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Can't follow this
At first look, I can't follow this. Maybe some further explanation would help. For instance, showing the relationship between the 12-note 7-limit scale and crossbone. Also, it's simply asserted that two primes separated by 12 have a special relationship.
- genewardsmith July 15, 2014, 08:22:41 PM UTC-0700
Thanks for the feedback and suggestions Gene. I can see where explicitly bridging tosee gaps would clear up a lot, especially since I included all three implementations in rapid succession; I'll get to work on it tonight.
- joeydinardo2 July 16, 2014, 06:24:28 AM UTC-0700
Bridging those gaps*
- joeydinardo2 July 16, 2014, 06:27:12 AM UTC-0700
I think it's important to mention that if A = 7^(1/19) abd B = 5^(1/17), then 2 is approximately A^4 * B^3. If we assume this equivalence, then we are in a tuning of a rank two 2.5.7 temperament tempering out |-323 0 57 68>. We might want to also use 3 as approximately B^19/A^5. Assuming both, we are in this temperament, in the 5 and 7 eigenmonzo tuning:
Alternatively, there's this:
At any rate, an 88 note scale would seem natural for crossbone.
- genewardsmith July 16, 2014, 09:35:42 AM UTC-0700
That's a great interpretation, though I'd like to somehow make clear that my intentions with Crossbone are not to be in reference to or approximate an octave equivalency, but instead to use the septave and pentave together in keyspace (physical space on the keyboard, not pitch space) repeating the 'sepent' -a combination in keyspace of the pentave (in 17steps) and the septave (in 19 steps)- every 36 keys.
I'd like to stay away from classifying the EDT temperament in relation to an octave approximation, but that's absolutely reasonable for the octave-based just scale approximation.
- joeydinardo2 July 16, 2014, 10:14:33 AM UTC-0700
Oops, I was under the impression EDT meant "Equally-Divided Temperament" meaning "any temperament not octave-repeating." In this case, I actually mean EDP (equally divided pentave) and EDS (equally divided septave)
- joeydinardo2 July 17, 2014, 09:38:13 AM UTC-0700
I'm still not finding an actual specification of which notes belong to Crossbone.
- genewardsmith July 17, 2014, 05:58:05 PM UTC-0700
Working on it; adding sections detailing the sepent, a pitch table, detailing the prime assertion you mention, and reworking the just scale documentation.
- joeydinardo2 July 17, 2014, 07:58:59 PM UTC-0700
Are the notes:
(1) A^n plus B^n for various integers n
(2) A^n * B^m for integers n and m
(3) Something else?
- genewardsmith July 18, 2014, 05:58:07 PM UTC-0700
In reference to the just approximates? The key assignment/layout? Or are you asking if each order is something composite/polymicrotonal?
- joeydinardo2 July 18, 2014, 09:28:35 PM UTC-0700