Alpharabian tuning: Difference between revisions

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* Intervals that are in the 2.11 subgroup are all considered Axirabian intervals as 2.11 forms a core navigational axis of Alpharabian tuning.

* The intervals [[3/2]], [[4/3]], [[9/8]], [[16/9]], and so forth, have the same functions as in [[Pythagorean tuning]].

* 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.

* 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.

* Since 1089/1024 is (33/32)^2, ~~modifying a Pythagorean interval by~~ [[33/32]] ~~results in an interval that is considered Alpharabian unless the resulting interval lies along the 2.11 axis, thus~~, ~~intervals that result from~~ the modification ~~of a Pythagorean interval~~ by [[1089/1024~~]] are labeled similarly to those modified in the equivalent fashion~~ by [[2187/2048]]~~, the only difference being~~ that modification by 1089/1024 results in an Alpharabian interval rather than a Pythagorean interval.

* Since 1089/1024 is (33/32)^2, and since [[2187/2048]] only differs from 1089/1024 by 243/242, the only difference between modification by 1089/1024 and modification by [[2187/2048]] is that modification by 1089/1024 results in an Alpharabian interval rather than a Pythagorean interval.

The following premise has currently not been finalized:

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 * Intervals that are in the 2.11 subgroup are all considered Axirabian intervals as 2.11 forms a core navigational axis of Alpharabian tuning.
 * The intervals [[3/2]], [[4/3]], [[9/8]], [[16/9]], and so forth, have the same functions as in [[Pythagorean tuning]].
-* 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.
+* 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.
-* Since 1089/1024 is (33/32)^2, modifying a Pythagorean interval by [[33/32]] results in an interval that is considered Alpharabian unless the resulting interval lies along the 2.11 axis, thus, intervals that result from the modification of a Pythagorean interval by [[1089/1024]] are labeled similarly to those modified in the equivalent fashion by [[2187/2048]], the only difference being that modification by 1089/1024 results in an Alpharabian interval rather than a Pythagorean interval.
+* Since 1089/1024 is (33/32)^2, and since [[2187/2048]] only differs from 1089/1024 by 243/242, the only difference between modification by 1089/1024 and modification by [[2187/2048]] is that modification by 1089/1024 results in an Alpharabian interval rather than a Pythagorean interval.
 The following premise has currently not been finalized: