User talk:TallKite: Difference between revisions

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Thanks in advance for having a look into [[Talk:Fifthspan #About ringy confusion]]. --[[User:Xenwolf|Xenwolf]] ([[User talk:Xenwolf|talk]]) 16:55, 20 November 2020 (UTC)

== System for Describing Alpharabian Tuning ==

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 either 33/32, 1331/1296 or 1089/1024- are all considered "Alpharabian".

* 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 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.

* Generally, 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.

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)

@@ Line 126: / Line 126: @@
 Thanks in advance for having a look into [[Talk:Fifthspan #About ringy confusion]]. --[[User:Xenwolf|Xenwolf]] ([[User talk:Xenwolf|talk]]) 16:55, 20 November 2020 (UTC)
+== System for Describing Alpharabian Tuning ==
+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 either 33/32, 1331/1296 or 1089/1024- are all considered "Alpharabian".
+* 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 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.
+* Generally, 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.
+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)