10 ms·

What Is a Major Chord?

78 points by mhb 5y ago

revskill 5y ago
In simple terms, intuitively, major sounds more funny, it's good to cheer up listeners.
kevinventullo 5y ago
There’s a bit more to this: a “perfect” fifth is not actually two notes differing by a factor of 2^(7/12), but rather by a factor of 1.5. It just so happens that 2^(7/12) is very close to 1.5, which makes it possible to tune a piano so that all fifths and all octaves sound approximately right. Theoretically, though, there will always be some error: any non-integer power of two is necessarily irrational. Thus, there is no perfect way to divide an octave into equally hz-spaced increments so that you hit the fifth along the way to doing the whole octave.
- deleted 5y ago
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- VBprogrammer 5y ago
  I believe it's also one of the reasons the G-string is hardest to tune by ear because in equal temperament it's actually the furthest away from the true note.
  - hunter2_ 5y ago
    Yes, between most guitar strings is a perfect 4th interval (where equal temperament ratio [0] and the integer ratio it approximates [1] are quite close to each other) but between the G string and B string is a major 3rd interval (where equal temperament ratio [3] and the integer ratio it approximates [4] are a bit farther from each other). When using a tuner to tune a guitar, you get the equal temperament normally desired for it's ability to play equally in any key. When tuning by ear, if you are just minimizing the beating you hear (instead of targeting the beating that exists in equal temperament, like good piano technicians are trained to do) you'll end up with integer ratios. Accidentally ending up at the integer ratio of a major third is "farther off" than doing so for a perfect fourth. Typically this manifests as a difficult time tuning the B string though, not the G string, if you go low to high. Solution: tune low to high for the E,A,D,G and tune high to low for the high E,B (doing a perfect octave for the E to E where the equal temperament ratio [4] perfectly matches the integer ratio [5]). [0] 1.334840:1 or 2^(5/12):1 [1] 1.333333:1 or 4:3 [2] 1.259921:1 or 2^(4/12):1 [3] 1.25:1 or 5:4 [4] 2:1 or 2^(12/12):1 [5] 2:1
    - ghostpepper 5y ago
      Does this mean there's actually a scientific reason to tune by ear instead of with an electronic tuner? I feel like I naturally do some of these things, like tuning low to high but then (seemingly arbitrarily) tune the high e against the low E.
      - hunter2_ 5y ago
        Yes, integer ratios sound better than equal temperament ratios. The downside is that you end up with an instrument that has some integer ratios and some disgusting wolf intervals because it's mathematically impossible to have all integer ratios between every possible interval in every possible key you might decide to play in. That problem is what equal temperament solves for, and is a good reason to use an electronic tuner unless you know your songs will sound better without.
    - narag 5y ago
      When tuning by ear, if you are just minimizing the beating you hear... I assume you are talking about fretless instruments. With a guitar you just play a unison using the frets and the thicker string.
      - hunter2_ 5y ago
        No, my entire comment is about tuning a typical fretted guitar. Playing a unison as you say, and turning the peg until beating completely disappears, yields integer ratios instead of equal temperament ratios. The result of that can sound nicer than equal temperament for some keys/chords but terrible for other keys/chords.
        narag 5y ago
        Unison means same sound. There's no ratio, unless you mean 1:1.
        hunter2_ 5y ago
  - osigurdson 5y ago
    I've always found the B string hardest to tune by ear. Generally I need to fine tune it in the context of a few chords.
    - hunter2_ 5y ago
      Whether G is hard or B is hard depends on whether you're going high-to-low or low-to-high, as the issue is the interval between them, so it's just a matter of which one you're using as a known-good reference and which one you're trying to tune. There's an easier solution than taking multiple passes as you play different chords: see my other comment.
      - osigurdson 5y ago
        Thanks. I understand your approach but what method do you use to tune the high E? I assume you mean that the low E is used to tune the high E but perhaps you pick an E on the G string for this purpose. Is there any "best" E on the low side to use as a reference?
        hunter2_ 5y ago
        You always need some point of reference to start with, or if you don't have an external reference, you can just go with anything at all. I would typically choose either of the E strings, just to be able to immediately match the other E string to it, and then go inward (up to G and down to B).
        osigurdson 5y ago
        I tried it and it works pretty well. One thing that I noticed is I subconsciously have been tuning GBE open because it’s a pain to reach around to the tuning pegs. How does this impact things?
        hunter2_ 5y ago
        When you play G and B open and tune them to eliminate beating, you're in pretty bad shape because you're making a "just" (integer ratio) major 3rd which is quite far from an equal temperament major 3rd. When you play B and E open and tune them to eliminate beating, you're in okay shape because you're making a "just" (integer ratio) perfect 4th which is not terribly far from an equal temperament perfect 4th. See my earlier comment [0] with all the numbers if you want to quantity "pretty bad" vs "okay". In that comment, my initial references to footnotes 3 and 4 should actually be 2 and 3, but it's too late to correct it. [0] https://news.ycombinator.com/item?id=31145233 https://news.ycombinator.com/item?id=31145233
  - efortis 5y ago
    That's interesting. I start with "A" on the G-string, and then use its "B" to tune the B-string and so on.
- ghostpepper 5y ago
  This is super interesting and I feel like reading it helped a few concepts click for me, so thank you.
- hunter2_ 5y ago
  > all fifths and all octaves sound approximately right Octaves are actually 100% right regardless of equal temperament versus perfect/just/etc. The only real exception is when you get into octave stretching to compensate for string inharmonicity, but that's a whole separate matter.
sunaurus 5y ago
Nice summary. The fact that 7 of the 12 notes in an octave are assigned letters has always bothered me. It's quite arbitrary, we could just as easily have 6 letters + 6 in-between notes, or just 12 discrete letters.
- emerged 5y ago
  The naming makes perfect sense with C Major, or A minor. Because the in-key notes are letters. The weirdness is how we then apply those same names to every other key. I tend to be very C Major focused when playing piano, and just use the transpose function to change keys. Things are much simpler that way IMO.
  - sunaurus 5y ago
    I just tend to think of scales in terms of numbers and not letters, so the pain of having an "uneven" naming for the notes is worse for me than any pain from no longer having letters line up perfectly with two specific scales. But I can see why the current naming is useful for piano players.
    - waqf 5y ago
      As a piano player, let's figure out the best way to arrange the keys on the keyboard first, and figure out the names afterwards.
      - jefftk 5y ago
        My favorite arrangement: https://en.wikipedia.org/wiki/Wicki%E2%80%93Hayden_note_layout https://en.wikipedia.org/wiki/Wicki%E2%80%93Hayden_note_layo...
  - jakelazaroff 5y ago
    I think it makes sense for the other keys, too. Let’s say we had twelve distinct letters, A–L. Here’s a key: H J K A C E F First of all, which key is it? We know it starts with H. But is it major or minor? We have to mentally calculate all the intervals, rather than just looking for the sharps and flats. And calculating the intervals is annoying! You could go 2122212, which doesn’t correspond to major or minor — it’s dorian. Meanwhile, in current notation, you’d just look at the sharps (C# and F# = D major) and the starting note (E).
adamnemecek 5y ago
I’m working on an IDE for music composition. Chords and music theory will be very much front and and center. Launching next month. https://ngrid.io https://ngrid.io Join the discord https://discord.gg/a5ttYuG https://discord.gg/a5ttYuG
- colejohnson66 5y ago
  Do you have any screenshots? That webpage is very bare.
  - adamnemecek 5y ago
    I’m polishing the UI as we speak.
flurie 5y ago
This is an odd post, because the author starts in the right place, harmonics, and then veers off into scale degrees without really answering the question. The best place to get the answer is Schönberg’s Theory of Harmony, but we can do something quick here. The main harmonic series of music is what happens when one applies integer multiplication to a given frequency, which we’ll call a root. As the author described, an octave, or the same perceived sound but higher, is a 2x, and a 3x, or 1.5x the previous value, is called a “fifth” due to it being the fifth major scale degree in the twelve tone system described by the author. 4x is 2^2, another octave, and then 5x is the (major) third. Because all of these integer harmonics are present in the root, though at greatly reduced force, these sounds serve to bolster the natural harmonics of the root.
- deleted 5y ago
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- odyssey7 5y ago
  While it's an interesting derivation, Schoenberg was eager to explain that his book was about teaching practical skills and understanding. He prefaced his derivation with the statement: "Therefore, whenever I theorize, it is less important whether these theories be right than whether they be useful as comparisons to clarify the object and to give the study perspective." This is something I find compelling about Schoenberg. He doesn't claim to know more than he does, he's just presenting a useful mental model.
  - flurie 5y ago
    It sounds like we agree? I recommend that intro because it's practical, especially for someone who is likely an adult asking what a major chord is.
    - odyssey7 5y ago
      This might just be a word choice thing, I think I took issue with it being labeled the answer -- Schoenberg didn't want it to be considered definitive, but merely useful. An overarching theme of the book was his philosophy that no eternal aesthetic laws were known to exist, so he was careful not to make definitive claims unless he could really be sure about them.
f38zf5vdt 5y ago
It's harmony produced the root (any frequency), the major third (5/4 ratio), the 5th (3/2 ratio). They're approximated in the 12TET scale so that they harmonize across keys and octaves. I always say I hate musical notation (letters and classical notation) being it so horrifically obscures the mathematical relationships of the 12TET scale. It's literally just approximations of: Major Scale Root frequency (C 262hz, whatever) 2: 9/8 root (D) 3: 5/4 root (E) 4: 4/3 root (F) 5: 3/2 root (G) 6: 5/3 root (A) 7: 15/8 root (B) 2x root (C, 524 hz) 2: 9/8 2x root and so on. Minor scale is simply the starting the whole thing at the Major 6th instead of at the root. 12TET in comparison to just temperament is slightly harder to explain because of the way it allows harmonies to scale without distorting when changing keys, but there really isn't much more to western music than that.
zw123456 5y ago
The more interesting question to me, is not what makes a major or minor, that is a simple google search away, there are tons of references about that; the more interesting question in my mind is why do certain harmonic intervals sound more pleasing to humans (perhaps animals as well) than other intervals. Is it arbitrary? Perhaps not. There has been a lot of research on that as well, for example: https://www.newscientist.com/article/dn20930-why-harmony-pleases-the-brain/ https://www.newscientist.com/article/dn20930-why-harmony-ple... So, once you figure out what a major and minor are, then the next question is why does that sound better than other combinations of notes?
- parenthesis 5y ago
  How a chord sounds depends greatly on the timbre of the instrument or instruments. For example, a major or minor triad played on a heavily distorted electric guitar sounds pretty uncomfortable (hence power chords), but played on strings sounds pretty calm. How a chord sounds also depends greatly on what came before it. For example, in typical common practice period harmony, dominant seventh chords do not sound resolved. On the other hand, many songs in popular music have moments that resolve to a dominant seventh chord.
  - mrob 5y ago
    A distorted guitar distorts the components of the power chord after mixing them. This means that you get intermodulation distortion between different notes. The sum and different tones generated by this distortion form a harmonic series when combined with the original notes. A power chord is root + fifth, which is a 1:1.5 ratio of frequencies (exactly in just intonation, and very nearly in equal temperament). Intermodulation distortion produces tones of frequency ratio 1.5 + 1 and 1.5 - 1, giving 2 and 0.5. Combine them with the existing tones and you get 0.5:1:1.5:2. This is just the harmonic series 1:2:3:4, but pitched down an octave (all frequencies divided by two). A distorted power chord contains the harmonics of a single note pitched an octave lower, which is why it sounds "heavy". There are many other harmonics in the notes, so the timbre is much more complicated that that, but the fundamentals are most prominent, so the distorted power chord sounds consonant. And if you have a guitar with a hexaphonic pickup and distort each string individually you don't get intermodulation distortion between the notes, so you can play much more complicated chords without it sounding dissonant.
analog31 5y ago
Granted, I'm a musician, so take everything I say with a grain of salt. And I don't know what the author's background is. But I've noticed that the people who tend to have the biggest problem with music theory are engineers. I think it comes from an assumption that music should be learned like engineering, where you start with fundamentals, and then build upon them. And then they're horrified to discover that even the fundamentals are arbitrary and approximate. Most musicians don't start out with fundamentals. We started by choosing an instrument and somehow learning to play it. For the most part, musicians don't care about temperaments. Equal temperament only applies to a handful of instruments that can be kept in tune long enough for it to matter, and that can play the same note, the same way, twice. An orchestra, jazz band, or solo fiddler, have no temperament in any meaningful sense. Yes, musical notation is a cluster. But it serves its purpose well enough to be useful to support a symbiosis between the composer and the performer. If any composer chooses to try a bespoke notation, they'll discover that nobody will ever perform their composition. It's like a programming language that nobody likes, but that is supported by a job market and labor pool. My advice for any engineer wanting to get into music is, get an instrument and learn to play it. Preferably a non-electronic one, so you won't be tempted to turn music into a numbers game.
- k__ 5y ago
  As educator for engineers, I would even go so far as to say your approach is good for engineering too. I had the impression that fundamentals are much easier if you played around with some real world tech. But to go back to music theory. I think, it helps when you already started a song and you're stuck. If you got a catchy melody, some theory gives you the tools to add fitting harmonies to it, etc.
- defanor 5y ago
  As a programmer studying music, I found the "music theory for nerds" article [1] very helpful to get started, and then kept noticing how many general music learning materials for beginners skip the fundamentals/justification, suggesting to just remember many non-arbitrary things that can be deduced, without explaining why they are that way. As the article itself mentions, the hard part is to figure which parts are arbitrary and which ones are not quite so arbitrary, but pretty sure an engineer can get an easy start by studying those bits first. Playing an instrument is nice and fun too, of course, but I think it's more helpful for intuition rather than actual understanding -- and those are usually best to combine. [1] https://eev.ee/blog/2016/09/15/music-theory-for-nerds/ https://eev.ee/blog/2016/09/15/music-theory-for-nerds/
jdontillman 5y ago
Sorry, but I have to say that none of this will make a particle of sense to someone who would be asking such a question. A rudimentary question is a wonderful an opportunity to distill everything down to a simple understandable concept. Here's how I would do it: --- Western music is based on simple frequency ratios. 2:1 is so basic that we call it the same note, but an octave up. Three pitches with ratios 4:5:6 make a major chord. These are the simplest possible ratios within an octave, so a major chord is the most basic chord, and all other chords are derived from that
- mrob 5y ago
  >Western music is based on simple frequency ratios. Western music is based on simple frequency ratios, played by instruments with harmonic timbres (meaning that when you decompose the sound of a single note into sine waves using a Fourier transform, the frequencies of the sine waves are all integer multiples of the lowest frequency sine wave). This is true for wind and string instruments, but not true with tuned percussion unless you go to special effort to shape the instrument to make it so (as is done by bell makers). Musical styles that use inharmonic timbres, e.g. Indonesian gamelan music, need different tuning to sound best. And this also happens in Western music. Piano is technically tuned percussion, and the sound of a piano is slightly inharmonic. Pianos are tuned with stretched octave to compensate: https://en.wikipedia.org/wiki/Stretched_tuning https://en.wikipedia.org/wiki/Stretched_tuning
  - jdontillman 5y ago
    That's all very interesting... But the harmonic or inharmonic content of the instrument does not address the original question. And it leads to confusion; putting your first and last sentences together implies that a piano is not a western musical instrument. We know that's not true.
    - mrob 5y ago
      Piano timbre is approximately harmonic. The inharmonicity is subtle enough that you can ignore it and it will still sound okay. Same is true with plucked string instruments. You're still using Western music theory.
jimhefferon 5y ago
In case some folks have not seen it: along something of the same lines but in very much more depth is Music: A Mathematical Offering by Dave Benson, at https://logosfoundation.org/kursus/music_math.pdf https://logosfoundation.org/kursus/music_math.pdf
jdwyah 5y ago
Chuckle. This is why people can’t stand engineers. (Said with love, but still). The idea that mhz is even worth mentioning… Fwiw, huge shout out to https://improviseforreal.com https://improviseforreal.com which for me was the happy medium between “major chord is happy” (huh?, whyyy?) and “C0 is 16 mhz”.
- jefftk 5y ago
  Hz, not MHz. The upper limit of human hearing is only 20 KHz.
sizzzzlerz 5y ago
I've been a musician since I learned to play the clarinet beginning in 4th grade, almost 57 years ago. During that time, I've learned to play the saxophone, guitar, and the piano. I learned how to read music from the very start and have been totally accustomed to the western notation. Is it the best? I have no idea. It's the only way I know. That said, anybody attempting to design a new, better, notation is facing long odds in it every being widely adopted, even if it can demonstrate some advantages. Trying to persuade the music community would be like trying to convince typists to use the Dvorak keyboard instead of the standard. Yes, some will adopt it and sing its praises but most will not want to relearn how to type.
osigurdson 5y ago
One thing they do not mention is a stringed instrument creates a standing wave which produces many octaves simultaneously when playing a single note. This sounds considerably different from a pure sine wave and is possible to leverage in a creative way on guitar/guitar like instruments.
- jefftk 5y ago
  Not just many octaves: many harmonics. With an ideal string, these are all multiples of the fundamental frequency, because they each represent a different way of dividing the whole string into equal parts.
efortis 5y ago
A chord-maker JS kata: https://github.com/ericfortis/chord-maker https://github.com/ericfortis/chord-maker
ridaj 5y ago
As a tentatively more minimalistic explanation, the musical ear perceives specific geometric relationships between frequencies as strong stimuli, and a major chord consists of simultaneously striking frequencies x, x times the cube root of 2, and x times 3/2.
reggieband 5y ago
I wonder what it is about music that makes people accept these simplifications. I imagine an alternate universe where an article on the optics of color is posted. Someone mentions that all light are frequencies, the color red is such-and-such frequency, blue is whatever Hz, etc. We observe that a color wheel creates some theory of adjacency, compliments of color etc. And some artists use this in their work to enhance the effect. Would an article like that warrant a comment section filled with a bunch of people acting like that gave them sufficient tools to understand the works of Da Vinci, Van Gogh, Picasso? Pitch, melody and harmony are integral aspects to music but they are by no means sufficient to provide an understanding of music. Just as a purely mathematical description of the optics of color is not sufficient to understand painting. I would argue that the overwhelming majority of music you have enjoyed in your life was written with literally zero regard to these details. In my own opinion, music programs that raise these mathematical details above all others lead to the dullest and least inspired music.
cato_the_elder 5y ago
I'm not much of a musician, but all the explanations about why the major scale is the way is, or octave equivalence, etc. always sound suspiciously similar to the good old "nature abhors a vacuum" [1] to me. I feel like it has much more to do with convention than music theorists like to confess. [1]: https://en.m.wikipedia.org/wiki/Horror_vacui_(physics) https://en.m.wikipedia.org/wiki/Horror_vacui_(physics)
dr_dshiv 5y ago
Does anyone know the legend of Pythagoras? It is the best. First scientific experiment in history, too…
taylodl 5y ago
You want to learn music theory? Check out Rick Beato’s book. https://rickbeato.com/products/the-beato-book-4-0-pdf https://rickbeato.com/products/the-beato-book-4-0-pdf It’s comprehensive. It’s also frequently on sale for 40% or more off. He sends you updates when he releases new versions.
museme 5y ago
There is something cruel about having the base unit of your counting system be 1/2. But then again, pi.

78 points by mhb 5y ago

In simple terms, intuitively, major sounds more funny, it's good to cheer up listeners.

There’s a bit more to this: a “perfect” fifth is not actually two notes differing by a factor of 2^(7/12), but rather by a factor of 1.5. It just so happens that 2^(7/12) is very close to 1.5, which makes it possible to tune a piano so that all fifths and all octaves sound approximately right. Theoretically, though, there will always be some error: any non-integer power of two is necessarily irrational. Thus, there is no perfect way to divide an octave into equally hz-spaced increments so that you hit the fifth along the way to doing the whole octave.

deleted 5y ago
[deleted]
VBprogrammer 5y ago
I believe it's also one of the reasons the G-string is hardest to tune by ear because in equal temperament it's actually the furthest away from the true note.
- hunter2_ 5y ago
  Yes, between most guitar strings is a perfect 4th interval (where equal temperament ratio [0] and the integer ratio it approximates [1] are quite close to each other) but between the G string and B string is a major 3rd interval (where equal temperament ratio [3] and the integer ratio it approximates [4] are a bit farther from each other). When using a tuner to tune a guitar, you get the equal temperament normally desired for it's ability to play equally in any key. When tuning by ear, if you are just minimizing the beating you hear (instead of targeting the beating that exists in equal temperament, like good piano technicians are trained to do) you'll end up with integer ratios. Accidentally ending up at the integer ratio of a major third is "farther off" than doing so for a perfect fourth. Typically this manifests as a difficult time tuning the B string though, not the G string, if you go low to high. Solution: tune low to high for the E,A,D,G and tune high to low for the high E,B (doing a perfect octave for the E to E where the equal temperament ratio [4] perfectly matches the integer ratio [5]). [0] 1.334840:1 or 2^(5/12):1 [1] 1.333333:1 or 4:3 [2] 1.259921:1 or 2^(4/12):1 [3] 1.25:1 or 5:4 [4] 2:1 or 2^(12/12):1 [5] 2:1
  - ghostpepper 5y ago
    Does this mean there's actually a scientific reason to tune by ear instead of with an electronic tuner? I feel like I naturally do some of these things, like tuning low to high but then (seemingly arbitrarily) tune the high e against the low E.
    - hunter2_ 5y ago
      Yes, integer ratios sound better than equal temperament ratios. The downside is that you end up with an instrument that has some integer ratios and some disgusting wolf intervals because it's mathematically impossible to have all integer ratios between every possible interval in every possible key you might decide to play in. That problem is what equal temperament solves for, and is a good reason to use an electronic tuner unless you know your songs will sound better without.
  - narag 5y ago
    When tuning by ear, if you are just minimizing the beating you hear... I assume you are talking about fretless instruments. With a guitar you just play a unison using the frets and the thicker string.
    - hunter2_ 5y ago
      No, my entire comment is about tuning a typical fretted guitar. Playing a unison as you say, and turning the peg until beating completely disappears, yields integer ratios instead of equal temperament ratios. The result of that can sound nicer than equal temperament for some keys/chords but terrible for other keys/chords.
      - narag 5y ago
        Unison means same sound. There's no ratio, unless you mean 1:1.
        hunter2_ 5y ago
- osigurdson 5y ago
  I've always found the B string hardest to tune by ear. Generally I need to fine tune it in the context of a few chords.
  - hunter2_ 5y ago
    Whether G is hard or B is hard depends on whether you're going high-to-low or low-to-high, as the issue is the interval between them, so it's just a matter of which one you're using as a known-good reference and which one you're trying to tune. There's an easier solution than taking multiple passes as you play different chords: see my other comment.
    - osigurdson 5y ago
      Thanks. I understand your approach but what method do you use to tune the high E? I assume you mean that the low E is used to tune the high E but perhaps you pick an E on the G string for this purpose. Is there any "best" E on the low side to use as a reference?
      - hunter2_ 5y ago
        You always need some point of reference to start with, or if you don't have an external reference, you can just go with anything at all. I would typically choose either of the E strings, just to be able to immediately match the other E string to it, and then go inward (up to G and down to B).
        osigurdson 5y ago
        I tried it and it works pretty well. One thing that I noticed is I subconsciously have been tuning GBE open because it’s a pain to reach around to the tuning pegs. How does this impact things?
        hunter2_ 5y ago
        When you play G and B open and tune them to eliminate beating, you're in pretty bad shape because you're making a "just" (integer ratio) major 3rd which is quite far from an equal temperament major 3rd. When you play B and E open and tune them to eliminate beating, you're in okay shape because you're making a "just" (integer ratio) perfect 4th which is not terribly far from an equal temperament perfect 4th. See my earlier comment [0] with all the numbers if you want to quantity "pretty bad" vs "okay". In that comment, my initial references to footnotes 3 and 4 should actually be 2 and 3, but it's too late to correct it. [0] https://news.ycombinator.com/item?id=31145233 https://news.ycombinator.com/item?id=31145233
- efortis 5y ago
  That's interesting. I start with "A" on the G-string, and then use its "B" to tune the B-string and so on.
ghostpepper 5y ago
This is super interesting and I feel like reading it helped a few concepts click for me, so thank you.
hunter2_ 5y ago
> all fifths and all octaves sound approximately right Octaves are actually 100% right regardless of equal temperament versus perfect/just/etc. The only real exception is when you get into octave stretching to compensate for string inharmonicity, but that's a whole separate matter.

sunaurus 5y ago

Nice summary. The fact that 7 of the 12 notes in an octave are assigned letters has always bothered me. It's quite arbitrary, we could just as easily have 6 letters + 6 in-between notes, or just 12 discrete letters.

emerged 5y ago
The naming makes perfect sense with C Major, or A minor. Because the in-key notes are letters. The weirdness is how we then apply those same names to every other key. I tend to be very C Major focused when playing piano, and just use the transpose function to change keys. Things are much simpler that way IMO.
- sunaurus 5y ago
  I just tend to think of scales in terms of numbers and not letters, so the pain of having an "uneven" naming for the notes is worse for me than any pain from no longer having letters line up perfectly with two specific scales. But I can see why the current naming is useful for piano players.
  - waqf 5y ago
    As a piano player, let's figure out the best way to arrange the keys on the keyboard first, and figure out the names afterwards.
    - jefftk 5y ago
      My favorite arrangement: https://en.wikipedia.org/wiki/Wicki%E2%80%93Hayden_note_layout https://en.wikipedia.org/wiki/Wicki%E2%80%93Hayden_note_layo...
- jakelazaroff 5y ago
  I think it makes sense for the other keys, too. Let’s say we had twelve distinct letters, A–L. Here’s a key: H J K A C E F First of all, which key is it? We know it starts with H. But is it major or minor? We have to mentally calculate all the intervals, rather than just looking for the sharps and flats. And calculating the intervals is annoying! You could go 2122212, which doesn’t correspond to major or minor — it’s dorian. Meanwhile, in current notation, you’d just look at the sharps (C# and F# = D major) and the starting note (E).

adamnemecek 5y ago

I’m working on an IDE for music composition. Chords and music theory will be very much front and and center. Launching next month. https://ngrid.io https://ngrid.io Join the discord https://discord.gg/a5ttYuG https://discord.gg/a5ttYuG

colejohnson66 5y ago
Do you have any screenshots? That webpage is very bare.
- adamnemecek 5y ago
  I’m polishing the UI as we speak.

flurie 5y ago

This is an odd post, because the author starts in the right place, harmonics, and then veers off into scale degrees without really answering the question. The best place to get the answer is Schönberg’s Theory of Harmony, but we can do something quick here. The main harmonic series of music is what happens when one applies integer multiplication to a given frequency, which we’ll call a root. As the author described, an octave, or the same perceived sound but higher, is a 2x, and a 3x, or 1.5x the previous value, is called a “fifth” due to it being the fifth major scale degree in the twelve tone system described by the author. 4x is 2^2, another octave, and then 5x is the (major) third. Because all of these integer harmonics are present in the root, though at greatly reduced force, these sounds serve to bolster the natural harmonics of the root.

deleted 5y ago
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odyssey7 5y ago
While it's an interesting derivation, Schoenberg was eager to explain that his book was about teaching practical skills and understanding. He prefaced his derivation with the statement: "Therefore, whenever I theorize, it is less important whether these theories be right than whether they be useful as comparisons to clarify the object and to give the study perspective." This is something I find compelling about Schoenberg. He doesn't claim to know more than he does, he's just presenting a useful mental model.
- flurie 5y ago
  It sounds like we agree? I recommend that intro because it's practical, especially for someone who is likely an adult asking what a major chord is.
  - odyssey7 5y ago
    This might just be a word choice thing, I think I took issue with it being labeled the answer -- Schoenberg didn't want it to be considered definitive, but merely useful. An overarching theme of the book was his philosophy that no eternal aesthetic laws were known to exist, so he was careful not to make definitive claims unless he could really be sure about them.

f38zf5vdt 5y ago

It's harmony produced the root (any frequency), the major third (5/4 ratio), the 5th (3/2 ratio). They're approximated in the 12TET scale so that they harmonize across keys and octaves. I always say I hate musical notation (letters and classical notation) being it so horrifically obscures the mathematical relationships of the 12TET scale. It's literally just approximations of: Major Scale Root frequency (C 262hz, whatever) 2: 9/8 root (D) 3: 5/4 root (E) 4: 4/3 root (F) 5: 3/2 root (G) 6: 5/3 root (A) 7: 15/8 root (B) 2x root (C, 524 hz) 2: 9/8 2x root and so on. Minor scale is simply the starting the whole thing at the Major 6th instead of at the root. 12TET in comparison to just temperament is slightly harder to explain because of the way it allows harmonies to scale without distorting when changing keys, but there really isn't much more to western music than that.

zw123456 5y ago

The more interesting question to me, is not what makes a major or minor, that is a simple google search away, there are tons of references about that; the more interesting question in my mind is why do certain harmonic intervals sound more pleasing to humans (perhaps animals as well) than other intervals. Is it arbitrary? Perhaps not. There has been a lot of research on that as well, for example: https://www.newscientist.com/article/dn20930-why-harmony-pleases-the-brain/ https://www.newscientist.com/article/dn20930-why-harmony-ple... So, once you figure out what a major and minor are, then the next question is why does that sound better than other combinations of notes?

parenthesis 5y ago
How a chord sounds depends greatly on the timbre of the instrument or instruments. For example, a major or minor triad played on a heavily distorted electric guitar sounds pretty uncomfortable (hence power chords), but played on strings sounds pretty calm. How a chord sounds also depends greatly on what came before it. For example, in typical common practice period harmony, dominant seventh chords do not sound resolved. On the other hand, many songs in popular music have moments that resolve to a dominant seventh chord.
- mrob 5y ago
  A distorted guitar distorts the components of the power chord after mixing them. This means that you get intermodulation distortion between different notes. The sum and different tones generated by this distortion form a harmonic series when combined with the original notes. A power chord is root + fifth, which is a 1:1.5 ratio of frequencies (exactly in just intonation, and very nearly in equal temperament). Intermodulation distortion produces tones of frequency ratio 1.5 + 1 and 1.5 - 1, giving 2 and 0.5. Combine them with the existing tones and you get 0.5:1:1.5:2. This is just the harmonic series 1:2:3:4, but pitched down an octave (all frequencies divided by two). A distorted power chord contains the harmonics of a single note pitched an octave lower, which is why it sounds "heavy". There are many other harmonics in the notes, so the timbre is much more complicated that that, but the fundamentals are most prominent, so the distorted power chord sounds consonant. And if you have a guitar with a hexaphonic pickup and distort each string individually you don't get intermodulation distortion between the notes, so you can play much more complicated chords without it sounding dissonant.

analog31 5y ago

Granted, I'm a musician, so take everything I say with a grain of salt. And I don't know what the author's background is. But I've noticed that the people who tend to have the biggest problem with music theory are engineers. I think it comes from an assumption that music should be learned like engineering, where you start with fundamentals, and then build upon them. And then they're horrified to discover that even the fundamentals are arbitrary and approximate. Most musicians don't start out with fundamentals. We started by choosing an instrument and somehow learning to play it. For the most part, musicians don't care about temperaments. Equal temperament only applies to a handful of instruments that can be kept in tune long enough for it to matter, and that can play the same note, the same way, twice. An orchestra, jazz band, or solo fiddler, have no temperament in any meaningful sense. Yes, musical notation is a cluster. But it serves its purpose well enough to be useful to support a symbiosis between the composer and the performer. If any composer chooses to try a bespoke notation, they'll discover that nobody will ever perform their composition. It's like a programming language that nobody likes, but that is supported by a job market and labor pool. My advice for any engineer wanting to get into music is, get an instrument and learn to play it. Preferably a non-electronic one, so you won't be tempted to turn music into a numbers game.

k__ 5y ago
As educator for engineers, I would even go so far as to say your approach is good for engineering too. I had the impression that fundamentals are much easier if you played around with some real world tech. But to go back to music theory. I think, it helps when you already started a song and you're stuck. If you got a catchy melody, some theory gives you the tools to add fitting harmonies to it, etc.
defanor 5y ago
As a programmer studying music, I found the "music theory for nerds" article [1] very helpful to get started, and then kept noticing how many general music learning materials for beginners skip the fundamentals/justification, suggesting to just remember many non-arbitrary things that can be deduced, without explaining why they are that way. As the article itself mentions, the hard part is to figure which parts are arbitrary and which ones are not quite so arbitrary, but pretty sure an engineer can get an easy start by studying those bits first. Playing an instrument is nice and fun too, of course, but I think it's more helpful for intuition rather than actual understanding -- and those are usually best to combine. [1] https://eev.ee/blog/2016/09/15/music-theory-for-nerds/ https://eev.ee/blog/2016/09/15/music-theory-for-nerds/

jdontillman 5y ago

Sorry, but I have to say that none of this will make a particle of sense to someone who would be asking such a question. A rudimentary question is a wonderful an opportunity to distill everything down to a simple understandable concept. Here's how I would do it: --- Western music is based on simple frequency ratios. 2:1 is so basic that we call it the same note, but an octave up. Three pitches with ratios 4:5:6 make a major chord. These are the simplest possible ratios within an octave, so a major chord is the most basic chord, and all other chords are derived from that

mrob 5y ago
>Western music is based on simple frequency ratios. Western music is based on simple frequency ratios, played by instruments with harmonic timbres (meaning that when you decompose the sound of a single note into sine waves using a Fourier transform, the frequencies of the sine waves are all integer multiples of the lowest frequency sine wave). This is true for wind and string instruments, but not true with tuned percussion unless you go to special effort to shape the instrument to make it so (as is done by bell makers). Musical styles that use inharmonic timbres, e.g. Indonesian gamelan music, need different tuning to sound best. And this also happens in Western music. Piano is technically tuned percussion, and the sound of a piano is slightly inharmonic. Pianos are tuned with stretched octave to compensate: https://en.wikipedia.org/wiki/Stretched_tuning https://en.wikipedia.org/wiki/Stretched_tuning
- jdontillman 5y ago
  That's all very interesting... But the harmonic or inharmonic content of the instrument does not address the original question. And it leads to confusion; putting your first and last sentences together implies that a piano is not a western musical instrument. We know that's not true.
  - mrob 5y ago
    Piano timbre is approximately harmonic. The inharmonicity is subtle enough that you can ignore it and it will still sound okay. Same is true with plucked string instruments. You're still using Western music theory.

jimhefferon 5y ago

In case some folks have not seen it: along something of the same lines but in very much more depth is Music: A Mathematical Offering by Dave Benson, at https://logosfoundation.org/kursus/music_math.pdf https://logosfoundation.org/kursus/music_math.pdf

jdwyah 5y ago

Chuckle. This is why people can’t stand engineers. (Said with love, but still). The idea that mhz is even worth mentioning… Fwiw, huge shout out to https://improviseforreal.com https://improviseforreal.com which for me was the happy medium between “major chord is happy” (huh?, whyyy?) and “C0 is 16 mhz”.

jefftk 5y ago
Hz, not MHz. The upper limit of human hearing is only 20 KHz.

sizzzzlerz 5y ago

I've been a musician since I learned to play the clarinet beginning in 4th grade, almost 57 years ago. During that time, I've learned to play the saxophone, guitar, and the piano. I learned how to read music from the very start and have been totally accustomed to the western notation. Is it the best? I have no idea. It's the only way I know. That said, anybody attempting to design a new, better, notation is facing long odds in it every being widely adopted, even if it can demonstrate some advantages. Trying to persuade the music community would be like trying to convince typists to use the Dvorak keyboard instead of the standard. Yes, some will adopt it and sing its praises but most will not want to relearn how to type.

osigurdson 5y ago

One thing they do not mention is a stringed instrument creates a standing wave which produces many octaves simultaneously when playing a single note. This sounds considerably different from a pure sine wave and is possible to leverage in a creative way on guitar/guitar like instruments.

jefftk 5y ago
Not just many octaves: many harmonics. With an ideal string, these are all multiples of the fundamental frequency, because they each represent a different way of dividing the whole string into equal parts.

efortis 5y ago

A chord-maker JS kata: https://github.com/ericfortis/chord-maker https://github.com/ericfortis/chord-maker

ridaj 5y ago

As a tentatively more minimalistic explanation, the musical ear perceives specific geometric relationships between frequencies as strong stimuli, and a major chord consists of simultaneously striking frequencies x, x times the cube root of 2, and x times 3/2.

reggieband 5y ago

I wonder what it is about music that makes people accept these simplifications. I imagine an alternate universe where an article on the optics of color is posted. Someone mentions that all light are frequencies, the color red is such-and-such frequency, blue is whatever Hz, etc. We observe that a color wheel creates some theory of adjacency, compliments of color etc. And some artists use this in their work to enhance the effect. Would an article like that warrant a comment section filled with a bunch of people acting like that gave them sufficient tools to understand the works of Da Vinci, Van Gogh, Picasso? Pitch, melody and harmony are integral aspects to music but they are by no means sufficient to provide an understanding of music. Just as a purely mathematical description of the optics of color is not sufficient to understand painting. I would argue that the overwhelming majority of music you have enjoyed in your life was written with literally zero regard to these details. In my own opinion, music programs that raise these mathematical details above all others lead to the dullest and least inspired music.

cato_the_elder 5y ago

I'm not much of a musician, but all the explanations about why the major scale is the way is, or octave equivalence, etc. always sound suspiciously similar to the good old "nature abhors a vacuum" [1] to me. I feel like it has much more to do with convention than music theorists like to confess. [1]: https://en.m.wikipedia.org/wiki/Horror_vacui_(physics) https://en.m.wikipedia.org/wiki/Horror_vacui_(physics)

dr_dshiv 5y ago

Does anyone know the legend of Pythagoras? It is the best. First scientific experiment in history, too…

taylodl 5y ago

You want to learn music theory? Check out Rick Beato’s book. https://rickbeato.com/products/the-beato-book-4-0-pdf https://rickbeato.com/products/the-beato-book-4-0-pdf It’s comprehensive. It’s also frequently on sale for 40% or more off. He sends you updates when he releases new versions.

museme 5y ago

There is something cruel about having the base unit of your counting system be 1/2. But then again, pi.