Common Problems for Comma Drifters

I wanted to thank Paul Erlich for taking the time to make the interesting
chart last week with "common" harmonic progressions that were having
"comma" problems in just intonation.

It was fascinating to see the difference between the two systems he
illustrates, one which observed "common" tones. (Which I GUESS are "puns"
or "homophones" -- I am unclear)

If I understand the Vincentino system he proposes, it is ESSENTIALLY in
meantone, since the roots are in meantone. However, if the progression
were more elaborate, with more roots involved, would this mean that the
comma drift would be re-distributed AGAIN, divided by the number of roots??
I imagine it would.

Of course, this kind of system including just intonation would not work
with any fixed keyboard mechanism (standard), but only with instruments
that could "adapt" in real time. (??)

I would enjoy seeing harmonic progression charts like this that go a bit
further -- let's say at least to the vi of the common harmonic progression.
So far, we've only been dealing with I, IV, ii, V, I, which seems a tad
limited.

By the way, the Alan Forte harmony book, which has been resurfacing in so
many ways on the list of late, is really a fine volume, for what it is. It
is one of the few harmony texts that didn't incite immediate vomit with me,
and I used it for review in my doctoral studies. I particularly remember a
large number of exercises in four-part harmony, which were good practice.
I do have a copy of the book, but it is one of those books that stays in my
library. Unfortunately, the Walter Piston harmony text, in contrast, did
not have a salutary effect. (His orch. book is pretty decent, though...)

Thanks again for the posts, and I would be interested in seeing further
efforts that try to combine traditional tonal practice with just intonation
theory...

Joseph Pehrson

Joesph Pehrson wrote,

>Of course, this kind of system including just intonation would not work
>with any fixed keyboard mechanism (standard), but only with instruments
>that could "adapt" in real time. (??)

Actually, Vicentino implemented his 1555 system on a 36-tone keyboard: 19
tones of meantone, and 17 tones of meantone transposed by 1/4-comma.

>I would enjoy seeing harmonic progression charts like this that go a bit
>further -- let's say at least to the vi of the common harmonic progression.
>So far, we've only been dealing with I, IV, ii, V, I, which seems a tad
>limited.

Joseph, I'd be happy to produce a chart like that for any progression you
care to name, but lat me say this: the adaptive JI system we've been
discussing (Vicentino's) will work for _any_ triadic progression that
"works" in (extended) meantone. That is, the only ones which won't work are
ones which use enharmonic equivalents, e.g., G#=Ab. These types of
progressions became important with Schubert and his successors. In meantone,
this is a shift of about 40 cents. To learn more about what works and what
doesn't work in meantone and why most things don't work in strict JI, read
Blackwood's _Structure of Recognizable Diatonic Tunings_.

>Thanks again for the posts, and I would be interested in seeing further
>efforts that try to combine traditional tonal practice with just intonation
>theory...

This is a multifaceted issue and