Talk:Chromatic pairs: Difference between revisions

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::: 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)

== Huxley ==

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::: --[[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 38: / Line 38: @@
 ::: 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)
 == Huxley ==
@@ Line 65: / Line 68: @@
 ::: --[[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)