Talk:Consistency

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About Terminology

Hey, Inthar, I must admit that I'm having trouble seeing terminology such as "minimal consistent EDOs" and "maximal consistent set" as being correct, seeing as I'm a native English speaker. I would think such terms would be better written as "minimally consistent EDOs" and "maximally consistent set". In addition, I'd sooner see the term "move" rather than "walk away" in the phrase "a chord is consistent to distance d in an edo, if the chord is consistent and you can "walk away" up to distance d from the chord consistently," seeing as "walk away" doesn't sound quite right. The trouble is that fixing some of these involves moving a page, and I don't have the permission to do that. --Aura (talk) 20:53, 20 January 2021 (UTC)

I changed the wording to move. I wish regular users could move pages without leaving redirects. Inthar (talk) 21:05, 20 January 2021 (UTC)

Thanks. I must point out, however, that this permissions business seems to have a lot to to with preventing vandalism. --Aura (talk) 21:06, 20 January 2021 (UTC)

I don't see what would be bad about leaving redirects when renaming. This way users who have the pages saved in their bookmarks can find them even after a rename. --Xenwolf (talk) 23:32, 20 January 2021 (UTC)

On the definition of consistency to distance d

I really like the concept and it's something I was thinking about before in my theoretical investigations into the approximative capabilities of EDOs of interest to me. However, I don't understand why the definition of consistency to distance d isn't just the maximum step error of all intervals being less than 1/(2d), because this would allow picking a multiset of any d intervals within a chord and multiplying them together and having the result be consistent, including picking one interval d times. I strongly suggest this alternative definition for the sake of simplicity, intuitiveness and ease of understanding.
(It also means "consistency to distance 1/2" can be seen as guaranteeing - at worst - a second-best mapping of an interval, and that consistency to distance k as k approaches 0 implies infinite inconsistency, thus representing ever-weaker consistency, and ultimately, no consistency, as you can't move anywhere without being inconsistent, AKA you can move 0 distance while being consistent.) --Godtone (talk) 04:20, 22 January 2021 (UTC)

Not going to lie, I'm somewhat against this proposed alternative definition at this point because I'm not settling for second-best mappings in when it comes to the definition of things like telicity. Perhaps if this definition can meet the strict requirements behind my idea of telicity, then I can get behind this idea. --Aura (talk) 06:11, 22 January 2021 (UTC)

Assimilate or Occupy?

I have the impression that this article originally tried to explain consistency in odd-limit-diamonds. I'm not sure if it's a good idea to occupy the term for a different concept. Would it be possible to share the term and turn the article into an overview of different concepts of consistency? If the answer is yes, then this approach should also be reflected in the introduction. As soon as these concepts need more space than a section, we can add dedicated articles with unique names. --Xenwolf (talk) 20:51, 22 January 2021 (UTC)

From what I gather, Inthar's second concept integrated the original concept into it. That said, I think it really is possible to share the term and turn the article into an overview of different concepts of consistency. --Aura (talk) 20:53, 22 January 2021 (UTC)

Now that I'm thinking about it, I think you should talk to Inthar to see just how these two concepts of consistency are related, and if it really turns out that I was right about Inthar's second concept being an expansion on the original, well, I'll let you two decide how to handle things from there. That said, I should mention that the different concepts of consistency need to be disambiguated in some way, even though they share this same article. --Aura (talk) 21:02, 22 January 2021 (UTC)

My new definition of consistency (to distance 0) just reformulates the term to be applicable to chords, rather than sets of notes not viewed as a chord. By my definition of chord consistency, an edo approximates chord C consistently iff it is consistent in S (according to the old definition) where S = diamond(C) where C is viewed as a set of notes from tonic. Inthar (talk) 22:51, 22 January 2021 (UTC)