User:CritDeathX/Sam's Musings: Difference between revisions

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== Stepped Temperament ==

Stepped temperament is the name I give to the '''2.3.5.9.10.11.13.29.31'''-limit temperament with a generator of a flat 5/4 that tempers out 967458816/847425747, 16325867520/13841287201, 823543/629856, etc. Obviously, this is a high complexity temperament, though the good thing is that you have two major thirds that you can choose from; a 12c sharp third (appears after 13 generators) or a 15c flat third (the generator). I tried to demonstrate this fact in the limit, though I have a feeling there's a more accurate way of writing it. A similar occurrence happens in [[pseudo-semaphore]], where the 3rd harmonic has 2 different mappings.

Stepped temperament is the name I give to the '''2.3.5.9.10.11.13.29.31'''-limit temperament with a generator of a flat 5/4 that tempers out 967458816/847425747, 16325867520/13841287201, 823543/629856, etc. Obviously, this is a high complexity temperament, though the good thing is that you have two major thirds that you can choose from; a 12c sharp third (appears after 15 generators) or a 15c flat third (the generator). I tried to demonstrate this fact in the limit, though I have a feeling there's a more accurate way of writing it. A similar occurrence happens in [[pseudo-semaphore]], where the 3rd harmonic has 2 different mappings.

Another thing you may notice is the size of the limit; this is the largest limit that I've seen as of 4/8/2020. Considering I'm only sticking under 31, this is still a sizable limit.

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 == Stepped Temperament ==
-Stepped temperament is the name I give to the '''2.3.5.9.10.11.13.29.31'''-limit temperament with a generator of a flat 5/4 that tempers out <small>967458816/847425747</small>, <small>16325867520/13841287201</small>, <small>823543/629856</small>, etc. Obviously, this is a high complexity temperament, though the good thing is that you have two major thirds that you can choose from; a 12c sharp third (appears after 13 generators) or a 15c flat third (the generator). I tried to demonstrate this fact in the limit, though I have a feeling there's a more accurate way of writing it. A similar occurrence happens in [[pseudo-semaphore]], where the 3rd harmonic has 2 different mappings.
+Stepped temperament is the name I give to the '''2.3.5.9.10.11.13.29.31'''-limit temperament with a generator of a flat 5/4 that tempers out <small>967458816/847425747</small>, <small>16325867520/13841287201</small>, <small>823543/629856</small>, etc. Obviously, this is a high complexity temperament, though the good thing is that you have two major thirds that you can choose from; a 12c sharp third (appears after 15 generators) or a 15c flat third (the generator). I tried to demonstrate this fact in the limit, though I have a feeling there's a more accurate way of writing it. A similar occurrence happens in [[pseudo-semaphore]], where the 3rd harmonic has 2 different mappings.
 Another thing you may notice is the size of the limit; this is the largest limit that I've seen as of 4/8/2020. Considering I'm only sticking under 31, this is still a sizable limit.