33/32: Difference between revisions
→See also: added another sound example |
Expansion |
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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 = al-Farabi (Alpharabius) quarter | | Name = undecimal comma<br>undecimal quarter tone<br>al-Farabi (Alpharabius) quarter tone | ||
| Color name = | | Color name = | ||
| FJS name = P1<sup>11</sup> | |||
| Sound = jid_33_32_pluck_adu_dr220.mp3 | | Sound = jid_33_32_pluck_adu_dr220.mp3 | ||
}} | }} | ||
'''33/32''', the '''undecimal comma''', '''undecimal quarter tone''', or '''al-Farabi (Alpharabius) quarter tone''', is a [[superparticular]] [[ratio]] which differs by a [[385/384|keenanisma (385/384)]], from the [[36/35|septimal quarter tone (36/35)]]. Raising a just [[4/3|perfect fourth (4/3)]] by the al-Farabi quarter-tone leads to the [[11/8|undecimal super-fourth (11/8)]]. Raising it instead by 36/35 leads to the [[48/35|septimal super-fourth (48/35)]] which approximates 11/8. | |||
Arguably | 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]]. | |||
== See also == | == See also == | ||
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* [[Gallery of just intervals]] | * [[Gallery of just intervals]] | ||
* [[32/31]] | * [[32/31]] | ||
[[Category:11-limit]] | [[Category:11-limit]] | ||
Revision as of 08:45, 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.