16-19-24 minor chord

DWolf wrote
> D 1/1
> F 19/16
> A 3/2
> (from John Link)
> <<
> Although D is clearly the root, as opposed to Bb (8/5 relative to D), I
> don't think that that's what good singers would do, because of the large
> third between F and A involving the primes 3, 5, and 19.
> >>

I think that singers do 16-19-24 for a really minor chord if the three
notes sound together. If the tonic isn't here, for separate work for
example, 24/19 would be too near of 5/4 and singers would have very
difficult to do 24/19. But I have no experience of that, it's only that
I suppose.

But with my violin I have long years of practice. When I play a minor
third, I always make a choice between 6/5, 19/16 and 7/6 with the help
of difference tone (for diatonic music, chromatism is another problem).
With bB/G, I hear bE for 6/5, D for 19/16, C for 7/6. For 6/5 and 7/6
it's quite easy, for 19/16, if the third is enough high, it's possible,
if not, I play a "little" 6/5 which "seams" minor...
For the 6th it's more difficult. In the first sonate of Bach, for
example, when I play the first (or last) chord G-D-bB-G, I must play
bB-G for a long time, if I hear a bE, it proove that I'm playing 5/3,
and this bE isn't very good for G minor!

DWolf wrote
> While the minor triad 16:19:24 is very much more pleasant (it was either Lou
> Harrison or Tom Stone who called the 19:16 "nature's own minor third") than
> the Major triad found by inversion:
> 38:48:57, the latter is extremely close to the 12tet and certainly better
> than the pythagorean 64:81:96!

For me (the theorist and the violinist) a major chord is always 4-5-6,
for C-bE-G-bB chord it's probably
32-38-48-57 (a fifth 3/2 with 19/16 on 2 and 19/16 on 3 then 3/2 between
both 19) but here I have no real practice experience of this kind of
chord.

May I have more details for "Lou Harrison and Tom Stone" and 16-19-24
minor chord?

>For me (the theorist and the violinist) a major chord is always 4-5-6,
>for C-bE-G-bB chord it's probably
>32-38-48-57 (a fifth 3/2 with 19/16 on 2 and 19/16 on 3 then 3/2 between
>both 19) but here I have no real practice experience of this kind of
>chord.

For a minor seventh chord I think the two real choices are 10:12:15:18 and
12:14:18:21. 57 is just way too high a number to ever have any practical
relevance for tuning.

> [Paul Erlich, TD 392.16]
>
> 57 is just way too high a number to ever have any
> practical relevance for tuning.

Hold on there, Paul... 57 is simply 19 x 3.
So the 3:2 'perfect 5th' above 19/16 is 57/32.

It's plausible to add a '7th' to a 16:19:24 minor
chord which is a 3:2 above the 19/16 'minor 3rd'.
This gives you the 32:38:48:57 chord mentioned
by Xavier. It's virtually indistinguishable from
the 12-eq 'minor 7th chord':

RATIO CENTS DEVIATION FROM 12-EQ

57/32 - ~0.532
3/2 + ~1.955
19/16 - ~2.487
1/1 0

-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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>> 57 is just way too high a number to ever have any
>> practical relevance for tuning.

>Hold on there, Paul... 57 is simply 19 x 3.
>So the 3:2 'perfect 5th' above 19/16 is 57/32.

I should have said, 'practical relevance for perception'.