Talk:Minimal consistent EDOs: Difference between revisions
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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. | 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) | 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) | ||
: There should be an infinite number of EDOs with a higher consistency limit than distinct consistency limit, though I don't know anything about rarity of high consistency limits. You are right though 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 names are idiosyncratic here? == | ||
Revision as of 17:36, 10 September 2026
The limits of indistinct consistency
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? --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. Iywuqety (talk) 17:25, 21 November 2023 (UTC)
- There should be an infinite number of EDOs with a higher consistency limit than distinct consistency limit, though I don't know anything about rarity of high consistency limits. You are right though 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
efficient_edos( ivs, inconsistencies=0, min_simplifications=1, edos=range(1,1000) )in User:Godtone#My Python 3 code. --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)? --BudjarnLambeth (talk) 08:06, 9 September 2026 (UTC)