Talk:39edo - Revision history

Overthink: /* 39 isn't a dual-7 edo */ alright

2026-06-04T20:02:10Z

39 isn't a dual-7 edo: alright

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	:: —[[User:FloraC\|FloraC]] ([[User talk:FloraC\|talk]]) 13:28, 3 June 2026 (UTC)		:: —[[User:FloraC\|FloraC]] ([[User talk:FloraC\|talk]]) 13:28, 3 June 2026 (UTC)

			::: Seems like an okay solution, worth a try. --[[User:Overthink\|Overthink]] ([[User talk:Overthink\|talk]]) 20:02, 4 June 2026 (UTC)

	: I have no opinion on 39et in particular, but I will agree that "patentness" is a completely arbitrary quality and the procedure of rounding is merely heuristic to get something that usually works. – [[User:Sintel\|Sintel🎏]] ([[User_talk:Sintel\|talk]]) 19:47, 30 May 2026 (UTC)		: I have no opinion on 39et in particular, but I will agree that "patentness" is a completely arbitrary quality and the procedure of rounding is merely heuristic to get something that usually works. – [[User:Sintel\|Sintel🎏]] ([[User_talk:Sintel\|talk]]) 19:47, 30 May 2026 (UTC)

FloraC: /* 39 isn't a dual-7 edo */ +++

2026-06-03T13:29:15Z

39 isn't a dual-7 edo: +++

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	:: —[[User:FloraC\|FloraC]] ([[User talk:FloraC\|talk]]) 20:30, 30 May 2026 (UTC)		:: —[[User:FloraC\|FloraC]] ([[User talk:FloraC\|talk]]) 20:30, 30 May 2026 (UTC)

			:: So, as I'm editing the table for a 39c column, I've realized 39c isn't significantly better than 39. In light of this, I propose two tables. First for 39d as we had before (plus primes 13 and 19 via 39df), and a second table for a comparison on various other mappings: 39 in 2.25.35.11, 39c, 39, and 39d. This will cater to more demands than ever. Those who don't think of 39 as a dual-prime system get their cleaner table, and those who do get their table too.

			:: —[[User:FloraC\|FloraC]] ([[User talk:FloraC\|talk]]) 13:28, 3 June 2026 (UTC)

	: I have no opinion on 39et in particular, but I will agree that "patentness" is a completely arbitrary quality and the procedure of rounding is merely heuristic to get something that usually works. – [[User:Sintel\|Sintel🎏]] ([[User_talk:Sintel\|talk]]) 19:47, 30 May 2026 (UTC)		: I have no opinion on 39et in particular, but I will agree that "patentness" is a completely arbitrary quality and the procedure of rounding is merely heuristic to get something that usually works. – [[User:Sintel\|Sintel🎏]] ([[User_talk:Sintel\|talk]]) 19:47, 30 May 2026 (UTC)

FloraC at 11:06, 3 June 2026

2026-06-03T11:06:22Z

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	:: I agree with Overthink on this front. At the very least, the patent val should be given in the interval table, and it should probably be discussed in other parts of the page, but I recognize 39d as a legitimate interpretation as well. Most people looking for an edo to use don't really care about TE either. -- [[User:VectorGraphics\|VectorGraphics]] ([[User talk:VectorGraphics\|talk]]) 10:12, 3 June 2026 (UTC)		:: I agree with Overthink on this front. At the very least, the patent val should be given in the interval table, and it should probably be discussed in other parts of the page, but I recognize 39d as a legitimate interpretation as well. Most people looking for an edo to use don't really care about TE either. -- [[User:VectorGraphics\|VectorGraphics]] ([[User talk:VectorGraphics\|talk]]) 10:12, 3 June 2026 (UTC)

			::: > I agree with Overthink on this front. […]

			::: This is not a poll. Address my points and back your own points with reasoning.

			::: > Most people looking for an edo to use don't really care about TE either.

			::: You don't have to "care about TE" to see why 39d is clearly the best val. I showed three aspects for it, only one of which deals with TE errors, so my other two aspects still stand. TE errors here are but a math model to quantify the general observation that 39d is the most accurate mapping, considerably more so than the second place, and that 39 patent isn't necessarily the second place.

			::: —[[User:FloraC\|FloraC]] ([[User talk:FloraC\|talk]]) 11:05, 3 June 2026 (UTC)

	:: That sounds very sensible — put my vote in for that as well. [[User:Lucius Chiaraviglio\|Lucius Chiaraviglio]] ([[User talk:Lucius Chiaraviglio\|talk]]) 18:36, 30 May 2026 (UTC)		:: That sounds very sensible — put my vote in for that as well. [[User:Lucius Chiaraviglio\|Lucius Chiaraviglio]] ([[User talk:Lucius Chiaraviglio\|talk]]) 18:36, 30 May 2026 (UTC)

VectorGraphics at 10:12, 3 June 2026

2026-06-03T10:12:18Z

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	: Overall, I think 39 and 39d should have about equal coverage, with structures in both presented. The page definitely should explain how 39d improves accuracy of many intervals, and it should be up to the reader to decide which perspective they agree with, and which mapping to use. --[[User:Overthink\|Overthink]] ([[User talk:Overthink\|talk]]) 17:08, 30 May 2026 (UTC)		: Overall, I think 39 and 39d should have about equal coverage, with structures in both presented. The page definitely should explain how 39d improves accuracy of many intervals, and it should be up to the reader to decide which perspective they agree with, and which mapping to use. --[[User:Overthink\|Overthink]] ([[User talk:Overthink\|talk]]) 17:08, 30 May 2026 (UTC)

			:: I agree with Overthink on this front. At the very least, the patent val should be given in the interval table, and it should probably be discussed in other parts of the page, but I recognize 39d as a legitimate interpretation as well. Most people looking for an edo to use don't really care about TE either. -- [[User:VectorGraphics\|VectorGraphics]] ([[User talk:VectorGraphics\|talk]]) 10:12, 3 June 2026 (UTC)
	:: That sounds very sensible — put my vote in for that as well. [[User:Lucius Chiaraviglio\|Lucius Chiaraviglio]] ([[User talk:Lucius Chiaraviglio\|talk]]) 18:36, 30 May 2026 (UTC)		:: That sounds very sensible — put my vote in for that as well. [[User:Lucius Chiaraviglio\|Lucius Chiaraviglio]] ([[User talk:Lucius Chiaraviglio\|talk]]) 18:36, 30 May 2026 (UTC)

FloraC: /* 39 isn't a dual-7 edo */ re

2026-05-30T20:30:39Z

39 isn't a dual-7 edo: re

← Older revision		Revision as of 20:30, 30 May 2026
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	:: That sounds very sensible — put my vote in for that as well. [[User:Lucius Chiaraviglio\|Lucius Chiaraviglio]] ([[User talk:Lucius Chiaraviglio\|talk]]) 18:36, 30 May 2026 (UTC)		:: That sounds very sensible — put my vote in for that as well. [[User:Lucius Chiaraviglio\|Lucius Chiaraviglio]] ([[User talk:Lucius Chiaraviglio\|talk]]) 18:36, 30 May 2026 (UTC)


			:: > Not everyone agrees that more accurate necessarily means "better", and that patent vals are completely arbitrary.

			:: That's why I need these ppl to hear me out.

			:: > The patent val isn't completely uninteresting, supporting structures like immunity and triforce.

			:: I think it's less interesting than 39c. I think Leri has made a case for 39d vs 39c, so dual-5 dual-7, which is more acceptable than dual-7 alone. I should add that the prime 17 in 39c doesn't really work given it tunes 17/16 < 18/17, and that 39d might benefit more from a 19 than 13 tho I don't really mind 39df. I also think 2.3.25.35.11 is too sparse a subgroup to be interesting. Overall I'm willing to take the compromise of two columns, one based on 39d and the other based on 39c, with the patent val deducible from them.

			:: —[[User:FloraC\|FloraC]] ([[User talk:FloraC\|talk]]) 20:30, 30 May 2026 (UTC)

	: I have no opinion on 39et in particular, but I will agree that "patentness" is a completely arbitrary quality and the procedure of rounding is merely heuristic to get something that usually works. – [[User:Sintel\|Sintel🎏]] ([[User_talk:Sintel\|talk]]) 19:47, 30 May 2026 (UTC)		: I have no opinion on 39et in particular, but I will agree that "patentness" is a completely arbitrary quality and the procedure of rounding is merely heuristic to get something that usually works. – [[User:Sintel\|Sintel🎏]] ([[User_talk:Sintel\|talk]]) 19:47, 30 May 2026 (UTC)

Sintel at 19:47, 30 May 2026

2026-05-30T19:47:57Z

← Older revision		Revision as of 19:47, 30 May 2026
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	:: That sounds very sensible — put my vote in for that as well. [[User:Lucius Chiaraviglio\|Lucius Chiaraviglio]] ([[User talk:Lucius Chiaraviglio\|talk]]) 18:36, 30 May 2026 (UTC)		:: That sounds very sensible — put my vote in for that as well. [[User:Lucius Chiaraviglio\|Lucius Chiaraviglio]] ([[User talk:Lucius Chiaraviglio\|talk]]) 18:36, 30 May 2026 (UTC)

			: I have no opinion on 39et in particular, but I will agree that "patentness" is a completely arbitrary quality and the procedure of rounding is merely heuristic to get something that usually works. – [[User:Sintel\|Sintel🎏]] ([[User_talk:Sintel\|talk]]) 19:47, 30 May 2026 (UTC)

Lucius Chiaraviglio: /* 39 isn't a dual-7 edo */ Coverage of alternative vals

2026-05-30T18:36:39Z

39 isn't a dual-7 edo: Coverage of alternative vals

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	: Overall, I think 39 and 39d should have about equal coverage, with structures in both presented. The page definitely should explain how 39d improves accuracy of many intervals, and it should be up to the reader to decide which perspective they agree with, and which mapping to use. --[[User:Overthink\|Overthink]] ([[User talk:Overthink\|talk]]) 17:08, 30 May 2026 (UTC)		: Overall, I think 39 and 39d should have about equal coverage, with structures in both presented. The page definitely should explain how 39d improves accuracy of many intervals, and it should be up to the reader to decide which perspective they agree with, and which mapping to use. --[[User:Overthink\|Overthink]] ([[User talk:Overthink\|talk]]) 17:08, 30 May 2026 (UTC)

			:: That sounds very sensible — put my vote in for that as well. [[User:Lucius Chiaraviglio\|Lucius Chiaraviglio]] ([[User talk:Lucius Chiaraviglio\|talk]]) 18:36, 30 May 2026 (UTC)

Overthink: /* 39 isn't a dual-7 edo */Reply

2026-05-30T17:08:53Z

39 isn't a dual-7 edo: Reply

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	—[[User:FloraC\|FloraC]] ([[User talk:FloraC\|talk]]) 21:51, 29 May 2026 (UTC)		—[[User:FloraC\|FloraC]] ([[User talk:FloraC\|talk]]) 21:51, 29 May 2026 (UTC)

			: Overall, I agree that 39d feels more natural to use. However, the wiki is supposed to present info from a neutral point of view rather than pushing a perspective. Not everyone agrees that more accurate necessarily means "better", and that patent vals are completely arbitrary. People often think of the octave as the equivalence interval, so they want to keep it pure. The pure-octave patent val with prime harmonics as basis entries feels like the most natural mapping to use for many people, even if it is less accurate overall. The patent val isn't completely uninteresting, supporting structures like immunity and triforce. 39edo is a medium-sized edo, and someone who uses it very much may not be focused on accuracy.

			: Overall, I think 39 and 39d should have about equal coverage, with structures in both presented. The page definitely should explain how 39d improves accuracy of many intervals, and it should be up to the reader to decide which perspective they agree with, and which mapping to use. --[[User:Overthink\|Overthink]] ([[User talk:Overthink\|talk]]) 17:08, 30 May 2026 (UTC)

FloraC at 21:51, 29 May 2026

2026-05-29T21:51:35Z

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	: Also, when you added the second table you added an extra line between the templates, which makes them more spaced apart than they should be. --[[User:Overthink\|Overthink]] ([[User talk:Overthink\|talk]]) 03:57, 2 April 2026 (UTC)		: Also, when you added the second table you added an extra line between the templates, which makes them more spaced apart than they should be. --[[User:Overthink\|Overthink]] ([[User talk:Overthink\|talk]]) 03:57, 2 April 2026 (UTC)

			== 39 isn't a dual-7 edo ==
			39d is clearly the best val up to the 11-limit and 39 patent should not be put in the interval table as a competing column (39df might be considered as the 13-limit mapping tho that's besides the point), for mostly the same reason 44d should not as I showed in Talk: 44edo.

			To be clear, the question of a dual-prime edo concerns whether two mappings are nearly equally valid. If one mapping is considerably more accurate, it is hard for one to hear the other mapping as a valid approximation to the same set of intervals, since their presence in the same tuning system means the difference in quality is highlighted thru contrast. As such, for many edo articles we present a main mapping most useful for composition. This mapping is discussed at length in the theory section and put in the interval table. The distinction of a main mapping and various ancillary mappings is a consistent feature of edo articles on this wiki.

			The ancillary mappings can also be used, and may be interesting for various reasons. I think they deserve to be discussed briefly in the theory section. However, we can't afford to put whatever we think is potentially or marginally useful in the interval table, cuz human readers have limited attention resource and wish to spend it on the best things. A less valid mapping in the interval table means divided attention and less efficiency of presenting information.

			For example, in 145edo, there is this short sentence discussing the utility of a less accurate mapping: "The 145c val provides a tuning for magic which is nearly identical to the POTE tuning." But the main mapping is discussed in the rest of the article.

			The reasons that 39d commends itself as the main mapping are mostly the same as that for 44. Specifically:
			* The sharp 3, 5, 11 justifies the sharp 7. The interactions of 7 with 3, 5, 9, 11, and 15 all favor the sharp mapping. Iow 7 itself is the only inconsistently mapped interval in the 11-limit 15-odd-limit. While this is also true for 34edo, which is treated as dual-7, 39edo differs from 34edo in that the other primes and especially the 5 are very sharp, which brings us to …
			* With the flat 7, the 7/5 will have 93% error and the 15/14 will have ''112%'' error, whereas with the sharp 7, the maximum error comes from 7 itself, only 51%.
			* TE error for 39d: 2.43 cents; 39dee: 3.13 cents; 39: 3.79 cents. Note that 39dee has a lower error than 39, so if 39dee isn't reasonable to consider, neither is 39 logically.

			The only difference here is that the flat-7 mapping is a patent val. On that account one might argue that the mapping is of some special importance. I think the value of patentness has been overstated in the community at large. What we mean by a patent val is really using the closest approximation for the basis elements, but basis elements can change. For example, many ppl consider 5/3 and/or 7/6 to be as important in composition as 5/4 and 7/4, and one can generate the 7-limit with 2, 3, 5/3, and 7/6. In this basis, the patent val for 39edo isn't the same as the one found for 2, 3, 5, and 7. In fact it's the sharp-7 mapping. That reveals the lack of unique significance of patent vals in practice (and in math, as every GPV is demonstrably patent in some way); as such the importance of a mapping solely from being a patent val in this specific case is baseless from a broader perspective.

			—[[User:FloraC\|FloraC]] ([[User talk:FloraC\|talk]]) 21:51, 29 May 2026 (UTC)

Overthink: /* 39dfgijk */ add on

2026-04-02T03:57:58Z

39dfgijk: add on

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	: Octave compression certainly makes the higher harmonics more accurate, though one needs to be careful about intervals with many powers of 2 (and also 11, since it loses accuracy at that level of compression). A second row won't do too much harm, so I guess adding it back is fine. [[User:Overthink\|Overthink]] ([[User talk:Overthink\|talk]]) 03:54, 2 April 2026 (UTC)		: Octave compression certainly makes the higher harmonics more accurate, though one needs to be careful about intervals with many powers of 2 (and also 11, since it loses accuracy at that level of compression). A second row won't do too much harm, so I guess adding it back is fine. [[User:Overthink\|Overthink]] ([[User talk:Overthink\|talk]]) 03:54, 2 April 2026 (UTC)

			: Also, when you added the second table you added an extra line between the templates, which makes them more spaced apart than they should be. --[[User:Overthink\|Overthink]] ([[User talk:Overthink\|talk]]) 03:57, 2 April 2026 (UTC)

← Older revision		Revision as of 20:02, 4 June 2026
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	:: —[[User:FloraC\|FloraC]] ([[User talk:FloraC\|talk]]) 13:28, 3 June 2026 (UTC)		:: —[[User:FloraC\|FloraC]] ([[User talk:FloraC\|talk]]) 13:28, 3 June 2026 (UTC)

			::: Seems like an okay solution, worth a try. --[[User:Overthink\|Overthink]] ([[User talk:Overthink\|talk]]) 20:02, 4 June 2026 (UTC)

	: I have no opinion on 39et in particular, but I will agree that "patentness" is a completely arbitrary quality and the procedure of rounding is merely heuristic to get something that usually works. – [[User:Sintel\|Sintel🎏]] ([[User_talk:Sintel\|talk]]) 19:47, 30 May 2026 (UTC)		: I have no opinion on 39et in particular, but I will agree that "patentness" is a completely arbitrary quality and the procedure of rounding is merely heuristic to get something that usually works. – [[User:Sintel\|Sintel🎏]] ([[User_talk:Sintel\|talk]]) 19:47, 30 May 2026 (UTC)

← Older revision		Revision as of 10:12, 3 June 2026
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	: Overall, I think 39 and 39d should have about equal coverage, with structures in both presented. The page definitely should explain how 39d improves accuracy of many intervals, and it should be up to the reader to decide which perspective they agree with, and which mapping to use. --[[User:Overthink\|Overthink]] ([[User talk:Overthink\|talk]]) 17:08, 30 May 2026 (UTC)		: Overall, I think 39 and 39d should have about equal coverage, with structures in both presented. The page definitely should explain how 39d improves accuracy of many intervals, and it should be up to the reader to decide which perspective they agree with, and which mapping to use. --[[User:Overthink\|Overthink]] ([[User talk:Overthink\|talk]]) 17:08, 30 May 2026 (UTC)

			:: I agree with Overthink on this front. At the very least, the patent val should be given in the interval table, and it should probably be discussed in other parts of the page, but I recognize 39d as a legitimate interpretation as well. Most people looking for an edo to use don't really care about TE either. -- [[User:VectorGraphics\|VectorGraphics]] ([[User talk:VectorGraphics\|talk]]) 10:12, 3 June 2026 (UTC)
	:: That sounds very sensible — put my vote in for that as well. [[User:Lucius Chiaraviglio\|Lucius Chiaraviglio]] ([[User talk:Lucius Chiaraviglio\|talk]]) 18:36, 30 May 2026 (UTC)		:: That sounds very sensible — put my vote in for that as well. [[User:Lucius Chiaraviglio\|Lucius Chiaraviglio]] ([[User talk:Lucius Chiaraviglio\|talk]]) 18:36, 30 May 2026 (UTC)