Reply to Jim Savage

>(i) play E major so it has 1 5/4 3/2 ratios, then Ab is played as 25/16 =
>1.56 of C instead of the "original" ratio of 8/5 = 1.6 of C

That's good but the third of E major is G#, not Ab. G# is usually considered
to be 25/16 relative to C in JI anyway.

>(ii) play E major with 1 5/4 3/2 ratios, but shift E down slightly so that
>none of E Ab or B are played as 5/4, 8/5 and 15/8 of C respectively, but a
>centered shift is done (like John A. deLaubenfels example in following
>replies to my question - that's how I know what it's called :)).

That may be necessary if you're going to continue modulating in major thirds
(like Schubert) and want to get back to C. But then you'd shift E up
slightly, not down slightly. I can't think of a case where you'd want to
shift it down slightly.

>(iii) Play E major using the 5/4, 8/5 and 15/8 of C (the original
pitches),
>so the major third is no longer 5/4 but is 32/25 = 1.28

That's Ken Overton's way, and it sucks. I'd never do that. Again, you're
using Ab instead of G#.

>Continue the progression given above (Cmaj - Emaj) to Abmin, so Ab and B
are
>held. If Abmin is to have ratios of 1 6/5 3/2, one has to play B at 48/25
>=1.92 of C instead of the original 15/8, or shift both Ab and B (maybe
using
>again John's centered shift).

Again, depends on context. There's no reason to shift G# and B from the E
major, since they already form the same interval they should in G#min,
unless you're going to try to get back to C by going up a major third.

>>That doesn't work so well for certain chords. For example, a C6/9 chord
>>(C E G A D) would have the fifth between A and D as 40:27 if you tuned it
>>according to "the JI major scale" on C

>Do you mean the 4th of 27/20 = 1.35 between A and D?

Same thing.

>For 9, 11, 13
>chords, etc., does the dominant harmonies come from the upper note
>intervals, or from the correspondence with the root harmonics?

I've done a lot of experimentation and usually I prefer the former. The only
chords where I _might_ use a ratio of 11 are a 9#11 chord (4:5:6:7:9:11) and
a m9b5 chord (5:6:7:9:11), and only the first of these correspond to root
harmonics. I would never use a ratio of 13 in a jazz chord.

>I don't know
>much about this area - I tend to go for the simple harmonies.

But C6/9 _is_ a simple harmony, considered fairly consonant. It's not
consonant in JI, though.

>I find that Ab F C Eb (descend from Ab, rise to Eb) depends quite a bit on
>the minor third intervals. Played high on the keyboard, it sounds awful to
>me in 12Tet, and takes on a different feel depending on the minor third
>intervals played.

So you like the melody better when the minor third intervals are tuned as
_________?

>From: "Paul H. Erlich" <PErlich@Acadian-Asset.com>
>...I would never use a ratio of 13 in a jazz chord.

No? As the b13 in a V7 chord in a minor key I think you'll find that it's
just the thing. E.g., the note F in A7b9b13 in the key of D minor. It's
just a little higher than the F in a D minor chord. How much? Well:

((13*3)/32) / (6/5) = 1.5625%

John Link
ALMOST ACAPPELLA

>>...I would never use a ratio of 13 in a jazz chord.

>No? As the b13 in a V7 chord in a minor key I think you'll find that it's
>just the thing. E.g., the note F in A7b9b13 in the key of D minor.

Nah, I'd put it a perfect fifth above the b9.

>From: "Paul H. Erlich" <PErlich@Acadian-Asset.com>
>
>>>...I would never use a ratio of 13 in a jazz chord.
>
>>No? As the b13 in a V7 chord in a minor key I think you'll find that it's
>>just the thing. E.g., the note F in A7b9b13 in the key of D minor.
>
>Nah, I'd put it a perfect fifth above the b9.

And how would you tune the b9? I say that good singers would use 17/16
relative to the root. That way, in A7b9b13 we have nothing but prime
numbers for lots of tension:

A 1
C# 5
G 7
Bb 17
F 13

And if we were to add b5, it would tune as 11, another prime. And I say #9
would be 19. And there we have the altered scale!

A Bb B C# Eb (E) F G
1 17 19 5 11 (5) 13 7

I'm guessing that you would make Bb 16/15 relative to A. If so, then we
have the following:

A 15
C# 75
G ?
Bb 1
F 3

(I wonder how you think G would tune. Maybe 6/5 relative to Bb?)

or a lattice diagram as follows:

C#

A

F

Bb

I that A7b9b13 tuned that way has too many pretty intervals to function as
an earth-splitting dominant 7th chord (now I'm getting poetic). Tuned
according to my conjecture I think it would be a fabulous set-up for the D
minor triad to follow.

John Link
ALMOST ACAPPELLA

>> [Jim Savage, TD 386.12]
>>
>> (iii) Play E major using the 5/4, 8/5 and 15/8 of C (the
>> original pitches), so the major third is no longer 5/4 but
>> is 32/25 = 1.28

> [Paul Erlich, TD 386.13]
>
> That's Ken Overton's way, and it sucks. I'd never do that.
> Again, you're using Ab instead of G#.

Of course, how one tunes a particular harmony is one's own
prerogative, but I think it's wrong to use such strongly
disapproving language in a *categorical* way.

What tuning sounds best in any particular instant is highly
dependent on many contextual factors, including the timbres
of the instruments, the movement of individual voices in the
musical texture, and one's own disposition. I'm sure Paul
himself would agree with this.

An example that is readily at hand comes from the middle
section of my piece _A Noiseless Patient Spider_.

Here is a lattice of the 5-limit system used in this section.
Plain letter-names indicate Pythagorean tuning, with '-'
and '+' indicating one syntonic comma deviation from
Pythagorean, and '<' and '>' two commas, higher and lower
respectively:

E#<
|
F#- --- C#- --- G#-
| | |
G ----- D ----- A ----- E ----- B
| | |
Bb+ ---- F+ ---- C+
|
Db>

I quote from my program notes (from the May 1999 AFMM Microthon)
to illustrate a tuning like the one Paul disputed:

> The 'Meditation', where the poet's thoughts turn inward,
> is tuned to the symmetrical 5-limit system centered on 'A'
> portrayed on the prime-factor lattice diagram - one kind
> of ultimate rational understanding of musical harmony - with
> a very soft drone on a low 'A'. The entire section uses only
> three main instrumental parts which each hold a pitch for six
> very slow beats as they move around the lattice.
>
> These three parts overlap and explore various 5-limit triad
> subsets of the total lattice of 13 pitches, and about two-thirds
> of the way thru this section they form a 'first inversion
> A major' triad, but the '3rd of the chord' (in the bass) is
> not the 'correct' 5:8 ratio with the pitch C#-, but rather the
> 16:25 Db>, giving a proportion for the whole triad of 32:50:75,
> instead of 5:8:12, so the exploration continues.

The point I'm making here is that it *still* sounds like an
'A major triad', and in the context in which I use it here,
it is important to the dynamic musical movement of the voices
that it is *not* tuned in the usual JI way.

The complete program notes, and a MIDI sequence of the
instrumental tracks (without the vocal part) can be found at:
http://www.ixpres.com/interval/monzo/spider/spider.htm

(The chord in question occurs at 4'21" into the piece, but
in order to have the instrument patches play properly, you
have to start listening no later than the beginning of this
section, which starts at 2'20".)

-monz

Joseph L. Monzo Philadelphia monz@juno.com
http://www.ixpres.com/interval/monzo/homepage.html
|"...I had broken thru the lattice barrier..."|
| - Erv Wilson |
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>From: Joe Monzo <monz@juno.com>
>
>Of course, how one tunes a particular harmony is one's own
>prerogative, but I think it's wrong to use such strongly
>disapproving language in a *categorical* way.

Well, it is impolite to speak such language, but I know that MY experience
is often best described by something like "thats sucks" (not really my
style of language) or "that's horribly out of tune" (more the way I would
put it). And yes, it is an artist's perogative to tune however he wishes,
but if you sing F as 8/5 (rather than 13/8) relative to A in an A7b9b13
chord in the key of D minor, don't be surprised if you're told that you're
flat.

>What tuning sounds best in any particular instant is highly
>dependent on many contextual factors, including the timbres
>of the instruments, the movement of individual voices in the
>musical texture, and one's own disposition. I'm sure Paul
>himself would agree with this.

I agree, including with the concept of "what sounds best". I have found
with my vocal quintet that there is hardly ever any disagreement about
whether we're really in tune. So I don't think that it is very much a
matter of taste. I believe that there actually is such a thing as good
intonation, and that it is not such a subjective notion as one might think.

John Link
ALMOST ACAPPELLA

I wrote,

>> That's Ken Overton's way, and it sucks. I'd never do that.
>> Again, you're using Ab instead of G#.

Joe Monzo wrote,

>Of course, how one tunes a particular harmony is one's own
>prerogative, but I think it's wrong to use such strongly
>disapproving language in a *categorical* way.

I agree and thaks for the reprimand. What I meant to say is that the chord
5/4:8/5:15/8 is not appropriate if you're trying to take common-practice
music and render it in JI to improve the consonance. It completely defeats
_that_ purpose of JI to tune a major chord that way; it won't sound like JI
in any way and won't be qualitatively any different from a major chord that
is simply out-of-tune.