4172edo: Difference between revisions

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==Theory==

== Theory ==

The first 8 prime harmonics below 25% in 4172edo are 2, 5, 13, 17, 31, 37, 53, 61. Therefore, 4172edo can be thought of as a 2.5.13.17.31.37.53.61 subgroup temperament~~, on which it is consistent. Other than that, it offers satisfactory representation of the 13-odd-limit (<28% error)~~.

The first 8 prime harmonics below 25% in 4172edo are 2, 5, 13, 17, 31, 37, 53, 61. Therefore, 4172edo can be thought of as a 2.5.13.17.31.37.53.61 subgroup temperament.

4172's divisors are {{EDOs|1, 2, 4, 7, 14, 28, 149, 298, 596, 1043, 2086}}. Notable member of the group is 149edo, which is the smallest edo uniquely consistent in the 17-odd limit~~. Therefore from a logarithmic pitch or highly composite EDO theory perspective~~, ~~4172edo can be thought of as a compound~~ of ~~28 149edos interlocked together~~.

=== Subsets and supersets ===

4172's divisors are {{EDOs|1, 2, 4, 7, 14, 28, 149, 298, 596, 1043, 2086}}. Notable member of the group is 149edo, which is the smallest edo uniquely consistent in the 17-odd limit, although its approximations have long been diluted by edo of this size.

=== ~~Harmonics~~ ===

=== Odd harmonics ===

[[Category:Equal divisions of the octave|####]]

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 {{Infobox ET}}
-{{EDO intro|4172}}
+{{ED intro}}
-==Theory==
+== Theory ==
-The first 8 prime harmonics below 25% in 4172edo are 2, 5, 13, 17, 31, 37, 53, 61. Therefore, 4172edo can be thought of as a 2.5.13.17.31.37.53.61 subgroup temperament, on which it is consistent. Other than that, it offers satisfactory representation of the 13-odd-limit (<28% error).
+The first 8 prime harmonics below 25% in 4172edo are 2, 5, 13, 17, 31, 37, 53, 61. Therefore, 4172edo can be thought of as a 2.5.13.17.31.37.53.61 subgroup temperament.
-'s divisors are {{EDOs|1, 2, 4, 7, 14, 28, 149, 298, 596, 1043, 2086}}. Notable member of the group is 149edo, which is the smallest edo uniquely consistent in the 17-odd limit. Therefore from a logarithmic pitch or highly composite EDO theory perspective, 4172edo can be thought of as a compound of 28 149edos interlocked together.
+=== Subsets and supersets ===
+'s divisors are {{EDOs|1, 2, 4, 7, 14, 28, 149, 298, 596, 1043, 2086}}. Notable member of the group is 149edo, which is the smallest edo uniquely consistent in the 17-odd limit, although its approximations have long been diluted by edo of this size.
-=== Harmonics ===
+=== Odd harmonics ===
-{{Odd harmonics in equal|4172}}
+{{harmonics in equal|4172}}
 <!-- 4-digit number -->
 [[Category:Equal divisions of the octave|####]]
+{{todo|inline=1|explain its xenharmonic value}}