Topic: Three more well-temperaments

3 scales

Thread (1 messages)

From: Herman Miller (2003-09-24)
Subject: Three more well-temperaments

Here are a few more well-temperaments I've found. These all have maximum
errors less than 20 cents in the thirds (both major and minor), and 6 cents
in the fifths.

"Butterfly I" (from the shape of the graph)

C-G, E-B tempered 3/20 Pyth. comma
G-D, A-E tempered 1/5 Pyth. comma
D-A, C#-G#, Eb-Bb tempered 1/10 Pyth. comma
B-F#-C#, Ab-Eb, Bb-F-C just

"Butterfly II"

G-D, A-E tempered 1/4 Pyth. comma
D-A, C#-G#, Eb-Bb tempered 1/10 Pyth. comma
F-C-G, E-B-F# tempered 1/20 Pyth. comma
F#-C#, Ab-Eb, Bb-F just

"Bug I"

C-G, A-E tempered 3/20 Pyth. comma
G-D-A tempered 1/4 Pyth. Comma
F#-C#, Eb-Bb tempered 1/10 Pyth. Comma
E-B-F#, C#-G#-D#, Bb-F-C just

I like this one. The C-E third is less than 3 cents sharp, it has lots of
just fifths, and a nice progression from "good" to "bad" thirds.

! butterfly1.scl
!
"Butterfly I" well-temperament
 12
!
 94.92188
 195.70313
 296.48438
 392.57813
 498.04688
 592.96875
 698.43750
 794.53125
 895.31250
 996.09375
 1091.01560
 2/1

! butterfly2.scl
!
"Butterfly II" well-temperament
 12
!
 96.09375
 196.87500
 297.65625
 392.57813
 499.21875
 594.14063
 700.78125
 795.70313
 896.48438
 997.26565
 1093.35935
 2/1

! bug.scl
!
"Bug I" well-temperament
 12
!
 92.57812
 194.53125
 296.48438
 389.06250
 498.04688
 592.96875
 698.43750
 794.53125
 890.62500
 996.09375
 1091.01560
 2/1