Re: Sesquisexta -- another correction

Hello, there, everyone, and as I noted in my first corrections,
discussing a new (or sometimes actually "newly rediscovered") tuning
is often an opportunity to make errors in either note spellings or
indications for the size of intervals.

In my first correction on the Sesquisexta tuning with its two
Pythagorean keyboards tuned a pure 7:6 apart, I addressed some initial
glitches with note spellings but unfortunately introduced new bugs
concerning interval sizes. Here is a debugging:

> Contractive 7-flavor quad (12:14:18:21)
>
> Intensive Remissive
>
> B&3/D@4 --- -63 --- A&3/C@4 G&3/Bb@3 --- -63 --- A3
> (267) (0) (267) (0)
> B3 --- +204 --- A&3/C@4 G3 --- +204 --- A3
> (498,435) (702,702) (498,435) (702,702)
> E&3/G@3 --- -63 --- D&3/F@3 C&3/Eb@3 --- -63 --- D3
>(969,702,267) (702,702,0) (969,702,267) (702,702,0)
> E3 --- +63 --- D&3/F@3 C3 --- +204 --- D3

An intensive neo-Gothic cadence involves descending whole-tones (here
the usual Pythagorean 9:8, ~203.91 cents) and ascending semitones
(here at the 7-based ratio of 28:27, ~62.96 cents), so the indicated
melodic motions in cents are very clearly wrong. Here's a corrected
version:

Contractive 7-flavor quad (12:14:18:21)

Intensive Remissive

B&3/D@4 --- -204 --- A&3/C@4 G&3/Bb@3 --- -63 --- A3
(267) (0) (267) (0)
B3 --- +63 --- A&3/C@4 G3 --- +204 --- A3
(498,435) (702,702) (498,435) (702,702)
E&3/G@3 --- -204 --- D&3/F@3 C&3/Eb@3 --- -63 --- D3
(969,702,267) (702,702,0) (969,702,267) (702,702,0)
E3 --- +63 --- D&3/F@3 C3 --- +204 --- D3

As explained in my previous corrections, notes of the upper manual are
indicated with two alternate notations. The first or "&" notation
simply shows the visual location of the key used to play the note:
thus "E&3" means "the E3 key on the upper manual," a pure 7:6 above
the same key on the lower manual.

The "@" notation shows a note a comma lower -- here the septimal comma
of 64:63 (~27.26 cents) in relation to the same note on the lower
keyboard: thus E&3=G@3, the note a septimal comma lower than G3.

As the other spellings in this example also illustrate, a note on the
upper manual is a septimal comma lower than a note visually appearing
a regular minor third higher on the lower keyboard: C&3=Eb@3,
G&3=Bb@3, etc.

Anyway, thanks to people for bearing with these early notational
"bugs" in attempting to describe what I find a very exciting new
tuning -- even if it turns out to be another "rediscovery."

Most appreciatively,

Margo Schulter
mschulter@value.net