Talk:Minimal consistent EDOs: Difference between revisions

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I note that all the edos here that are 5 digits or above have the same consistency and distinct consistency, as the number of steps to define different intervals increases faster than their ability to all line up in a well-tuned way. This implies that the number of edos that have a consistency greater than their distinct consistency is probably a finite number. Has anyone calculated what that number is and the highest edo that does this? --[[User:Yourmusic Productions|Yourmusic Productions]] ([[User talk:Yourmusic Productions|talk]]) 15:31, 13 October 2022 (UTC)

I am not aware of any handy formula to calculate the consistency or distinct consistency of edos. However, after flipping through individual edo pages, I managed to gather 34 edos (<400) which have greater consistency than distinct consistency limits:

1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 12, 15, 16, 18, 19, 22, 26, 27, 29, 31, 41, 46, 50, 58, 72, 80, 87, 94, 111, 121, 217, 282, 311, 388.

Despite the lack of mathematical verification, I doubt there are any more such edos. [[User:Iwuqety|Iywuqety]] ([[User talk:Iwuqety|talk]]) 17:25, 21 November 2023 (UTC)

: You are right that a high consistency limit may not be achievable until a very large EDO, thus always requiring distinct consistency (at least after a certain point) if the minimum EDO needed is large enough. Therefore, you have potentially made a valuable observation: there is a finite number of EDOs that are ''not'' distinctly consistent for a given odd-limit (or more generally, a set of target intervals). Based on this idea I added the function {{nowrap| <code>efficient_edos( ivs, inconsistencies{{=}}0, min_simplifications{{=}}1, edos{{=}}range(1,1000) )</code> }} in {{nowrap| [[User:Godtone#My Python 3 code]]. }} {{nowrap| --[[User:Godtone|Godtone]] ([[User talk:Godtone|talk]]) 17:35, 10 September 2026 (UTC) }}

== Which names are idiosyncratic here? ==

Which of the terms on this page are 'mainstream' and which ones are 'idiosyncratic' (and who are the terms attributed to)? --[[User:BudjarnLambeth|BudjarnLambeth]] ([[User talk:BudjarnLambeth|talk]]) 08:06, 9 September 2026 (UTC)

: User: ArrowHead294 coined the idiosyncratic term ''purely consistent''. —[[User:FloraC|FloraC]] ([[User talk:FloraC|talk]]) 08:46, 9 September 2026 (UTC)

:: Thank you FloraC :) --[[User:BudjarnLambeth|BudjarnLambeth]] ([[User talk:BudjarnLambeth|talk]]) 22:29, 10 September 2026 (UTC)

== Link first mention of each edo in every collumn ==

It is slightly unintuitive having to check all collumns instead of only the one you are interested in to find the link. Was the edit done in an automated way? Otherwise I will change it when I have time. [[User:Currywurst44|Currywurst44]] ([[User talk:Currywurst44|talk]]) 17:15, 23 September 2026 (UTC)

: Changes applied [[User:Currywurst44|Currywurst44]] ([[User talk:Currywurst44|talk]]) 21:26, 23 September 2026 (UTC)

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 I note that all the edos here that are 5 digits or above have the same consistency and distinct consistency, as the number of steps to define different intervals increases faster than their ability to all line up in a well-tuned way. This implies that the number of edos that have a consistency greater than their distinct consistency is probably a finite number. Has anyone calculated what that number is and the highest edo that does this? --[[User:Yourmusic Productions|Yourmusic Productions]] ([[User talk:Yourmusic Productions|talk]]) 15:31, 13 October 2022 (UTC)
+I am not aware of any handy formula to calculate the consistency or distinct consistency of edos. However, after flipping through individual edo pages, I managed to gather 34 edos (<400) which have greater consistency than distinct consistency limits:
+, 2, 3, 4, 5, 6, 7, 8, 9, 10, 12, 15, 16, 18, 19, 22, 26, 27, 29, 31, 41, 46, 50, 58, 72, 80, 87, 94, 111, 121, 217, 282, 311, 388.
+Despite the lack of mathematical verification, I doubt there are any more such edos. [[User:Iwuqety|Iywuqety]] ([[User talk:Iwuqety|talk]]) 17:25, 21 November 2023 (UTC)
+: You are right that a high consistency limit may not be achievable until a very large EDO, thus always requiring distinct consistency (at least after a certain point) if the minimum EDO needed is large enough. Therefore, you have potentially made a valuable observation: there is a finite number of EDOs that are ''not'' distinctly consistent for a given odd-limit (or more generally, a set of target intervals). Based on this idea I added the function {{nowrap| <code>efficient_edos( ivs, inconsistencies{{=}}0, min_simplifications{{=}}1, edos{{=}}range(1,1000) )</code> }} in {{nowrap| [[User:Godtone#My Python 3 code]]. }} {{nowrap| --[[User:Godtone|Godtone]] ([[User talk:Godtone|talk]]) 17:35, 10 September 2026 (UTC) }}
+== Which names are idiosyncratic here? ==
+Which of the terms on this page are 'mainstream' and which ones are 'idiosyncratic' (and who are the terms attributed to)? --[[User:BudjarnLambeth|BudjarnLambeth]] ([[User talk:BudjarnLambeth|talk]]) 08:06, 9 September 2026 (UTC)
+: User: ArrowHead294 coined the idiosyncratic term ''purely consistent''. —[[User:FloraC|FloraC]] ([[User talk:FloraC|talk]]) 08:46, 9 September 2026 (UTC)
+:: Thank you FloraC :) --[[User:BudjarnLambeth|BudjarnLambeth]] ([[User talk:BudjarnLambeth|talk]]) 22:29, 10 September 2026 (UTC)
+== Link first mention of each edo in every collumn ==
+It is slightly unintuitive having to check all collumns instead of only the one you are interested in to find the link. Was the edit done in an automated way? Otherwise I will change it when I have time. [[User:Currywurst44|Currywurst44]] ([[User talk:Currywurst44|talk]]) 17:15, 23 September 2026 (UTC)
+: Changes applied [[User:Currywurst44|Currywurst44]] ([[User talk:Currywurst44|talk]]) 21:26, 23 September 2026 (UTC)