Talk:847/845: Difference between revisions

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:::: —[[User:FloraC|FloraC]] ([[User talk:FloraC|talk]]) 08:23, 22 May 2026 (UTC)

::::: I think I understand what you mean. Here's my attempt to formulate my logic more precisely: The 5.7.11.13 subgroup is musically significant; 847/845 plays an important role in that subgroup; this interval relationship is a relevant description of that role.

::::: The significance of the 5.7.11.13 subgroup is primarily due to its lack of primes 2 and 3, which play unique roles in traditional music and much of microtonal music. This forces the exploration of new harmony. (It is also significant in part because it strongly suggests tempering one comma above all others, much more than most subgroups do.)

::::: I believe I have already explained 847/845's importance in the 5.7.11.13 subgroup, but for what it's worth, sintel's temperament search is more quantitative. Searching for 5.7.11.13 rank-3 temperaments gives 847/845 with a badness of 0.58, and the second result has a badness of 1.25, more than double the first's. (For comparison, I did the same search in about 20% of the 125 other four-prime 23-limit subgroups, and found only one other similarly extreme comma: 325/323 in the 5.13.17.19 subgroup.) 847/845 is a very significant interval in a significant subgroup, which merits a description of its role in that subgroup.

::::: The small intervals present in a subgroup are relevant to the structure and use of that subgroup. In the 5.7.11.13 subgroup, there are four simple ones: 125/121 and 175/169; and 637/605 and 343/325. 637/625 (33¢) separates the pairs from each other, and 847/845 (4¢) separates the intervals within each pair. This is an important part of 847/845's role in the 5.7.11.13 subgroup, so it belongs on this page.

::::: [[User:Squib|Squib]] ([[User talk:Squib|talk]]) 02:14, 23 May 2026 (UTC)

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 :::: —[[User:FloraC|FloraC]] ([[User talk:FloraC|talk]]) 08:23, 22 May 2026 (UTC)
+::::: I think I understand what you mean. Here's my attempt to formulate my logic more precisely: The 5.7.11.13 subgroup is musically significant; 847/845 plays an important role in that subgroup; this interval relationship is a relevant description of that role.
+::::: The significance of the 5.7.11.13 subgroup is primarily due to its lack of primes 2 and 3, which play unique roles in traditional music and much of microtonal music. This forces the exploration of new harmony. (It is also significant in part because it strongly suggests tempering one comma above all others, much more than most subgroups do.)
+::::: I believe I have already explained 847/845's importance in the 5.7.11.13 subgroup, but for what it's worth, sintel's temperament search is more quantitative. Searching for 5.7.11.13 rank-3 temperaments gives 847/845 with a badness of 0.58, and the second result has a badness of 1.25, more than double the first's. (For comparison, I did the same search in about 20% of the 125 other four-prime 23-limit subgroups, and found only one other similarly extreme comma: 325/323 in the 5.13.17.19 subgroup.) 847/845 is a very significant interval in a significant subgroup, which merits a description of its role in that subgroup.
+::::: The small intervals present in a subgroup are relevant to the structure and use of that subgroup. In the 5.7.11.13 subgroup, there are four simple ones: 125/121 and 175/169; and 637/605 and 343/325. 637/625 (33¢) separates the pairs from each other, and 847/845 (4¢) separates the intervals within each pair. This is an important part of 847/845's role in the 5.7.11.13 subgroup, so it belongs on this page.
+::::: [[User:Squib|Squib]] ([[User talk:Squib|talk]]) 02:14, 23 May 2026 (UTC)