4296edo: Difference between revisions

Overthink (talk | contribs)
+ brief description of higher limits
Overthink (talk | contribs)
Undo revision 211363 by Overthink (talk) not very notable (also easily seen from table)
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4296 = 12 × 358, and is potentially of use as a device for constructing 5-limit 12-note circulating temperaments, and
4296 = 12 × 358, and is potentially of use as a device for constructing 5-limit 12-note circulating temperaments, and
which means that one cent is exactly 3.58 steps of 4296edo. From that point of view, one might note that 81/80 is 77 steps, 531441/524288, the Pythagorean comma, 84 steps, and 32805/32768, the schisma, 7 steps, making it exactly 1/12 of a Pythagorean comma and 1/11 of a syntonic comma, useful approximations when dealing with this problem. Senior, {{monzo| -17 62 -35 }}, fortune, {{monzo| -107 47 14 }} and the [[monzisma]], {{monzo| 54 -37 2 }}, are all one step of 4296et.
which means that one cent is exactly 3.58 steps of 4296edo. From that point of view, one might note that 81/80 is 77 steps, 531441/524288, the Pythagorean comma, 84 steps, and 32805/32768, the schisma, 7 steps, making it exactly 1/12 of a Pythagorean comma and 1/11 of a syntonic comma, useful approximations when dealing with this problem. Senior, {{monzo| -17 62 -35 }}, fortune, {{monzo| -107 47 14 }} and the [[monzisma]], {{monzo| 54 -37 2 }}, are all one step of 4296et.
It is also a strong system in the 2.3.5.13.17.19.23.29.31 subgroup, being consistent to the 31-odd-limit in that subgroup.


=== Prime harmonics ===
=== Prime harmonics ===
{{Harmonics in equal|4296|prec=4}}
{{Harmonics in equal|4296|prec=4}}