E-flat sound the same, but they function differently, and the spelling communicates this functional difference.” This explanation always bothered me, because if the “function” is limited to the page and isn’t audible, then is it even a real thing? A feature of notated music (which is what most of us mean when we say "[western] classical music") is that there can be things notated and not heard. Similarly, there are also different notations which correspond to the same sound. Notation is ambiguous, and this can be a source of both frustration (for the students) and invention (for the composers). Charles Rosen opens his book The Romantic Generation with a fascinating discussion about music which is seen and not heard which deals with this philosophical issue. Of course this practice goes back much further. Composers have been playing with notation for a long time and it reached a peak of sophistication in the 15th century, as Emily Zazulia demonstrated in her PhD thesis and book[1]. This quality is obviously absent in musical cultures which do not rely on notation. I imagine to the outsider it appears as if the notation itself has taken on a life of its own to the detriment of the sounding music. Of course there is a certain elitism involved as well since explaining subtleties in notation is also a sure way of ostentatiously demonstrating one's erudition, which may explain why these kind of discussions are perennially popular here ;). [1] https://global.oup.com/academic/product/where-sight-meets-sound-9780197551912 https://global.oup.com/academic/product/where-sight-meets-so...

vcxy 4y ago
I would argue the difference is heard in music that broadly follows tonal harmony. Sure, the note it self sounds the same, but the difference is context. That context is there regardless of whether it is heard or seen. Edit: just to add some detail: you can definitely hear if something sounds Lydian. If it sounds Lydian, you know that's a sharp 4, not a flat 5. Put it in C e.g., then it's an F# and not a Gb, and you can hear that.
- Aidevah 4y ago
  Yes, exactly. A note is rarely found by itself, and looking at the context surrounding the note usually clears up the function of a note pretty quickly. Now that I think about it, the notation actually reduces ambiguity in this case since it specifies the function of notes which have the same sound.

kortex 4y ago

Anyone who is interested in going down the beyond-12-equal-temperment rabbit hole: - xeharmonic wiki: https://en.xen.wiki/w/Main_Page https://en.xen.wiki/w/Main_Page - xenharmonic playlist: https://open.spotify.com/playlist/1OcPPq0ohnUarvDCERaxaR?si=lIAZAVOFSb-Eczl2v7Re5Q&utm_source=copy-link https://open.spotify.com/playlist/1OcPPq0ohnUarvDCERaxaR?si=... - Tolgahan Çoğulu and his awesome microtonal guitar creations: https://youtu.be/iRsSjh5TTqI https://youtu.be/iRsSjh5TTqI Some bands with more "approachable" sounds (vs the xenharmonic playlist, which gets spicy) known for microtonal work: Psychedelic rock: - King Gizzard and the Lizard Wizard (namely albums Flying Microtonal Banana, KG, LW) - Altin Gün - Gaye su Akyol Classic blues rock (Led Zeppelin and the like, but also OG blues like Robert Johnson, that's another rabbit hole) also has a surprising amount of off-12Tet notes, because of the blues scale In the electronic realm, Aphex Twin does some interesting stuff with microtones - Jacob Collier - musical prodigy, mostly a capella/vocal arranging, but is a genre polymath, does some incredible stuff with just harmony If anyone has anything to add, please do! I can't get enough of this stuff

exabrial 4y ago

With TTET, we really need to drop note names just use scale degrees (aka ‘Nashville Number System’). This would remove a ton of confusion when texting music theory.

rdtennent 4y ago

>Bach wrote The Well-Tempered Clavier to show off how one well temperament system (no one knows which one) sounds okay in every major and minor key. The keys closer to C sound sweeter and more euphonious, while the more distant keys sound darker and edgier. Fairly recent research has shown that Bach may have been very explicit in specifying a temperament system. A series of what appear to be decorative swirls at the top of the title page of the WTC has been conjectured to actually be instructions for tuning to the temperament system he favoured.

ethanhein 4y ago
I wrote a blog post summarizing this research. The idea is that the swirls specify turns of the tuning pegs to modify meantone temperament. It's more or less pure speculation, but it does produce a very nice-sounding tuning, almost equal temperament but not uniform across the keys. https://www.ethanhein.com/wp/2020/what-does-the-well-tempered-clavier-sound-like-in-actual-well-temperament/ https://www.ethanhein.com/wp/2020/what-does-the-well-tempere...

AlbertCory 4y ago

There's a ton of good information here, but it seems to assume a guitar or piano, where there's only one key or fretted space for each note. For a fretless stringed instrument, they are indeed different notes, and the same note within a single piece can sound different depending on whether the line is moving up or down. If that sounds heretical: I got this from the Alexander String Quartet, in the Q&A session after their performance. They have a measurement of microtones (I think they're called "clicks" but I forget), and all four of them have to agree on how many clicks up or down from the center of the note they're using.

palimpsests 4y ago
the unit of measurement is called a “cent”. there are 100 cents between each 1/2 step in 12-tone equal temperament.
- AlbertCory 4y ago
  Thanks. I thought "clicks" didn't sound right.
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wizofaus 4y ago
I find that a little odd when vibrato can be as wide as 70 cents (70% of a semitone) further up the fingerboard. It makes sense for certain chords in highly tonal music though.
- AlbertCory 4y ago
  They coordinate that, too. I asked about the movie A Late Quartet (a great movie, btw, with the immortal Phillip Seymour Hoffman), and they said, "in the movie, they say 'our vibratos aren't lining up' and that's something I actually would say in a rehearsal."

AlbertCory 4y ago

I searched the whole thread for "Autotune" and didn't find it, so let me start: I'm assuming, but I want to check with you all: does Autotune always "correct" to the exact center of the note? I assume the answer is probably Yes. If so, that's a bug, is it not?

MikeBattaglia 4y ago
You are correct. For instance, traditionally, in barbershop vocal music, singers are trained to deliberately deviate from 12 equal, towards an ever-shifting kind of just intonation, in order to maximize the extent to which the voices blend. Auto tune, on the other hand, just tunes things straight to 12 equal. Melodyne fares a little bit better in that it lets you tune to custom microtonal scales, or fudge things a little bit here and there, etc. Interestingly, Logic Pro X has a "Hermode Tuning algorithm" that will basically do the dynamic adjustment toward just intonation for you, but it only works for MIDI instruments and not auto tune as far as I know.
filoeleven 4y ago
Autotune software has different parameters available to it. These include pitch correction speed, how close a singer has to be to the note in order to start/stop pitch-correction, which pitches to correct for. The T-Pain effect, which is the autotune sound you’re probably thinking of, cranks most of those parameters all the way up in order to get to that robot voice: “instantly lock the vocals to one of these set pitches, if the singer goes lower than X, immediately switch to the next lower pitch in the set.” More subtle usage makes for a performance that is more in tune overall but keeps much more of the vocalist’s expression and pitch variation intact. Its goal usually is to not be noticed. I don’t think I understand your question (edit: about it being a bug), so I won’t attempt to answer it directly, but maybe the above info is helpful in thinking about it.
- AlbertCory 4y ago
  > about it being a bug The comment was asserting (or questioning) the T-Pain effect. I honestly didn't know if that was what everyone was using in Autotune or not.

willnonya 4y ago

"This confusion applies to all of the black keys" Music theory must be racist!!! /sarc

lloydatkinson 4y ago

You can tell they are different because of the way they are

tzs 4y ago

Suppose we start with 12-TET and ask what simple integer ratios each note is close to. To do that we need some notion of what it means for a simple integer ratio to be a good approximation to some arbitrary given number. Consider trying to approximate some number x with an integer ratio n/m. For a given m all we can guarantee is that we can find some m so to |x-n/m| <= 1/2m. One way to define good approximation is if for a given m, we can get a lot closer than 1/2m to x then that is close. For example if we want to approximate pi with m = 6, 7, or 8, the closest we can get is 19/6, 22/7, and 25/8. The absolute errors are about 1/40, 1/790, and 1/60, respectively. They are all doing better than 1/2m, but 6 and 7 are only about 3.5 times better 1/2m, but 7 is 56 times better than 1/2m. So we say that 22/7 is a good approximation to Pi. That doesn't mean it is particular close--just that it is way closer than other approximations with similar sized denominators. For a given number x there is a way to find such good approximations. You figure out the continued fraction for x. For Pi that is 3 + 1/(7 + 1/(15 + 1/(1 + 1/(292 + 1/(1 + ..., then even though that goes on forever you type ")))))" so that the unbalanced parens don't drive you crazy, and take the sequence you get by taking finite sections from the left side of that continued fraction. So for Pi we get 3, 1 + 1/7, 3 + 1/(7 + 1/15), ..., which when simplified give 3, 22/7, 333/106, 355/113, 103993/33102, .... Note that 22/7 is in there, which is the good approximation from early. All of those numbers from taking the left parts of the continued fraction, which are called convergents of the continued fraction, are good approximation in the sense above: they are way closer to Pi than anything else with similar denominators. What we can do then to find good integer ratios that are close to the notes of 12-TET is for each 12-TET note, take its frequency divided by C's frequency, compute the continued fraction of that, and compute the first few convergents. Here are the results. I've omitted convergents with a denominator of 1 or with a denominator > 500. C#/Db: {17/16, 18/17, 89/84, 196/185} D: { 9/8, 55/49} D#/Eb: { 6/5, 19/16, 25/21, 44/37} E: { 4/3, 5/4, 29/23 34/27, 63/50, 286/227, 349/277} F: { 3/2, 4/3, 295/221} F#/Gb: { 3/2, 7/5, 17/12, 41/29, 99/70, 239/169, 577/408} G: { 3/2, 442/295} G#/Ab: { 3/2, 8/5, 19/12, 27/17, 100/63, 227/143, 781/492} A: { 5/3, 37/22} A#/Bb: { 7/4, 9/5, 16/9, 41/23, 57/32, 98/55} B: {15/8, 17/9, 168/89, 185/98}

beefman 4y ago

Great question but some unfortunate errors here. > Before the advent of temperament systems, D-sharp and E-flat were two different notes. D# and Eb were defined as elements of a temperament system, namely meantone temperament. > My track is tuned in a system called five-limit just intonation ... It's the basis for all the tuning systems used in Western Europe between about 1500 and 1900. The basis for tuning systems in Western Europe between 1400 and 1800 was meantone temperament. 5-limit JI has never been the basis of a common practice music culture anywhere or at any time in world history. > We can do this because Western people consider octaves to be equivalent. All people experience octave equivalence. > Ultimately, split black keys did not catch on. Split keys were fairly common on keyboard instruments for about a century. > Bach wrote The Well-Tempered Clavier to show off how one well temperament system (no one knows which one) sounds okay in every major and minor key. Bach was a proponent of well temperaments in general, not any specific one.

ethanhein 4y ago
Meantone is a modification of three-limit just intonation to try to better approximate the thirds from five-limit just intonation. I know that it is historically inaccurate to say that meantone follows from five-limit, but in order to understand the point of meantone's existence, you have to know about five-limit as the standard that meantone is aiming for. I should probably rephrase my post to say that meantone follows logically from five-limit, not that it follows historically. All humans (and some monkeys) can detect octaves, but that does not mean that all humans consider octaves to be equivalent. That's a culturally specific convention. It's a very widespread convention thanks to Europe's wide cultural reach, but it's very much not a universal one. Split keys may have been common for a while, but I think we can agree that in the long term, they did not catch on.

bewaretheirs 4y ago

Related in a distant way: https://news.ycombinator.com/item?id=31476078 https://news.ycombinator.com/item?id=31476078 my TL;DR, as a western classically-trained amateur musician largely unfamiliar with Indian music: Harmonium (a small reed organ) is widely used in Indian classical music but its use is controversial because it doesn't allow for the fine adjustments in pitch (roughly analogous to the D#/Eb distinction discussed here) that is seen as central to most/all Indian styles.

wforfang 4y ago

D-sharp and E-flat are two different notes used to describe the same physical vibration for the same reason "father" and "son" are two different words that could describe the same person. It's just a way to communicate contextual relation.

marton78 4y ago
This is false. D-sharp and E-flat have (slightly) different frequencies. Read the article!
- dehrmann 4y ago
  ...in certain temperaments, but not the ubiquitous 12-TET.
  - noslenwerdna 4y ago
    ... as thoroughly explained in the article.
    - P_I_Staker 4y ago
      Well I haven't read the article, so IDK

deleted 4y ago

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vram22 4y ago

Sort of related, and may be interesting, for the comments in this post about a Python piano app I had done some years ago: Play the piano on your computer with Python: https://jugad2.blogspot.com/2013/04/play-piano-on-your-computer-with-python.html?m=0 https://jugad2.blogspot.com/2013/04/play-piano-on-your-compu... Some of the comments gave some interesting music theory info.

d1sxeyes 4y ago

The author asks an interesting question which I didn’t see the answer to in his reply: what DO you call this note in the A minor blues scale? He says you’re only supposed to use each letter once, so am I supposed to call this an E flat and then refer to the following note as an F flat? I struggle a bit with considering the ‘blue note’ a variation of the fifth - it feels more to me like a variation of the fourth, so is it in fact a D sharp? But then the fourth would be C double-sharp, and the (flat) third would be B sharp… right? All of that just sounds mad.

JIMS_Music_Sys 4y ago

Ethan, You wrote, "your choices were these: you could limit your harpsichord playing to certain keys, or you could have a bewilderingly complex instrument that you would spend half your life tuning." May I respectfully suggest that an alternative option exist now, which did not exist then? First, please note that the tunings that you are describing are all extended meantone tunings (more or less), derived from stacking perfect fifths (P5's) that have been more-or-less tempered away from their just ratio (702 cents). If you widen the P5 to 720 cents, you get 5-tone equal temperament (5-tet). If you narrow the P5 to 686 cents, you get 7-tet. In between, you get the historical meantone tunings and today's 12-tet (P5=700). They are all defined by the same three elements: 1. Their period of repetition, the perfect octave (P8) which maps the 2nd partial to the P8. 2. Their generator, the tempered P5, which maps the 3rd partial to the P5. 3. Their comma sequence, which starts with the syntonic comma, which maps the 5th partial to the M3.(If the first comma in the sequence were the schisma, then the 5th partial would be mapped to the d4, defining the schismatic temperament.) This combination of a P8 period, P5 generator, and comma sequence that starts with the syntonic comma, is called the "syntonic temperament" in "Dynamic Tonality" (see Wikipedia for both quoted terms). An "isomorphic keyboard" is a keyboard that is generated by the same period, generator, and comma sequence as the temperament with which it is said to be isomorphic. Isomorphic keyboards had not yet been discovered before the West standardized on 12-tet. Had they been known then, then the course of musical history might have been quite different. With brings me back to your quote. A keyboard that is isomorphic with the syntonic temperament is brain-dead simple. It has the same fingering in every octave of every key of every tuning of the syntonic temperament. 12-tet, 1/4 meantone, 32-tet, 53-tet, infinity-tet -- same fingering. One can even bias the mapping of pitches to notes to support irregular tunings such as well-temperaments. Therefore, IF ISOMORPHIC KEYBOARDS HAD EXISTED during the period that you describe, then they would have had a shot at becoming the de facto standard keyboard instrument subsequently. Today, isomorphic keyboards DO exist. Anyone who is serious about exploring the frontiers of tonality should check them out (and Dynamic Tonality, which requires an isomorphic keyboard). Respectfully, Jim Plamondon