Aberrismic theory: Difference between revisions

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Certain scales with aberrismas may be endowed with JI interpretations via RTT temperaments, such as [[equal temperament]]s. Under groundfault's use of edos (usually patent vals) as RTT temperaments, the aberrisma tends to become [[81/80]] in a 2.3.5 context and a [[64/63]] in a 2.3.7 context. Some scales such as 5L2m5s and 5L2m7s admit a more accurate 2.3.5.7 interpretation that tempers neither 81/80 nor 64/63 but identifies the two commas, tempering out [[5120/5103]].

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.

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 [[Ultrapyth]] temperament.

=== 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.

The following table shows two different temperament interpretations for the same aberrismic scale pattern blackdye (sLmLsLmLsL), under untempered 2.3.5 and Ultrapyth 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.~~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~~, thereby tempering 9 fifths to a 14/11 rather~~ than ~~a 5/4~~. ~~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~~.

* [[Ultrapyth]], 2.3.5.7.11.13[32 & 37], is a diatonic temperament generated by a fifth even sharper than in Superpyth. [[37edo]] provides a nearly optimal tuning.

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

|+ Blackdye intervals in two temperaments

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! Sizes

! Untempered 2.3.5

! ~~Flutterpyth~~

! Ultrapyth

|-

!|[[TAMNAMS|1-steps]]

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 Certain scales with aberrismas may be endowed with JI interpretations via RTT temperaments, such as [[equal temperament]]s. Under groundfault's use of edos (usually patent vals) as RTT temperaments, the aberrisma tends to become [[81/80]] in a 2.3.5 context and a [[64/63]] in a 2.3.7 context. Some scales such as 5L2m5s and 5L2m7s admit a more accurate 2.3.5.7 interpretation that tempers neither 81/80 nor 64/63 but identifies the two commas, tempering out [[5120/5103]].
-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.
+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 [[Ultrapyth]] temperament.
 === 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.
+The following table shows two different temperament interpretations for the same aberrismic scale pattern blackdye (sLmLsLmLsL), under untempered 2.3.5 and Ultrapyth 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, 2.3.14/11[32 & 37], is a rank-2 diatonic temperament that is a neogothic analogue to 5-limit Superpyth and tunes the 3/2 even sharper, thereby tempering 9 fifths to a 14/11 rather than a 5/4. 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.
+* [[Ultrapyth]], 2.3.5.7.11.13[32 & 37], is a diatonic temperament generated by a fifth even sharper than in Superpyth. [[37edo]] provides a nearly optimal tuning.
 {| class="wikitable right-2 right-3 right-4 right-5"
 |+ Blackdye intervals in two temperaments
@@ Line 19: / Line 19: @@
 ! Sizes
 ! Untempered 2.3.5
-! Flutterpyth
+! Ultrapyth
 |-
 !|[[TAMNAMS|1-steps]]