33/32: Difference between revisions
No edit summary |
Added color name, fixed typo, misc. edits, categories |
||
| Line 1: | Line 1: | ||
{{Infobox Interval | {{Infobox Interval | ||
| Ratio = 33/32 | | Ratio = 33/32 | ||
| Monzo = -5 1 0 0 1 | | Monzo = -5 1 0 0 1 | ||
| Cents = 53.27294 | | Cents = 53.27294 | ||
| Name = al-Farabi quarter tone, <br>undecimal quarter tone, <br>undecimal comma, <br>Alpharabian parachroma, <br>Alpharabian ultraprime | | Name = al-Farabi quarter tone, <br>undecimal quarter tone, <br>undecimal comma, <br>Alpharabian parachroma, <br>Alpharabian ultraprime | ||
| Color name = | | Color name = 1o1, ilo unison | ||
| FJS name = P1<sup>11</sup> | | 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 '''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 | '''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 superfourth (11/8)]]. Raising it instead by 36/35 leads to the [[48/35|septimal superfourth (48/35)]] which approximates 11/8. Apart from this, it is also the interval between [[32/27]] and [[11/9]], and between [[9/8]] and [[12/11]]. | ||
Because of its close proximity to [[28/27]], form which it differs only by [[Pentacircle comma|896/891]], one could reasonably argue that 33/32 is the undecimal counterpart to 28/27 in a way, particularly if treated as an interval in its own right. However, despite this, 33/32 generally has properties more akin to a chromatic interval than to anything resembling a diatonic interval. In addition, 33/32 could arguably have been used as a melodic interval in the Greek Enharmonic Genus, and if so, there are several possibilities for the resulting tetrachord. The most obvious of these possibilities would be to include 32:33:34 within the interval of a perfect fourth, in which case this ancient Greek scale can be approximated in [[22edo]] and [[24edo]], with the comma 1089/1088 being tempered out so that 33/32 and 34/33 are equated. Another possibility, however, is that the semitone was [[16/15]], which, according to [https://en.wikipedia.org/wiki/Genus_(music) Wikipedia], is indirectly attested to in the writings of Ptolemy, and thus, if 33/32 was in fact used, it would have been paired with [[512/495]]. | Because of its close proximity to [[28/27]], form which it differs only by [[Pentacircle comma|896/891]], one could reasonably argue that 33/32 is the undecimal counterpart to 28/27 in a way, particularly if treated as an interval in its own right. However, despite this, 33/32 generally has properties more akin to a chromatic interval than to anything resembling a diatonic interval. In addition, 33/32 could arguably have been used as a melodic interval in the Greek Enharmonic Genus, and if so, there are several possibilities for the resulting tetrachord. The most obvious of these possibilities would be to include 32:33:34 within the interval of a perfect fourth, in which case this ancient Greek scale can be approximated in [[22edo]] and [[24edo]], with the comma 1089/1088 being tempered out so that 33/32 and 34/33 are equated. Another possibility, however, is that the semitone was [[16/15]], which, according to [https://en.wikipedia.org/wiki/Genus_(music) Wikipedia], is indirectly attested to in the writings of Ptolemy, and thus, if 33/32 was in fact used, it would have been paired with [[512/495]]. | ||
The interval 33/32 is significant in [[Functional Just System]] and [[Helmholtz-Ellis notation]] as the undecimal formal comma which translates a Pythagorean interval to a nearby undecimal interval. However, it should be noted that in some significant respects, treating 33/32 as a comma rather than as an important musical interval in its own right sells it short, and results in the failure to correctly define the properties of certain intervals. Namely, a stack of two 33/32 intervals equals [[1089/1024]], a type of chromatic semitone that has [[128/121]] as its diatonic counterpart. Furthermore, 33/32 is one of two distinct 11-limit quartertone intervals required to add up to a whole tone, with [[4096/3993]] being the other- specifically, adding 4096/3993 to a stack of three 33/32 quartertones yields [[9/8]]. In addition to all this, 33/32 finds a special place in [[Alpharabian tuning]] and it is from this area of microtonal theory, among a select few others, that 33/32 acquires the names "'''Alpharabian parachroma'''" and "''' | The interval 33/32 is significant in [[Functional Just System]] and [[Helmholtz-Ellis notation]] as the undecimal formal comma which translates a Pythagorean interval to a nearby undecimal interval. However, it should be noted that in some significant respects, treating 33/32 as a comma rather than as an important musical interval in its own right sells it short, and results in the failure to correctly define the properties of certain intervals. Namely, a stack of two 33/32 intervals equals [[1089/1024]], a type of chromatic semitone that has [[128/121]] as its diatonic counterpart. Furthermore, 33/32 is one of two distinct 11-limit quartertone intervals required to add up to a whole tone, with [[4096/3993]] being the other- specifically, adding 4096/3993 to a stack of three 33/32 quartertones yields [[9/8]]. In addition to all this, 33/32 finds a special place in [[Alpharabian tuning]] and it is from this area of microtonal theory, among a select few others, that 33/32 acquires the names "'''Alpharabian parachroma'''" and "'''Alpharabian ultraprime'''", names that at this point are only used in said theoretical contexts. While many may be accustomed to thinking of 33/32 and [[729/704]] as "semiaugmented primes", this analysis is only completely accurate when [[243/242]] is tempered out. | ||
== See also == | == See also == | ||
| Line 28: | Line 27: | ||
[[Category:11-limit]] | [[Category:11-limit]] | ||
[[Category:Superparticular]] | [[Category:Superparticular]] | ||
[[Category:Quartertone]] | [[Category:Quartertone]] | ||
[[Category:Alpharabian]] | [[Category:Alpharabian]] | ||
[[Category:Medium comma]] | [[Category:Medium comma]] | ||
[[Category: | [[Category:Octave-reduced harmonics]] | ||
[[Category: | [[Category:Pages with internal sound examples]] | ||
Revision as of 03:28, 20 December 2021
| Interval information |
undecimal quarter tone,
undecimal comma,
Alpharabian parachroma,
Alpharabian ultraprime
reduced,
reduced harmonic
[sound info]
33/32, the al-Farabi quarter tone[1], undecimal quarter tone, or undecimal comma, 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 superfourth (11/8). Raising it instead by 36/35 leads to the septimal superfourth (48/35) which approximates 11/8. Apart from this, it is also the interval between 32/27 and 11/9, and between 9/8 and 12/11.
Because of its close proximity to 28/27, form which it differs only by 896/891, one could reasonably argue that 33/32 is the undecimal counterpart to 28/27 in a way, particularly if treated as an interval in its own right. However, despite this, 33/32 generally has properties more akin to a chromatic interval than to anything resembling a diatonic interval. In addition, 33/32 could arguably have been used as a melodic interval in the Greek Enharmonic Genus, and if so, there are several possibilities for the resulting tetrachord. The most obvious of these possibilities would be to include 32:33:34 within the interval of a perfect fourth, in which case this ancient Greek scale can be approximated in 22edo and 24edo, with the comma 1089/1088 being tempered out so that 33/32 and 34/33 are equated. Another possibility, however, is that the semitone was 16/15, which, according to Wikipedia, is indirectly attested to in the writings of Ptolemy, and thus, if 33/32 was in fact used, it would have been paired with 512/495.
The interval 33/32 is significant in Functional Just System and Helmholtz-Ellis notation as the undecimal formal comma which translates a Pythagorean interval to a nearby undecimal interval. However, it should be noted that in some significant respects, treating 33/32 as a comma rather than as an important musical interval in its own right sells it short, and results in the failure to correctly define the properties of certain intervals. Namely, a stack of two 33/32 intervals equals 1089/1024, a type of chromatic semitone that has 128/121 as its diatonic counterpart. Furthermore, 33/32 is one of two distinct 11-limit quartertone intervals required to add up to a whole tone, with 4096/3993 being the other- specifically, adding 4096/3993 to a stack of three 33/32 quartertones yields 9/8. In addition to all this, 33/32 finds a special place in Alpharabian tuning and it is from this area of microtonal theory, among a select few others, that 33/32 acquires the names "Alpharabian parachroma" and "Alpharabian ultraprime", names that at this point are only used in said theoretical contexts. While many may be accustomed to thinking of 33/32 and 729/704 as "semiaugmented primes", this analysis is only completely accurate when 243/242 is tempered out.
See also
- 64/33 – its octave complement
- 16/11 – its fifth complement
- Gallery of just intervals
- 32/31
- File:Ji-33-32-csound-foscil-220hz.mp3
- 23-EDO – its step size is a good (albeit inconsistent) approximation of 33/32
References
- ↑ The name goes back to Abu Nasr Al-Farabi (in Western reception also Alpharabius), see Wikipedia: Al-Farabi.