22edo: Difference between revisions

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| en = 22edo
| en = 22edo
| de = 22-EDO
| de = 22-EDO
| es = 22 EDO
| 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
!5-limit commas
|-
|-
| 1
| 1
| 1\22
| 1\22
| [[Escapade]] / [[escaped]]<br>[[Chromo]]<br>[[Ceratitid]]
| [[Escapade]] / [[escaped]]<br>[[Chromo]]<br>[[Ceratitid]]
|[[1220703125/1146617856]]<br>[[4294967296/4271484375]]
|-
|-
| 1
| 1
| 3\22
| 3\22
| [[Porcupine]]
| [[Porcupine]]
|[[250/243]]
|-
|-
| 1
| 1
| 5\22
| 5\22
| [[Orwell]] (22) / blair (22) / winston (22f)
| [[Orwell]] (22) / blair (22) / winston (22f)
|[[2109375/2097152]]
|-
|-
| 1
| 1
| 7\22
| 7\22
| [[Magic]] / telepathy
| [[Magic]] / telepathy
|[[3125/3072]]
|-
|-
| 1
| 1
| 9\22
| 9\22
| [[Superpyth]] / [[suprapyth]]
| [[Superpyth]] / [[suprapyth]]
|[[20480/19683]]<br>[[8388608/7971615]]
|-
|-
| 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
|[[2048/2025]]
|-
|-
| 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]]
|[[2197265625/2147483648]]
|-
|-
| 2
| 2
| 5\22
| 5\22
| [[Doublewide]] / fleetwood
| [[Doublewide]] / fleetwood
|[[390625/373248]]
|-
|-
| 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 ==
# Barbour, James Murray, ''Tuning and temperament, a historical survey'', East Lansing, Michigan State College Press, 1953 [c1951]
<references>
# 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 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]]