33/32: Difference between revisions
Expansion |
added commas to separate alternative interval names, re-introduced alternative sound file (now only linking to the description page) |
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| Line 4: | Line 4: | ||
| Monzo = -5 1 0 0 1 | | Monzo = -5 1 0 0 1 | ||
| Cents = 53.27294 | | Cents = 53.27294 | ||
| Name = undecimal comma<br>undecimal quarter tone<br>al-Farabi (Alpharabius) quarter tone | | Name = undecimal comma, <br>undecimal quarter tone, <br>al-Farabi (Alpharabius) quarter tone | ||
| Color name = | | Color name = | ||
| FJS name = P1<sup>11</sup> | | FJS name = P1<sup>11</sup> | ||
| Line 20: | Line 20: | ||
* [[Gallery of just intervals]] | * [[Gallery of just intervals]] | ||
* [[32/31]] | * [[32/31]] | ||
* [[:File:Ji-33-32-csound-foscil-220hz.mp3]] | |||
[[Category:11-limit]] | [[Category:11-limit]] | ||
Revision as of 09:25, 26 July 2020
| Interval information |
undecimal quarter tone,
al-Farabi (Alpharabius) quarter tone
reduced,
reduced harmonic
[sound info]
33/32, the undecimal comma, undecimal quarter tone, or al-Farabi (Alpharabius) quarter tone, is a superparticular ratio which differs by a keenanisma (385/384), from the septimal quarter tone (36/35). Raising a just perfect fourth (4/3) by the al-Farabi quarter-tone leads to the undecimal super-fourth (11/8). Raising it instead by 36/35 leads to the septimal super-fourth (48/35) which approximates 11/8.
Arguably 33/32 could have been used as a melodic interval in the Greek Enharmonic Genus. The resulting tetrachord would include 32:33:34 within the interval of a perfect fourth. This ancient Greek scale can be approximated in 22edo and 24edo, if the comma 1089/1088 is tempered so that 33/32 and 34/33 are equated.
33/32 is significant in Functional Just System as the undecimal formal comma which translates a Pythagorean interval to a nearby undecimal interval. Apart from the aforementioned relationship between 4/3 and 11/8, it is also the interval between 32/27 and 11/9, and between 9/8 and 12/11.