Alpharabian tuning: Difference between revisions

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* 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; 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, 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.

* 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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The following rules are directly derived from the above premises:

* Generally, intervals that result from the modification of a Pythagorean interval by 33/32 take either the 'ultra' or 'infra' prefixes- for example [[891/512]], which is the Alpharabian Ultramajor Sixth, and 512/297, which is the Alpharabian Inframinor Seventh- however, there are a number of special cases...

* Generally, intervals that result from the modification of a Pythagorean interval by 33/32 take either the 'ultra' or 'infra' prefixes- for example [[891/512]], which is the Alpharabian Ultramajor Sixth, and [[512/297]], which is the Alpharabian Inframinor Seventh- however, there are a number of special cases...

:* Augmentation of a Perfect Fourth or Perfect Fifth by 33/32 results in a Paramajor interval

:* Dimunition of a Perfect Fourth or Perfect Fifth by 33/32 results in a Paraminor interval

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 * 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; 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, 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.
+* 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:
@@ Line 26: / Line 26: @@
 The following rules are directly derived from the above premises:
-* Generally, intervals that result from the modification of a Pythagorean interval by 33/32 take either the 'ultra' or 'infra' prefixes- for example [[891/512]], which is the Alpharabian Ultramajor Sixth, and 512/297, which is the Alpharabian Inframinor Seventh- however, there are a number of special cases...
+* Generally, intervals that result from the modification of a Pythagorean interval by 33/32 take either the 'ultra' or 'infra' prefixes- for example [[891/512]], which is the Alpharabian Ultramajor Sixth, and [[512/297]], which is the Alpharabian Inframinor Seventh- however, there are a number of special cases...
 :* Augmentation of a Perfect Fourth or Perfect Fifth by 33/32 results in a Paramajor interval
 :* Dimunition of a Perfect Fourth or Perfect Fifth by 33/32 results in a Paraminor interval