Talk:Sensipent family - Revision history

FloraC at 13:16, 29 September 2026

2026-09-29T13:16:12Z

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	::: FWIW, IMO there is no unique best extension of sensipent beyond the one from 2.3.5 to 2.3.5.31, that I know of at least. It'd have to not look strange relative to the 2.3.5.31 version if found. --[[User:Godtone\|Godtone]] ([[User talk:Godtone\|talk]]) 13:11, 29 September 2026 (UTC)		::: FWIW, IMO there is no unique best extension of sensipent beyond the one from 2.3.5 to 2.3.5.31, that I know of at least. It'd have to not look strange relative to the 2.3.5.31 version if found. --[[User:Godtone\|Godtone]] ([[User talk:Godtone\|talk]]) 13:11, 29 September 2026 (UTC)

			:::: Thank you for clarifying.

			:::: Tbh I'm okay either way, but the case for making it canon seems slightly stronger than not. My interpretation of the optimal ET sequence is that the big gap after 65 shows the optimum is essentially around 65, and those larger entries are only minor improvements in accuracy thus negligible. The main equal temps supporting 5-limit sensipent are 46, 65, and 84, as well as their sums, 111 and 149. All but 149 support this extension so it seems good enough to me.

			:::: Meanwhile, since I believe only the add-11 temps should be at the top, yet you insist whatever is canon should be, I figured: why not making sensible canon so that we can settle this for now?

			:::: —[[User:FloraC\|FloraC]] ([[User talk:FloraC\|talk]]) 13:16, 29 September 2026 (UTC)

Godtone at 13:11, 29 September 2026

2026-09-29T13:11:47Z

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	::: I thought you was saying 2.3.5.31 sensipent shouldn't be canon. --[[User:Godtone\|Godtone]] ([[User talk:Godtone\|talk]]) 13:10, 29 September 2026 (UTC)		::: I thought you was saying 2.3.5.31 sensipent shouldn't be canon. --[[User:Godtone\|Godtone]] ([[User talk:Godtone\|talk]]) 13:10, 29 September 2026 (UTC)

			::: FWIW, IMO there is no unique best extension of sensipent beyond the one from 2.3.5 to 2.3.5.31, that I know of at least. It'd have to not look strange relative to the 2.3.5.31 version if found. --[[User:Godtone\|Godtone]] ([[User talk:Godtone\|talk]]) 13:11, 29 September 2026 (UTC)

Godtone: clarify

2026-09-29T13:10:20Z

clarify

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	:: —[[User:FloraC\|FloraC]] ([[User talk:FloraC\|talk]]) 12:32, 29 September 2026 (UTC)		:: —[[User:FloraC\|FloraC]] ([[User talk:FloraC\|talk]]) 12:32, 29 September 2026 (UTC)

			::: I thought you was saying 2.3.5.31 sensipent shouldn't be canon. --[[User:Godtone\|Godtone]] ([[User talk:Godtone\|talk]]) 13:10, 29 September 2026 (UTC)

FloraC: /* Make sensible canon */

2026-09-29T12:32:29Z

Make sensible canon

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	: 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. --[[User:Godtone\|Godtone]] ([[User talk:Godtone\|talk]]) 11:19, 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. --[[User:Godtone\|Godtone]] ([[User talk:Godtone\|talk]]) 11:19, 29 September 2026 (UTC)

			:: I'm confused. You seem to suggest sensible should not be canon based on the optimal ET sequences, but in our DM, you said:

			:: > i see no reason for it to not qualify a sensible canon

			:: Could you clarify your exact take on this again?

			:: —[[User:FloraC\|FloraC]] ([[User talk:FloraC\|talk]]) 12:32, 29 September 2026 (UTC)

Godtone: /* Make sensible canon */ clarify and correct

2026-09-29T11:39:36Z

Make sensible canon: clarify and correct

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	—[[User:FloraC\|FloraC]] ([[User talk:FloraC\|talk]]) 08:28, 29 September 2026 (UTC)		—[[User:FloraC\|FloraC]] ([[User talk: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, ~~already~~ taking a different path after 65, 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. --[[User:Godtone\|Godtone]] ([[User talk:Godtone\|talk]]) 11:19, 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. --[[User:Godtone\|Godtone]] ([[User talk:Godtone\|talk]]) 11:19, 29 September 2026 (UTC)

Godtone: /* Make sensible canon */ correction, but in my defence these always looked very similar to me

2026-09-29T11:33:41Z

Make sensible canon: correction, but in my defence these always looked very similar to me

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	—[[User:FloraC\|FloraC]] ([[User talk:FloraC\|talk]]) 08:28, 29 September 2026 (UTC)		—[[User:FloraC\|FloraC]] ([[User talk: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 ''~~'''~~identical~~'''~~'' except it 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, already taking a different path after 65, 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. --[[User:Godtone\|Godtone]] ([[User talk:Godtone\|talk]]) 11:19, 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, already taking a different path after 65, 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. --[[User:Godtone\|Godtone]] ([[User talk:Godtone\|talk]]) 11:19, 29 September 2026 (UTC)

Godtone: /* Make sensible canon */ wrong val

2026-09-29T11:29:20Z

Make sensible canon: wrong val

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	—[[User:FloraC\|FloraC]] ([[User talk:FloraC\|talk]]) 08:28, 29 September 2026 (UTC)		—[[User:FloraC\|FloraC]] ([[User talk: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 '''''identical''''' except it adds ~~604c~~. 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, already taking a different path after 65, 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. --[[User:Godtone\|Godtone]] ([[User talk:Godtone\|talk]]) 11:19, 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 '''''identical''''' except it 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, already taking a different path after 65, 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. --[[User:Godtone\|Godtone]] ([[User talk:Godtone\|talk]]) 11:19, 29 September 2026 (UTC)

Godtone: /* Make sensible canon */ ?

2026-09-29T11:19:31Z

Make sensible canon: ?

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	—[[User:FloraC\|FloraC]] ([[User talk:FloraC\|talk]]) 08:28, 29 September 2026 (UTC)		—[[User:FloraC\|FloraC]] ([[User talk: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 '''''identical''''' except it adds 604c. 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, already taking a different path after 65, 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. --[[User:Godtone\|Godtone]] ([[User talk:Godtone\|talk]]) 11:19, 29 September 2026 (UTC)

FloraC at 08:28, 29 September 2026

2026-09-29T08:28:21Z

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	::::::::: Alright, thank you! —[[User:FloraC\|FloraC]] ([[User talk:FloraC\|talk]]) 01:54, 27 August 2026 (UTC)		::::::::: Alright, thank you! —[[User:FloraC\|FloraC]] ([[User talk: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)<sup>2</sup>⋅(16384/16335).

			—[[User:FloraC\|FloraC]] ([[User talk:FloraC\|talk]]) 08:28, 29 September 2026 (UTC)

FloraC at 01:54, 27 August 2026

2026-08-27T01:54:18Z

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	:::::::: 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. --[[User:Godtone\|Godtone]] ([[User talk:Godtone\|talk]]) 21:00, 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. --[[User:Godtone\|Godtone]] ([[User talk:Godtone\|talk]]) 21:00, 26 August 2026 (UTC)

			::::::::: Alright, thank you! —[[User:FloraC\|FloraC]] ([[User talk:FloraC\|talk]]) 01:54, 27 August 2026 (UTC)