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, (very improper) [[1L 4s]] is the haplotonic scale, [[1L 6s]] is the albitonic scale, and [[7L 8s]] is the chromatic scale.

: 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, (very improper) [[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". I don't think any naming system will ever be able to get rid of these types of terms, because, even if we forced the haplotonic, albitonic, and chromatic scales to be next to each other in the chain (e.g. 7, 8, and 15 notes for porcupine), we would still need to worry about "mini-haplotonic" and "mega-chromatic" scales. If these terms are inevitably required, we should come up with some standard definition of them, instead of using them in weird ways, e.g. how Shoe[5] is "mini-haplotonic" instead of "haplotonic", and Slendric has two haplotonic scales with 5 and 6 notes instead of the 6 note one being "mega-haplotonic". [[User:CompactStar|CompactStar]] ([[User talk:CompactStar|talk]]) 01:06, 25 May 2023 (UTC)

::: Sorry, I might not have been clear, I didn't mean to imply that these 4 assumptions were Ganaram inukshuk's; rather, they are most likely Gene Ward Smith's, assuming he's the one to have come up with the terms ''albitonic'' an such (although I think ''haplotonic'' came later), and I'm stating them as general properties one is likely to generalize out of the diatonic scale in general.

: 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". I don't think any naming system will ever be able to get rid of these types of terms, because, even if we forced the haplotonic, albitonic, and chromatic scales to be next to each other in the chain (e.g. 7, 8, and 15 notes for porcupine), we would still need to worry about "mini-haplotonic" and "mega-chromatic" scales. If these terms are inevitably required, we should come up with some standard definition of them, instead of using them in weird ways, e.g. how Shoe[5] is "mini-haplotonic" instead of "haplotonic", and Slendric has two haplotonic scales with 5 and 6 notes instead of the 6 note one being "mega-haplotonic". [[User:CompactStar|CompactStar]] ([[User talk:CompactStar|talk]]) 01:06, 25 May 2023 (UTC)

::: Anyway, I believe it's important to keep in mind that another way to think of "albitonic" is "what scale should go on the white keys of a piano-like keyboard", and similarly "haplotonic" describes the scale that goes on the black keys, such that the combination of all keys is the corresponding chromatic scale. In the porcupine example, you would use 1L 6s for haplotonic (7 notes), 7L 1s for albitonic (8 notes) and 7L 8s for chromatic (15 notes). This corresponds to the usual porcupine keyboard layout. I think the structure of decomposing a chromatic scale in two subscales is more important, especially since it is actually possible to preserve that property integrally, while the number of notes is fated to fall outside of the usual 5/7/12-note forms, so I don't think we should try to enforce it artificially. In fact, the 3rd assumption, which ensures that the chromatic scale's size is equal to the sum of the other two scales' sizes, could be used to solve otherwise weird cases, such as Barton, which would be decomposed as 11+13=24 instead of 5/7/11, even though it's very tempting to treat 5 and 7 as haplotonic and albitonic respectively; it wouldn't make sense to me to try building a piano-like layout with scales of size 5/7/11, but 11+13 would be an almost trivial generalization of the diatonic layout. --[[User:Fredg999|Fredg999]] ([[User talk:Fredg999|talk]]) 02:58, 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, (very improper) [[1L 4s]]  is the haplotonic scale, [[1L 6s]] is the albitonic scale, and [[7L 8s]] is the chromatic scale.
-: 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, (very improper) [[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". I don't think any naming system will ever be able to get rid of these types of terms, because, even if we forced the haplotonic, albitonic, and chromatic scales to be next to each other in the chain (e.g. 7, 8, and 15 notes for porcupine), we would still need to worry about "mini-haplotonic" and "mega-chromatic" scales. If these terms are inevitably required, we should come up with some standard definition of them, instead of using them in weird ways, e.g. how Shoe[5] is "mini-haplotonic" instead of "haplotonic", and Slendric has two haplotonic scales with 5 and 6 notes instead of the 6 note one being "mega-haplotonic". [[User:CompactStar|CompactStar]] ([[User talk:CompactStar|talk]]) 01:06, 25 May 2023 (UTC)
+::: Sorry, I might not have been clear, I didn't mean to imply that these 4 assumptions were Ganaram inukshuk's; rather, they are most likely Gene Ward Smith's, assuming he's the one to have come up with the terms ''albitonic'' an such (although I think ''haplotonic'' came later), and I'm stating them as general properties one is likely to generalize out of the diatonic scale in general.
-: 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". I don't think any naming system will ever be able to get rid of these types of terms, because, even if we forced the haplotonic, albitonic, and chromatic scales to be next to each other in the chain (e.g. 7, 8, and 15 notes for porcupine), we would still need to worry about "mini-haplotonic" and "mega-chromatic" scales. If these terms are inevitably required, we should come up with some standard definition of them, instead of using them in weird ways, e.g. how Shoe[5] is "mini-haplotonic" instead of "haplotonic", and Slendric has two haplotonic scales with 5 and 6 notes instead of the 6 note one being "mega-haplotonic". [[User:CompactStar|CompactStar]] ([[User talk:CompactStar|talk]]) 01:06, 25 May 2023 (UTC)
+::: Anyway, I believe it's important to keep in mind that another way to think of "albitonic" is "what scale should go on the white keys of a piano-like keyboard", and similarly "haplotonic" describes the scale that goes on the black keys, such that the combination of all keys is the corresponding chromatic scale. In the porcupine example, you would use 1L 6s for haplotonic (7 notes), 7L 1s for albitonic (8 notes) and 7L 8s for chromatic (15 notes). This corresponds to the usual porcupine keyboard layout. I think the structure of decomposing a chromatic scale in two subscales is more important, especially since it is actually possible to preserve that property integrally, while the number of notes is fated to fall outside of the usual 5/7/12-note forms, so I don't think we should try to enforce it artificially. In fact, the 3rd assumption, which ensures that the chromatic scale's size is equal to the sum of the other two scales' sizes, could be used to solve otherwise weird cases, such as Barton, which would be decomposed as 11+13=24 instead of 5/7/11, even though it's very tempting to treat 5 and 7 as haplotonic and albitonic respectively; it wouldn't make sense to me to try building a piano-like layout with scales of size 5/7/11, but 11+13 would be an almost trivial generalization of the diatonic layout. --[[User:Fredg999|Fredg999]] ([[User talk:Fredg999|talk]]) 02:58, 25 May 2023 (UTC)