Talk:Sensipent family: Difference between revisions

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—[[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)

:: 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)

::: 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)

:::: 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)

@@ Line 38: / Line 38: @@
 —[[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)
+:: 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)
+::: 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)
+:::: 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)