33/32: Difference between revisions

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'''33/32''', '''al-Farabi quarter tone'''<ref>The name goes back to Abu Nasr Al-Farabi (in Western reception also Alpharabius), see [[wikipedia:Al-Farabi]] </ref>, '''undecimal quarter tone''', or '''undecimal comma''', 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.

'''33/32''', the '''al-Farabi quarter tone'''<ref>The name goes back to Abu Nasr Al-Farabi (in Western reception also Alpharabius), see [[wikipedia:Al-Farabi]] </ref>, '''undecimal quarter tone''', or '''undecimal comma''', 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 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.

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-'''33/32''', '''al-Farabi quarter tone'''<ref>The name goes back to Abu Nasr Al-Farabi (in Western reception also Alpharabius), see [[wikipedia:Al-Farabi]] </ref>, '''undecimal quarter tone''', or '''undecimal comma''', 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.
+'''33/32''', the '''al-Farabi quarter tone'''<ref>The name goes back to Abu Nasr Al-Farabi (in Western reception also Alpharabius), see [[wikipedia:Al-Farabi]] </ref>, '''undecimal quarter tone''', or '''undecimal comma''', 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 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.