Talk:Sensipent family

Is 2.3.5.31 sensipent not accurate enough to be canonical?

I ask because the optimal ET sequence starts 8, 11c, 19, 46, 65 for both but 5-limit sensipent finishes with 539, 604c, 669c while 2.3.5.31 finishes with 344, 409, 474, 539, 604c, so both reach the constrained range implied by 539 and 604c. Also, it looked prettier and presented interesting information up-front in its previous form. Take a look at this diff. I certainly understand moving the sendai section but the 2.3.5.31 subgroup should rightly be categorised as an extension, no? --Godtone (talk) 23:18, 19 August 2026 (UTC)

It's canonical. Just that I decided that any subgroup temp that skips two or more primes should be placed at the bottom of the page, so that you see the 7-limit temps sooner and see the 2.3.5.11 and 2.3.5.7.11 temps both immediately at the H3 level:

== 2.3.5 ==
=== 2.3.5.11 ===
== 2.3.5.7 ==
=== 2.3.5.7.11 ===

—FloraC (talk) 07:55, 20 August 2026 (UTC)

If you agree a subgroup extension is canonical s.t there's no ambiguity (meaning it's unique among alternatives) then I believe it should be presented as such (as an extension proper, but with a subheader indicating it's a subgroup extension, as it was before). Furthermore, your reason seems backwards to me; shouldn't a subgroup extension that isn't in the increasing order of primes be prioritised at the very top, as it represents unique information? --Godtone (talk)

I believe subgroup extensions may be prioritized if they skip one prime. Any more than one, they tend to be esoteric, and there's not much logic to putting them at the top organizationally. Instead, the overview section should be expanded to inform the readers of a subgroup extensions section. —FloraC (talk) 16:04, 21 August 2026 (UTC)

It isn't an esoteric extension. It gives interpretation to the gen as ~40/31~31/24, which is an extremely accurate (S31 difference) harmonical interpretation of the sqrt(5/3) gen. It'd be easier to argue that the schismic extension to prime 41 is arbitrary due to the distance on the chain required to reach prime 41, although even that isn't that strange as it's via S81, so is good in any tuning with an accurate syntonic comma. --Godtone (talk) 16:55, 23 August 2026 (UTC)

It's esoteric cuz the subgroup is esoteric. —FloraC (talk) 03:48, 24 August 2026 (UTC)

It seems to me that this sense only serves to prioritise low-prime-limit temps with complete subgroups (which obviously did not need more prioritisation given that's the standard structure of the wiki), while shifting focus away from potentially significant unique opportunities (as judged by high accuracy, obvious mapping and completion of interpretations) in higher limits. for example, 5-limit diaschismic has an obvious subgroup extension to prime 17 which if not canonical is at least clearly relevant. And similarly, moving it to the end had the same effect ("shifting focus away from potentially significant unique opportunities (as judged by high accuracy, obvious mapping and completion of interpretations)"). I'd like for you to address this concern properly and solidly rather than reshifting focus on what you see as the best method of organisation. Did anyone other than you take issue with this organisation/motion towards what you suggested? --Godtone (talk) 16:11, 25 August 2026 (UTC)

I didn't came up with all the schemes. Subgroup extensions were originally completely separate from family/clan pages, or if they were in the same page, they were always at the bottom. See Meantone family as an example (I never moved any subgroup temp to the bottom in that page). I try to strike a balance by prioritizing subgroups that skip one prime, which covers a significant part of practical cases and makes organizational sense. I believe you should work on the theory of the subgroups themselves if you want more ppl to recognize your work cuz it's baseless to consider the so-called potentially significant unique opportunities otherwise. —FloraC (talk) 07:58, 26 August 2026 (UTC)

Oh nvm, I noticed there's a short discussion under a bolded Subgroup extensions: section that mentions the extensions, so I'm satisfied with this compromise, as I was worried that there would be no mention at all of the subgroup extensions relative to the head temp. --Godtone (talk) 21:00, 26 August 2026 (UTC)

Alright, thank you! —FloraC (talk) 01:54, 27 August 2026 (UTC)

Make sensible canon

The recent changes have made this page an organizational hell. I think one way to remedy it is to simplify these extensions and in particular I think sensible qualifies as the canonical extension of sensipent. Reasons:

• Significance of the subgroup: 2.3.5.11, as compared to 2.3.5.31.
• Precedence: despite being lower-accuracy, 2.3.5.11-subgroup würschmidt is established as canon, from its support by "core" equal temps 31, 34, and 65. The situation with sensible is similar. We can thus avoid the fuss of dealing with 2.3.5.31 separately.
• Practicality: 5-limit sensipent is basically optimal at 65edo (111 (= 46 + 65) and 149 (= 65 + 84) aren't more accurate than 65). Support by 46, 65, and 84 is also significant. These in combination make sensible the single sensible extension to use.
• Factorization: 78732/78125 = (6912/6875)⋅(8019/8000) = (8019/8000)²⋅(16384/16335).

—FloraC (talk) 08:28, 29 September 2026 (UTC)

The optimal ET sequence of sensipent (2.3.5.31) is 8, 11c, 19, 46, 65, 344, 409, 474, 539, 604c. The optimal ET sequence of the 5-limit version is near-identical except it has fewer vals in the hundreds; it misses 344, 409 and 474 but adds 669c. It occurs to me based on this fact, the extreme similarity in optimal tunings (being in fact slightly more constrained when adding prime 31) and the significant reduction in badness that it clearly is a great candidate for canonical extension, given the property of finding the sqrt(5/3) gen as sqrt(16/15) above 5/4 and sqrt(16/15) below 4/3, hence 32/31~31/30 and hence the gen's interpretation as spanning 5/3 with the chord 24:31:40, via 40/24 = 5/3. Furthermore, the optimal ET sequence of sensible is wildly different: 19, 46, 65, 111, 176g, taking a clearly different path after 65 as opposed to omitting some vals (as is common in optimal ET sequences of canonical extensions), and introducing a warted and final val early of 176g. I also must admit that I created sensible specifically because of taking issue with the inaccuracy of the 2.3.5.7.13 subgroup, but seeing potential in the temperament in higher limits that supported 5-limit sensi (hence the naming inspiration), so that the subgroup was to some degree opportunistic based on what worked; prime 29 is essentially the only prime that doesn't fit in sensible, and the primes 7 and 13 can fit only if you admit significant damage. --Godtone (talk) 11:19, 29 September 2026 (UTC)