31 eq 5ths

Hey Paul...you're quite correct, of course, the 19 tone 5ths are worse (but only by 2cents) than 31, and I do, indeed, notice it. My comment on 31 was not intended to be a big deal, I was sort of thinking out loud, so to speak. I think a lot about tunings and what they mean, and since I haven't composed yet in 31 (mainly cause I wanted to concentrate on 34, since not as many people have composed in 34 compared to 31), when I picked up the 31 tone guitar I went "oh, something sounds out of tune," and the whole subject of temperaments and why they came into being in the first place sort of went through my head...maybe putting this less than earthshaking insight on the forum wasn't a good idea, if I had been talking in person to someone about the flat 5ths, it would have been a one sentence casual remark and been gone in a second.
In 19, it's also interesting that the major 3rd is as flat as the 5th, so there's some sort of symmetry there at work. If one likes chordal, modulating music, as I do, using some sort of tempered tuning seems inevitible, so you have to live with the out of tune intervals. And, another subject which interests me is why Europeans, out of all the cultures on Earth, got interested in chordal music in the first place...it seems that most cultures were making music with melody and rhythm as the main structures, not chordal modulation. Maybe there's no good answer, but I've often reflected how much work has gone into creating temperaments so we can modulate through distant keys. And, of course, a lot of great music has come from those out of tune 5ths and 3rds. It's also fascinating how the natural structure of the overtone series does not seem to be made for modulating music...it's a deep and vast subject, it will surely keep me busy for the rest of this life...best...HHH

--- In tuning@yahoogroups.com, "Neil Haverstick" <microstick@m...>
wrote:
>
> Hey Paul...you're quite correct, of course, the 19 tone 5ths are
worse
> (but only by 2cents) than 31, and I do, indeed, notice it. My
comment on 31
> was not intended to be a big deal, I was sort of thinking out loud,
so to
> speak. I think a lot about tunings and what they mean, and since I
haven't
> composed yet in 31 (mainly cause I wanted to concentrate on 34,
since not as
> many people have composed in 34 compared to 31), when I picked up
the 31
> tone guitar I went "oh, something sounds out of tune," and the
whole subject
> of temperaments and why they came into being in the first place
sort of went
> through my head...maybe putting this less than earthshaking insight
on the
> forum wasn't a good idea, if I had been talking in person to
someone about
> the flat 5ths, it would have been a one sentence casual remark and
been gone
> in a second.

Sorry, didn't mean to take it as more than that!

> In 19, it's also interesting that the major 3rd is as flat as
the 5th, so
> there's some sort of symmetry there at work.

It's more than just some abstract symmetry -- this equality means
that the minor third and major sixth are just about pure in 19.
Musically, I think this is somewhat significant. These intervals
shouldn't be treated as less important than the major third itself,
as they occur in all major and minor triads . . . But overall, I
think the triads sound just a bit purer in 31, since both the 5th and
(especially) the major 3rd are better in 31.

> If one likes chordal,
> modulating music, as I do,

I see the "modulating" part as less important, and the use of chord
changes within the diatonic (or other 2D) scale as the real fly in
the JI ointment. See below.

> using some sort of tempered tuning seems
> inevitible, so you have to live with the out of tune intervals.

On a fretted guitar or any fixed-pitch instrument, this is basically
true. Though sometimes, you can do a bit better with "Middle Path"
tunings such as, say, (a slightly stretched) 1/4-comma meantone, than
you can with ETs, depending on which chord progressions and scales
you wish to use. This was what the paper I sent you was about.

With flexible-pitch instruments, such as human voices or fretted
guitars, or even fixed-pitch instruments with enough pitches (like
Vicentino's Archicembalo in his second tuning of 1555), you can
sometimes get around this problem by using adaptive JI. Adaptive JI
means each chord is perfectly just in itself, but the horizontal
(melodic) intervals are tempered, so that chord progressions that are
supposed to return to their starting point do just that, instead of
drifting or requiring full "comma"-sized shifts.

> And, another
> subject which interests me is why Europeans, out of all the
cultures on
> Earth, got interested in chordal music in the first place...

I think it might have evolved from polyphony, when it was slowly
realized that the succession of combinations made by the notes in the
various strands can have as much musical meaning as the melodies in
the strands themselves, and especially after the Western _tonal_
system crystallized around 1670.

> it seems that
> most cultures were making music with melody and rhythm as the main
> structures, not chordal modulation. Maybe there's no good answer,
but I've
> often reflected how much work has gone into creating temperaments
so we can
> modulate through distant keys.

I see temperament as most relevant even when we stay in one key! Just
changing chords in a single diatonic key can reveal the problems with
JI. No modulation is necessary.

> And, of course, a lot of great music has come
> from those out of tune 5ths and 3rds. It's also fascinating how the
natural
> structure of the overtone series does not seem to be made for
modulating
> music

I think I'd change "modulating music" to "diatonic music" (as well as
music based on other 2D scales). There's no trouble moving to
different key centers in JI if you have enough notes. The real
problems with strict JI show up plenty well in a single key. You're
right that _chord changes_ are typically what causes these problems
to arise, though.