Talk:Meantone: Difference between revisions

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::: Yes, excluding compton extensions, fifthspan +30 is the 11-limit extension with the lowest logflat badness (it's 0.0649609 gene smith tenney-euclidean badness, or 2.1475667 dirichlet badness). Similarly, my 13-limit extension with 3/1 at +39 generators is the 13-limit extension with the lowest logflat badness (0.0494043 smith TE, 2.0414469 dirichlet), excluding compton extensions. This 13-limit extension is supported by [[67edo]] unwarted; however, if you would like to get rid of the warts on 12edo and 55edo, [https://sintel.pythonanywhere.com/result?edos=12+%26+55&submit_edo=submit&subgroup=2.3.5.7.11.13 12 & 55] is an option, though it has much higher [[complexity]] and [[logflat badness]] because the 13/1 is reached with -28 fifths rather than a positive number of generators (and thus it cannot be played in otonal chords involving 7 and 11 without the use of the 67-note and larger MOS scales). [[User:Recentlymaterialized|Recentlymaterialized]] ([[User talk:Recentlymaterialized|talk]]) 16:03, 6 January 2025 (UTC)

:::: Those are some monster-high Badness values, for sure. But I went to the [[Lumatone mapping for 55edo]], and although I am not a Lumatone player, while the finger stretches with the Bosanquet layout look extremely awkward, the finger positionings with the 6L 1s layout actually look quite doable (or only mildly awkward) even for somebody with average hands, although I'll admit to having not yet analyzed more than a couple of chords that would include 11/8 and/or 13/8 (only had time for just a cursory inspection so far). Haven't seen a [[Lumatone mapping for 67edo]] yet, but since Bosanquet isn't going to work for this anyway, maybe whatever layout somebody eventually does come up (this won't even be the highest EDO with a Lumatone mapping, by a longshot) with will have those intervals be usable as well [[User:Lucius Chiaraviglio|Lucius Chiaraviglio]] ([[User talk:Lucius Chiaraviglio|talk]]) 20:25, 6 January 2025 (UTC)

Revision as of 16:03, 6 January 2025 view source Recentlymaterialized (talk \| contribs) 237 edits No edit summary ← Older edit		Revision as of 20:25, 6 January 2025 view source Lucius Chiaraviglio (talk \| contribs) 1,167 edits →Unlisted strong 7-limit Meantone extension (provisional name Mildtone)?: High-Badness, but still reasonably playable? Newer edit →
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	::: Yes, excluding compton extensions, fifthspan +30 is the 11-limit extension with the lowest logflat badness (it's 0.0649609 gene smith tenney-euclidean badness, or 2.1475667 dirichlet badness). Similarly, my 13-limit extension with 3/1 at +39 generators is the 13-limit extension with the lowest logflat badness (0.0494043 smith TE, 2.0414469 dirichlet), excluding compton extensions. This 13-limit extension is supported by [[67edo]] unwarted; however, if you would like to get rid of the warts on 12edo and 55edo, [https://sintel.pythonanywhere.com/result?edos=12+%26+55&submit_edo=submit&subgroup=2.3.5.7.11.13 12 & 55] is an option, though it has much higher [[complexity]] and [[logflat badness]] because the 13/1 is reached with -28 fifths rather than a positive number of generators (and thus it cannot be played in otonal chords involving 7 and 11 without the use of the 67-note and larger MOS scales). [[User:Recentlymaterialized\|Recentlymaterialized]] ([[User talk:Recentlymaterialized\|talk]]) 16:03, 6 January 2025 (UTC)		::: Yes, excluding compton extensions, fifthspan +30 is the 11-limit extension with the lowest logflat badness (it's 0.0649609 gene smith tenney-euclidean badness, or 2.1475667 dirichlet badness). Similarly, my 13-limit extension with 3/1 at +39 generators is the 13-limit extension with the lowest logflat badness (0.0494043 smith TE, 2.0414469 dirichlet), excluding compton extensions. This 13-limit extension is supported by [[67edo]] unwarted; however, if you would like to get rid of the warts on 12edo and 55edo, [https://sintel.pythonanywhere.com/result?edos=12+%26+55&submit_edo=submit&subgroup=2.3.5.7.11.13 12 & 55] is an option, though it has much higher [[complexity]] and [[logflat badness]] because the 13/1 is reached with -28 fifths rather than a positive number of generators (and thus it cannot be played in otonal chords involving 7 and 11 without the use of the 67-note and larger MOS scales). [[User:Recentlymaterialized\|Recentlymaterialized]] ([[User talk:Recentlymaterialized\|talk]]) 16:03, 6 January 2025 (UTC)

			:::: Those are some monster-high Badness values, for sure. But I went to the [[Lumatone mapping for 55edo]], and although I am not a Lumatone player, while the finger stretches with the Bosanquet layout look extremely awkward, the finger positionings with the 6L 1s layout actually look quite doable (or only mildly awkward) even for somebody with average hands, although I'll admit to having not yet analyzed more than a couple of chords that would include 11/8 and/or 13/8 (only had time for just a cursory inspection so far). Haven't seen a [[Lumatone mapping for 67edo]] yet, but since Bosanquet isn't going to work for this anyway, maybe whatever layout somebody eventually does come up (this won't even be the highest EDO with a Lumatone mapping, by a longshot) with will have those intervals be usable as well [[User:Lucius Chiaraviglio\|Lucius Chiaraviglio]] ([[User talk:Lucius Chiaraviglio\|talk]]) 20:25, 6 January 2025 (UTC)