Catakleismic: Difference between revisions

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== Interval chain ==

{| class="wikitable center-1 right-2"

! &#~~35;~~

! #

! Cents*

! Approximate ratios

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| 81/80

|}

<nowiki />* In 2.3.5.7.13 POTE tuning

<nowiki/>* In 2.3.5.7.13 POTE tuning

=== As a detemperament of 19et ===

[[File: Catakleismic 19et Detempering.png|thumb|Catakleismic as a 72-tone 19et detempering]]

Catakleismic is naturally considered as a [[detemperament]] of the [[19edo|19 equal temperament]]. The diagram on the right shows a 72-tone detempered scale, with a generator range of -35 to +36. 72 is the largest number of tones for a mos where intervals in the 19 categories do not overlap. Each category is divided into three or four qualities separated by 19 generator steps, which represent the syntonic comma. Combining this division with the minor and major diatonic qualities of the 19 equal temperament, catakleismic gives us seven or eight qualities for each diatonic category in addition to the four qualities for the categories corresponding to [[interseptimal interval]]s.

Notice also the little interval between the largest of a category and the smallest of the next. This interval spans 53 generator steps, so it vanishes in 53edo, but is tuned to the same size as the syntonic comma in 72edo. 125edo tunes it to one half the size of the syntonic comma, which may be seen as a good compromise.

== Chords ==

@@ Line 9: / Line 9: @@
 == Interval chain ==
 {| class="wikitable center-1 right-2"
-! &#35;
+! #
 ! Cents*
 ! Approximate ratios
@@ Line 93: / Line 93: @@
 | 81/80
 |}
-<nowiki />* In 2.3.5.7.13 POTE tuning
+<nowiki/>* In 2.3.5.7.13 POTE tuning
+=== As a detemperament of 19et ===
+[[File: Catakleismic 19et Detempering.png|thumb|Catakleismic as a 72-tone 19et detempering]]
+Catakleismic is naturally considered as a [[detemperament]] of the [[19edo|19 equal temperament]]. The diagram on the right shows a 72-tone detempered scale, with a generator range of -35 to +36. 72 is the largest number of tones for a mos where intervals in the 19 categories do not overlap. Each category is divided into three or four qualities separated by 19 generator steps, which represent the syntonic comma. Combining this division with the minor and major diatonic qualities of the 19 equal temperament, catakleismic gives us seven or eight qualities for each diatonic category in addition to the four qualities for the categories corresponding to [[interseptimal interval]]s.
+Notice also the little interval between the largest of a category and the smallest of the next. This interval spans 53 generator steps, so it vanishes in 53edo, but is tuned to the same size as the syntonic comma in 72edo. 125edo tunes it to one half the size of the syntonic comma, which may be seen as a good compromise.
 == Chords ==