22edo: Difference between revisions
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| en = 22edo | | en = 22edo | ||
| de = 22-EDO | | de = 22-EDO | ||
| es = | | es = | ||
| ja = 22平均律 | | ja = 22平均律 | ||
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== History == | == History == | ||
The idea of dividing the octave into 22 steps of equal size seems to have originated with nineteenth century music theorist {{w|Robert Holford Macdowall Bosanquet|R. H. M. Bosanquet}}. Inspired by the supposed division of the octave into 22 unequal parts in the [[Indian music|music theory of India]], Bosanquet noted that such an equal division was capable of representing 5-limit music with tolerable accuracy. In this he was followed in the twentieth century by theorist José Würschmidt, who noted it as a possible next step after [[19edo]], and {{w|James Murray Barbour|J. Murray Barbour}} in his classic survey of tuning history, ''Tuning and Temperament''. | The idea of dividing the octave into 22 steps of equal size seems to have originated with nineteenth century music theorist {{w|Robert Holford Macdowall Bosanquet|R. H. M. Bosanquet}}. Inspired by the supposed division of the octave into 22 unequal parts in the [[Indian music|music theory of India]], Bosanquet noted that such an equal division was capable of representing 5-limit music with tolerable accuracy.<ref name="bosanquet1879hindoo" /> In this he was followed in the twentieth century by theorist José Würschmidt, who noted it as a possible next step after [[19edo]], and {{w|James Murray Barbour|J. Murray Barbour}} in his classic survey of tuning history, ''Tuning and Temperament''.<ref name="wurschmidt1931tonleitern" /><ref name="barbour1953tuning /> | ||
== Theory == | == Theory == | ||
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! Generator | ! Generator | ||
! Temperaments | ! Temperaments | ||
|- | |- | ||
| 1 | | 1 | ||
| 1\22 | | 1\22 | ||
| [[Escapade]] / [[escaped]]<br>[[Chromo]]<br>[[Ceratitid]] | | [[Escapade]] / [[escaped]]<br>[[Chromo]]<br>[[Ceratitid]] | ||
|- | |- | ||
| 1 | | 1 | ||
| 3\22 | | 3\22 | ||
| [[Porcupine]] | | [[Porcupine]] | ||
|- | |- | ||
| 1 | | 1 | ||
| 5\22 | | 5\22 | ||
| [[Orwell]] (22) / blair (22) / winston (22f) | | [[Orwell]] (22) / blair (22) / winston (22f) | ||
|- | |- | ||
| 1 | | 1 | ||
| 7\22 | | 7\22 | ||
| [[Magic]] / telepathy | | [[Magic]] / telepathy | ||
|- | |- | ||
| 1 | | 1 | ||
| 9\22 | | 9\22 | ||
| [[Superpyth]] / [[suprapyth]] | | [[Superpyth]] / [[suprapyth]] | ||
|- | |- | ||
| 2 | | 2 | ||
| 1\22 | | 1\22 | ||
| [[Shrutar]] / hemipaj<br>[[Comic]] | | [[Shrutar]] / hemipaj<br>[[Comic]] | ||
|- | |- | ||
| 2 | | 2 | ||
| 2\22 | | 2\22 | ||
| [[Srutal]] / [[pajara]] / pajarous | | [[Srutal]] / [[pajara]] / pajarous | ||
|- | |- | ||
| 2 | | 2 | ||
| 3\22 | | 3\22 | ||
| [[Hedgehog]] / [[echidna]] | | [[Hedgehog]] / [[echidna]] | ||
|- | |- | ||
| 2 | | 2 | ||
| 4\22 | | 4\22 | ||
| [[Astrology]]<br>[[Antikythera]]<br>[[Wizard]] | | [[Astrology]]<br>[[Antikythera]]<br>[[Wizard]] | ||
|- | |- | ||
| 2 | | 2 | ||
| 5\22 | | 5\22 | ||
| [[Doublewide]] / fleetwood | | [[Doublewide]] / fleetwood | ||
|- | |- | ||
| 11 | | 11 | ||
| 1\22 | | 1\22 | ||
| [[Undeka]]<br>[[Hendecatonic (temperament)|Hendecatonic]] | | [[Undeka]]<br>[[Hendecatonic (temperament)|Hendecatonic]] | ||
|} | |} | ||
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== Instruments == | == Instruments == | ||
== Scordatura piano == | === Scordatura piano === | ||
Although it does not allow for much in the way of modulation, it is possible to make some music using a piano tuned to a 12 note subset of 22edo, as shown by [[Juhani Nuorvala]]'s [https://www.youtube.com/watch?v=raRiTvogBBA ''Improvisations on a piano tuned to 22edo''] (2026). | Although it does not allow for much in the way of modulation, it is possible to make some music using a piano tuned to a 12 note subset of 22edo, as shown by [[Juhani Nuorvala]]'s [https://www.youtube.com/watch?v=raRiTvogBBA ''Improvisations on a piano tuned to 22edo''] (2026). | ||
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== References == | == References == | ||
<references> | |||
<ref name="barbour1953tuning"> | |||
Barbour, James Murray, ''[https://archive.org/details/tuningtemperamen00barb Tuning and temperament, a historical survey]'', East Lansing, Michigan State College Press, 1953 [c1951] | |||
</ref> | |||
<ref name="bosanquet1879hindoo"> | |||
Bosanquet, R.H.M. [https://www.webcitation.org/5kjJcrhEx ''On the Hindoo division of the octave, with additions to the theory of higher orders''], Proceedings of the Royal Society of London vol. 26, 1879, pp. 272-284. Reproduced in Tagore, Sourindro Mohun, ''Hindu Music from Various Authors'', Chowkhamba Sanskrit Series, Varanasi, India, 1965 | |||
</ref> | |||
<ref name="wurschmidt1931tonleitern"> | |||
Würschmidt, J., ''[https://www.zobodat.at/pdf/Sitzber-physik-med-Soc-Erlangen_63-64_0133-0238.pdf Tonleitern, Tonarten und Tonsysteme]''. Sitzungsberichte der Physikalisch-Medizinischen Sozietät zu Erlangen – 63-64: 133 - 238., 1931-1932 | |||
</ref> | |||
</references> | |||
[[Category:Twentuning]] | [[Category:Twentuning]] | ||