Talk:Tenney–Euclidean tuning: Difference between revisions

← Older edit Newer edit →

VisualWikitext

@@ Line 133: / Line 133: @@
 ::: So we can name errors/tunings in this format:
 ::: '''([weight eponym](-weighted)(-)([norm eponym adjective](-normed))'''
-::: And if you use the word "weighted" or "normed" explicitly and the other term is present, you should use "weighted" or "normed" explicitly for that term too.
+::: And if you use the word "weighted" or "normed" explicitly and the other term is present, you should use "weighted" or "normed" explicitly for that term too ''(edit: I recognize that this bit is way less important and more of a stylistic suggestion)''.
 ::: I'll give some examples.
@@ Line 149: / Line 149: @@
 ::: - - Tenney-weighted tuning
 ::: - - Tenney-weighted-Minkowskian-normed tuning
-::: - '''not okay names:'''
+::: - <s>'''not okay names:'''</s> '''okay, but stylistically concerning names:''' ''(edit: per Flora's thoughts, these names are fine. My concerns are merely stylistic)''
 ::: - - Tenney-weighted-Minkowksian tuning
 ::: - - Tenney-Minkowskian-normed tuning
@@ Line 158: / Line 158: @@
 ::: - - Tenney-Euclidean tuning
 ::: - - Tenney-weighted-Euclidean-normed tuning
+::: - - Tenney-Euclidean-normed tuning ''(edit: as per later comment, "Tenney" can be used unbound from weight, as an adjective for divide-by-log-of-prime, so this one has been moved to the "okay" category)''
+::: - '''okay, but stylistically concerning names:'''
+::: - - Tenney-weighted-Euclidean tuning ''(edit: per Flora's thoughts, this name is fine. My concerns are merely stylistic)''
 ::: - '''not okay names:'''
-::: - - Tenney-weighted-Euclidean tuning
-::: - - Tenney-Euclidean-normed tuning
 ::: - - Tenney-Euclidean-weighted tuning
 ::: - - Tenney-normed-Euclidean tuning
@@ Line 176: / Line 177: @@
 :::: Woa your table is really enlightening! I mostly agree with you. As I figured "Tenney" was the weighting method and "Euclidean" was the norm method, on that basis I'd be more lax about calling them. I think Tenney-weighted-Euclidean tuning and Tenney-Euclidean-normed tuning are ok. [[User:FloraC|FloraC]] ([[User talk:FloraC|talk]]) 12:26, 27 January 2022 (UTC)
+::::: Nice! I'm glad it was helpful. And thanks for making the requested change. (Nice work on the Tenney height article yesterday, too).
+::::: You're right about "Tenney-weighted-Euclidean tuning". I realized that my recommendation against that type of name was way less important, merely a stylistic concern, so I made changes in my previous post here accordingly.
+::::: And I've moved "Tenney-Euclidean-normed" up into the completely okay category. I suggested it myself in my previous post but just didn't update my first post yet. I realized I have another way to explain why that one's okay. If you look at the Tenney-Euclidean error as <math>(eW)(i/||i||)</math> then that's a primes error map <math>e</math> with Tenney-weighted primes per the <math>W</math>, multiplied with <math>i/||i||</math> which could also be written <math>î</math> "i-hat", being the "normalized vector" or "unit vector" for the interval, specifically using the Euclidean norm. But we can group things a slightly different way, too: <math>(e)(Wi/||i||)</math>, in which case you've just got a plain old primes error map, but then the other thing you got is a ''Tenney-''Euclidean normed interval, because the <math>W</math> ("Tenney") matrix just has a diagonal of <math>1/log₂p</math>, so it puts stuff in the denominator along with that <math>||i||</math>, resulting in an interval essentially divided by its TE-height AKA TE-norm. So that's basically just a mathematical rendition of the fact I stated in the previous post that Tenney in our context simply means that <math>1/log₂p</math> thing, and is not necessarily bound to weight. --[[User:Cmloegcmluin|Cmloegcmluin]] ([[User talk:Cmloegcmluin|talk]]) 16:32, 27 January 2022 (UTC)