User:FloraC/Temperament extension issues

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A list of issues with temperament extensions.

Open issues

Rank-2 temperaments

Alphatrident

7-limit → 11-limit

11-limit alphatrident should be decanonicalized. 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:

Dicot

5-limit → 7-limit

7-limit dicot should be decanonicalized. 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: pending community reaction.

Diminished

7-limit → 11-limit

11-limit diminished should be decanonicalized. It flips the optimal tuning from flat to sharp of just.

Proposed solution:

Keemun

11-limit → 13-limit

13-limit keemun should be decanonicalized. Kema, which maps prime 13 to +14 steps, is the right extension to use, as in all kleismic temperaments.

Proposed solution:

Pajara

11-limit → 13-limit

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

Proposed solution:

Parakleismic

7-limit → 11-limit

11-limit parakleismic should be decanonicalized. 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:

Secund

11-limit → 13-limit

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

Proposed solution:

Tertiaseptal

7-limit → 11-limit

11-limit tertiaseptal should be decanonicalized. 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. Tertia and tertiaseptia are bad-tasted names so we might wanna reconsider these names too.

Proposed solution:

Schismatic family

Various dubious extensions. Will eventually collect them and add to the talk page.

Tetracot family

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

Rank-3 temperaments

Agni

11-limit → 13-limit

13-limit agni should be decanonicalized. There's no reason to favor 31 & 72 over 41 & 72.

Proposed solution:

Artemis

11-limit → 13-limit

13-limit artemis should be decanonicalized, 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 decanonicalized. See the case with artemis.

Proposed solution:

Closed issues

Rank-2 temperaments

Augmented/augene

5-limit → 7-limit

7-limit augene should be canonicalized while 13-limit augene should be decanonicalized. 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.

Ennealimmal

7-limit → 11-limit → 13-limit

11-limit ennealimmal should be decanonicalized. Further, 13-limit ennealimmal should be decanonicalized 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 undistinguishable. 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 decanonicalized. 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 decanonicalized. 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 decanonicalized. 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 decanonicalized. 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 decanonicalized. 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 decanonicalized. 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.

Rank-3 temperaments

Aphrodite

11-limit → 13-limit

13-limit aphrodite should be decanonicalized. 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 canonicalized. 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 decanonicalized. 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 decanonicalized. 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 decanonicalized. Thrush is a better extension.

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