User:Aura/Aura's Ideas on Tonality: Difference between revisions

Line 269:

|}

From this particular sample, we can deduce that there are ~~three~~ fundamental premises of the Alpharabian tuning system:

From this particular sample, we can deduce that there are several fundamental premises of the Alpharabian tuning system:

* 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.

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

* Since 1089/1024 is (33/32)^2, modifying a Pythagorean interval by 33/32 always results in an interval that is considered "Alpharabian".

* 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".

~~I should also point out 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.

* As both the rastma and 1331/1296 are 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 latter of which will be covered in the next section~~.

The following rules are directly derived from the above premises:

@@ Line 269: / Line 269: @@
 |}
-From this particular sample, we can deduce that there are three fundamental premises of the Alpharabian tuning system:
+From this particular sample, we can deduce that there are several fundamental premises of the Alpharabian tuning system:
 * 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.
+* The intervals [[3/2]], [[4/3]], [[9/8]], [[16/9]], and so forth, have the same functions as in [[Pythagorean tuning]].
-* Since 1089/1024 is (33/32)^2, modifying a Pythagorean interval by 33/32 always results in an interval that is considered "Alpharabian".
+* 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".
-I should also point out 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.
-* As both the rastma and 1331/1296 are 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 latter of which will be covered in the next section.
 The following rules are directly derived from the above premises: