Cassandra triads: Difference between revisions

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The '''cassandra triads''' are triads in which the two step sizes are (tempered versions of) [[13/11]] and [[14/11]] and the total span is a tempered [[3/2|perfect fifth]]. There are two of them, ~~one of which is~~ intermediate between major and supermajor, and ~~the other~~ intermediate between minor and subminor.

The '''cassandra triads''' or neogothic triads are triads in which the two step sizes are (tempered versions of) [[13/11]] and [[14/11]] and the total span is a tempered [[3/2|perfect fifth]]. There are two of them, a major triad intermediate between classical major and supermajor, and likewise a minor triad intermediate between classical minor and subminor.

This tempers out the [[364/363]], which is one of the [[pentacircle comma]]s. Cassandra triads appear in [[17edo]], and even more closely in [[29edo]]. Cassandra chords are closely related to the 19-limit rootsubminor, rootminor, rootmajor, and roostsupermajor triads; in fact, a Cassandra minor triad could be considered to function as both rootsubminor ''and'' as rootminor, and similarly the cassandra major chord functions as both rootmajor and rootsupermajor.

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== Consonance of cassandra triads ==

=== JI-based explanation ===

The 13:11 and 14:11 dyads both reside near local [[harmonic entropy]] maxima due to falling almost halfway between a septimal and a pental consonance. This, as well as the fact that the triadic just approximations are 242:286:364, do not make the Cassandra triads sound appealing as consonances.

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-The '''cassandra triads''' are triads in which the two step sizes are (tempered versions of) [[13/11]] and [[14/11]] and the total span is a tempered [[3/2|perfect fifth]]. There are two of them, one of which is intermediate between major and supermajor, and the other intermediate between minor and subminor.
+The '''cassandra triads''' or neogothic triads are triads in which the two step sizes are (tempered versions of) [[13/11]] and [[14/11]] and the total span is a tempered [[3/2|perfect fifth]]. There are two of them, a major triad intermediate between classical major and supermajor, and likewise a minor triad intermediate between classical minor and subminor.
 This tempers out the [[364/363]], which is one of the [[pentacircle comma]]s. Cassandra triads appear in [[17edo]], and even more closely in [[29edo]]. Cassandra chords are closely related to the 19-limit rootsubminor, rootminor, rootmajor, and roostsupermajor triads; in fact, a Cassandra minor triad could be considered to function as both rootsubminor ''and'' as rootminor, and similarly the cassandra major chord functions as both rootmajor and rootsupermajor.
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 == Consonance of cassandra triads ==
+=== JI-based explanation ===
 The 13:11 and 14:11 dyads both reside near local [[harmonic entropy]] maxima due to falling almost halfway between a septimal and a pental consonance. This, as well as the fact that the triadic just approximations are 242:286:364, do not make the Cassandra triads sound appealing as consonances.