User:FloraC/Temperament extension issues

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A list of issues with temperament extensions.

Preliminaries

Objectives

"It's just labeling mathematical objects." I hear you say.

The goal is to make the scope of a temp name more coherent so that you need less modification and explanation to the names you use, ultimately to facilitate exploring the space of useful ideas and to reduce the friction in the communication of these ideas.

Terms

Segment

For rank-2 temps, refers to a tuning range of an extension, often bounded by equal temps. Segments often zigzag, i.e., the tuning of the added element changes direction as the tuning of the generator crosses a boundary, entering the range of another extension. A central segment is a range, among many, that takes the middle part of the original tuning range, and thus is most fit for a canonical extension.

Other notes

• The equal-temperament joins used here imply tuning ranges.

Open issues

Rank-2 temperaments

Alphatrident

7-limit → 11-limit

11-limit alphatrident should be decanonized. The tuning is not very representative of 7-limit alphatrident. Specifically, alphatrident has three 11-limit extensions: 176 & 229, 229 & 282, and 282 & 335d. The first and last are supported by 53 which means they are simpler, but they are not representative of the 7-limit optimum. The middle one is representative of the 7-limit optimum, but is very complex. Therefore, the situation is similar to slendric, where none of the extensions should be canon.

Proposed solution:

Chlorine

7-limit → 11-limit

11-limit chlorine should be decanonized. The 612 & 935 extension isn't more complex (with the same Graham complexity in the 11-odd-limit) but is way more accurate.

Proposed solution:

Diminished

7-limit → 11-limit

11-limit diminished should be decanonized. While it's natural to temper out 99/98 and 100/99 as a jubilismic temperament, the 36/35 (= S8⋅S9) in the comma list makes this less accurate since we're equating 8/7~10/9 with 11/10. Besides, it flips the optimal tuning from flat to sharp of just. Diminished could arguably be more naturally defined on 2.3.5.7.17.19.

Proposed solution: 11-limit diminished → diminutive. Status: pending community reactions.

Gammic

7-limit → 11-limit

11-limit gammic should be decanonized. It's a low-accuracy extension.

Proposed solution:

Grendel

11-limit → 13-limit

13-limit grendel should be decanonized. The tuning is not very representative of 11-limit grendel. Specifically, grendel has three 13-limit extensions: 121 & 152f, 152f & 183, and 183 & 214. The first and last are supported by 31 which means they are simpler, but they are not representative of the 11-limit optimum. The middle one is representative of the 11-limit optimum, but somewhat more complex than the last. Therefore, the situation is similar to slendric, where none of the extensions should be canon.

Proposed solution:

Hemiwürschmidt

11-limit → 13-limit

13-limit hemiwürschmidt should be decanonized. While the 11-limit extension is a significant drop in accuracy, it doesn't shift the optimum too much (from between 99 and 130 to somewhere near 130, as 291 (= 130 + 161) isn't more accurate), and it can be reasoned based on it using the same mapping as the 2.3.5.11-subgroup version of würschmidt, the latter of which is supported by the "core" equal temps, 31, 34 and 65. The 13-limit version is where the shift of optimum becomes qualitative difference and the 31 and 99e vals are both questionable anyway.

Proposed solution:

Keemun

11-limit → 13-limit

13-limit keemun should be decanonized. Kema, which maps 15/13 to the hemifourth (and hence prime 13 to +14 steps), is the right extension to use, as in all kleismic temperaments and all semaphoresmic temperaments. Besides, kema's equal-temperament join is 15 & 19, while the currently canonical 13-limit extension is 15f & 19, and 15 is better than 15f. Kema is additionally supported by patent 34, while the currently canonical extension uses the much less accurate 34f. The mapping of prime 13 to -5 generators is inaccurate and in the opposite direction compared to primes 3, 5, and 7, making other intervals of 13 more complex.

Kema and kumbaya are etymologically unrelated to keemun, so it seems okay to rename the currently canonical 13-limit keemun to something unrelated too.

Proposed solution: 13-limit keemun → kimah. Kema → 13-limit keemun. Status: pending community reactions.

Lunatic

7-limit → 11-limit

11-limit lunatic should be decanonized. Lunatic has at least three extensions: 205 & 323, 323 & 441, and 441 & 559. Perhaps, the canonicity of 441 & 559 could be argued on the basis that the 7-limit optimum is very close to 441; however, compared to the good efficiency and portability of the 7-limit temperament, this 11-limit extension is pretty mid.

Proposed solution:

Maquila

5-limit → 7-limit

7-limit maquila should be decanonized, or alternatively the 5-limit restriction should. In either case, it's a low-accuracy, high-badness extension that uses the dual-7 65edo.

Proposed solution:

Neptune

7-limit → 11-limit

11-limit neptune should be decanonized. It's a low-accuracy extension. Neptune is also described as a 2.3.5.7.17-subgroup temperament, which is more natural. However, the 2.3.5.7.17.31-subgroup extension is a significant drop in accuracy, so that one should at least be dual-named, like triceneptune.

Proposed solution:

Pajara

11-limit → 13-limit

13-limit pajara should be decanonized. It's way too inaccurate. Pajara should be a no-13 17-limit temperament.

Proposed solution: 13-limit pajara → paja. Status: pending community reactions.

Parakleismic

7-limit → 11-limit

11-limit parakleismic should be decanonized. Extending parakleismic to the 11- and 13-limit is complicated, mainly cuz both 99edo and 118edo have ambiguous interpretations, but paralytic (99e & 118) is the "main" extension here, since septimal parakleismic is really an interpolation between 99 and 118, with 217 giving a good middle ground. Note that 217 is more accurate than both 99 and 118 in the 7-limit, showing that the optimum isn't very near 99. Paralytic uses the 19e val, which is reasonable, and the other extensions zigzag around this segment: 80 & 99e, called paradigmic, 118 & 137d, which is our "undecimal parakleismic" tho the optimum is sharp of 87\118, making it 99 & 118, and finally 61de & 80, called parkleismic, tho the optimum is flat of 59\80, making it 80 & 99.

Paralytic has four notable 13-limit extensions: 99ef & 118, 99e & 118, 99ef & 118f, and 99e & 118f. Note that 99e & 118 and 99ef & 118f are the more accurate ones, supported by 217, and the other two are less accurate, but use the simpler 19e-form in the 13-limit. The 13-odd-limit Graham complexities of 99e & 118 and 99ef & 118f are 157 and 142, respectively, showing that 99e & 118 isn't simpler than 99ef & 118f; thus 13-limit paralytic needs a distinct name too.

Paradigmic has two notable 13-limit extensions: 80 & 99e and 80 & 99ef, and like above, 80 & 99e is the simpler 19-form whereas 80 & 99ef is more accurate. 80 & 99ef also supports 13-limit parapyth, which is an extra point. It follows that 13-limit paradigmic needs a distinct name too.

Proposed solution:

Sengagen

11-limit → 13-limit

13-limit sengagen should be decanonized. The 49f & 50 extension, which maps prime 13 to +35 steps, is simpler as all the other primes are positive (Graham complexity 58 vs 73), and nearly as accurate, compared to the currently canonical extension. This should be very clear in the badness values, where the difference is significant. But more importantly, 49f and 50 show a duality: 50 tunes 11/9 a step wider than 27/22, and 49f tunes 39/32 a step wider than 16/13, both due to the vanishment of 144/143, and then 99ef is where they all converge to the true neutral third. In this sense, 49f & 50 is the result of applying a consistent logic to primes 11 and 13, so should be more natural than 49 & 50.

Proposed solution: 13-limit sengagen → sengageny; sengage → 13-limit sengagen. Status: pending community reactions.

Spell

11-limit → 13-limit

13-limit spell should be decanonized. Cantrip, which maps 15/13 to the hemifourth (and hence prime 13 to +17 steps), is the right extension to use, as in all semaphoresmic temperaments. Besides, cantrip's equal-temperament join is 19 & 25e, which makes more sense than whatever the currently canonical extension is.

Proposed solution: 13-limit spell → spellcraft; cantrip → 13-limit spell. Status: pending community reactions.

Tertiaseptal

7-limit → 11-limit

11-limit tertiaseptal should be decanonized. Tertiaseptal has three 11-limit extensions: 109 & 140, 140 & 171, and 171 & 202. Perhaps, the canonicity of 171 & 202 could be argued on the basis that the 7-limit optimum is very close to 171; however, compared to the absolute supremacy of the 7-limit temperament, this 11-limit extension is plain bad. Tertiaseptal is also described as a no-11 13- and 17-limit temperament, which further justifies the change.

Currently, the other 11-limit extensions are called tertia and tertiaseptia, which, despite the confusing form (sounds like commas rather than temps), suggests that the extension 171 & 202 might be septia.

Proposed solution: 11-limit tertiaseptal → septia. Status: pending community reactions.

Wesley

5-limit → 7-limit

7-limit wesley should be decanonized. The tuning is not very representative of 5-limit wesley. Roman (26 & 29) is most representative, even tho it's a little more complex.

Proposed solution:

Würschmidt

5-limit → 7-limit

7-limit würschmidt should be decanonized. Almost all the notable supporting equal temperaments are dual-7: 34, 65, 96, and 127, and that speaks something about it. Würschmidt is also described as a 2.3.5.11.(23)-subgroup temperament, which is more natural.

Proposed solution:

Schismatic family

Various dubious extensions. See Talk: Schismatic family #Extensions. Pending public reactions.

Tetracot family

Various dubious extensions to the 17-limit. See Talk: Tetracot family #17- and 19-limit extensions. Pending public reactions.

Rank-3 temperaments

Artemis

11-limit → 13-limit

13-limit artemis should be decanonized, as diana is a very competitive extension. This is a series of awkward cases related to orwell, which doesn't have a simple and accurate 13-limit extension, but since the more accurate one, 31 & 53, was dubbed tridecimal orwell over the simpler 22f & 31, these rank-3 temperaments should not be utterly at odds with that. Related temperaments include guanyin and zeus, both go with the 31 & 53 path.

Proposed solution:

Big brother

11-limit → 13-limit

13-limit big brother should be decanonized. See the case with artemis.

Proposed solution:

Freya

11-limit → 13-limit

13-limit freya should be decanonized. 11-limit freya has three extensions: 31 & 41 & 270, 31 & 72 & 270, and 41 & 72 & 270. 31 & 41 & 270 is a pretty neutral choice, but is also the least efficient out of all three.

Proposed solution:

Closed issues

Rank-2 temperaments

Augmented/augene

5-limit → 7-limit

7-limit augene should be canonized while 13-limit augene should be decanonized. Tempering out 126/125 is natural for diaschismic, augmented and diminished, and since both diaschismic and diminished have canonical 7-limit extensions, so should augmented (even tho septimal diaschismic is essentially grandfathered in). Furthermore, the 11-limit extension should remain as canon, for the 11-odd-limit diamond monotone range is the same as 9-odd-limit. The name augene may remain as an alias for this temperament, but the 13-limit extension should eventually have its name changed cuz that one is much worse.

Proposed solution: 7-, 11-, and 13-limit augene → augmented (augene). Status: changed.

Dicot

5-limit → 7-limit

7-limit dicot should be decanonized. It has been clear that it's difficult to discuss these as a single temperament. The 7-limit extension is in fact the best extension of 2.3.7-subgroup {54/49} (in the same way beep is the best extension of bug), known as mujannabic, so it may inherit that name.

Proposed solution: 7- and 11-limit dicot → mujannabic. Status: changed.

Ennealimmal

7-limit → 11-limit → 13-limit

11-limit ennealimmal should be decanonized. Further, 13-limit ennealimmal should be decanonized with respect to the 11-limit to make way for the other extension to be canon. Compared to the absolute supremacy of the 7-limit temperament, the 11-limit is mid, and the 13-limit is just utterly wrong. This should be obvious from the badness values and the optimal GPV sequences, but also the Graham complexities: 225 for 99e & 171e vs 189 for 99ef & 171ef.

The names of the ennealimmal extensions demonstrate an absolute devoidness of creativity. The same morpheme combination ennealimma is re-used again and again, making all the extension names almost indistinguishable. Therefore I believe in rectifying these names we should inject new morphemes into the scene, while keeping the ennea- part to remind users of their relations. 11-limit ennealimmal (99e & 171e) tempers out the symbiotic comma, so it can be called enneabiotic. Further, since 13-limit 99e & 171e is the worse extension, it can be enneabio. The other high-accuracy 11-limit extension, 99 & 171, tempers out the olympic comma, so it can be called ennealympic. Ennealimnic and ennealiminal were named earlier so I think they can stay.

Semiennealimmal is extremely misleading. It tempers out the pine comma so it can be ennealimmapine. This name is a little long but the temp itself isn't very notable anyway.

Proposed solution: 11-limit ennealimmal, 13-limit ennealimmalis → enneabiotic; 13-, 17-, 19-limit ennealimmal → enneabio; ennealimmia → ennealympic; semiennealimmal → ennealimmapine. Status: changed.

Hendecatonic

7-limit → 11-limit

11-limit hendecatonic should be decanonized. It's not better than 22 & 99e, known as cohendecatonic.

Proposed solution: 11-, 13- and 17-limit hendecatonic → hendecaton. Status: changed.

Ketchup

17-limit → 19-limit

19-limit ketchup should be decanonized. Ketchup should be a no-19 23-limit temperament.

Proposed solution: replace 19- and 23-limit ketchup with no-19 23-limit. Status: changed.

Leapday

17-limit → 19-limit

19-limit leapday should be decanonized. Leapday should be a no-19 23-limit temperament.

Proposed solution: replace 19- and 23-limit leapday and leapling with no-19 23-limit leapday. Status: changed.

Magus

7-limit → 5-limit

5-limit magus should be decanonized. The 5-limit temperament's optimum is between 43edo and 46edo, which corresponds to the tuning range of amigo (43 & 46), not magus (46 & 49).

Proposed solution: 5-limit magus → amigo. Status: suspended.

Misty

7-limit → 11-limit

11-limit misty should be decanonized. Misty is more naturally a 2.3.5.7.17.19-subgroup temperament. Besides, 99 & 111, 99ef & 111, and 87 & 99 are all competitive extensions. Proposing these extensions as murky (87 & 99ef), smoky (87 & 99), hazy (99 & 111), and ashy (99ef & 111).

Proposed solution: 11-, 13-, 17-, and 19-limit misty → murky, delete mystic (87 & 99e). Status: changed.

Nessafof

7-limit → 11-limit

11-limit nessafof should be decanonized. Extending nessafof to the 11-limit is complicated since both 84edo and 99edo have ambiguous interpretations (see the case with parakleismic). Currently we have catalogued the two low-complexity 15-form extensions, which makes sense. One is being called nessa so the other may simply be fof.

Proposed solution: 11-limit nessafof → fof. Status: changed.

Secund

11-limit → 13-limit

13-limit secund should be decanonized, for the other extension is obviously way better.

Proposed solution: delete 13-limit secund. Secundly → 13-limit secund. Status: changed.

Rank-3 temperaments

Agni

11-limit → 13-limit

13-limit agni should be decanonized. There's no reason to favor 31 & 72 over 41 & 72, even tho the latter has a little higher badness. Proposing to rename it to pavaka, after another name of Agni.

Proposed solution: 13-limit agni → pavaka. Status: changed.

Aphrodite

11-limit → 13-limit

13-limit aphrodite should be decanonized. It's the worst of the four catalogued extensions. Eros is perhaps the best extension, and based on that, it would make sense to name the other extensions after the Erotes (Eros, Anteros, Himeros, Pothos). However, the other extensions are named after the equivalent deities of Aphrodite in other mythologies, so if we follow that pattern, the temperament in question may be named astarte, after Phoenician goddess Astarte.

Proposed solution: 13-limit aphrodite → astarte. Status: changed.

Jubilismic/jubilee

7-limit → 11-limit

Jubilee should be canonized. This is obvious. We should spare the name jubilee for the 2.5.7-subgroup temp, mirroring semaphore.

Proposed solution: 11-limit jubilee → jubilismic; 2.5.7-subgroup jubilic → jubilee. Status: changed/suspended.

Laka

13-limit → 17-limit

17-limit laka should be decanonized. Laka should be a no-17 19-limit temperament.

Proposed solution: delete 17-limit laka. Status: changed.

Marvel

11-limit → 13-limit

13-limit marvel should be decanonized. Hecate is a very competitive extension, and based on that one could consider naming the temperament in question after Greek deities such as Helios, Hebe, Hermes, or Hephaestus.

Proposed solution: 13-limit marvel → helios. Status: changed.

Starling

7-limit → 11-limit

11-limit starling should be decanonized. Thrush is a better extension.

Proposed solution: undecimal starling → starnova. Status: changed.