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.

:: 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.

::: 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)

:::: Adopting the definition (haplotonic) + (albitonic) = (chromatic) reinforces the position that they are a pair rather than a triple, because haplotonic is not necessarily the direct parent of albitonic, and multiple albitonic-chromatic pairs will share the same haplotonic. Extreme case: (1L)+(1L 2s)=(3L 1s), (1L)+(1L 6s)=(7L 1s), ... Known case: (2L 3s)+(5L 2s)=(5a 7b), (2L 3s)+(5L 7s)=(5a 12b), ... --[[User:Dummy index|Dummy index]] ([[User talk:Dummy index|talk]]) 15:40, 18 November 2024 (UTC)

:::: On Barton example, for the 5/7/9/11/13-note scale we are interested in, the equations to be taken up would be 2+5=7 or 2+7=9 or 2+9=11. In other words, Barton[2] is positioned as haplotonic. Why don't we call Barton[5] mini-albitonic? --[[User:Dummy index|Dummy index]] ([[User talk:Dummy index|talk]]) 13:11, 19 November 2024 (UTC)

:::: If we take haplotonic roughly to mean "semitone-free MOS", then only Barton[2] can be haplotonic for Barton. --[[User:Dummy index|Dummy index]] ([[User talk:Dummy index|talk]]) 14:57, 20 November 2024 (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~~.

== Huxley ==

There are a lot of pages on the wiki that link to "Huxley". Based on what pages link there, I'm pretty sure Huxley is a temperament.

: 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 way~~ of ~~naming them~~, ~~although~~ I ~~am not sure how~~ to do that. [[User:~~CompactStar~~|~~CompactStar~~]] ([[User talk:~~CompactStar~~|talk]]) 01:06, ~~25 May 2023~~ (UTC)

However, I am not sure what Huxley temperament is, whether or not it belongs on this page or a different page, or whether or not it is different from [[Lovecraft]]?

I have searched every instance of the word "Huxley" on the wiki, and tried a bunch of different Google searches and queries in x31eq, but I just keep making myself more confused.

If any of you know what Huxley temperament is, please create a page for it so I can educate myself. Thank you :)

--[[User:BudjarnLambeth|BudjarnLambeth]] ([[User talk:BudjarnLambeth|talk]]) 09:11, 19 September 2024 (UTC)

: Have you tried searching the Yahoo Groups tuning list archives? https://github.com/YahooTuningGroupsUltimateBackup/YahooTuningGroupsUltimateBackup --[[User:Cmloegcmluin|Cmloegcmluin]] ([[User talk:Cmloegcmluin|talk]]) 15:59, 19 September 2024 (UTC)

:: Thank you for the recommendation, that was a very good idea. It will be a helpful resource when I'm looking for things in the future :)

:: Unfortunately I couldn't find anything about Huxley temperament in any of the files (I used Spotlight to search them). I did find mentions of "Huxley", but they were all talking about his book, Brave New World, not about the temperament. --[[User:BudjarnLambeth|BudjarnLambeth]] ([[User talk:BudjarnLambeth|talk]]) 08:30, 20 September 2024 (UTC)

::: Just an update to share with everyone. I'm continuing to research this. Here are some things that have been noted by people on the XA Facebook:

::: '''Steve Martin''': "''Hi Bud, I can't find a definition of Huxley (it is not in Graham's database afaics), I'll look at the numbers when I get a chance. Orwell has 8/5 from 3 generators, and a 4s9L mos, whereas garibertet (not heard of it before) has 5/3 from 3 generators, and a 4L9s mos, so there are some differences.''"

::: '''Ville-Pekka Turpeinen''': "''Judging by the name it appears to be riffing on Orwell by having a sharper 7/6 that gives 4/3 with six generators instead of Orwell's 7 generators of 3/2. According to Xen Wiki revision history, that name has been there as long as some pages have existed, which indicates that it comes from some earlier documentation that precedes the wiki itself.''"

::: Also very noteworthy is this archived discussion on the wiki from 2011: [[Talk:Map of linear temperaments/WikispacesArchive#Lovecraft and Huxley]]. It seems that even by that point, what "Huxley" referred to exactly had been forgotten. But it does appear to be almost identical (or completely identical) to [[Lovecraft]]. But it might have been different in its mapping of 5 or 7 or something. Still gotta try to figure that out.

::: --[[User:BudjarnLambeth|BudjarnLambeth]] ([[User talk:BudjarnLambeth|talk]]) 08:11, 24 September 2024 (UTC)

:::: The original discoverer of Huxley temperament - [[Deja Igliashon]] - saw my post on Facebook, and said the following:

:::: “''Hi Budjarn Lambeth, this temperament is one I discovered. It's an extension of Lovecraft, which is the 9&13 (edit: whoops, 4p&13p, not 9&13!) 2.11.13 subgroup temperament where two 13/11's stack to reach 11/8. Lovecraft itself is a restriction of 13-limit Orwell down to the 2.11.13 subgroup IIRC*. Huxley extends Lovecraft to add prime 3 in a different mapping than Orwell, specifically -6 generators. I mainly encountered it via 17edo. The extensions to include prime 5 or prime 7 thus aren't very good, but it's a very nice 2.3.11.13 temperament and 17edo is pretty close to optimal for it IIRC.''

:::: ''*Edit: nope, I was wrong about the Orwell connection! 13-limit Orwell has a different mapping for 13. Lovecraft actually has no real relationship to Orwell except that both have moments of symmetry at 4, 9, and 13-note scales and are generated by a subminor 3rd tuned a bit sharp of 7/6. Lovecraft's 13-note MOS is 4L9s, while Orwell's is 9L4s. Huxley follows Lovecraft's MOS sequence. Gods, but I'm rusty at this stuff!''”

:::: They then went on to write a page for the wiki about Huxley:

:::: “''I have created a very rudimentary version of the page. I may come back and add more to it later, but probably not; the xenwiki is really not my project. TBH it's probably the most potentially-useful temperament that I personally discovered! It also works in 21edo where it more meaningfully extends to the full 13-limit and connects with Delorean temperament. But it's really better to leave prime 5 out of its extensions, IMO. Getting prime 7 into the mix is a lot easier and I'm actually kind of surprised I didn't include it when I named it originally. It maps so easily to -5 generators and that doesn't even increase the error all that much.''”

:::: This is about the best possible outcome I could have hoped for! A huge thank you to Deja and to everyone else who helped throughout this whole process. I’m glad this temperament won’t be lost to time.

:::: --[[User:BudjarnLambeth|BudjarnLambeth]] ([[User talk:BudjarnLambeth|talk]]) 03:45, 28 September 2024 (UTC)

@@ Line 34: / Line 34: @@
 : 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.
+:: 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.
+::: 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)
+:::: Adopting the definition (haplotonic) + (albitonic) = (chromatic) reinforces the position that they are a pair rather than a triple, because haplotonic is not necessarily the direct parent of albitonic, and multiple albitonic-chromatic pairs will share the same haplotonic. Extreme case: (1L)+(1L 2s)=(3L 1s), (1L)+(1L 6s)=(7L 1s), ... Known case: (2L 3s)+(5L 2s)=(5a 7b), (2L 3s)+(5L 7s)=(5a 12b), ...  --[[User:Dummy index|Dummy index]] ([[User talk:Dummy index|talk]]) 15:40, 18 November 2024 (UTC)
+:::: On Barton example, for the 5/7/9/11/13-note scale we are interested in, the equations to be taken up would be 2+5=7 or 2+7=9 or 2+9=11. In other words, Barton[2] is positioned as haplotonic. Why don't we call Barton[5] mini-albitonic? --[[User:Dummy index|Dummy index]] ([[User talk:Dummy index|talk]]) 13:11, 19 November 2024 (UTC)
+:::: If we take haplotonic roughly to mean "semitone-free MOS", then only Barton[2] can be haplotonic for Barton. --[[User:Dummy index|Dummy index]] ([[User talk:Dummy index|talk]]) 14:57, 20 November 2024 (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.
+== Huxley ==
+There are a lot of pages on the wiki that link to "Huxley". Based on what pages link there, I'm pretty sure Huxley is a temperament.
-: 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 way of naming them, although I am not sure how to do that.  [[User:CompactStar|CompactStar]] ([[User talk:CompactStar|talk]]) 01:06, 25 May 2023 (UTC)
+However, I am not sure what Huxley temperament is, whether or not it belongs on this page or a different page, or whether or not it is different from [[Lovecraft]]?
+I have searched every instance of the word "Huxley" on the wiki, and tried a bunch of different Google searches and queries in x31eq, but I just keep making myself more confused.
+If any of you know what Huxley temperament is, please create a page for it so I can educate myself. Thank you :)
+--[[User:BudjarnLambeth|BudjarnLambeth]] ([[User talk:BudjarnLambeth|talk]]) 09:11, 19 September 2024 (UTC)
+: Have you tried searching the Yahoo Groups tuning list archives? https://github.com/YahooTuningGroupsUltimateBackup/YahooTuningGroupsUltimateBackup --[[User:Cmloegcmluin|Cmloegcmluin]] ([[User talk:Cmloegcmluin|talk]]) 15:59, 19 September 2024 (UTC)
+:: Thank you for the recommendation, that was a very good idea. It will be a helpful resource when I'm looking for things in the future :)
+:: Unfortunately I couldn't find anything about Huxley temperament in any of the files (I used Spotlight to search them). I did find mentions of "Huxley", but they were all talking about his book, Brave New World, not about the temperament. --[[User:BudjarnLambeth|BudjarnLambeth]] ([[User talk:BudjarnLambeth|talk]]) 08:30, 20 September 2024 (UTC)
+::: Just an update to share with everyone. I'm continuing to research this. Here are some things that have been noted by people on the XA Facebook:
+::: '''Steve Martin''': "''Hi Bud, I can't find a definition of Huxley (it is not in Graham's database afaics), I'll look at the numbers when I get a chance. Orwell has 8/5 from 3 generators, and a 4s9L mos, whereas garibertet (not heard of it before) has 5/3 from 3 generators, and a 4L9s mos, so there are some differences.''"
+::: '''Ville-Pekka Turpeinen''': "''Judging by the name it appears to be riffing on Orwell by having a sharper 7/6 that gives 4/3 with six generators instead of Orwell's 7 generators of 3/2. According to Xen Wiki revision history, that name has been there as long as some pages have existed, which indicates that it comes from some earlier documentation that precedes the wiki itself.''"
+::: Also very noteworthy is this archived discussion on the wiki from 2011: [[Talk:Map of linear temperaments/WikispacesArchive#Lovecraft and Huxley]]. It seems that even by that point, what "Huxley" referred to exactly had been forgotten. But it does appear to be almost identical (or completely identical) to [[Lovecraft]]. But it might have been different in its mapping of 5 or 7 or something. Still gotta try to figure that out.
+::: --[[User:BudjarnLambeth|BudjarnLambeth]] ([[User talk:BudjarnLambeth|talk]]) 08:11, 24 September 2024 (UTC)
+:::: The original discoverer of Huxley temperament - [[Deja Igliashon]] - saw my post on Facebook, and said the following:
+:::: “''Hi Budjarn Lambeth, this temperament is one I discovered. It's an extension of Lovecraft, which is the 9&13 (edit: whoops, 4p&13p, not 9&13!) 2.11.13 subgroup temperament where two 13/11's stack to reach 11/8. Lovecraft itself is a restriction of 13-limit Orwell down to the 2.11.13 subgroup IIRC*. Huxley extends Lovecraft to add prime 3 in a different mapping than Orwell, specifically -6 generators. I mainly encountered it via 17edo. The extensions to include prime 5 or prime 7 thus aren't very good, but it's a very nice 2.3.11.13 temperament and 17edo is pretty close to optimal for it IIRC.''
+:::: ''*Edit: nope, I was wrong about the Orwell connection! 13-limit Orwell has a different mapping for 13. Lovecraft actually has no real relationship to Orwell except that both have moments of symmetry at 4, 9, and 13-note scales and are generated by a subminor 3rd tuned a bit sharp of 7/6. Lovecraft's 13-note MOS is 4L9s, while Orwell's is 9L4s. Huxley follows Lovecraft's MOS sequence. Gods, but I'm rusty at this stuff!''”
+:::: They then went on to write a page for the wiki about Huxley:
+:::: “''I have created a very rudimentary version of the page. I may come back and add more to it later, but probably not; the xenwiki is really not my project. TBH it's probably the most potentially-useful temperament that I personally discovered! It also works in 21edo where it more meaningfully extends to the full 13-limit and connects with Delorean temperament. But it's really better to leave prime 5 out of its extensions, IMO. Getting prime 7 into the mix is a lot easier and I'm actually kind of surprised I didn't include it when I named it originally. It maps so easily to -5 generators and that doesn't even increase the error all that much.''”
+:::: This is about the best possible outcome I could have hoped for! A huge thank you to Deja and to everyone else who helped throughout this whole process. I’m glad this temperament won’t be lost to time.
+:::: --[[User:BudjarnLambeth|BudjarnLambeth]] ([[User talk:BudjarnLambeth|talk]]) 03:45, 28 September 2024 (UTC)