Keenan Pepper Optimal rank range MOS scales copied from XA

Keenan Pepper
Optimal rank range MOS scales

The following scales have optimal "rank range" which means all the different intervals between pairs of notes in the scale are as evenly spread out as possible. In most cases this means L/s=3/2, but if there is only one small step per period, it means L/s=1/2 instead.

In the case that you have two small steps per octave, you can use L/s=1/2 and there is only one ambiguity in the scale, a 600 cent interval. For example the diatonic scale in 12edo is like this. You don't know if 600 cents is an augmented fourth or a diminished fifth. So for these cases I give both possible choices.

Father[5] in 13edo (or 8edo if you don't mind one ambiguity)
Bug[5] in 9edo
Augmented[6] in 9edo
Machine[5] and [6] in 11edo
Pentatonic in 12edo
Diatonic in 19edo (or 12edo if you don't mind one ambiguity)
Diminished[8] in 12edo (aka familiar octatonic)
6- and 7-note scales generated by 2\13 in 13edo (Name, Igs?)
Hedgehog[8] in 14edo
Porcupine[7] and [8] in 15edo
Blackwood[10] in 15edo
Mavila[7] in 16edo
Mavila[9] in 25edo (or 16edo if you don't mind one ambiguity)
Neutral thirds [7] in 17edo
Bleu[8] and [9] in 17edo
Sensi[8] in 19edo
Negri[9] and [10] in 19edo
Father[8] in 21edo
Orwell[9] in 22edo
Decatonic and pajara[12] in 22edo
Bug[9] in 23edo
Decimal[10] in 24edo
Lemba[10] in 26edo
Beatles[10] in 27edo
Pythagorean[12] (cassandra/leapday/whatever) in 29edo

Cool list, thanks. Any reason Keenan's name is attached
to it? -C.

Gene wrote:

>Keenan Pepper
>Optimal rank range MOS scales
>Father[5] in 13edo (or 8edo if you don't mind one ambiguity)
>Bug[5] in 9edo
>Augmented[6] in 9edo
>Machine[5] and [6] in 11edo
>Pentatonic in 12edo
>Diatonic in 19edo (or 12edo if you don't mind one ambiguity)
>Diminished[8] in 12edo (aka familiar octatonic)
>6- and 7-note scales generated by 2\13 in 13edo (Name, Igs?)
>Hedgehog[8] in 14edo
>Porcupine[7] and [8] in 15edo
>Blackwood[10] in 15edo
>Mavila[7] in 16edo
>Mavila[9] in 25edo (or 16edo if you don't mind one ambiguity)
>Neutral thirds [7] in 17edo
>Bleu[8] and [9] in 17edo
>Sensi[8] in 19edo
>Negri[9] and [10] in 19edo
>Father[8] in 21edo
>Orwell[9] in 22edo
>Decatonic and pajara[12] in 22edo
>Bug[9] in 23edo
>Decimal[10] in 24edo
>Lemba[10] in 26edo
>Beatles[10] in 27edo
>Pythagorean[12] (cassandra/leapday/whatever) in 29edo

It could be useful to have the difference in TE error between
these tunings and the TE-optimal ones... -Carl

At 07:13 AM 8/29/2011, you wrote:
>Father[5] in 13edo (or 8edo if you don't mind one ambiguity)
>Bug[5] in 9edo
>Augmented[6] in 9edo
>Machine[5] and [6] in 11edo
>Pentatonic in 12edo
>Diatonic in 19edo (or 12edo if you don't mind one ambiguity)
>Diminished[8] in 12edo (aka familiar octatonic)
>6- and 7-note scales generated by 2\13 in 13edo (Name, Igs?)
>Hedgehog[8] in 14edo
>Porcupine[7] and [8] in 15edo
>Blackwood[10] in 15edo
>Mavila[7] in 16edo
>Mavila[9] in 25edo (or 16edo if you don't mind one ambiguity)
>Neutral thirds [7] in 17edo
>Bleu[8] and [9] in 17edo
>Sensi[8] in 19edo
>Negri[9] and [10] in 19edo
>Father[8] in 21edo
>Orwell[9] in 22edo
>Decatonic and pajara[12] in 22edo
>Bug[9] in 23edo
>Decimal[10] in 24edo
>Lemba[10] in 26edo
>Beatles[10] in 27edo
>Pythagorean[12] (cassandra/leapday/whatever) in 29edo

Ah, I see you weren't kidding when you said you'd archive
facebook posts over here. *confusing*

At 10:54 AM 8/29/2011, you wrote:
>Cool list, thanks. Any reason Keenan's name is attached
>to it? -C.
>
>Gene wrote:
>
>>Keenan Pepper
>>Optimal rank range MOS scales
>>Father[5] in 13edo (or 8edo if you don't mind one ambiguity)
>>Bug[5] in 9edo
>>Augmented[6] in 9edo
>>Machine[5] and [6] in 11edo
>>Pentatonic in 12edo
>>Diatonic in 19edo (or 12edo if you don't mind one ambiguity)
>>Diminished[8] in 12edo (aka familiar octatonic)
>>6- and 7-note scales generated by 2\13 in 13edo (Name, Igs?)
>>Hedgehog[8] in 14edo
>>Porcupine[7] and [8] in 15edo
>>Blackwood[10] in 15edo
>>Mavila[7] in 16edo
>>Mavila[9] in 25edo (or 16edo if you don't mind one ambiguity)
>>Neutral thirds [7] in 17edo
>>Bleu[8] and [9] in 17edo
>>Sensi[8] in 19edo
>>Negri[9] and [10] in 19edo
>>Father[8] in 21edo
>>Orwell[9] in 22edo
>>Decatonic and pajara[12] in 22edo
>>Bug[9] in 23edo
>>Decimal[10] in 24edo
>>Lemba[10] in 26edo
>>Beatles[10] in 27edo
>>Pythagorean[12] (cassandra/leapday/whatever) in 29edo
>

--- In tuning-math@yahoogroups.com, Carl Lumma <carl@...> wrote:
>
> Ah, I see you weren't kidding when you said you'd archive
> facebook posts over here. *confusing*

I'm trying it experimentally to see how people react, so I'd be interested to know why you think it is confusing.

The way the subject reads, "Keenan Pepper Optimal ... ", discards the
screen formatting from the Facebook group, making it seem as though
your name were some kind of nomenclature, rather than the person who
originally posted the topic on XA. (That is what happened, right?)

It would be good to establish some kind of subject-line convention for
material copied from XA, to be used as consistently as is practical
among the group. Something like "From XA:" at the beginning of the
subject line, to indicate to those who haven't been following (or who
aren't on FB) that the new list thread continues an ongoing topic, and
to make it easier to search by subject in the future.

/jc

On Mon, Aug 29, 2011 at 17:45, genewardsmith
<genewardsmith@sbcglobal.net> wrote:
>
>
> --- In tuning-math@yahoogroups.com, Carl Lumma <carl@...> wrote:
>>
>> Ah, I see you weren't kidding when you said you'd archive
>> facebook posts over here. *confusing*
>
> I'm trying it experimentally to see how people react, so I'd be interested to know why you think it is confusing.
>
>
>
>
> ------------------------------------
>
> Yahoo! Groups Links
>
>
>
>

Gene wrote:

>> Ah, I see you weren't kidding when you said you'd archive
>> facebook posts over here. *confusing*
>
>I'm trying it experimentally to see how people react, so I'd be
>interested to know why you think it is confusing.

I thought it was a post from you, for starters. If you really
want to use this list to backup facebook, I suggest making a
special Yahoo! account for the purpose, or at least tagging the
subject line with something like [facebook backup].

-Carl

Facebook has not the only Xenharmonic Alliance around.
Please say [facebookXA] or similar. -Carl

At 06:22 PM 8/29/2011, you wrote:
>The way the subject reads, "Keenan Pepper Optimal ... ", discards the
>screen formatting from the Facebook group, making it seem as though
>your name were some kind of nomenclature, rather than the person who
>originally posted the topic on XA. (That is what happened, right?)
>
>It would be good to establish some kind of subject-line convention for
>material copied from XA, to be used as consistently as is practical
>among the group. Something like "From XA:" at the beginning of the
>subject line, to indicate to those who haven't been following (or who
>aren't on FB) that the new list thread continues an ongoing topic, and
>to make it easier to search by subject in the future.
>
>/jc
>