Alpharabian comma: Difference between revisions
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{{Infobox Interval | {{Infobox Interval | ||
| Ratio = 131769/131072 | | Ratio = 131769/131072 | ||
| Name = Alpharabian comma | | Name = Alpharabian comma | ||
| Color name = | | Color name = L1o<sup>4</sup>-2, Laquadlo comma | ||
| | | Comma = yes | ||
}} | }} | ||
The '''Alpharabian comma''' is | The '''Alpharabian comma''' ({{monzo|legend=1| -17 2 0 0 4 }}, [[ratio]]: 131769/131072) is an [[11-limit]] (also 2.3.11 [[subgroup]]) [[comma]] measuring about 9.2{{cent}}. It is the amount by which a stack of two [[128/121]] diatonic semitones falls short of a [[9/8]] whole tone, and the amount by which a stack of four [[33/32]] quartertones exceeds a 9/8 whole tone. The term "Alpharabian" comes from Alpharabius – another name for Al-Farabi – and was chosen due to the fact that 33/32, also known as the the Al-Farabi Quartertone, is the primary parachroma of the 11-limit, a fact which lends itself to the idea of just 2.3.11 tuning being called "[[Alpharabian tuning]]" in the same way that just 3-limit tuning is called "[[Pythagorean tuning]]". Of note is that the Alpharabian comma and the [[Pythagorean comma]] are similar in that both commas represent the difference between two of their respective ''p''-limit's primary diatonic semitones and a 9/8 whole tone. | ||
== Temperaments == | |||
Tempering out the Alpharabian comma in the 11-limit results in the '''alphaxenic temperament''', or in the 2.3.11 subgroup the '''alphaxenean temperament'''. | |||
== See also == | == See also == | ||
* [[Alphaxenic rank three clan]] | |||
* [[Small comma]] | * [[Small comma]] | ||
[[Category:Alpharabian]] | [[Category:Alpharabian]] | ||
[[Category:Alphaxenic]] | |||
[[Category:Commas named for their regular temperament properties]] | |||
[[Category:Commas named after polymaths]] | |||
Latest revision as of 20:40, 5 November 2024
| Interval information |
reduced harmonic
The Alpharabian comma (monzo: [-17 2 0 0 4⟩, ratio: 131769/131072) is an 11-limit (also 2.3.11 subgroup) comma measuring about 9.2 ¢. It is the amount by which a stack of two 128/121 diatonic semitones falls short of a 9/8 whole tone, and the amount by which a stack of four 33/32 quartertones exceeds a 9/8 whole tone. The term "Alpharabian" comes from Alpharabius – another name for Al-Farabi – and was chosen due to the fact that 33/32, also known as the the Al-Farabi Quartertone, is the primary parachroma of the 11-limit, a fact which lends itself to the idea of just 2.3.11 tuning being called "Alpharabian tuning" in the same way that just 3-limit tuning is called "Pythagorean tuning". Of note is that the Alpharabian comma and the Pythagorean comma are similar in that both commas represent the difference between two of their respective p-limit's primary diatonic semitones and a 9/8 whole tone.
Temperaments
Tempering out the Alpharabian comma in the 11-limit results in the alphaxenic temperament, or in the 2.3.11 subgroup the alphaxenean temperament.