Another historical question

I think one of the most inportant scales in history after the Pythagorean scale is the scale:
9/8 10/9 16/15 9/8 9/8 ( or 10/9 ) 10/9 ( or 9/8 ) 16/15

I want to know where did this scale come from? Zarlino or prior to Zarlino? Or there is no known source?

Rami Vitale

> Message: 7
> Date: Wed, 17 Oct 2001 11:20:24 -0400
> From: "Rami Vitale" <alfred1@scs-net.org>
> Subject: Another historical question
>
> I think one of the most inportant scales in history after the
> Pythagorean scale is the scale: 9/8 10/9 16/15 9/8 9/8 ( or 10/9 )
> 10/9 ( or 9/8 ) 16/15
>
> I want to know where did this scale come from? Zarlino or prior to
> Zarlino? Or there is no known source?
>
> Rami Vitale

Rami - here's a copy of something I wrote before to the list on this:

----------------
Fogliano, in _Musica Theorica_, 1529, already presents a C-c species for
his monochord tuning. He acknowledges Ptolemy, and sets it out like
this:

C D E F G A B
10:9 9:8 16:15 9:8 10:9 9:8 16:15

|_____|___|____|
(Ptolemy's diaton syntonon)

This same tuning can be found even earlier, in _Musica practica_ by
Ramos de Pareja of Bologna, in 1482. He lays it out from A-a though.
His student Spataro reported that he arrived at this division
independently from Ptolemy. It's indeed unlikely Ramos would have had
access to the Greek sources.

So Zarlino, who acknowledges Fogliano as an excellent writer on music,
certainly knew Fogliano sets the octave division out from C to c. He
gives his division, likewise from C to c, which permutes the 9:8 and
10:9 from the beginning of Fogliano's, and
[snip]
------------------------------------

So Zarlino was first with the one you quote (1558), but it is very similar
to Fogliano's and Ramos's a little earlier. They had the "bad" fifth as
G-D; Zarlino has it as D-A. I don't know of any writers that give G-A as
9/8 and A-B as 10/9. This would make A-E the bad fifth.

Ptolemy gave as one of his tunings for a tetrachord: 16/15 9/8 10/9, but
if you combine this tetrachord with one starting a 9/8 wholetone above it,
as was the practice in forming octave scales, you actually do get the
scale Zarlino gives.

By the way, a similar reversal of the 9/8 and 10/9 happens in a diatonic
tuning of the tetrachord by Didymus (earlier than Ptolemy), who gives
16/15 10/9 9/8.

Best --Jon