Salinas

[Christopher Stembridge via Bill Alves, TD 204.5]
>
> As you may know Salinas had an organ made for him in Rome wch
> he took back to Spain.
> Unfortunately he never described it. From his discussion of
> tuning I infer that this instrument had a keyboard with enough
> split keys (including 2 different Ds) to give just intonation.
> Have you, or do you know anyone who has, dealt with this aspect
> of Salinas?

I don't have any specific info on Salinas's keyboard handy,
but this is a lattice of the 24-tone tuning system he described,
from my book:

('inf' and 'sup' are abbreviations for 'inferius' and 'superius'
respectively: these 5 pairs of notes were separated by the
syntonic comma. 'DIA', 'CHR', and 'ENH' refer to the genera
to which any individual note belonged, with 'C' as the 1/1,
and they refer to 'diatonic', 'chromatic', and 'enharmonic', resp.)

125:72 125:96 125:64
A# inf ----- E# ----- B#
ENH ENH ENH
| | |
| | |
25:18 25:24 25:16 75:64 225:128
F# inf ----- C# ----- G# ----- D# ----- A# sup
CHR CHR CHR ENH ENH
| | | | |
| | | | |
10:9 5:3 5:4 15:8 45:32
D inf ----- A ----- E ----- B ----- F# sup
DIA DIA DIA DIA CHR
| | | | |
| | | | |
16:9 4:3 1:1 3:2 9:8
b inf ----- F ----- C ----- G ----- D sup
CHR DIA DIA DIA DIA
| | | | |
| | | | |
64:45 16:15 8:5 6:5 9:5
Gb inf ----- Db ----- Ab ----- Eb ----- b sup
ENH ENH ENH CHR CHR
|
|
36:25
Gb sup
ENH

This was first published in Salinas's _De musica libri septem_
(Salamanca, Spain) in 1577. I got it from Arthur Daniels's
excellent two-part article _Microtonality and Mean-tone
Temperament in the Harmonic System of Francisco Salinas_,
published in 1965 in the _Journal of Music Theory_, vol 9,
# 1 and 2. The system described above is given on p 238 in
issue #2.

This is a very long and detailed article, and I would
have to re-read it carefully again to get accurate info
on Salinas's keyboard, but Daniels does describe Salinas's
use of temperament, so it seems doubtful to me that it
would have two 'D's. Then again, that's exactly what his
JI system (in the above lattice) gives, so maybe...

Hope that helps.

-monz

Joseph L. Monzo monz@juno.com
http://www.ixpres.com/interval/monzo/homepage.html
|"...I had broken thru the lattice barrier..."|
| - Erv Wilson |
--------------------------------------------------

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