Alpharabian comma: Difference between revisions

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The '''Alpharabian comma''' (~~about 9.18177[[Cent|¢]]), is the interval '''131769/131072''' or~~ {{~~Monzo~~| -17 2 0 0 4}} in [[~~monzo~~]] ~~notation~~. It is the amount by which a stack of two [[128/121]] diatonic semitones falls short of 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 ~~interval~~ of the 11-limit, a fact which lends itself to the idea of just 11~~-limit~~ tuning being called "Alpharabian tuning" in the same way that just 3-limit tuning is called "Pythagorean tuning". ~~Given~~ 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~~, it follows that tempering~~ out the Alpharabian comma results in ~~a member of~~ the '''~~Alpharabian family~~'''.

{{Infobox Interval

| Ratio = 131769/131072

| Name = Alpharabian comma

| Color name = L1o<sup>4</sup>-2, Laquadlo comma

| Comma = yes

}}

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 ==

* [[Alphaxenic rank three clan]]

* [[Small comma]]

[[Category:Alpharabian]]

[[Category:Alphaxenic]]

[[Category:Commas named for their regular temperament properties]]

[[Category:Commas named after polymaths]]

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-The '''Alpharabian comma''' (about 9.18177[[Cent|¢]]), is the interval '''131769/131072''' or {{Monzo| -17 2 0 0 4}} in [[monzo]] notation.  It is the amount by which a stack of two [[128/121]] diatonic semitones falls short of 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 interval of the 11-limit, a fact which lends itself to the idea of just 11-limit tuning being called "Alpharabian tuning" in the same way that just 3-limit tuning is called "Pythagorean tuning".  Given 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, it follows that tempering out the Alpharabian comma results in a member of the '''Alpharabian family'''.
+{{Infobox Interval
+| Ratio = 131769/131072
+| Name = Alpharabian comma
+| Color name = L1o<sup>4</sup>-2, Laquadlo comma
+| Comma = yes
+}}
+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 ==
+* [[Alphaxenic rank three clan]]
+* [[Small comma]]
+[[Category:Alpharabian]]
+[[Category:Alphaxenic]]
+[[Category:Commas named for their regular temperament properties]]
+[[Category:Commas named after polymaths]]