Alpharabian tuning: Difference between revisions

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The '''Alpharabian tuning''' is an [[11-limit]] version of [[just intonation]]- specifically the version that is limited to the 2.3.11 subgroup. ~~Although the core of Alpharabian tuning consists~~ of ~~those intervals with ratios involving integers whose only prime factors are 2 and 11, Alpharabian~~ tuning can also contain powers of 3 in their ratios. That said, within Alpharabian tuning, there's a distinction between "Alpharabian" and "Betarabian" intervals, with "Alpharabian" intervals generally either outright belonging to the 2.11 core subgroup or being ~~simpler and or nearer to 3-limit intervals than the nearby "Betarabian" intervals~~, ~~which often differ from their Alpharabian counterparts by a~~ [[~~243~~/~~242~~|~~rastma~~]]~~. There are other distinctions as well, but a proper descriptor~~ for ~~these other intervals has yet to be chosen~~.

The '''Alpharabian tuning''' is an [[11-limit]] version of [[just intonation]]- specifically the version that is limited to the 2.3.11 subgroup. As a significant portion of this tuning system is currently being pioneered by [[User:Aura|Aura]], see [[User:Aura/Aura's Ideas on Tonality|Aura's Ideas on Tonality]] for more details.

~~As a significant portion~~ of ~~this~~ tuning ~~system~~ is ~~currently being pioneered~~ by [[~~User~~:~~Aura~~|~~Aura~~]]~~, see~~ [[~~User~~:~~Aura~~/~~Aura~~'~~s Ideas on Tonality|Aura~~'~~s Ideas on Tonality]] for more details~~.

In terms of the interval naming scheme, there are several fundamental premises in Alpharabian tuning:

* Intervals that are in the 2.11 subgroup are all considered Alpharabian intervals.

* 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, modifying a Pythagorean interval by [[33/32]] always results in an interval that is considered "Alpharabian".

In addition to that, there's also at least one known secondary premise at play:

* 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 Pythagorean, Alpharabian and Betarabian intervals.

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 'parasuper' or 'parasub' prefixes, 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

:* Augmentation of a Pythagorean Minor interval by 33/32 results in a Lesser Neutral interval

:* Dimunition of a Pythagorean Major interval by 33/32 results in a Greater Neutral interval

* Generally, intervals that result that result from the modification of a Pythagorean interval by 1331/1296 take either the 'super' or 'sub' prefixes, with these prefixes generally being stacked where multiple such modifications occur, however, there are some significant caveats...

:* Augmentation of a Pythagorean Minor interval by a single 1331/1296 results in a Supraminor interval, but a second such augmentation results in a Betarabian Major interval due to said interval differing from the nearby Alpharabian Major (covered under modifications by 1089/1024) by a rastma.

:* Dimunition of a Pythagorean Major interval by a single 1331/1296 results in a Submajor interval, but a second such dimunition results in a Betarabian Minor interval due to said interval differing from the nearby Alpharabian Minor (covered under modifications by 1089/1024) by a rastma.

[[Category:Tuning]]

[[Category:Alpharabian| ]]

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-The '''Alpharabian tuning''' is an [[11-limit]] version of [[just intonation]]- specifically the version that is limited to the 2.3.11 subgroup.  Although the core of Alpharabian tuning consists of those intervals with ratios involving integers whose only prime factors are 2 and 11, Alpharabian tuning can also contain powers of 3 in their ratios.  That said, within Alpharabian tuning, there's a distinction between "Alpharabian" and "Betarabian" intervals, with "Alpharabian" intervals generally either outright belonging to the 2.11 core subgroup or being simpler and or nearer to 3-limit intervals than the nearby "Betarabian" intervals, which often differ from their Alpharabian counterparts by a [[243/242|rastma]].  There are other distinctions as well, but a proper descriptor for these other intervals has yet to be chosen.
+The '''Alpharabian tuning''' is an [[11-limit]] version of [[just intonation]]- specifically the version that is limited to the 2.3.11 subgroup.  As a significant portion of this tuning system is currently being pioneered by [[User:Aura|Aura]], see [[User:Aura/Aura's Ideas on Tonality|Aura's Ideas on Tonality]] for more details.
-As a significant portion of this tuning system is currently being pioneered by [[User:Aura|Aura]], see [[User:Aura/Aura's Ideas on Tonality|Aura's Ideas on Tonality]] for more details.
+In terms of the interval naming scheme, there are several fundamental premises in Alpharabian tuning:
+* Intervals that are in the 2.11 subgroup are all considered Alpharabian intervals.
+* 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, modifying a Pythagorean interval by [[33/32]] always results in an interval that is considered "Alpharabian".
+In addition to that, there's also at least one known secondary premise at play:
+* 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 Pythagorean, Alpharabian and Betarabian intervals.
+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 'parasuper' or 'parasub' prefixes, 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
+:* Augmentation of a Pythagorean Minor interval by 33/32 results in a Lesser Neutral interval
+:* Dimunition of a Pythagorean Major interval by 33/32 results in a Greater Neutral interval
+* Generally, intervals that result that result from the modification of a Pythagorean interval by 1331/1296 take either the 'super' or 'sub' prefixes, with these prefixes generally being stacked where multiple such modifications occur, however, there are some significant caveats...
+:* Augmentation of a Pythagorean Minor interval by a single 1331/1296 results in a Supraminor interval, but a second such augmentation results in a Betarabian Major interval due to said interval differing from the nearby Alpharabian Major (covered under modifications by 1089/1024) by a rastma.
+:* Dimunition of a Pythagorean Major interval by a single 1331/1296 results in a Submajor interval, but a second such dimunition results in a Betarabian Minor interval due to said interval differing from the nearby Alpharabian Minor (covered under modifications by 1089/1024) by a rastma.
 [[Category:Tuning]]
 [[Category:Alpharabian| ]] <!-- main article -->