Aberrismic theory: Difference between revisions

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=== Example: blackdye ===

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.

* ''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. This also implies that there is only one JI ratio for each interval under this interpretation, unlike in temperaments that temper out commas.

* [[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. Note that we chose to regard the 3-step 2L + s as a 14/11 rather than as a 5/4, lest the interpretation merely be an extension of the untempered 2.3.5 one.

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

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| 143/80<br/>21/11<br/>280/143

|}

== Musical open problems ==

# Investigate counterpoint in diatonic-based aberrismic scales.

[[Category:Terms]]

[[Category:Aberrismic theory|*]]

@@ Line 14: / Line 14: @@
 === Example: blackdye ===
 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.
+* ''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. This also implies that there is only one JI ratio for each interval under this interpretation, unlike in temperaments that temper out commas.
 * [[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. Note that we chose to regard the 3-step 2L + s as a 14/11 rather than as a 5/4, lest the interpretation merely be an extension of the untempered 2.3.5 one.
 {| class="wikitable right-2 right-3 right-4 right-5"
@@ Line 69: / Line 69: @@
 | 143/80<br/>21/11<br/>280/143
 |}
 == Musical open problems ==
 # Investigate counterpoint in diatonic-based aberrismic scales.
 [[Category:Terms]]
 [[Category:Aberrismic theory|*]]