ennealimmal

Am I correct that the first ennealimmal scale with an octave
is simply 9-equal, and the next is this 17-tone one...

50.
133.3
183.3
266.7
316.7
400.
450.
533.3
583.3
666.7
716.7
800.
850.
933.3
983.3
1066.7
1116.7

...?

Manuel, is there a convenient way to get MOS-like scales with
non-octave periods in Scala?

-Carl

--- In tuning-math@yahoogroups.com, Carl Lumma <ekin@l...> wrote:
> Am I correct that the first ennealimmal scale with an octave
> is simply 9-equal, and the next is this 17-tone one...

should be 18-tone . . . apparently you don't count 0 *or* 1200?

>
> 50.
> 133.3
> 183.3
> 266.7
> 316.7
> 400.
> 450.
> 533.3
> 583.3
> 666.7
> 716.7
> 800.
> 850.
> 933.3
> 983.3
> 1066.7
> 1116.7
>
> ...?
>
> Manuel, is there a convenient way to get MOS-like scales with
> non-octave periods in Scala?
>
> -Carl

>> Am I correct that the first ennealimmal scale with an octave
>> is simply 9-equal, and the next is this 17-tone one...
>
>should be 18-tone . . . apparently you don't count 0 *or* 1200?

d'oh.

>> 50.
>> 133.3
>> 183.3
>> 266.7
>> 316.7
>> 400.
>> 450.
>> 533.3
>> 583.3
>> 666.7
>> 716.7
>> 800.
>> 850.
>> 933.3
>> 983.3
>> 1066.7
>> 1116.7
// 2/1
>>
>> ...?
>>
>> Manuel, is there a convenient way to get MOS-like scales with
>> non-octave periods in Scala?

-Carl

Carl wrote:
>Manuel, is there a convenient way to get MOS-like scales with
>non-octave periods in Scala?

Sure, create them with PYTHAGOREAN specifying the period as
formal octave, and then use EXTEND to change the number of tones.
The SHOW DATA command now also shows whether repeating blocks have
Myhill's property.

>Am I correct that the first ennealimmal scale with an octave
>is simply 9-equal, and the next is this 17-tone one...

You probably mean 18-tone. The generator doesn't need to be
exactly 50 cents, but if I understand your question correctly, yes.

Manuel

--- In tuning-math@yahoogroups.com, "Manuel Op de Coul"
<manuel.op.de.coul@e...> wrote:

> You probably mean 18-tone. The generator doesn't need to be
> exactly 50 cents, but if I understand your question correctly, yes.

In fact, a generator of 25/612 makes more sense.