User talk:TallKite: Difference between revisions

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In evaluating my work on Alpharabian tuning, you asked if one can work backwards from my interval names, and if there a formula or an algorithm for that. So, I've decided to try and answer the question. After going through the list of names, and reevaluating the names in my system, yes, there 'is' a set of rules for how the names of the intervals in Alpharabian tuning are derived. However, there appears to be some modifications to my system that are required, and I will attempt to make some of them here.

* Intervals that are ~~either~~ in the 2.11 subgroup~~, as well as intervals that are derived from Pythagorean intervals by a single instance of either 33/32, 1331/1296 or 1089/1024,~~ are all considered "Alpharabian"~~- this is a hard and fast rule that takes precedence over other rules~~.

There are three fundamental premises of the Alpharabian tuning system:

* 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- this ~~is another hard rule~~ and ~~fast rule~~.

* Intervals that are in the 2.11 subgroup are all 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".

There's also an additional idea at play which seems to be of slightly lesser importance:

* 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 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

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:* 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 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...

* 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.

Modifying by combinations of 1331/1296 and 1089/1024 yields interesting results, but I have yet to properly create the part of the system for dealing with these sorts of things. I think we could afford to work together to develop this and to fix remaining flaws if you have the time. --[[User:Aura|Aura]] ([[User talk:Aura|talk]]) 16:43, 22 November 2020 (UTC)

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 In evaluating my work on Alpharabian tuning, you asked if one can work backwards from my interval names, and if there a formula or an algorithm for that.  So, I've decided to try and answer the question.  After going through the list of names, and reevaluating the names in my system, yes, there 'is' a set of rules for how the names of the intervals in Alpharabian tuning are derived.  However, there appears to be some modifications to my system that are required, and I will attempt to make some of them here.
-* Intervals that are either in the 2.11 subgroup, as well as intervals that are derived from Pythagorean intervals by a single instance of either 33/32, 1331/1296 or 1089/1024, are all considered "Alpharabian"- this is a hard and fast rule that takes precedence over other rules.
+There are three fundamental premises of the Alpharabian tuning system:
-* 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- this is another hard rule and fast rule.
+* Intervals that are in the 2.11 subgroup are all 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".
+There's also an additional idea at play which seems to be of slightly lesser importance:
+* 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 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
@@ Line 138: / Line 148: @@
 :* 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 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...
+* 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.
 Modifying by combinations of 1331/1296 and 1089/1024 yields interesting results, but I have yet to properly create the part of the system for dealing with these sorts of things.  I think we could afford to work together to develop this and to fix remaining flaws if you have the time. --[[User:Aura|Aura]] ([[User talk:Aura|talk]]) 16:43, 22 November 2020 (UTC)