Petrmic chords: Difference between revisions

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~~The~~ ''[[~~petrmic~~]] [[~~triad~~]]'' is a [[13-limit]], ~~[[Dyadic_chord|essentially tempered dyadic chord]]~~ consisting of two [[13/10]] intervals followed by a [[13/11]], in other words a 13/10-13/10-13/11 ~~chord, tempered by the petrma, [[2200/2197]], so that it closes at the [[octave]]~~. ~~Another way~~ to ~~say this is that it is~~ the ~~petrmic tempering of 1-~~13/10~~-22~~/13 ~~or 1-~~13/11~~-20/13~~. [[~~EDO|~~Equal ~~temperaments~~]] with petrmic ~~triads~~ include ~~[[29edo~~|29]], ~~[[37edo|~~37]], ~~[[50edo|~~50]], ~~[[53edo|~~53]], ~~[[58edo|~~58]], ~~[[84edo|~~84]], ~~[[87edo|~~87]], ~~[[111edo|~~111]], ~~[[121edo|~~121]], ~~[[140edo|~~140]], ~~[[190edo|~~190]], ~~[[198edo|~~198]], ~~[[224edo|~~224]], ~~[[311edo|~~311]], ~~[[414edo|~~414]], ~~[[422edo|~~422]], and ~~[[612edo|~~612]]. 37, 50 and especially 29 have notably good petrmic triads.

'''Petrmic chords''' are [[essentially tempered dyadic chord]]s tempered by the petrma, [[2200/2197]].

[[Category:13-limit]]

[[Category:~~petrmic~~]]

The petrmic triad is a palindrome in the 2.5.11.13 [[subgroup]] [[13-odd-limit]], consisting of two [[13/10]] intervals followed by a [[13/11]], closing at the [[octave]]. In other words:

[[Category:~~triad~~]]

* 1–13/10–22/13 with steps 13/10, 13/10, 13/11.

It can be extended to the following palindromic tetrad:

* 1–11/10–13/10–22/13 with steps 11/10, 13/11, 13/10, 13/11.

[[Equal temperament]]s with petrmic chords include {{EDOs| 29, 37, 50, 53, 58, 84, 87, 111, 121, 140, 190, 198, 224, 311, 414, 422, and 612 }}. 37, 50 and especially 29 have notably good petrmic triads.

[[Category:13-odd-limit chords]]

[[Category:Essentially tempered chords]]

[[Category:Triads]]

[[Category:Tetrads]]

[[Category:Petrmic]]

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-The ''[[petrmic]] [[triad]]'' is a [[13-limit]], [[Dyadic_chord|essentially tempered dyadic chord]] consisting of two [[13/10]] intervals followed by a [[13/11]], in other words a 13/10-13/10-13/11 chord, tempered by the petrma, [[2200/2197]], so that it closes at the [[octave]]. Another way to say this is that it is the petrmic tempering of 1-13/10-22/13 or 1-13/11-20/13. [[EDO|Equal temperaments]] with petrmic triads include [[29edo|29]], [[37edo|37]], [[50edo|50]], [[53edo|53]], [[58edo|58]], [[84edo|84]], [[87edo|87]], [[111edo|111]], [[121edo|121]], [[140edo|140]], [[190edo|190]], [[198edo|198]], [[224edo|224]], [[311edo|311]], [[414edo|414]], [[422edo|422]], and [[612edo|612]]. 37, 50 and especially 29 have notably good petrmic triads.
+'''Petrmic chords''' are [[essentially tempered dyadic chord]]s tempered by the petrma, [[2200/2197]].
-[[Category:13-limit]]
-[[Category:petrmic]]
+The petrmic triad is a palindrome in the 2.5.11.13 [[subgroup]] [[13-odd-limit]], consisting of two [[13/10]] intervals followed by a [[13/11]], closing at the [[octave]]. In other words:
-[[Category:triad]]
+* 1–13/10–22/13 with steps 13/10, 13/10, 13/11.
+It can be extended to the following palindromic tetrad:
+* 1–11/10–13/10–22/13 with steps 11/10, 13/11, 13/10, 13/11.
+[[Equal temperament]]s with petrmic chords include {{EDOs| 29, 37, 50, 53, 58, 84, 87, 111, 121, 140, 190, 198, 224, 311, 414, 422, and 612 }}. 37, 50 and especially 29 have notably good petrmic triads.
+[[Category:13-odd-limit chords]]
+[[Category:Essentially tempered chords]]
+[[Category:Triads]]
+[[Category:Tetrads]]
+[[Category:Petrmic]]