Talk:Chromatic pairs: Difference between revisions

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: In Ganaram inukshuk's proposition, the elements of the pair are the haplotonic and the albitonic scale (which, should I remind, is not Smith's original definition, should it matter), and they are related to a chromatic scale which contains at least one copy of each, and possibly multiple copies of one of them (the idea of "containing copies" comes from the [[recursive structure of MOS scales]]). That definition bakes in assumption 2, but does nothing about assumption 1. Assumption 3 is treated in the difference between the "strict" and the "weak" variants. Assumption 4 isn't treated either, but since it's only used to observe irregularities with edge cases, it's not as fundamental as the previous three. So by this proposition, I could call meantone[2] haplotonic, meantone[3] albitonic and meantone[5] chromatic. Maybe it would be wise to systematically skip 2 and 3, which are always mosses (and are rather trivial too) and skip right ahead to whatever size comes next. That would make it retro-compatible with common temperaments such as meantone, and it would sort of solve the issue with assumption 1.

: To sum up, I think it's fundamentally flawed to try to apply all 4 assumptions baked into the "traditional mosses" to all other mosses, but should someone try, I would go with Ganaram inukshuk's proposition and add the starting point rule I stated above (always start with the first size after 3). This will inevitably lead to 6-tone chromatic scales in extreme cases and to a lot of weak chromatic pairs despite the existence of "strong chromatic pairs" at higher sizes (see Barton example above), but that's the kind of information loss to be expected when taking too many variables at once. It's the problems of temperament all over again! --[[User:Fredg999|Fredg999]] ([[User talk:Fredg999|talk]]) 06:01, 21 May 2023 (UTC)

: Since we can rarely apply all of Ganaram inukshuk's assumptions at once to non-diatonic MOSses, I suggest we should give priority to the first assumption, because the scales closest to 5, 7, and 12 notes are the ones most melodically similar to the pentatonic, diatonic, and chromatic scales. For example, for porcupine, [[1L 4s]] is the haplotonic scale, [[1L 6s]] is the albitonic scale, and [[7L 8s]] is the chromatic scale. However, this approach would still require the intermediate terms–using the porcupine example again, the [[1L 5s]] and [[7L 1s]] scales would need to use terms like "mega-haplotonic" and "mega-albitonic".[[User:CompactStar|CompactStar]] ([[User talk:CompactStar|talk]]) 01:02, 25 May 2023 (UTC)

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 : In Ganaram inukshuk's proposition, the elements of the pair are the haplotonic and the albitonic scale (which, should I remind, is not Smith's original definition, should it matter), and they are related to a chromatic scale which contains at least one copy of each, and possibly multiple copies of one of them (the idea of "containing copies" comes from the [[recursive structure of MOS scales]]). That definition bakes in assumption 2, but does nothing about assumption 1. Assumption 3 is treated in the difference between the "strict" and the "weak" variants. Assumption 4 isn't treated either, but since it's only used to observe irregularities with edge cases, it's not as fundamental as the previous three. So by this proposition, I could call meantone[2] haplotonic, meantone[3] albitonic and meantone[5] chromatic. Maybe it would be wise to systematically skip 2 and 3, which are always mosses (and are rather trivial too) and skip right ahead to whatever size comes next. That would make it retro-compatible with common temperaments such as meantone, and it would sort of solve the issue with assumption 1.
 : To sum up, I think it's fundamentally flawed to try to apply all 4 assumptions baked into the "traditional mosses" to all other mosses, but should someone try, I would go with Ganaram inukshuk's proposition and add the starting point rule I stated above (always start with the first size after 3). This will inevitably lead to 6-tone chromatic scales in extreme cases and to a lot of weak chromatic pairs despite the existence of "strong chromatic pairs" at higher sizes (see Barton example above), but that's the kind of information loss to be expected when taking too many variables at once. It's the problems of temperament all over again! --[[User:Fredg999|Fredg999]] ([[User talk:Fredg999|talk]]) 06:01, 21 May 2023 (UTC)
+: Since we can rarely apply all of Ganaram inukshuk's assumptions at once to non-diatonic MOSses, I suggest we should give priority to the first assumption, because the scales closest to 5, 7, and 12 notes are the ones most melodically similar to the pentatonic, diatonic, and chromatic scales. For example, for porcupine, [[1L 4s]] is the haplotonic scale, [[1L 6s]] is the albitonic scale, and [[7L 8s]] is the chromatic scale. However, this approach would still require the intermediate terms–using the porcupine example again, the [[1L 5s]] and [[7L 1s]] scales would need to use terms like "mega-haplotonic" and "mega-albitonic".[[User:CompactStar|CompactStar]] ([[User talk:CompactStar|talk]]) 01:02, 25 May 2023 (UTC)