Catakleismic/13-limit chords: Difference between revisions

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Below are listed the 15-limit [[~~Dyadic_chord|~~dyadic ~~chords~~]] of [[~~Kleismic_family#Catakleismic-~~13-limit|tridecimal catakleismic ~~temperament~~]], subject to the condition that no interval smaller than [[~~12/11|~~12/11]], at 150 cents, appears. The essentially just chords are typed as otonal, utonal, or ambitonal. Those requiring tempering only by 225/224 are labeled marvel, by 385/384 keenanismic, by 540/539 swetismic, by 169/168 dhanvantarismic, by 325/324 marveltwin, by 351/350 ratwolfsmic, by 676/675 island, by 729/728 squbemic, by 1001/1000 sinbadmic and by 1287/1280 catadictmic. [[~~Rank_and_codimension~~|Codimension]] ~~two~~ temperaments are labeled marveltwin-island, ratwolfsmic-island, marvel-marveltwin, dhanvantarismic-marveltwin, dhanvantarismic-marvel, keenanismic-ratwolfsmic, swetismic-ratwolfsmic, and marvel-catadictmic. Rank ~~three~~ temperaments are labeled [[~~Ragisma_family~~#Beyla~~-13-limit~~|beyla]], [[~~Marvel_family~~#Hestia|hestia]], [[~~Swetismic_temperaments~~#Hypnos~~-13-limit~~|hypnos]], [[~~Marvel_family~~#Catakleismoid|catakleismoid]], [[~~Kleismic_rank_three_family~~#Isimud|isimud]], [[~~Marvel_family~~#~~Marvel~~|unimarvel]] and [[~~Marvel_family~~#~~Marvel~~|tridecimal marvel]]. Finally, if the full tridecimal catakleismic temperament is required, the chord is labeled catakleismic.

Below are listed the 15-limit [[dyadic chord]]s of [[13-limit|tridecimal]] [[catakleismic]] temperament, subject to the condition that no interval smaller than [[12/11]], at 150 cents, appears. The essentially just chords are typed as otonal, utonal, or ambitonal. Those requiring tempering only by [[225/224]] are labeled [[Marvel chords|marvel]], by [[385/384]] [[Keenanismic chords|keenanismic]], by [[540/539]] [[Swetismic chords|swetismic]], by [[169/168]] [[Dhanvantarismic chords|dhanvantarismic]], by [[325/324]] [[Marveltwin triad|marveltwin]], by [[351/350]] [[Ratwolf triad|ratwolfsmic]], by [[676/675]] [[Island tetrad|island]], by [[729/728]] [[Squbemic chords|squbemic]], by [[1001/1000]] [[Sinbadmic tetrad|sinbadmic]] and by [[1287/1280]] [[Catadictmic chords|catadictmic]]. [[Rank and codimension|Codimension]]-2 temperaments are labeled marveltwin-island, ratwolfsmic-island, marvel-marveltwin, dhanvantarismic-marveltwin, dhanvantarismic-marvel, keenanismic-ratwolfsmic, swetismic-ratwolfsmic, and marvel-catadictmic. Rank-3 temperaments are labeled [[Ragisma family #Beyla|beyla]], [[Marvel family #Hestia|hestia]], [[Swetismic temperaments #Hypnos|hypnos]], [[Marvel family #Catakleismoid|catakleismoid]], [[Kleismic rank three family #Isimud|isimud]], [[Marvel family #Undecimal marvel (unimarv)|unimarvel]] and [[Marvel family #Undecimal marvel (unimarv)|tridecimal marvel]]. Finally, if the full tridecimal catakleismic temperament is required, the chord is labeled catakleismic.

Tridecimal catakleismic is more richly endowed with chords, and in particular chords of lower complexity, than 7- or 11-limit catakleismic, with harmonies including but not limited to those of marvel temperament and [[~~The_Archipelago|~~the Archipelago]]. It has MOS of size 7, 11, 15, 19, 34 and 53. Triads and tetrads abound even in the 7-note MOS, and with the 11-note MOS pentads appear.

Tridecimal catakleismic is more richly endowed with chords, and in particular chords of lower complexity, than 7- or 11-limit catakleismic, with harmonies including but not limited to those of marvel temperament and [[the Archipelago]]. It has MOS of size 7, 11, 15, 19, 34 and 53. Triads and tetrads abound even in the 7-note MOS, and with the 11-note MOS pentads appear.

=Triads=

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-Below are listed the 15-limit [[Dyadic_chord|dyadic chords]] of [[Kleismic_family#Catakleismic-13-limit|tridecimal catakleismic temperament]], subject to the condition that no interval smaller than [[12/11|12/11]], at 150 cents, appears. The essentially just chords are typed as otonal, utonal, or ambitonal. Those requiring tempering only by 225/224 are labeled marvel, by 385/384 keenanismic, by 540/539 swetismic, by 169/168 dhanvantarismic, by 325/324 marveltwin, by 351/350 ratwolfsmic, by 676/675 island, by 729/728 squbemic, by 1001/1000 sinbadmic and by 1287/1280 catadictmic. [[Rank_and_codimension|Codimension]] two temperaments are labeled marveltwin-island, ratwolfsmic-island, marvel-marveltwin, dhanvantarismic-marveltwin, dhanvantarismic-marvel, keenanismic-ratwolfsmic, swetismic-ratwolfsmic, and marvel-catadictmic. Rank three temperaments are labeled [[Ragisma_family#Beyla-13-limit|beyla]], [[Marvel_family#Hestia|hestia]], [[Swetismic_temperaments#Hypnos-13-limit|hypnos]], [[Marvel_family#Catakleismoid|catakleismoid]], [[Kleismic_rank_three_family#Isimud|isimud]], [[Marvel_family#Marvel|unimarvel]] and [[Marvel_family#Marvel|tridecimal marvel]]. Finally, if the full tridecimal catakleismic temperament is required, the chord is labeled catakleismic.
+Below are listed the 15-limit [[dyadic chord]]s of [[13-limit|tridecimal]] [[catakleismic]] temperament, subject to the condition that no interval smaller than [[12/11]], at 150 cents, appears. The essentially just chords are typed as otonal, utonal, or ambitonal. Those requiring tempering only by [[225/224]] are labeled [[Marvel chords|marvel]], by [[385/384]] [[Keenanismic chords|keenanismic]], by [[540/539]] [[Swetismic chords|swetismic]], by [[169/168]] [[Dhanvantarismic chords|dhanvantarismic]], by [[325/324]] [[Marveltwin triad|marveltwin]], by [[351/350]] [[Ratwolf triad|ratwolfsmic]], by [[676/675]] [[Island tetrad|island]], by [[729/728]] [[Squbemic chords|squbemic]], by [[1001/1000]] [[Sinbadmic tetrad|sinbadmic]] and by [[1287/1280]] [[Catadictmic chords|catadictmic]]. [[Rank and codimension|Codimension]]-2 temperaments are labeled marveltwin-island, ratwolfsmic-island, marvel-marveltwin, dhanvantarismic-marveltwin, dhanvantarismic-marvel, keenanismic-ratwolfsmic, swetismic-ratwolfsmic, and marvel-catadictmic. Rank-3 temperaments are labeled [[Ragisma family #Beyla|beyla]], [[Marvel family #Hestia|hestia]], [[Swetismic temperaments #Hypnos|hypnos]], [[Marvel family #Catakleismoid|catakleismoid]], [[Kleismic rank three family #Isimud|isimud]], [[Marvel family #Undecimal marvel (unimarv)|unimarvel]] and [[Marvel family #Undecimal marvel (unimarv)|tridecimal marvel]]. Finally, if the full tridecimal catakleismic temperament is required, the chord is labeled catakleismic.
-Tridecimal catakleismic is more richly endowed with chords, and in particular chords of lower complexity, than 7- or 11-limit catakleismic, with harmonies including but not limited to those of marvel temperament and [[The_Archipelago|the Archipelago]]. It has MOS of size 7, 11, 15, 19, 34 and 53. Triads and tetrads abound even in the 7-note MOS, and with the 11-note MOS pentads appear.
+Tridecimal catakleismic is more richly endowed with chords, and in particular chords of lower complexity, than 7- or 11-limit catakleismic, with harmonies including but not limited to those of marvel temperament and [[the Archipelago]]. It has MOS of size 7, 11, 15, 19, 34 and 53. Triads and tetrads abound even in the 7-note MOS, and with the 11-note MOS pentads appear.
 =Triads=