Talk:44edo: Difference between revisions

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:::::::::::: I don't get why you're calling what I say "circular reasoning". 44edo has 2 quite flat and 3 quite sharp prime harmonics in the range up to 13, of which the 7th harmonic is the one that sticks out the most, so it makes sense to toggle that one between flat and sharp as needed. [[User:Lucius Chiaraviglio|Lucius Chiaraviglio]] ([[User talk:Lucius Chiaraviglio|talk]]) 15:41, 11 May 2026 (UTC)

::::::::::::: > I don't get why you're calling what I say "circular reasoning".

::::::::::::: I've made it very clear. You said: "does it consider the use of alternate vals in combination, or only in isolation? If the latter, then it would not show the benefits of switching between flat 7 and sharp 7." You essentially need the temperament finder to consider the system dual-prime to justify doing so. That is circular reasoning.

::::::::::::: > 44edo has 2 quite flat and 3 quite sharp prime harmonics in the range up to 13, of which the 7th harmonic is the one that sticks out the most, …

::::::::::::: Let's not go in circles cuz Overthink and I have done a more comprehensive analysis. To summarize:

:::::::::::::# The interactions of harmonic 7 with most low harmonics favor the sharp mapping. These are 1, 3, 9, 13, 15, 17, and 19, vs 5 and 11. The sharpness of 3 in particular implies a sharp tendency, which the harmonic 7 follows.

:::::::::::::# In terms of monotonicity limits, 44 has 19 whereas 44d only 13, tuning 14/13 < 15/14.

:::::::::::::# In terms of TE errors, 44 < 44e < 44d in the 11- to 19-limit.

:::::::::::::# In terms of maximum errors, 44d's 9/7 is more than 100% off.

::::::::::::: I hope that helps.

::::::::::::: —[[User:FloraC|FloraC]] ([[User talk:FloraC|talk]]) 17:23, 11 May 2026 (UTC)

:::::::::::::: I was looking for a temperament that uses 44d (by way of 22/21 ~ 21/20), and mapped out some pretty good intervals it hits, and when I went down to the rank-2 temperaments table in the 44edo article, there it is: [[Nautilus]] (and if you map it as dual-7 rather than as strict 44d, some of the intervals get simpler mappings, like 7#/4).

:::::::::::::: Added: [[User:Lucius Chiaraviglio|Lucius Chiaraviglio]] ([[User talk:Lucius Chiaraviglio|talk]]) 15:02, 13 May 2026 (UTC)

:::::::::::::: Last modified: [[User:Lucius Chiaraviglio|Lucius Chiaraviglio]] ([[User talk:Lucius Chiaraviglio|talk]]) 15:24, 13 May 2026 (UTC)

@@ Line 35: / Line 35: @@
 :::::::::::: I don't get why you're calling what I say "circular reasoning".  44edo has 2 quite flat and 3 quite sharp prime harmonics in the range up to 13, of which the 7th harmonic is the one that sticks out the most, so it makes sense to toggle that one between flat and sharp as needed.  [[User:Lucius Chiaraviglio|Lucius Chiaraviglio]] ([[User talk:Lucius Chiaraviglio|talk]]) 15:41, 11 May 2026 (UTC)
+::::::::::::: > I don't get why you're calling what I say "circular reasoning".
+::::::::::::: I've made it very clear. You said: "does it consider the use of alternate vals in combination, or only in isolation? If the latter, then it would not show the benefits of switching between flat 7 and sharp 7." You essentially need the temperament finder to consider the system dual-prime to justify doing so. That is circular reasoning.
+::::::::::::: > 44edo has 2 quite flat and 3 quite sharp prime harmonics in the range up to 13, of which the 7th harmonic is the one that sticks out the most, …
+::::::::::::: Let's not go in circles cuz Overthink and I have done a more comprehensive analysis. To summarize:
+:::::::::::::# The interactions of harmonic 7 with most low harmonics favor the sharp mapping. These are 1, 3, 9, 13, 15, 17, and 19, vs 5 and 11. The sharpness of 3 in particular implies a sharp tendency, which the harmonic 7 follows.
+:::::::::::::# In terms of monotonicity limits, 44 has 19 whereas 44d only 13, tuning 14/13 < 15/14.
+:::::::::::::# In terms of TE errors, 44 < 44e < 44d in the 11- to 19-limit.
+:::::::::::::# In terms of maximum errors, 44d's 9/7 is more than 100% off.
+::::::::::::: I hope that helps.
+::::::::::::: —[[User:FloraC|FloraC]] ([[User talk:FloraC|talk]]) 17:23, 11 May 2026 (UTC)
+:::::::::::::: I was looking for a temperament that uses 44d (by way of 22/21 ~ 21/20), and mapped out some pretty good intervals it hits, and when I went down to the rank-2 temperaments table in the 44edo article, there it is:  [[Nautilus]] (and if you map it as dual-7 rather than as strict 44d, some of the intervals get simpler mappings, like 7#/4).
+:::::::::::::: Added:    [[User:Lucius Chiaraviglio|Lucius Chiaraviglio]] ([[User talk:Lucius Chiaraviglio|talk]]) 15:02, 13 May 2026 (UTC)
+:::::::::::::: Last modified:  [[User:Lucius Chiaraviglio|Lucius Chiaraviglio]] ([[User talk:Lucius Chiaraviglio|talk]]) 15:24, 13 May 2026 (UTC)