22edo: Difference between revisions

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== Theory ==
== Theory ==
 
{{Odd harmonics in edo|edo=22}}
{| class="wikitable center-all"
! colspan="2" | <!-- empty cell -->
! prime 2
! prime 3
! prime 5
! prime 7
! prime 11
! prime 13
! prime 17
|-
! rowspan="2" | error
! absolute (¢)
| 0
| +7.2
| -4.5
| +13.0
| -5.9
| -22.3
| +4.1
|-
! [[Relative error|relative]] (%)
| 0
| +13
| -8
| +24
| -11
| -40
| +7
|-
! colspan="2" | [[Nearest edomapping]]
| 22
| 13
| 7
| 18
| 10
| 15
| 2
|-
! colspan="2" | [[Fifthspan]]
| 0
| +1
| +9
| -2
| -6
| -9
| -10
|}


The idea of dividing the octave into 22 steps of equal size seems to have originated with nineteenth century music theorist RHM Bosanquet. Inspired by the division of the octave into 22 unequal parts in the [[Indian|music theory of India]], Bosenquet 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|19 equal temperament]], and 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 RHM Bosanquet. Inspired by the division of the octave into 22 unequal parts in the [[Indian|music theory of India]], Bosenquet 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|19 equal temperament]], and J. Murray Barbour in his classic survey of tuning history, ''Tuning and Temperament''.
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| -2.597¢
| -2.597¢
|}
|}
== Properties of 22 equal temperament ==
== Properties of 22 equal temperament ==