1/4-comma meantone interval matrix and list

Hello all.

Yesterday, Denny Genovese played for me Dave Hill's CD
of piano pieces tuned in JI and meantone.

My favorite ones were a JI piece by Dave about a cat,
and an improvisation he did exploiting the close approximations
to 7- and 11-limit harmonics in 1/4-comma meantone.

I was so intrigued by the latter that I made an interval matrix
and list of available intervals for a 12-tone version of
1/4-comma meantone:

http://www.ixpres.com/interval/dict/1-4cmt.htm

For those without web access who find it useful:

(if line-breaks have been added which shorten the lines,
copy these tables to a text editor and delete the line-breaks
to arrive at the correct format)

INTERVAL MATRIX OF 12-TONE 1/4-COMMA MEANTONE, IN
SEMITONES
G# G F# F E Eb D C# C B Bb
A

3^x 5 -2 3 -4 1 -6 -1 4 -3 2 -5
0

G# 5 0.00 11.24 10.07 9.31 8.14 7.38 6.21 5.03 4.27 3.10 2.34
1.17

G -2 0.76 0.00 10.83 10.07 8.90 8.14 6.97 5.79 5.03 3.86 3.10
1.93

F# 3 1.93 1.17 0.00 11.24 10.07 9.31 8.14 6.97 6.21 5.03 4.27
3.10

F -4 2.69 1.93 0.76 0.00 10.83 10.07 8.90 7.73 6.97 5.79 5.03
3.86

E 1 3.86 3.10 1.93 1.17 0.00 11.24 10.07 8.90 8.14 6.97 6.21
5.03

Eb -6 4.62 3.86 2.69 1.93 0.76 0.00 10.83 9.66 8.90 7.73 6.97
5.79

D -1 5.79 5.03 3.86 3.10 1.93 1.17 0.00 10.83 10.07 8.90 8.14
6.97

C# 4 6.97 6.21 5.03 4.27 3.10 2.34 1.17 0.00 11.24 10.07 9.31
8.14

C -3 7.73 6.97 5.79 5.03 3.86 3.10 1.93 0.76 0.00 10.83 10.07
8.90

B 2 8.90 8.14 6.97 6.21 5.03 4.27 3.10 1.93 1.17 0.00 11.24
10.07

Bb -5 9.66 8.90 7.73 6.97 5.79 5.03 3.86 2.69 1.93 0.76 0.00
10.83

A 0 10.83 10.07 8.90 8.14 6.97 6.21 5.03 3.86 3.10 1.93 1.17
0.00

LIST OF ALL INTERVALS IN 12-TONE 1/4-COMMA MEANTONE
3^(-6�5), 1/1=A
left=lower note:right=higher note

diminished 8ve 11.24 G#:G, F#:F, E:Eb, C#:C, B:Bb

major 7th 10.83 G:F#, F:E, Eb:D, D:C#, C:B, Bb:A, A:G#

minor 7th 10.07 G#:F#, G:F, F#:E, F:Eb, E:D, D:C, C#:B, C:Bb, B:A,
A:G

augmented 6th 9.66 Eb:C#, Bb:G#

diminshed 7th 9.31 G#:F, F#:Eb, C#:Bb

major 6th 8.90 G:E, F:D, E:C#, Eb:C, D:B, C:A, B:G#, Bb:G, A:F#

minor 6th 8.14 G#:E, G:Eb, F#:D, E:C, D:B, C#:A, B:G, A:F

augmented 5th 7.73 F:C#, Eb:B, C:G#, Bb:F#

wolf 5th 7.38 G#:Eb

'perfect' 5th 6.97 G:D, F#:C#, F:C, E:B, Eb:Bb, D:A, C#:G#, C:G,
B:F#, Bb:F, A:E

diminished 5th 6.21 G#:D, F#:C, E:Bb, C#:G, B:F, A:Eb

augmented 4th 5.79 G:C#, F:B, Eb:A, D:G#, C:F#, Bb:E

'perfect' 4th 5.03 G#:C#, G:C, F#:B, F:Bb, E:A, D:G, C#:F#, C:F, B:E,
Bb:Eb, A:D

wolf 4th 4.62 Eb:G#

diminished 4th 4.27 G#:C, F#:Bb, C#:F, B:Eb

major 3rd 3.86 G:B, F:A, E:G#, Eb:G, D:F#, C:E, Bb:D, A:C#

minor 3rd 3.10 G#:B, G:Bb, F#:A, E:G, D:F, C#:E, C:Eb, B:D, A:C

augmented 2nd 2.69 F:G#, Eb:F#, Bb:C#

diminished 3rd 2.34 G#:Bb, C#:Eb

major 2nd 1.93 G:A, F#:G#, F:G, E:F#, Eb:F, D:E, C:D, B:C#, Bb:C,
A:B

minor 2nd 1.17 G#:A, F#:G, E:F, D:Eb, C#:D, B:C, A:Bb

augmented unison 0.76 G:G#, F:F#, Eb:E, C:C#, Bb:B

unison / 8ve 0, 12 G#:G#, G:G, F#:F#, F:F, E:E, Eb:Eb, D:D, C#:C#,
C:C, B:B, Bb:Bb, A:A

-monz

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

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