43edo: Difference between revisions

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Ringer scale should go under the well temperament section
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== Ringer 43 ==
The metaphorical color palette that the intervals of [[43edo]] present can be quite appealing (for various reasons such as being meantone and splitting 4/3 into 6 equal parts and 3/2 into 5 equal parts) 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 ==
== Notation ==
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== Well temperaments ==
=== Ringer 43 ===
The metaphorical color palette that the intervals of [[43edo]] present can be quite appealing for various reasons such as being meantone and splitting 4/3 into 6 equal parts and 3/2 into 5 equal parts, 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


== Music ==
== Music ==
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<references/>
<references/>


[[Category:43edo| ]] <!-- main article -->
[[Category:Equal divisions of the octave|##]] <!-- 2-digit number -->
[[Category:Meantone]]
[[Category:Meantone]]
[[Category:Prime EDO]]
[[Category:Quartismic]]
[[Category:Quartismic]]