Singing through the syntonic comma
On a Thummer-like keyboard, from C, count up four perfect fifths (from F through C, G, and D, to A). In Just Intonation tuning—which perfectly aligns notes with the harmonic series’ partials—the perfect fifth is 701.955 cents wide, so that’s (4*701.955=) 2807.82 cents. Subtract a couple of octaves (2*1200=2400 cents) from that and you get a remainder of 407.82 cents.
Now, another way to get from F to A on a Thummer-like keyboard is to got rightward by a single major third. In Just intonation, a major third is 386.31 cents wide. Subtracting this major third from your octave-reduced stack of four perfect fifths, you get (407.82-386.31=) 21.51 cents, which is the syntonic comma, which is the difference between a 10/9 major second (Re) and a 9/8 major second (also Re). The ratio of 10/9 over 9/8 is (9*9)/(10*8) = 81/80, which works out to this exact same 21.51 cents. (I don't want to go into more of the math here.)
21.5 cents is a LOT – more than one-fifth of a semi-tone. It is very audible, even to untrained musicians. If two singers are out of tune by a syntonic comma, you and everyone else in the audience WILL hear the difference, as a strong beating between the two singer’s voices.
This is a significant problem for vocal groups (if they actually want to sound good), especially when singing in close harmonies a capella, as (for example) barbershop quartets do.
If you sing the I-vi-ii-V-I chord progression in Just Intonation, for example, the I chord that you end on will be a syntonic comma lower than the I chord that you started on. This is called “commatic drift.” To avoid this drift, singers must learn to distinguish between two different Re’s: the 10/9 Re at the root of the ii chord and the 9/8 Re in the 5th of the V chord. This requires singers to be able to sing the two different notes correctly, and–at least as importantly–know when to sing each one and not the other.
I don't see how the use of Do-based minor either helps or hinders a singers ability to correctly choose and sing the right Re. I would welcome having someone explain this to me. I can't find much discussion of this issue on the Web, which suggests that I my misunderstanding of the issues is so deep that I can't even choose the right search terms. Either that, or writing about singing is like dancing about architecture, so none of the relevant discussion is written down.
One of the great advantages of the syntonic temperament is that it tempers out the syntonic comma (hence its name), so chord progressions like the one above “work” without either two Re’s or commatic drift. The cost of this tempering is that the notes of such a temperament are not perfectly aligned with the partials of the Harmonic Series.
There are two ways to address this. One is to adapt the pitches of the notes as they are played to align them with the proper JI intervals. There has been a ton of work on this kind of adaptive tuning. It presumes that the only timbre that’s interesting is the harmonic series, and that all tuning should be adjusted to align with harmonic partials.
Dynamic Tonality supports this. You can use the Tonality Diamond in the TransFormSynth to choose a “major JI” tuning or a “minor JI” tuning, at either vertical end of the tonality diamond. This keeps the tuning at a 5-limit JI, and adjust the 5th partial to align with the 10/9ths Re (in major) or 9/8ths Re (in minor). Of course, if you do this, then moving the tuning slider has no effect, because your use of the tonality diamond has indicated that you want to use a JI tuning, not a tempered tuning.
On the other hand, Dynamic Tonality can also address the problem by tempering the timbre to match the current tuning. Just keep the tonality diamond’s dot a near the vertical center of the tonality diamond, along the axis from “fully harmonic” timbres to “fully tempered” timbres, and you can adjust the tuning slider to your heart’s content. This option was not available to previous generations of theorists, because they didn’t have the necessary computing power. But it’s available to us. Even singers, singing into microphones, can have their amplified timbres adjusted in real time to fit the current syntonic tuning (such as 12-tet).
(I have this recurring nightmare that the only popular use of Dynamic Tonality will be to make 12-tet more consonant, thereby locking it in as the de facto standard forever.)
Point being, that Dynamic Tonality makes the problem of the syntonic comma completely disappear by tempering it out of the harmonic series, thus eliminating the syntonic comma at its source.
Now, another way to get from F to A on a Thummer-like keyboard is to got rightward by a single major third. In Just intonation, a major third is 386.31 cents wide. Subtracting this major third from your octave-reduced stack of four perfect fifths, you get (407.82-386.31=) 21.51 cents, which is the syntonic comma, which is the difference between a 10/9 major second (Re) and a 9/8 major second (also Re). The ratio of 10/9 over 9/8 is (9*9)/(10*8) = 81/80, which works out to this exact same 21.51 cents. (I don't want to go into more of the math here.)
21.5 cents is a LOT – more than one-fifth of a semi-tone. It is very audible, even to untrained musicians. If two singers are out of tune by a syntonic comma, you and everyone else in the audience WILL hear the difference, as a strong beating between the two singer’s voices.
This is a significant problem for vocal groups (if they actually want to sound good), especially when singing in close harmonies a capella, as (for example) barbershop quartets do.
If you sing the I-vi-ii-V-I chord progression in Just Intonation, for example, the I chord that you end on will be a syntonic comma lower than the I chord that you started on. This is called “commatic drift.” To avoid this drift, singers must learn to distinguish between two different Re’s: the 10/9 Re at the root of the ii chord and the 9/8 Re in the 5th of the V chord. This requires singers to be able to sing the two different notes correctly, and–at least as importantly–know when to sing each one and not the other.
I don't see how the use of Do-based minor either helps or hinders a singers ability to correctly choose and sing the right Re. I would welcome having someone explain this to me. I can't find much discussion of this issue on the Web, which suggests that I my misunderstanding of the issues is so deep that I can't even choose the right search terms. Either that, or writing about singing is like dancing about architecture, so none of the relevant discussion is written down.
One of the great advantages of the syntonic temperament is that it tempers out the syntonic comma (hence its name), so chord progressions like the one above “work” without either two Re’s or commatic drift. The cost of this tempering is that the notes of such a temperament are not perfectly aligned with the partials of the Harmonic Series.
There are two ways to address this. One is to adapt the pitches of the notes as they are played to align them with the proper JI intervals. There has been a ton of work on this kind of adaptive tuning. It presumes that the only timbre that’s interesting is the harmonic series, and that all tuning should be adjusted to align with harmonic partials.
Dynamic Tonality supports this. You can use the Tonality Diamond in the TransFormSynth to choose a “major JI” tuning or a “minor JI” tuning, at either vertical end of the tonality diamond. This keeps the tuning at a 5-limit JI, and adjust the 5th partial to align with the 10/9ths Re (in major) or 9/8ths Re (in minor). Of course, if you do this, then moving the tuning slider has no effect, because your use of the tonality diamond has indicated that you want to use a JI tuning, not a tempered tuning.
On the other hand, Dynamic Tonality can also address the problem by tempering the timbre to match the current tuning. Just keep the tonality diamond’s dot a near the vertical center of the tonality diamond, along the axis from “fully harmonic” timbres to “fully tempered” timbres, and you can adjust the tuning slider to your heart’s content. This option was not available to previous generations of theorists, because they didn’t have the necessary computing power. But it’s available to us. Even singers, singing into microphones, can have their amplified timbres adjusted in real time to fit the current syntonic tuning (such as 12-tet).
(I have this recurring nightmare that the only popular use of Dynamic Tonality will be to make 12-tet more consonant, thereby locking it in as the de facto standard forever.)
Point being, that Dynamic Tonality makes the problem of the syntonic comma completely disappear by tempering it out of the harmonic series, thus eliminating the syntonic comma at its source.
Labels: intonation, music theory, singing
posted by JimPlamondon | 3:40 PM
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