311edo: Difference between revisions

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== Intervals ==

The 41-limit add-73 add-89 add-101 add-109 add-113 123-odd-limit is represented very close to completely ~~consistently~~, and as aforementioned, the 77-odd-limit subset of that odd-limit is perfectly consistent, to which a variety of odds can be added that keep perfect consistency, but for comprehensiveness and practical use as a temperament approximating the low-to-mid end of the harmonic series, we consider a larger odd-limit than that which seeks to be more complete.

The 41-limit add-73 add-89 add-101 add-109 add-113 123-odd-limit is represented very close to completely [[consistent]]ly, and as aforementioned, the 77-[[odd-limit]] subset of that odd-limit is perfectly consistent, to which a variety of odds can be added that keep perfect consistency, but for comprehensiveness and practical use as a temperament approximating the low-to-mid end of the harmonic series, we consider a larger odd-limit than that which seeks to be more complete.

There are 884 interval pairs in that [[odd limit]] (the [[41-limit]] add-73 add-89 add-101 add-109 add-113 123-odd-limit), where "pairs" refers to that each interval has an [[octave complement]] with equal and opposite error. That odd limit can be described explicitly as the [[tonality diamond]] of {1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29, 31, 33, 35, 37, 39, 41, 45, 49, 51, 55, 57, 63, 65, 69, 73, 75, 77, 81, 85, 87, 89, 91, 93, 95, 99, 101, 105, 109, 111, 113, 115, 117, 119, 121, 123}. We can also express that odd-limit as the 123-odd-limit minus only the following twelve prime odds: {43, 47, 53, 59, 61, 67, 71, 79, 83, 97, 103, 107}.

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 == Intervals ==
-The 41-limit add-73 add-89 add-101 add-109 add-113 123-odd-limit is represented very close to completely consistently, and as aforementioned, the 77-odd-limit subset of that odd-limit is perfectly consistent, to which a variety of odds can be added that keep perfect consistency, but for comprehensiveness and practical use as a temperament approximating the low-to-mid end of the harmonic series, we consider a larger odd-limit than that which seeks to be more complete.
+The 41-limit add-73 add-89 add-101 add-109 add-113 123-odd-limit is represented very close to completely [[consistent]]ly, and as aforementioned, the 77-[[odd-limit]] subset of that odd-limit is perfectly consistent, to which a variety of odds can be added that keep perfect consistency, but for comprehensiveness and practical use as a temperament approximating the low-to-mid end of the harmonic series, we consider a larger odd-limit than that which seeks to be more complete.
 There are 884 interval pairs in that [[odd limit]] (the [[41-limit]] add-73 add-89 add-101 add-109 add-113 123-odd-limit), where "pairs" refers to that each interval has an [[octave complement]] with equal and opposite error. That odd limit can be described explicitly as the [[tonality diamond]] of {1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29, 31, 33, 35, 37, 39, 41, 45, 49, 51, 55, 57, 63, 65, 69, 73, 75, 77, 81, 85, 87, 89, 91, 93, 95, 99, 101, 105, 109, 111, 113, 115, 117, 119, 121, 123}. We can also express that odd-limit as the 123-odd-limit minus only the following twelve prime odds: {43, 47, 53, 59, 61, 67, 71, 79, 83, 97, 103, 107}.