Ganassi, was: An Augmented Baker's Dozen

Hello all, monz here.

Sorry to have been so absent lately, but I discovered the
Mahler List last weekend and have been *REALLY* busy over there...
Those interested can find a link to info, here:
http://www.netaxs.com/~jgreshes/mahler/

Back to tuning...

[Paul Erlich, TD 233.9 & 10]
>
> Kraig Grady wrote,
>> With 12et I always preferred the minor chord so it is no
>> suprise my preference for subharmonics.
>
> I would think that for a keen-eared high-limit just intonation
> enthusiast, the 12-tET minor triad would sound like a nearly
> exact 16:19:24, which has a clear root, while a 12-tET major triad
> would sound like a very out-of-tune 4:5:6.

> Carl Lumma wrote,
>> Actually, Kraig, I am beginning to believe that the 12tET minor
>> triad approximates 16:19:24 more often than 10:12:15. You and
>> Wilson both told me about the 19-limit approximations in
>> 12-tone... I think you guys were right.
>
> I guess my comment to that effect came too late.

In 1543 Sylvestro Ganassi published a JI well-temperament
which made ingenious use of 17- and 19-limit ratios for the
'black notes'. It gave successive proportions for the series
of notes from C to F, from F to G, and from G to B (C).

Documented in Barbour.

[view in a fixed-width font]

NOTE CENTS RATIO PROPORTIONS
C 1200 2:1 30:15
B 1088 15:8 30:16
A#/Bb 983 30:17 30:17
A 884 5:3 30:18
G#/Ab 791 30:19 30:19
G 702 3:2 30:20 24:16
F#/Gb 597 24:17 24:17
F 498 4:3 24:18 20:15
E 386 5:4 20:16
D#/Eb 281 20:17 20:17
D 182 10:9 20:18
C#/Db 89 20:19 20:19
C 0 1:1 30:30 24:24 20:20

-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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