3 ms·

You might like the book "Equal Temperament Ruined Harmony." It makes the case that there is a long history of differentiating sharps and flats in western music

by kmill 5y ago

You might like the book "Equal Temperament Ruined Harmony." It makes the case that there is a long history of differentiating sharps and flats in western music (flats are just a bit sharper than sharps), while arguing that in practice the whole tone was subdivided into nine parts, with the major and minor half steps respectively 5 or 4 of those nine parts. I don't think the precise tuning system described by the book really happened, but it does collect evidence that "enharmonic" used to mean "finesse your intonation to make this sharp be that flat." In my own experimentation, the just intonation intervals are jarringly perfect, and I'd say that the 5:4 major third is too narrow. Has anyone checked that barbershop quartets are actually singing such narrow major thirds? My understand is that many studies have shown that string instrumentalists and singers, even when they claim to be using just intonation, play their major thirds somewhere between 5:4 and equal temperament. It's also extraordinarly difficult to really tune basic harmony justly. The ii V I progression is a fun one... if you're not careful you shift the tonic by a syntonic comma.

tshaddox 5y ago
> Has anyone checked that barbershop quartets are actually singing such narrow major thirds? I don’t know if anyone has checked, but why wouldn’t they want to? Surely the low integer ratios are best going to get the intended sound of barbershop harmony, unless there are other acoustic reasons why slightly changing the intervals would work better (something akin to octave stretching in pianos, although I’m not sure that sort of thing would be as relevant to barbershop harmony).
- kmill 5y ago
  That's a nice thought in theory, but I can assure you that string quartets do not play 5:4 major thirds -- they're significantly sharper (but not quite equal tempered major thirds). There's more to music than acoustics. Four-part harmony has a lot of moving parts (literally and figuratively), and you have to make concessions to acoustically pure intervals to make it sound like it's in tune through time.
  - zozbot234 5y ago
    This is true, there are even "comma pump" sequences that are literally impossible to play fully harmonically, being inherently based on conflating "close" ratios! (I think in theory, a very detailed Schenkerian-ish analysis of a piece would tell you quite a bit about where ratios should be made "nicer" and where they shouldn't - but that's a lot of work and involves a whole lot of personal judgment.)
    - kmill 5y ago
      I think one of the reasons ii V I is so compelling (versus IV V I) is that the ii (or ii7) is conflating many notes. In C major, using interval terms as a stand-in for "tuned justly": Is the D a fourth below G or a minor (or harmonic) seventh below C? Once you've chosen your D, is A a perfect fifth above it? If so, what kind of major second relation does it now have to G? Is the F a perfect fourth above C, or is it a major third above your D? Or is it supposed to be the minor (or harmonic) seventh above G? I think barbershop tends to skirt these questions by instead using a II V I progression (a secondary dominant), since the F# doesn't have to stand in careful relation to other notes of the plain C major scale. (That's interesting Schenkerian analysis can help understand these issues. I know only about it at a very thin surface level.)
      - zozbot234 5y ago
        I suppose a good rule of thumb is that "dissonant" notes (in the musical syntax sense) should be in a harmonic relation with the scale step they will ultimately resolve into - so D to C, A to G, F to C etc. This can and will create roughness in the vertical dimension, but that actually reflects their unstable "energy" that drives them to resolution. Of course one could just as well use microtonal shifts to play with this kind of stability whenever longer-range relations are involved. Perhaps this is part of what good performers do intuitively when playing a melodic instrument. The relevance of music-syntactical dissonance and resolution is what might make Schenkerian analysis a very useful tool to understand these possibilities!
  - tshaddox 5y ago
cousin_it 5y ago
I don't think it's very difficult. In the ii-V-I, slightly shifting the root of the ii sounds fine, and most other problems can be solved similarly. I've made plenty of music in just intonation, here's a recent example: https://www.youtube.com/watch?v=qkUs-BdxtN8 https://www.youtube.com/watch?v=qkUs-BdxtN8 To me it sounds like very standard harmony, but "cleaner".

by kmill 5y ago

tshaddox 5y ago

> Has anyone checked that barbershop quartets are actually singing such narrow major thirds? I don’t know if anyone has checked, but why wouldn’t they want to? Surely the low integer ratios are best going to get the intended sound of barbershop harmony, unless there are other acoustic reasons why slightly changing the intervals would work better (something akin to octave stretching in pianos, although I’m not sure that sort of thing would be as relevant to barbershop harmony).

kmill 5y ago
That's a nice thought in theory, but I can assure you that string quartets do not play 5:4 major thirds -- they're significantly sharper (but not quite equal tempered major thirds). There's more to music than acoustics. Four-part harmony has a lot of moving parts (literally and figuratively), and you have to make concessions to acoustically pure intervals to make it sound like it's in tune through time.
- zozbot234 5y ago
  This is true, there are even "comma pump" sequences that are literally impossible to play fully harmonically, being inherently based on conflating "close" ratios! (I think in theory, a very detailed Schenkerian-ish analysis of a piece would tell you quite a bit about where ratios should be made "nicer" and where they shouldn't - but that's a lot of work and involves a whole lot of personal judgment.)
  - kmill 5y ago
    I think one of the reasons ii V I is so compelling (versus IV V I) is that the ii (or ii7) is conflating many notes. In C major, using interval terms as a stand-in for "tuned justly": Is the D a fourth below G or a minor (or harmonic) seventh below C? Once you've chosen your D, is A a perfect fifth above it? If so, what kind of major second relation does it now have to G? Is the F a perfect fourth above C, or is it a major third above your D? Or is it supposed to be the minor (or harmonic) seventh above G? I think barbershop tends to skirt these questions by instead using a II V I progression (a secondary dominant), since the F# doesn't have to stand in careful relation to other notes of the plain C major scale. (That's interesting Schenkerian analysis can help understand these issues. I know only about it at a very thin surface level.)
    - zozbot234 5y ago
      I suppose a good rule of thumb is that "dissonant" notes (in the musical syntax sense) should be in a harmonic relation with the scale step they will ultimately resolve into - so D to C, A to G, F to C etc. This can and will create roughness in the vertical dimension, but that actually reflects their unstable "energy" that drives them to resolution. Of course one could just as well use microtonal shifts to play with this kind of stability whenever longer-range relations are involved. Perhaps this is part of what good performers do intuitively when playing a melodic instrument. The relevance of music-syntactical dissonance and resolution is what might make Schenkerian analysis a very useful tool to understand these possibilities!
- tshaddox 5y ago

cousin_it 5y ago

I don't think it's very difficult. In the ii-V-I, slightly shifting the root of the ii sounds fine, and most other problems can be solved similarly. I've made plenty of music in just intonation, here's a recent example: https://www.youtube.com/watch?v=qkUs-BdxtN8 https://www.youtube.com/watch?v=qkUs-BdxtN8 To me it sounds like very standard harmony, but "cleaner".