936/935: Difference between revisions
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'''936/935''', the '''ainos comma''' or '''ainma''', is | '''936/935''', the '''ainos comma''' or '''ainma''', is a [[17-limit]] [[unnoticeable comma]] with a size of roughly 1.85 cents. It arises when fitting [[18/17]] between [[5/4]] and [[13/11]] as well as when fitting [[17/16]] between [[13/11]] and [[10/9]]. Moreover, it is also the interval that differentiates [[17/13]] from [[72/55]], [[24/17]] from [[55/39]], and [[117/64]] from [[935/512]], the [[273/272|tannisma (273/272)]] from the [[385/384|keenanisma (385/384)]], and the [[256/255|septendecimal kleisma (256/255)]] from the [[352/351|minthma (352/351)]]. Thus, tempering out this comma is a good way to extend minthmic and gentle harmonies to the 17-limit, as well as a good way to bring keenanismic and tannismic harmonies together. When tempered out in a linearly independent fashion, the resulting temperaments are called "'''ainos temperaments'''", and are characterized by the presence of [[Dyadic chord|essentially tempered chord]]s called "'''[[ainic chords]]'''". | ||
This comma's names come from the Ancient Greek word "aînos" (meaning "tale", "story" or "fable"<ref>[[Wiktionary: αἶνος #Ancient Greek]]</ref>), which is fitting due to the comma serving as a viable 17-limit extension to minthmic temperaments, among others. Funny enough, this same Greek word is the source of the Ancient Greek word "aínigma" (meaning "riddle"<ref>[[Wiktionary: αἴνιγμα #Ancient Greek]]</ref>), from which we ultimately get our word "enigma", and this is also fitting due to the sheer difficulty that was involved in the initial process of working out both the name and the uses of this comma in a short span of time. | This comma's names come from the Ancient Greek word "aînos" (meaning "tale", "story" or "fable"<ref>[[Wiktionary: αἶνος #Ancient Greek]]</ref>), which is fitting due to the comma serving as a viable 17-limit extension to minthmic temperaments, among others. Funny enough, this same Greek word is the source of the Ancient Greek word "aínigma" (meaning "riddle"<ref>[[Wiktionary: αἴνιγμα #Ancient Greek]]</ref>), from which we ultimately get our word "enigma", and this is also fitting due to the sheer difficulty that was involved in the initial process of working out both the name and the uses of this comma in a short span of time. | ||
It factors into two superparticular intervals: [[1701/1700]] × [[2080/2079]]. | |||
== See also == | == See also == | ||
Revision as of 08:55, 15 January 2021
| Interval information |
ainma
reduced
936/935, the ainos comma or ainma, is a 17-limit unnoticeable comma with a size of roughly 1.85 cents. It arises when fitting 18/17 between 5/4 and 13/11 as well as when fitting 17/16 between 13/11 and 10/9. Moreover, it is also the interval that differentiates 17/13 from 72/55, 24/17 from 55/39, and 117/64 from 935/512, the tannisma (273/272) from the keenanisma (385/384), and the septendecimal kleisma (256/255) from the minthma (352/351). Thus, tempering out this comma is a good way to extend minthmic and gentle harmonies to the 17-limit, as well as a good way to bring keenanismic and tannismic harmonies together. When tempered out in a linearly independent fashion, the resulting temperaments are called "ainos temperaments", and are characterized by the presence of essentially tempered chords called "ainic chords".
This comma's names come from the Ancient Greek word "aînos" (meaning "tale", "story" or "fable"[1]), which is fitting due to the comma serving as a viable 17-limit extension to minthmic temperaments, among others. Funny enough, this same Greek word is the source of the Ancient Greek word "aínigma" (meaning "riddle"[2]), from which we ultimately get our word "enigma", and this is also fitting due to the sheer difficulty that was involved in the initial process of working out both the name and the uses of this comma in a short span of time.
It factors into two superparticular intervals: 1701/1700 × 2080/2079.