6 ms·

Now that we can have electronic instruments that "tune" themselves, could we compute song-optimal tunings that preserve the intervals used most in that song? D

Now that we can have electronic instruments that "tune" themselves, could we compute song-optimal tunings that preserve the intervals used most in that song? Does this have a name? As a guitarist we often swap guitars or retune to make certain songs easier to play, or to be able to get a certain tamber put of the note. But I never considered it as a way to address temperament. It's interesting to think how much of music theory emerges out of reconciliation with available instruments, as opposed to reconciliation with the ear.

ajross 4y ago
> Now that we can have electronic instruments that "tune" themselves, could we compute song-optimal tunings that preserve the intervals used most in that song? We've had self-tuning instruments for thousands of years. Vocal harmony has almost always been perfectly tuned for its key. Likewise orchestral strings are fretless and can produce perfect intervals. Equitemperment was an innovation in the 17th century because it approximated the perfect intervals very well ("sounded good") but also permitted the ability to simultaneously represent scales based on every note in the circle of fifths ("sounded interesting"). But the "real" chords were always (well, since the late middle ages) understood to be integer ratios.
- tengwar2 4y ago
  Brass instruments (not just the trombone) can have micro-adjustments in pitch through the embouchure (lip position/tension) of the musician.
  - analog31 4y ago
    Also, the tubes for the individual valves have their own tuning slides. A trumpet will typically have a little thumb-operated lever for one of those slides, to help with some of the notes. I saw a video of a tuba solo, and the tubist was working the tuning slides almost as much as the valves.
    - tengwar2 4y ago
      Those removable slides are usually just to get the spit out of the loops. I haven't seen the lever you mention - are you sure you are not just looking at the usual [water key](https://www.youtube.com/watch?v=vMbb8-WK_VM https://www.youtube.com/watch?v=vMbb8-WK_VM)?
    - dbcurtis 4y ago
      With valved brass instruments you are trying to approximate a logarithmic relationship with a linear sum of components. Trumpets have a high resonant Q, so not using the valve slides is going to produce out of tune notes. I played horn once upon a time. Horns have low resonant Q, so you just “lip it in”.
      - palimpsests 4y ago
        one of my favorite aspects of learning the tuba was when we covered logarithmic approximations via linear summing.
    - jnwatson 4y ago
      Thumb-operated levers on trumpets are uncommon (though, IMHO ergonomically superior). More common are a ring in which you place your left ring finger. The ring is directly attached to a slide on the third valve, so you can flatten notes by extending your left ring finger.
      - bewaretheirs 4y ago
        What I've seen is a thumb lever for the 1st valve, finger ring for the 3rd valve.
  - squarefoot 4y ago
    Does this apply also to sax? I've listened to some (mainly old) recordings where the sax seems clearly out of tune; sometimes it's subtle but there are recordings in which it's so off that one wonders if it's done on purpose (1) and personally I really dislike it. Back in the day there weren't digital effects or they were so primitive that applying pitch correction on the fly while maintaining sound quality and spectral integrity was out of question, still tape recorders allowed to finely set their speed, so tuning the song to a sax being recorded would have been trivial. (1) Example: "get up an get out" by Iggy Pop. https://www.youtube.com/watch?v=R1ld5jG3f-M https://www.youtube.com/watch?v=R1ld5jG3f-M
    - tengwar2 4y ago
      If you listen to the start of Acker Bilk's "Stranger on the Shore", you can hear him bending the notes deliberately.
    - colomon 4y ago
      As far as I know it applies to both brass and woodwinds, though the degree of difficulty involved probably varies between types of instruments and also (at least on the woodwinds I'm familiar with) note to note.
    - palimpsests 4y ago
      retuning via tape velocity modulation would be easiest if the instrument in question was consistently out of tune with the rest of the band - like if the sax was always 15 cents flat relative to the harmonic structure. usually that’s not the case though. typically it’s individual notes. much harder to precisely and accurately modulate tape velocity (especially by hand).
    - mr_tristan 4y ago
      A sax is really easy to control (or lose control) of the pitch. And in fact, many saxophonists will just shift various ranges around sharp or flat to suit their style (cough Phil Woods cough). So basically, a woodwind like a sax will tune a few notes with a piano or whatever, but it's really up to the player to keep playing in tune. I would not even bother trying to autotune or use post-processing; it'll just sound weird. This is also how you can get a room full of student musicians "tuned" but it still sounds like a disaster.
  - bewaretheirs 4y ago
    Yep. And - where musically appropriate - if you know which note of the chord you're playing, you can tweak the pitch towards the Pythagorean tuning and get the harmony to "ring" as the harmonics of each note reinforce each other. This sort of hybrid tuning is common in barbershop quartet singing as well.
- evrydayhustling 4y ago
  This is a cool insight! Can choruses be shown to dynamically adopt "optimal" tunings for a particular song? I.e. the singers settle onto frequencies that make the song's intervals sound best? To be clear, I'm trying to explore the idea that individual songs have optimal tunings because they only use certain intervals. So, something more fine grained even then singing for a particular key.
  - ajross 4y ago
    You can absolutely sing a perfect chord. That's most of the idea behind styles like barbershop, for example. But things start to fall apart when chords transition between each other. The first and third notes of the central chords in a key will line up on top of each other, but the middle notes of the chords and triads based on other notes don't. So just like an equitempered scale sounds a tiny bit off, harmony gets wonky too if you try to do interesting things. So the compromise we've all settled on is that we play music in the equitempered scale, and only adjust a little bit here and there to exploit perfect tunings in limited, style-dependent ways. Which is to say: perfect chords are interesting flavor, but at the end of the day kinda boring in isolation; "real" music needs more rules.
    - evrydayhustling 4y ago
      Awesome appreciate you explaining this. Hadn't considered the idea that transitions vs simultaneous notes "compete" on what the optimal note frequencies are. And very cool to understand that people are dealing with this pragmatically all the time.
      - kofejnik 4y ago
        For a demo, you can search YouTube for “Jacob collier g half-sharp”
  - geofft 4y ago
    Singers will do this via intuition - you don't think of, say, a perfect fifth as 2^(7/12) = 1.4983x over the root. You think of it as a particular pair of sounds that resonates well, much like when you picture "red" in your mind you're not thinking of exact HSV or Pantone values. At most, you'll think of a perfect fifth as exactly halfway between the octaves (1.5x over the root). As the sibling comment points out, this isn't the singers choosing a particular temperament for the entire song; it's them constantly tuning individual chords and intervals to each other and to their previous notes as the song goes on. The same note on paper can be several slightly-different frequencies in different parts of the song, and most singers won't even be able to tell you that they're doing that. (This is also the same mechanism at work when an entire choir singing an unaccompanied piece goes flat without realizing it. Someone will not quite make an ascending interval, and everyone else will adjust to cover it.)
andrepd 4y ago
There is a very similar thing: Just intonation http://alumni.media.mit.edu/~bdenckla/thesis/texts/htthe/node24.html http://alumni.media.mit.edu/~bdenckla/thesis/texts/htthe/nod...
bluGill 4y ago
Maybe, but it needs to be the whole band not just one instrument. What notes the bass us hitting changes how the guitar needs to sound and vice versa. If you have a large orchestra it's gets hard, and even worse if someone hits a wrong note.
mrob 4y ago
You can even dynamically adjust the tuning to maximize consonance throughout the song, e.g.: https://sethares.engr.wisc.edu/mp3s/three_ears.html https://sethares.engr.wisc.edu/mp3s/three_ears.html
- deleted 4y ago
  [deleted]
- dcow 4y ago
  This is really cool. It sounds weird for about the first 45-90 seconds but then my mind adjusts and it sounds really pleasant. Would make a good context/theme for a video game soundtrack.
  - AnonCoward42 4y ago
    It really is kool. However, I have the feeling you can transport only a very limited range of emotions with it as we are accustomed to certain harmonics I guess. Still, it's kinda like alien music and it's certainly creative.
  - drdeca 4y ago
    To me the individual notes sound fine and usually normal-ish (except for the really extended ones), but I have difficulty hearing the overall tune? Or, it sounds like there are parts of a tune with other parts on top which I don’t hear how they fit? I think a clearer demonstration might be to have a side by side comparison of a fairly simple tune in 12TET vs in this dynamical tuning.
    - thewebcount 4y ago
      Agreed! I’m not hearing a very definable or memorable melody or harmony. The synth sounds chosen are kind of grating, which doesn’t help. I’d love to hear something more coherent in this sort of tuning to get a better understanding of it.
- still_grokking 4y ago
  Is "maximized consonance" what causes those extreme sharp sounding ring tones? (After listening to this peace my ears are still ringing; 2 min. after the fact). Also the tonal glides sound like an old broken record player. (This creates a sensation of "wobbling speed", which sounds just wrong). Hmm, my ears are still ringing, even while writing this; that was not a pleasant experience to be honest… I guess I need some ear-bleach. Psytrance to the rescue! Let's see, maybe, hmm, Talpa¹, or maybe better that old Atma set²? ___ ¹ https://www.youtube.com/watch?v=wErFe-1dlg4 https://www.youtube.com/watch?v=wErFe-1dlg4 ² https://www.youtube.com/watch?v=HU9FDStUoT8 https://www.youtube.com/watch?v=HU9FDStUoT8
smrq 4y ago
Not trying to be "that guy", just figured you might want to know-- although it's pronounced "tamber" it's spelled "timbre". Thanks, english.
- kqr 4y ago
  I think this one you can blame on the French.
  - m-p-3 4y ago
    The word sounds exactly how it is written when you say it in French tho, not our fault you adopted the word and say it differently ;)
    - zdragnar 4y ago
      I blame the English aristocrats. Why eat cow like a peasant when you could have some beef like a fancy person?
      - kibwen 4y ago
        And why spell it "color" like the Romans did when you can blithely attempt to imitate the French aristocracy by injecting arbitrary "u"s into random words, thus giving you license to complain about CSS keywords for the rest of recorded history? :P
        willnonya 4y ago
        You're my new favorite person.
      - dudeguy3301 4y ago
        also, think the french started this. a name for the animal in the field, a different name for the animal on your plate.
        4y ago
xhevahir 4y ago
You might like to hear this proprietary algorithm: http://www.hermode.com/index_en.html http://www.hermode.com/index_en.html Since you're a guitarist, there's also this Swedish guitar, which purports to solve the tuning problem (which I tend to think is not a problem but an essential part of the instrument's sound) https://youtu.be/-penQWPHJzI https://youtu.be/-penQWPHJzI
- still_grokking 4y ago
  Wow, this guitar sounds so ultra-clean! Depending on song this could be pretty nice. But the normal, "imperfect" guitar does not sound bad. I would also say, this "imperfection" gives a guitar its typical sound in the first place, so it's not a "problem". Both guitars in that video are great, but indeed quite different.
  - smitty1e 4y ago
    The humanity is in the imperfections. Prediction: society demotes all of the auto-tuning and AI art to training status, and actual art produced by himans with pulses is preferred.
    - still_grokking 4y ago
      Here we're not on the same page, frankly. My favorite style of music (Psytrance) almost requires digital "perfection". It's even not really possible to create a "properly sounding" Psytrance bass-line¹, not even a most basic variant, without doing some math (or using tools that will do that math for you). Frequencies, pitch, tempo, and phase need to match constantly and absolutely perfect, or it won't sound properly. Any "humanization" on any preset would kill the sound instantly! For that reason creating Psytrance is a very "mechanical" task that only machines can perform with the required precision. (And not every machine is good enough for that actually. You need for example oscillators with very high precision or you will experience unwanted artifacts, especially on higher frequencies, that could destroy the sound). Something that could create "perfectly matching" chords that don't include any dissonance would be really useful to get the (most of the time) desired "ultra-clean" Psytrance sounds. The usual alternative is to filter out all dissonance. But that's a lot of work, or in "bigger" chords or soundscapes outright impossible (even when you slice the sound in the frequency spectrum with all kind of tricks; filters also produce artifacts… And trying to get rid of those artifacts, like phase imperfections, changes the sound again in often undesired ways. A "perfect" tuning form the get go would maybe help with such things). ___ ¹ Here two of the better tutorials for Psytrance bass-lines: https://www.youtube.com/watch?v=m40xkEkrEKo https://www.youtube.com/watch?v=m40xkEkrEKo https://www.youtube.com/watch?v=-4B1NcdNJjE https://www.youtube.com/watch?v=-4B1NcdNJjE And if you're lazy see here for a VST plugin send form the gods: https://fx23.net/psylab-pro/ https://fx23.net/psylab-pro/
MikeBattaglia 4y ago
This is called "adaptive just intonation." Logic Pro X has this feature built in, using a particular algorithm called Hermode Tuning. It sounds great
- thebeardisred 4y ago
  /me goes to explore this in Ableton...
golergka 4y ago
Apple Logic Pro has this function built in as Hermode tuning.

ajross 4y ago

> Now that we can have electronic instruments that "tune" themselves, could we compute song-optimal tunings that preserve the intervals used most in that song? We've had self-tuning instruments for thousands of years. Vocal harmony has almost always been perfectly tuned for its key. Likewise orchestral strings are fretless and can produce perfect intervals. Equitemperment was an innovation in the 17th century because it approximated the perfect intervals very well ("sounded good") but also permitted the ability to simultaneously represent scales based on every note in the circle of fifths ("sounded interesting"). But the "real" chords were always (well, since the late middle ages) understood to be integer ratios.

tengwar2 4y ago
Brass instruments (not just the trombone) can have micro-adjustments in pitch through the embouchure (lip position/tension) of the musician.
- analog31 4y ago
  Also, the tubes for the individual valves have their own tuning slides. A trumpet will typically have a little thumb-operated lever for one of those slides, to help with some of the notes. I saw a video of a tuba solo, and the tubist was working the tuning slides almost as much as the valves.
  - tengwar2 4y ago
    Those removable slides are usually just to get the spit out of the loops. I haven't seen the lever you mention - are you sure you are not just looking at the usual [water key](https://www.youtube.com/watch?v=vMbb8-WK_VM https://www.youtube.com/watch?v=vMbb8-WK_VM)?
  - dbcurtis 4y ago
    With valved brass instruments you are trying to approximate a logarithmic relationship with a linear sum of components. Trumpets have a high resonant Q, so not using the valve slides is going to produce out of tune notes. I played horn once upon a time. Horns have low resonant Q, so you just “lip it in”.
    - palimpsests 4y ago
      one of my favorite aspects of learning the tuba was when we covered logarithmic approximations via linear summing.
  - jnwatson 4y ago
    Thumb-operated levers on trumpets are uncommon (though, IMHO ergonomically superior). More common are a ring in which you place your left ring finger. The ring is directly attached to a slide on the third valve, so you can flatten notes by extending your left ring finger.
    - bewaretheirs 4y ago
      What I've seen is a thumb lever for the 1st valve, finger ring for the 3rd valve.
- squarefoot 4y ago
  Does this apply also to sax? I've listened to some (mainly old) recordings where the sax seems clearly out of tune; sometimes it's subtle but there are recordings in which it's so off that one wonders if it's done on purpose (1) and personally I really dislike it. Back in the day there weren't digital effects or they were so primitive that applying pitch correction on the fly while maintaining sound quality and spectral integrity was out of question, still tape recorders allowed to finely set their speed, so tuning the song to a sax being recorded would have been trivial. (1) Example: "get up an get out" by Iggy Pop. https://www.youtube.com/watch?v=R1ld5jG3f-M https://www.youtube.com/watch?v=R1ld5jG3f-M
  - tengwar2 4y ago
    If you listen to the start of Acker Bilk's "Stranger on the Shore", you can hear him bending the notes deliberately.
  - colomon 4y ago
    As far as I know it applies to both brass and woodwinds, though the degree of difficulty involved probably varies between types of instruments and also (at least on the woodwinds I'm familiar with) note to note.
  - palimpsests 4y ago
    retuning via tape velocity modulation would be easiest if the instrument in question was consistently out of tune with the rest of the band - like if the sax was always 15 cents flat relative to the harmonic structure. usually that’s not the case though. typically it’s individual notes. much harder to precisely and accurately modulate tape velocity (especially by hand).
  - mr_tristan 4y ago
    A sax is really easy to control (or lose control) of the pitch. And in fact, many saxophonists will just shift various ranges around sharp or flat to suit their style (cough Phil Woods cough). So basically, a woodwind like a sax will tune a few notes with a piano or whatever, but it's really up to the player to keep playing in tune. I would not even bother trying to autotune or use post-processing; it'll just sound weird. This is also how you can get a room full of student musicians "tuned" but it still sounds like a disaster.
- bewaretheirs 4y ago
  Yep. And - where musically appropriate - if you know which note of the chord you're playing, you can tweak the pitch towards the Pythagorean tuning and get the harmony to "ring" as the harmonics of each note reinforce each other. This sort of hybrid tuning is common in barbershop quartet singing as well.
evrydayhustling 4y ago
This is a cool insight! Can choruses be shown to dynamically adopt "optimal" tunings for a particular song? I.e. the singers settle onto frequencies that make the song's intervals sound best? To be clear, I'm trying to explore the idea that individual songs have optimal tunings because they only use certain intervals. So, something more fine grained even then singing for a particular key.
- ajross 4y ago
  You can absolutely sing a perfect chord. That's most of the idea behind styles like barbershop, for example. But things start to fall apart when chords transition between each other. The first and third notes of the central chords in a key will line up on top of each other, but the middle notes of the chords and triads based on other notes don't. So just like an equitempered scale sounds a tiny bit off, harmony gets wonky too if you try to do interesting things. So the compromise we've all settled on is that we play music in the equitempered scale, and only adjust a little bit here and there to exploit perfect tunings in limited, style-dependent ways. Which is to say: perfect chords are interesting flavor, but at the end of the day kinda boring in isolation; "real" music needs more rules.
  - evrydayhustling 4y ago
    Awesome appreciate you explaining this. Hadn't considered the idea that transitions vs simultaneous notes "compete" on what the optimal note frequencies are. And very cool to understand that people are dealing with this pragmatically all the time.
    - kofejnik 4y ago
      For a demo, you can search YouTube for “Jacob collier g half-sharp”
- geofft 4y ago
  Singers will do this via intuition - you don't think of, say, a perfect fifth as 2^(7/12) = 1.4983x over the root. You think of it as a particular pair of sounds that resonates well, much like when you picture "red" in your mind you're not thinking of exact HSV or Pantone values. At most, you'll think of a perfect fifth as exactly halfway between the octaves (1.5x over the root). As the sibling comment points out, this isn't the singers choosing a particular temperament for the entire song; it's them constantly tuning individual chords and intervals to each other and to their previous notes as the song goes on. The same note on paper can be several slightly-different frequencies in different parts of the song, and most singers won't even be able to tell you that they're doing that. (This is also the same mechanism at work when an entire choir singing an unaccompanied piece goes flat without realizing it. Someone will not quite make an ascending interval, and everyone else will adjust to cover it.)

andrepd 4y ago

There is a very similar thing: Just intonation http://alumni.media.mit.edu/~bdenckla/thesis/texts/htthe/node24.html http://alumni.media.mit.edu/~bdenckla/thesis/texts/htthe/nod...

bluGill 4y ago

Maybe, but it needs to be the whole band not just one instrument. What notes the bass us hitting changes how the guitar needs to sound and vice versa. If you have a large orchestra it's gets hard, and even worse if someone hits a wrong note.

mrob 4y ago

You can even dynamically adjust the tuning to maximize consonance throughout the song, e.g.: https://sethares.engr.wisc.edu/mp3s/three_ears.html https://sethares.engr.wisc.edu/mp3s/three_ears.html

deleted 4y ago
[deleted]
dcow 4y ago
This is really cool. It sounds weird for about the first 45-90 seconds but then my mind adjusts and it sounds really pleasant. Would make a good context/theme for a video game soundtrack.
- AnonCoward42 4y ago
  It really is kool. However, I have the feeling you can transport only a very limited range of emotions with it as we are accustomed to certain harmonics I guess. Still, it's kinda like alien music and it's certainly creative.
- drdeca 4y ago
  To me the individual notes sound fine and usually normal-ish (except for the really extended ones), but I have difficulty hearing the overall tune? Or, it sounds like there are parts of a tune with other parts on top which I don’t hear how they fit? I think a clearer demonstration might be to have a side by side comparison of a fairly simple tune in 12TET vs in this dynamical tuning.
  - thewebcount 4y ago
    Agreed! I’m not hearing a very definable or memorable melody or harmony. The synth sounds chosen are kind of grating, which doesn’t help. I’d love to hear something more coherent in this sort of tuning to get a better understanding of it.
still_grokking 4y ago
Is "maximized consonance" what causes those extreme sharp sounding ring tones? (After listening to this peace my ears are still ringing; 2 min. after the fact). Also the tonal glides sound like an old broken record player. (This creates a sensation of "wobbling speed", which sounds just wrong). Hmm, my ears are still ringing, even while writing this; that was not a pleasant experience to be honest… I guess I need some ear-bleach. Psytrance to the rescue! Let's see, maybe, hmm, Talpa¹, or maybe better that old Atma set²? ___ ¹ https://www.youtube.com/watch?v=wErFe-1dlg4 https://www.youtube.com/watch?v=wErFe-1dlg4 ² https://www.youtube.com/watch?v=HU9FDStUoT8 https://www.youtube.com/watch?v=HU9FDStUoT8

smrq 4y ago

Not trying to be "that guy", just figured you might want to know-- although it's pronounced "tamber" it's spelled "timbre". Thanks, english.

kqr 4y ago
I think this one you can blame on the French.
- m-p-3 4y ago
  The word sounds exactly how it is written when you say it in French tho, not our fault you adopted the word and say it differently ;)
  - zdragnar 4y ago
    I blame the English aristocrats. Why eat cow like a peasant when you could have some beef like a fancy person?
    - kibwen 4y ago
      And why spell it "color" like the Romans did when you can blithely attempt to imitate the French aristocracy by injecting arbitrary "u"s into random words, thus giving you license to complain about CSS keywords for the rest of recorded history? :P
      - willnonya 4y ago
        You're my new favorite person.
    - dudeguy3301 4y ago
      also, think the french started this. a name for the animal in the field, a different name for the animal on your plate.
      - 4y ago

xhevahir 4y ago

You might like to hear this proprietary algorithm: http://www.hermode.com/index_en.html http://www.hermode.com/index_en.html Since you're a guitarist, there's also this Swedish guitar, which purports to solve the tuning problem (which I tend to think is not a problem but an essential part of the instrument's sound) https://youtu.be/-penQWPHJzI https://youtu.be/-penQWPHJzI

still_grokking 4y ago
Wow, this guitar sounds so ultra-clean! Depending on song this could be pretty nice. But the normal, "imperfect" guitar does not sound bad. I would also say, this "imperfection" gives a guitar its typical sound in the first place, so it's not a "problem". Both guitars in that video are great, but indeed quite different.
- smitty1e 4y ago
  The humanity is in the imperfections. Prediction: society demotes all of the auto-tuning and AI art to training status, and actual art produced by himans with pulses is preferred.
  - still_grokking 4y ago
    Here we're not on the same page, frankly. My favorite style of music (Psytrance) almost requires digital "perfection". It's even not really possible to create a "properly sounding" Psytrance bass-line¹, not even a most basic variant, without doing some math (or using tools that will do that math for you). Frequencies, pitch, tempo, and phase need to match constantly and absolutely perfect, or it won't sound properly. Any "humanization" on any preset would kill the sound instantly! For that reason creating Psytrance is a very "mechanical" task that only machines can perform with the required precision. (And not every machine is good enough for that actually. You need for example oscillators with very high precision or you will experience unwanted artifacts, especially on higher frequencies, that could destroy the sound). Something that could create "perfectly matching" chords that don't include any dissonance would be really useful to get the (most of the time) desired "ultra-clean" Psytrance sounds. The usual alternative is to filter out all dissonance. But that's a lot of work, or in "bigger" chords or soundscapes outright impossible (even when you slice the sound in the frequency spectrum with all kind of tricks; filters also produce artifacts… And trying to get rid of those artifacts, like phase imperfections, changes the sound again in often undesired ways. A "perfect" tuning form the get go would maybe help with such things). ___ ¹ Here two of the better tutorials for Psytrance bass-lines: https://www.youtube.com/watch?v=m40xkEkrEKo https://www.youtube.com/watch?v=m40xkEkrEKo https://www.youtube.com/watch?v=-4B1NcdNJjE https://www.youtube.com/watch?v=-4B1NcdNJjE And if you're lazy see here for a VST plugin send form the gods: https://fx23.net/psylab-pro/ https://fx23.net/psylab-pro/

MikeBattaglia 4y ago

This is called "adaptive just intonation." Logic Pro X has this feature built in, using a particular algorithm called Hermode Tuning. It sounds great

thebeardisred 4y ago
/me goes to explore this in Ableton...

golergka 4y ago

Apple Logic Pro has this function built in as Hermode tuning.