The "Warped Canon" Page

(part 2: irregular 12-note scales)

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Circular 12-note temperaments

In some ways the canon is not a useful comparison of "well-tempered" and other irregular 12-note tunings, because the main differences in many of these temperaments are found in remote keys. For this reason, the canons on this page are available in four different versions: one in the original key of D, and the others in the keys of C, D-flat, and E-flat. Because these tunings are primarily designed for keyboard instruments (and because I'm sick of hearing the same arrangment over and over), I've changed the instrumentation of the three melodic lines.

This table gives the temperament of each fifth in fractions of a Pythagorean comma (fifths are narrow unless marked positive):

                  C-G   G-D   D-A   A-E   E-B   B-F# F#-C# C#-G# Ab-Eb Eb-Bb Bb-F   F-C
Barnes            1/6   1/6   1/6   1/6    0    1/6    0     0     0     0     0    1/6
Bendeler III      1/4   1/4    0     0    1/4    0     0     0    1/4    0     0     0
Lehman            1/6   1/6   1/6   1/6    0     0     0    1/12  1/12  1/12 +1/12  1/6
Kellner           1/5   1/5   1/5   1/5    0    1/5    0     0     0     0     0     0
Keyhole           1/20  1/4   1/4   1/20  1/20  1/20  1/20  1/20  1/20  1/20  1/20  1/20
Neidhardt S. City 1/6   1/6   1/6   1/6   1/12  1/12   0     0    1/12  1/12   0     0
Neidhardt Village 1/12  1/6   1/4   1/4    0    1/12   0    1/12   0     0    1/12   0
Sorge 1758        1/6   1/6   1/6   1/12   0    1/12  1/12   0    1/12  1/12  1/12   0
Vallotti          1/6   1/6   1/6   1/6   1/6    0     0     0     0     0     0    1/6
Werckmeister III  1/4   1/4   1/4    0     0    1/4    0     0     0     0     0     0

References