33/32: Difference between revisions

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'''33/32'''
{{Infobox Interval
|-5 1 0 0 1>
| Icon =
| Ratio = 33/32
| Monzo = -5 1 0 0 1
| Cents = 53.27294
| Name = al-Farabi (Alpharabius) quarter-tone
| Color name =
| Sound = jid_33_32_pluck_adu_dr220.mp3
}}


53.2729 cents
The '''al-Farabi (Alpharabius) quarter-tone''', '''33/32''', is a [[superparticular]] ratio which differs by a [[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]] super-fourth. Raising it instead by 36/35 leads to the [[48/35|septimal super-fourth (48/35)]] which approximates 11/8.


[[File:jid_33_32_pluck_adu_dr220.mp3]] [[:File:jid_33_32_pluck_adu_dr220.mp3|sound sample]]
Arguably the al-Farabia quarter-tone 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|22-edo]] and [[24edo|24-edo]], if the comma 1089/1088 is tempered so that 33/32 and 34/33 are equated.


The al-Farabi (Alpharabius) quarter-tone, 33/32, is a [[superparticular|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]] by the al-Farabi quarter-tone leads to the [[11/8|11/8]] super-fourth. Raising it instead by 36/35 leads to the [[48/35|septimal super-fourth]] which approximates 11/8.
== See also ==


Arguably the al-Farabia quarter-tone 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|22-edo]] and [[24edo|24-edo]], if the comma 1089/1088 is tempered so that 33/32 and 34/33 are equated.
* [[Gallery of just intervals]]
* [[32/31]]
 
[[Category:11-limit]]
[[Category:Interval ratio]]
[[Category:Superparticular]]
[[Category:Quartertone]]
[[Category:Listen]]

Revision as of 14:21, 21 June 2020

Interval information
Ratio 33/32
Factorization 2-5 × 3 × 11
Monzo [-5 1 0 0 1⟩
Size in cents 53.27294¢
Name al-Farabi (Alpharabius) quarter-tone
FJS name [math]\displaystyle{ \text{P1}^{11} }[/math]
Special properties superparticular,
reduced,
reduced harmonic
Tenney norm (log2 nd) 10.0444
Weil norm (log2 max(n, d)) 10.0888
Wilson norm (sopfr(nd)) 24

[sound info]
Open this interval in xen-calc

The al-Farabi (Alpharabius) quarter-tone, 33/32, 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 11/8 super-fourth. Raising it instead by 36/35 leads to the septimal super-fourth (48/35) which approximates 11/8.

Arguably the al-Farabia quarter-tone 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 22-edo and 24-edo, if the comma 1089/1088 is tempered so that 33/32 and 34/33 are equated.

See also

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