Talk:39edo: Difference between revisions

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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)

== 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)

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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)
+== 39 isn't a dual-7 edo ==
+d 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)