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Three more well-temperaments

🔗Herman Miller <hmiller@IO.COM>

9/24/2003 4:22:33 PM

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