43edo: Difference between revisions

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=== Prime harmonics ===

Although not [[consistent]], it performs quite decently in very high limits. It has unambiguous mappings for all prime harmonics up to ''64'', with the sole exceptions of 23 and, ~~perhaps, 41~~. The mappings for composite harmonics can then be derived from those for the primes, giving an almost-complete version of mode 32 of the harmonic series, although the aforementioned lack of consistency will give some unusual results. Indeed, the step size of 43edo is very close to the [[64/63|septimal comma (64/63)]], while two steps is close to [[32/31]], and four steps to [[16/15]].

Although not [[consistent]], it performs quite decently in very high limits. It has unambiguous mappings for all prime harmonics up to ''100'', with the sole exceptions of 23, 71 and 89, making a great [[#Ringer 43|Ringer scale]]. The mappings for composite harmonics can then be derived from those for the primes, giving an almost-complete version of mode 32 of the harmonic series, although the aforementioned lack of consistency will give some unusual results. Indeed, the step size of 43edo is very close to the [[64/63|septimal comma (64/63)]], while two steps is close to [[32/31]], and four steps to [[16/15]].

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| ''16.479''

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== Ringer 43 ==

The metaphorical color palette that the intervals of [[43edo]] present can be quite appealing especially given it is structured with meantone but the accuracy leaves one wanting in many cases, which is why an excellent alternative (given the unambiguity of mappings of all primes in the 97-limit except 71 and 89) is Ringer 43, a [[Ringer scale]] with 43 notes per octave period:

<pre>

55:56:57:58:59:60:61:62:63:64:65:66:67:68:69:70:72:73:74:75:76:78:79:80:82:83:84:86:87:88:90:91:92:94:96:97:98:100:102:104:106:108:109:110

</pre>

Or equivalently in the form of reduced, [[rooted interval]]s:

65/64, 33/32, 67/64, 17/16, 69/64, 35/32, 9/8, 73/64, 37/32, 75/64, 19/16, 39/32, 79/64, 5/4, 41/32, 83/64, 21/16, 43/32, 87/64, 11/8, 45/32, 91/64, 23/16, 47/32, 3/2, 97/64, 49/32, 25/16, 51/64, 13/8, 53/32, 27/16, 109/64, 55/32, 7/4, 57/32, 29/16, 59/32, 15/8, 61/32, 31/16, 63/32, 2/1

== Notation ==

@@ Line 14: / Line 14: @@
 === Prime harmonics ===
-Although not [[consistent]], it performs quite decently in very high limits. It has unambiguous mappings for all prime harmonics up to ''64'', with the sole exceptions of 23 and, perhaps, 41. The mappings for composite harmonics can then be derived from those for the primes, giving an almost-complete version of mode 32 of the harmonic series, although the aforementioned lack of consistency will give some unusual results. Indeed, the step size of 43edo is very close to the [[64/63|septimal comma (64/63)]], while two steps is close to [[32/31]], and four steps to [[16/15]].
+Although not [[consistent]], it performs quite decently in very high limits. It has unambiguous mappings for all prime harmonics up to ''100'', with the sole exceptions of 23, 71 and 89, making a great [[#Ringer 43|Ringer scale]]. The mappings for composite harmonics can then be derived from those for the primes, giving an almost-complete version of mode 32 of the harmonic series, although the aforementioned lack of consistency will give some unusual results. Indeed, the step size of 43edo is very close to the [[64/63|septimal comma (64/63)]], while two steps is close to [[32/31]], and four steps to [[16/15]].
 {{Harmonics in equal|43}}
@@ Line 501: / Line 501: @@
 | ''16.479''
 |}
+== Ringer 43 ==
+The metaphorical color palette that the intervals of [[43edo]] present can be quite appealing especially given it is structured with meantone but the accuracy leaves one wanting in many cases, which is why an excellent alternative (given the unambiguity of mappings of all primes in the 97-limit except 71 and 89) is Ringer 43, a [[Ringer scale]] with 43 notes per octave period:
+<pre>
+:56:57:58:59:60:61:62:63:64:65:66:67:68:69:70:72:73:74:75:76:78:79:80:82:83:84:86:87:88:90:91:92:94:96:97:98:100:102:104:106:108:109:110
+</pre>
+Or equivalently in the form of reduced, [[rooted interval]]s:
+/64, 33/32, 67/64, 17/16, 69/64, 35/32, 9/8, 73/64, 37/32, 75/64, 19/16, 39/32, 79/64, 5/4, 41/32, 83/64, 21/16, 43/32, 87/64, 11/8, 45/32, 91/64, 23/16, 47/32, 3/2, 97/64, 49/32, 25/16, 51/64, 13/8, 53/32, 27/16, 109/64, 55/32, 7/4, 57/32, 29/16, 59/32, 15/8, 61/32, 31/16, 63/32, 2/1
 == Notation ==