The five weakly CS 12-et scales

Balzano's weakening of CS struck me as ad-hoc, so I checked what
happens if you define weakly CS by replacing the less than with a less
than or equal for the various class elements. I get five weakly CS
scales, one of course the diatonic.

[2, 4, 6, 7, 8, 10, 12], [2, 4, 5, 8, 9, 11, 12],
[2, 4, 6, 7, 9, 10, 12], [2, 3, 6, 7, 9, 11, 12],
[1, 3, 5, 6, 8, 10, 12]

On 5/26/06, Gene Ward Smith <genewardsmith@coolgoose.com> wrote:
> Balzano's weakening of CS struck me as ad-hoc, so I checked what
> happens if you define weakly CS by replacing the less than with a less
> than or equal for the various class elements. I get five weakly CS
> scales, one of course the diatonic.
>
> [2, 4, 6, 7, 8, 10, 12], [2, 4, 5, 8, 9, 11, 12],
> [2, 4, 6, 7, 9, 10, 12], [2, 3, 6, 7, 9, 11, 12],
> [1, 3, 5, 6, 8, 10, 12]

Looks like we've got the diatonic, its two permutations, the "harmonic
minor" scale, and its inversion.

At 11:45 AM 5/26/2006, you wrote:
>On 5/26/06, Gene Ward Smith <genewardsmith@coolgoose.com> wrote:
>> Balzano's weakening of CS struck me as ad-hoc, so I checked what
>> happens if you define weakly CS by replacing the less than with a less
>> than or equal for the various class elements. I get five weakly CS
>> scales, one of course the diatonic.
>>
>> [2, 4, 6, 7, 8, 10, 12], [2, 4, 5, 8, 9, 11, 12],
>> [2, 4, 6, 7, 9, 10, 12], [2, 3, 6, 7, 9, 11, 12],
>> [1, 3, 5, 6, 8, 10, 12]
>
>Looks like we've got the diatonic, its two permutations, the "harmonic
>minor" scale, and its inversion.

Thanks for doing these, Keenan.

-Carl