Talk:Minimal consistent EDOs

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)

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 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)

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

Thank you FloraC :) --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. Currywurst44 (talk) 17:15, 23 September 2026 (UTC)

Changes applied Currywurst44 (talk) 21:26, 23 September 2026 (UTC)