7 ms·

A random suggestion to make for nicer, more interesting music: the article takes pitches from a table of equal tempered note frequencies relative to A440: > Fo

by elihu 6y ago

A random suggestion to make for nicer, more interesting music: the article takes pitches from a table of equal tempered note frequencies relative to A440: > For example, here’s a familiar riff “E B D E D B A B”. It uses only 4 notes - D and E from one octave and A + B from the other, lower octave. If we look at the note frequency table, the pitches of those notes in octaves 5 and 4 would be 659.2Hz (E), 587.3Hz (D), 440Hz (A) and 493.8Hz (B). Instead of equal tempered pitches (which are generated by repeatedly multiplying by the 12th root of 2), use pitches that form whole number ratios with respect to the root of your key. A decent 12-note chromatic scale would be something like 1:1, 16:15, 9:8, 6:5, 5:4, 4:3, 45:32, 3:2, 8:5, 5:3, 15:8, and 2:1. So, for instance if your root is C=256 hz, you'd have 256 hz for C, (25616)/15 for C#, (2569)/8 for D, and so on. This is a just intonation (JI) scale. An advantage of JI is that the musical intervals blend with each other better, whereas the advantage of equal temperament (ET) is that you can use any note as the root and change keys on the fly without causing problems. If you're doing electronic music, though, there's a lot less reason to stick with ET: you can always just multiply your whole tuning table by a constant if you want to switch key. JI scales can be made with any ratios: the above maps well to most conventional music, but there's no rule that you have to limit yourself to 12 steps per octave. Using the harmonic series is another option, or adding in ratios that have a 7 in them.

reitzensteinm 6y ago
Maybe a decade ago, I read a story here on HN where somebody was analyzing a singer's audio to detect how close their pitch was, coming to the conclusion that the root was spot on but other notes were slightly sharp or flat. Someone in the comments pointed out that the analysis was done assuming even temperament, and the singer was actually totally nailing just intonation. It's one of those anecdotes that has stuck with me since as a reminder to try to not get tunnel vision on a specific metric.
- andi999 6y ago
  Thats funny. I am generally surprised how singers actually practise with a piano player (which seems to be done here often), since the piano is equally tempered. Wouldnt it make more sense tonpractise with a violin player?
  - toolslive 6y ago
    I don't think it really matters: the piano or violin just offer a reference notes the vocalist needs to be able to match. For example, even though the piano is a limited instrument (frequency wise) it's perfectly possible for a violin player to practice "against" a piano. In the end, whatever the violinist plays is never going to be perfect. There are basically 3strategies to cope with that: micro-adjustments (correcting), add vibrato (masking) and stop playing that note and move to another note.
  - dri_ft 6y ago
    I mean in some sense yes, but more importantly, you probably want to practice with a harmony instrument, i.e. one that can play full chords, which probably means piano, guitar... I can't think of any such instruments where it's easy to tune on the fly as with a violin.
- kzrdude 6y ago
  It sounds like someone with a frequency measurement went to apply it to music without speaking with musicians. As long as they learned something eventually, I guess :)
  - PaulDavisThe1st 6y ago
    Actually, the other way around really. Someone looked up the musical information and measured and found a discrepancy. Given that most western music does in fact use 12TET, the claimed "out of tune-ness" was reasonable to note. The problem is that there are cultures and genres of music that do not use 12TET. In the west these are rare, and many musicians would not know about this. But the measurer had the misfortune to be measuring music that did, and thus was incorrect.
    - powersnail 6y ago
      I think Just intonation, or an approximation to that, is what people are instinctively using, unless they are consciously tuning themselves to a piano. It sounds much more "in tune" to the ear, because of the nice ratios. It really wouldn't surprise me that raw recordings of many singers are in fact more just than equal temperament.
      - PaulDavisThe1st 6y ago
        This makes sense, but it would imply that they have "instinctively solved" the fundamental problems with modulation and harmony that just intonation creates. This seems unlikely.
        elihu 6y ago
        Realistically, they probably just sing an approximation that's close to JI while unconsciously allowing the pitch to drift a little bit so that comma pumps aren't a problem. That seems more plausible than that people naturally sing in an artificial tuning based on repeated multiplication of the twelvth root of two, even if that's the musical context that people are most exposed to these days. Those whole-number ratios are just too good to resist, even if a singer isn't fully aware of what they're doing.
kmill 6y ago
I've had lots of fun experimenting with JI, but I think you're greatly understating the difficulty of using a scale like that for conventional music! Basic chords (like ii) are horribly out of tune due to the syntonic comma, and while you can retune things as you go (like a singer or string player would), it takes a lot of finesse -- the IV ii V I progression is tricky, and if you're not careful you create a comma pump, transposing things down just a little bit by the end. In practice, 5/4 major thirds are at the very low end of acceptible major thirds, with the Pythagorean 81/64 at the top. I find slightly sharper major thirds to sounds better generally [for western common practice harmony]. An interesting system, which I wish I've had more time experimenting with before suggesting it, is 55EDO, using a system where each whole tone is broken into nine equal parts; a five part interval is a major semitone and a four part interval a minor semitone. The major scale is made from whole tones and two major semitones. A C# is slightly flatter than a Db in this system, and you only have to worry about enharmonics (old meaning: futzing with the small distances between similar pitches) in complicated chord progressions. Not suggesting not to try JI of course, I'd recommend experimenting with it (including the suggested 7-limit JI as well)! Scales in the end can only be judged in the context of what you want to do with them -- they certainly all have tradeoffs.
- powersnail 6y ago
  One thing to note is that you don't have to always play a note at the same frequency, even in the same piece. On the violin, it's common to adjust intonation to different concerns: to bring out multiple voices, to put emphasis on the melodic line, or to nail the chords. I don't know how hard it would be to do this digitally though. I imagine it would be quite tedious to work on a fretless digital music software.
- Slow_Hand 6y ago
  Out of curiosity, how do you go about auditioning these systems in your own practice? Are you a performer playing an instrument by ear? Are you sequencing sounds in a DAW? Or are you tuning your sounds in a programming environment similar to the linked article? I ask because I'm an electronic musician working in a DAW (Ableton mostly) and am trying to find the best workflow to start exploring these concepts. Ideally, there would be an interface for switching between tuning systems that's as easy as drawing in a time-signature change, but micro-tuning seems to be a low priority for most DAWs. The only one I know to even begin integrating alternate tuning systems is Logic, and those settings are tucked away deep in the preferences. Does anyone here have a resource for starting to familiarize oneself with how to integrate alternate tunings into their composition? The simpler the better, I suppose. As soon as one sets their foot into the world of alternate tunings you're usually flooded with 40+ tunings. As someone who's worked in Equal Temperament their whole life I would like to pick ONE system and really drill down on it until I get a grip on how to integrate these tunings into programs that are built for ET.
meowface 6y ago
I like trying to make electronic music as a hobby, and I totally agree with your thoughts about just intonation. There's no reason to not at least try it once if you're making electronic music. I personally find it does often produce results that sound better or more interesting to me; chords and intervals are definitely (by definition and subjectively) more consonant and "pure". However, not only must one adjust the tuning each time you want to switch keys, just intonation actually doesn't work for all intervals even within a single key: https://music.stackexchange.com/a/22017 https://music.stackexchange.com/a/22017. This is something I often don't see mentioned. If you're programming the music entirely in software, you could avoid this by basically forgetting about the notion of notes/pitch classes/scales/keys entirely and focus solely on the frequencies and ratios. I wouldn't be surprised if a lot of the best music of the distant future is partly created in such a way (by humans, AIs, and/or both working together). But if you're working in a DAW, the best option may be to consider a few intervals off-limits, if you want everything to be pure.
- elihu 6y ago
  Regarding the "D-minor problem", the way I look at it is that problem is not with just intonation per se, but with how C major is defined and how it is used in equal temperament vs JI. The probelm is solved in JI by re-defining the key of C major to include both 10:9 and 9:8. So, instead of one D, you have two slightly different Ds. Equal temperament just uses a note almost half way in between to play the role of both notes, but that's just an approximation. (This double-role can be useful for certain chord progressions that work out in equal temperament even though mathematically they shouldn't.) JI definitely becomes a lot more useful and interesting if you allow for more than 12 notes per octave. I'd consider 16 to be about a reasonable minimum for conventional 5-limit music, but having more opens up more possibilities. In the context of the original article which seemed to be geared more to just implementing some sort of basic sequencer or picking random notes from a scale, I think picking notes from a JI scale rather than 12-tone equal temperament is an easy way to do something different from what everyone else does with a good chance of having a result that sounds good. More serious music composition or performance in JI generally requires more awareness of the various quirks of JI versus equal temperament. I do wish tooling was better; in some ways, MIDI kind of locked everyone into 12-tone equal temperament, and getting out of that rut is going to require some kind of large change. (MPE and Midi-2.0 are possibilities; time will tell if they pan out.)
sergeykish 6y ago
Equal tempered tuning dissonant on oscilloscope: https://www.youtube.com/watch?v=6NlI4No3s0M https://www.youtube.com/watch?v=6NlI4No3s0M Exploring the lattice, JI and ET: https://www.youtube.com/watch?v=I49bj-X7fH0 https://www.youtube.com/watch?v=I49bj-X7fH0 https://www.youtube.com/watch?v=M5OJgsHXSmY https://www.youtube.com/watch?v=M5OJgsHXSmY > the Tonnetz (German: tone-network) is a conceptual lattice diagram representing tonal space first described by Leonhard Euler in 1739. https://en.wikipedia.org/wiki/Tonnetz https://en.wikipedia.org/wiki/Tonnetz
zokier 6y ago
Just intonation is interesting, but it sort of explodes the composition complexity, because for each note the next (or concurrent) note can be based either on some root note or the current note. For example going up major thirds in C would be C-E-G#, but with just intonation you have to make the choice if that last note should be (C * 5/4) * 5/4 , or C * 8/5. The magic of equal temperament makes the distinction go away, so things are simpler.
- PaulDavisThe1st 6y ago
  Only if you insist on using harmony and/or modulation. There's plenty of musical cultures around the world that don't use harmony to the extent that western music does (if at all), and in these cultures, the issues caused by just intonation (or any tuning/scale system, really) are not anywhere near as much of a problem (if the exist at all).

by elihu 6y ago

reitzensteinm 6y ago

Maybe a decade ago, I read a story here on HN where somebody was analyzing a singer's audio to detect how close their pitch was, coming to the conclusion that the root was spot on but other notes were slightly sharp or flat. Someone in the comments pointed out that the analysis was done assuming even temperament, and the singer was actually totally nailing just intonation. It's one of those anecdotes that has stuck with me since as a reminder to try to not get tunnel vision on a specific metric.

andi999 6y ago
Thats funny. I am generally surprised how singers actually practise with a piano player (which seems to be done here often), since the piano is equally tempered. Wouldnt it make more sense tonpractise with a violin player?
- toolslive 6y ago
  I don't think it really matters: the piano or violin just offer a reference notes the vocalist needs to be able to match. For example, even though the piano is a limited instrument (frequency wise) it's perfectly possible for a violin player to practice "against" a piano. In the end, whatever the violinist plays is never going to be perfect. There are basically 3strategies to cope with that: micro-adjustments (correcting), add vibrato (masking) and stop playing that note and move to another note.
- dri_ft 6y ago
  I mean in some sense yes, but more importantly, you probably want to practice with a harmony instrument, i.e. one that can play full chords, which probably means piano, guitar... I can't think of any such instruments where it's easy to tune on the fly as with a violin.
kzrdude 6y ago
It sounds like someone with a frequency measurement went to apply it to music without speaking with musicians. As long as they learned something eventually, I guess :)
- PaulDavisThe1st 6y ago
  Actually, the other way around really. Someone looked up the musical information and measured and found a discrepancy. Given that most western music does in fact use 12TET, the claimed "out of tune-ness" was reasonable to note. The problem is that there are cultures and genres of music that do not use 12TET. In the west these are rare, and many musicians would not know about this. But the measurer had the misfortune to be measuring music that did, and thus was incorrect.
  - powersnail 6y ago
    I think Just intonation, or an approximation to that, is what people are instinctively using, unless they are consciously tuning themselves to a piano. It sounds much more "in tune" to the ear, because of the nice ratios. It really wouldn't surprise me that raw recordings of many singers are in fact more just than equal temperament.
    - PaulDavisThe1st 6y ago
      This makes sense, but it would imply that they have "instinctively solved" the fundamental problems with modulation and harmony that just intonation creates. This seems unlikely.
      - elihu 6y ago
        Realistically, they probably just sing an approximation that's close to JI while unconsciously allowing the pitch to drift a little bit so that comma pumps aren't a problem. That seems more plausible than that people naturally sing in an artificial tuning based on repeated multiplication of the twelvth root of two, even if that's the musical context that people are most exposed to these days. Those whole-number ratios are just too good to resist, even if a singer isn't fully aware of what they're doing.

kmill 6y ago

I've had lots of fun experimenting with JI, but I think you're greatly understating the difficulty of using a scale like that for conventional music! Basic chords (like ii) are horribly out of tune due to the syntonic comma, and while you can retune things as you go (like a singer or string player would), it takes a lot of finesse -- the IV ii V I progression is tricky, and if you're not careful you create a comma pump, transposing things down just a little bit by the end. In practice, 5/4 major thirds are at the very low end of acceptible major thirds, with the Pythagorean 81/64 at the top. I find slightly sharper major thirds to sounds better generally [for western common practice harmony]. An interesting system, which I wish I've had more time experimenting with before suggesting it, is 55EDO, using a system where each whole tone is broken into nine equal parts; a five part interval is a major semitone and a four part interval a minor semitone. The major scale is made from whole tones and two major semitones. A C# is slightly flatter than a Db in this system, and you only have to worry about enharmonics (old meaning: futzing with the small distances between similar pitches) in complicated chord progressions. Not suggesting not to try JI of course, I'd recommend experimenting with it (including the suggested 7-limit JI as well)! Scales in the end can only be judged in the context of what you want to do with them -- they certainly all have tradeoffs.

powersnail 6y ago
One thing to note is that you don't have to always play a note at the same frequency, even in the same piece. On the violin, it's common to adjust intonation to different concerns: to bring out multiple voices, to put emphasis on the melodic line, or to nail the chords. I don't know how hard it would be to do this digitally though. I imagine it would be quite tedious to work on a fretless digital music software.
Slow_Hand 6y ago
Out of curiosity, how do you go about auditioning these systems in your own practice? Are you a performer playing an instrument by ear? Are you sequencing sounds in a DAW? Or are you tuning your sounds in a programming environment similar to the linked article? I ask because I'm an electronic musician working in a DAW (Ableton mostly) and am trying to find the best workflow to start exploring these concepts. Ideally, there would be an interface for switching between tuning systems that's as easy as drawing in a time-signature change, but micro-tuning seems to be a low priority for most DAWs. The only one I know to even begin integrating alternate tuning systems is Logic, and those settings are tucked away deep in the preferences. Does anyone here have a resource for starting to familiarize oneself with how to integrate alternate tunings into their composition? The simpler the better, I suppose. As soon as one sets their foot into the world of alternate tunings you're usually flooded with 40+ tunings. As someone who's worked in Equal Temperament their whole life I would like to pick ONE system and really drill down on it until I get a grip on how to integrate these tunings into programs that are built for ET.

meowface 6y ago

I like trying to make electronic music as a hobby, and I totally agree with your thoughts about just intonation. There's no reason to not at least try it once if you're making electronic music. I personally find it does often produce results that sound better or more interesting to me; chords and intervals are definitely (by definition and subjectively) more consonant and "pure". However, not only must one adjust the tuning each time you want to switch keys, just intonation actually doesn't work for all intervals even within a single key: https://music.stackexchange.com/a/22017 https://music.stackexchange.com/a/22017. This is something I often don't see mentioned. If you're programming the music entirely in software, you could avoid this by basically forgetting about the notion of notes/pitch classes/scales/keys entirely and focus solely on the frequencies and ratios. I wouldn't be surprised if a lot of the best music of the distant future is partly created in such a way (by humans, AIs, and/or both working together). But if you're working in a DAW, the best option may be to consider a few intervals off-limits, if you want everything to be pure.

elihu 6y ago
Regarding the "D-minor problem", the way I look at it is that problem is not with just intonation per se, but with how C major is defined and how it is used in equal temperament vs JI. The probelm is solved in JI by re-defining the key of C major to include both 10:9 and 9:8. So, instead of one D, you have two slightly different Ds. Equal temperament just uses a note almost half way in between to play the role of both notes, but that's just an approximation. (This double-role can be useful for certain chord progressions that work out in equal temperament even though mathematically they shouldn't.) JI definitely becomes a lot more useful and interesting if you allow for more than 12 notes per octave. I'd consider 16 to be about a reasonable minimum for conventional 5-limit music, but having more opens up more possibilities. In the context of the original article which seemed to be geared more to just implementing some sort of basic sequencer or picking random notes from a scale, I think picking notes from a JI scale rather than 12-tone equal temperament is an easy way to do something different from what everyone else does with a good chance of having a result that sounds good. More serious music composition or performance in JI generally requires more awareness of the various quirks of JI versus equal temperament. I do wish tooling was better; in some ways, MIDI kind of locked everyone into 12-tone equal temperament, and getting out of that rut is going to require some kind of large change. (MPE and Midi-2.0 are possibilities; time will tell if they pan out.)

sergeykish 6y ago

Equal tempered tuning dissonant on oscilloscope: https://www.youtube.com/watch?v=6NlI4No3s0M https://www.youtube.com/watch?v=6NlI4No3s0M Exploring the lattice, JI and ET: https://www.youtube.com/watch?v=I49bj-X7fH0 https://www.youtube.com/watch?v=I49bj-X7fH0 https://www.youtube.com/watch?v=M5OJgsHXSmY https://www.youtube.com/watch?v=M5OJgsHXSmY > the Tonnetz (German: tone-network) is a conceptual lattice diagram representing tonal space first described by Leonhard Euler in 1739. https://en.wikipedia.org/wiki/Tonnetz https://en.wikipedia.org/wiki/Tonnetz

zokier 6y ago

Just intonation is interesting, but it sort of explodes the composition complexity, because for each note the next (or concurrent) note can be based either on some root note or the current note. For example going up major thirds in C would be C-E-G#, but with just intonation you have to make the choice if that last note should be (C * 5/4) * 5/4 , or C * 8/5. The magic of equal temperament makes the distinction go away, so things are simpler.

PaulDavisThe1st 6y ago
Only if you insist on using harmony and/or modulation. There's plenty of musical cultures around the world that don't use harmony to the extent that western music does (if at all), and in these cultures, the issues caused by just intonation (or any tuning/scale system, really) are not anywhere near as much of a problem (if the exist at all).