Alpharabian tuning: Difference between revisions

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* The interval 33/32, is the standard Alpharabian quartertone due to not only being the simplest quartertone in the 2.3.11 subgroup, but also due to the fact that stacking three of these and subtracting the resulting interval from 9/8 yields the simplest possible interval that can result from such as process; furthermore, modification of a Pythagorean interval by this quartertone generally results in an Alpharabian interval- the only two known exceptions to this being 11/8 and 16/11, which differ from 4/3 and 3/2 respectively by this interval.

* The rastma, [[243/242]], is functionally the simplest type of Alpharabian [[Diatonic, Chromatic, Enharmonic, Subchromatic|subchroma]] and since three instances of 243/242 are almost equal to 81/80 in JI, one can closely approach just [[5-limit]] intervals simply by moving three rastmas away from Pythagorean intervals in both JI and systems where the [[parimo]] is [[tempered out]]; furthermore, modification of a Pythagorean interval by this subchroma generally results in an Alpharabian interval- the only two known exceptions to this being 121/64 and 128/121, which differ from 243/128 and 256/243 respectively by this interval.

~~The following premise has currently not been finalized:~~

* As both the [[243/242|rastma]] and [[1331/1296]] are [[Diatonic, Chromatic, Enharmonic, Subchromatic|subchromas]] that form differences between members of the 2.11 subgroup and Pythagorean intervals, both of these subchromas belong to a set of intervals defining different interval sets within Alpharabian tuning, and subchromas within this particular interval set help define the differences between intervals classified as Pythagorean, Alpharabian, Betarabian and so forth.

The following rules are directly derived from the above premises:

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 * The interval 33/32, is the standard Alpharabian quartertone due to not only being the simplest quartertone in the 2.3.11 subgroup, but also due to the fact that stacking three of these and subtracting the resulting interval from 9/8 yields the simplest possible interval that can result from such as process; furthermore, modification of a Pythagorean interval by this quartertone generally results in an Alpharabian interval- the only two known exceptions to this being 11/8 and 16/11, which differ from 4/3 and 3/2 respectively by this interval.
 * The rastma, [[243/242]], is functionally the simplest type of Alpharabian [[Diatonic, Chromatic, Enharmonic, Subchromatic|subchroma]] and since three instances of 243/242 are almost equal to 81/80 in JI, one can closely approach just [[5-limit]] intervals simply by moving three rastmas away from Pythagorean intervals in both JI and systems where the [[parimo]] is [[tempered out]]; furthermore, modification of a Pythagorean interval by this subchroma generally results in an Alpharabian interval- the only two known exceptions to this being 121/64 and 128/121, which differ from 243/128 and 256/243 respectively by this interval.
-The following premise has currently not been finalized:
-* As both the [[243/242|rastma]] and [[1331/1296]] are [[Diatonic, Chromatic, Enharmonic, Subchromatic|subchromas]] that form differences between members of the 2.11 subgroup and Pythagorean intervals, both of these subchromas belong to a set of intervals defining different interval sets within Alpharabian tuning, and subchromas within this particular interval set help define the differences between intervals classified as Pythagorean, Alpharabian, Betarabian and so forth.
 The following rules are directly derived from the above premises: