Semi-Just Meantone C Scale

All, Copyright © 2002 by Pauline W.
Phillips

Here's the semi-just meantone C scale I calculated, where theoretically E =
386.316 (.002 long 386.314), G = 696.579 (5.376 short 701.955) cents, 7Bb =
965.790 (3.036 short 968.826), and requires white split digitals for five
harmonic minor 7ths. The harmonic minor 7th are calculated from F-7Eb.

C C# 7D D D#/7Eb E 7F
F F#
0 76.053 152.016 193.158 269.211 386.316 462.369 503.421
579.474

7G G G# /7Ab 7A A A#/7Bb B
7C
655.527 696.579 772.632 848.685 889.737 965.790 1082.895
1158.948

C2
1200

The major 3rds and minor 6ths are "pure," off the theoretical values just
enough to be out of phase.
Major triads are F-C-G-D-A-E-B-F#-C#-G#-D#/7Eb-A#/7Bb-7F-7C-5ths-7G-7D-7A.
The major triads F-C-G-D-A-E-B have harmonic minor 7ths.
The flat triads bII, bIII, bVI, and bVII are available.
The scale will play C, 7c and e.

This scale has the advantage over my JT scale in that the F7 chord is
included, thus allowing playing on one manual.

However, my JT scale has just-tempered 5ths worth 700 cents.And the major
3rds, minor 3rds, major 6ths, minor 6ths, minor 7ths, and diminished I, III,
IV, VII are all "pure"! And the flatted chords also have harmonic minor 7ths.
So my JT Phillips scale is superior to the Meantone scale.

I'd rather use three manuals, each with seven split digitals per octave per
key signature, to play my scale than to compromise as much as the Meantone
scale does.

MT suggests compositions are composed in whole in key signatures. When in
fact my scale proves key signatures apply to phrases. Thus music written in C
major may use the F, C, and G scales, and sometimes a flatted scale. And thus
justifies using up to three differently-tuned manuals to play a compositon.

Sincerely,
Pauline W. Phillips, Moderator, <A HREF="/JohannusOrgansSchool ">Johannus Organs eSchool</A>
Johannus Orgelbouw, Holland, builds pipe, pipe-digital, digital-sampled
organs.
Moderator, <A HREF="/JustIntonationOrganSchool/">Just Intonation Organ eSchool</A>