Aberrismic theory: Difference between revisions

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At times, a scale pattern has varying temperaments according to the tuning. For example, 5L2m3s may be given the temperament structure of either untempered 2.3.5 or Flutterpyth temperament.

~~<!--~~=== Example: blackdye ===

=== Example: blackdye ===

The following table shows two different temperament interpretations for the same aberrismic scale pattern blackdye (sLmLsLmLsL), under untempered 2.3.5 and [[Flutterpyth]] respectively.

* ''Untempered'' does not mean that the final tuning must be the JI tuning, but simply that there exists a tuning with no deviation from JI, or that the temperament before applying the tuning map has the same rank as the JI subgroup.

* Flutterpyth, 2.3~~.13/11~~.14/11[32 & 37], is a rank-2 diatonic temperament that is a neogothic analogue to 5-limit Superpyth and tunes the 3/2 even sharper, as a result tempering C-D# to a 14~~/11 and C-Fb to a 13~~/11. For sake of presentation, this table uses an extension, 2.3.5.7.11.13[32 & 37], incorporating 7/4 and 13/10; [[37edo]] provides a nearly optimal tuning for the extension.

* Flutterpyth, 2.3.14/11[32 & 37], is a rank-2 diatonic temperament that is a neogothic analogue to 5-limit Superpyth and tunes the 3/2 even sharper, as a result tempering C-D# to a 14/11. For sake of presentation, this table uses an extension, 2.3.5.7.11.13[32 & 37], incorporating 7/4, 13/11, and 13/10; [[37edo]] provides a nearly optimal tuning for the extension.

{| class="wikitable right-2 right-3 right-4 right-5"

|+ Blackdye intervals in two temperaments

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 At times, a scale pattern has varying temperaments according to the tuning. For example, 5L2m3s may be given the temperament structure of either untempered 2.3.5 or Flutterpyth temperament.
-<!--=== Example: blackdye ===
+=== Example: blackdye ===
 The following table shows two different temperament interpretations for the same aberrismic scale pattern blackdye (sLmLsLmLsL), under untempered 2.3.5 and [[Flutterpyth]] respectively.
 * ''Untempered'' does not mean that the final tuning must be the JI tuning, but simply that there exists a tuning with no deviation from JI, or that the temperament before applying the tuning map has the same rank as the JI subgroup.
-* Flutterpyth, 2.3.13/11.14/11[32 & 37], is a rank-2 diatonic temperament that is a neogothic analogue to 5-limit Superpyth and tunes the 3/2 even sharper, as a result tempering C-D# to a 14/11 and C-Fb to a 13/11. For sake of presentation, this table uses an extension, 2.3.5.7.11.13[32 & 37], incorporating 7/4 and 13/10; [[37edo]] provides a nearly optimal tuning for the extension.
+* Flutterpyth, 2.3.14/11[32 & 37], is a rank-2 diatonic temperament that is a neogothic analogue to 5-limit Superpyth and tunes the 3/2 even sharper, as a result tempering C-D# to a 14/11. For sake of presentation, this table uses an extension, 2.3.5.7.11.13[32 & 37], incorporating 7/4, 13/11, and 13/10; [[37edo]] provides a nearly optimal tuning for the extension.
 {| class="wikitable right-2 right-3 right-4 right-5"
 |+ Blackdye intervals in two temperaments