Alpharabian tuning: Difference between revisions

* 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 4096/3993 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 Parachromatic Semilimma, [[1331/1296]], is slightly over half of [[256/243]], the Pythagorean Limma, with the remainder being 4096/3993, and since 1331/1296 differs from 33/32 by the rastma, modification of a Pythagorean interval by this quartertone often results in an Alpharabian interval- the principle exceptions to this being 1331/1024 and 2048/1331, which differ from 81/64 and 128/81 respectively by this interval, though there are others.

* 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

:* Augmentation of a Pythagorean Minor interval by 33/32 results in an Artoneutral interval

The following rules have not yet been finalized in their entirety due to lack of details:

| Alpharabian infraoctave

| This interval is the octave-reduced 33rd subharmonic.

|-

|}