Xenharmonic Wiki

Talk:Marvel: Difference between revisions

← Older editNewer edit →
VisualWikitext
Godtone (talk | contribs)
autopatrolled, emailconfirmed
2,289 edits
add reasonings based on decreasing error of odd-limits rather than consistency
Godtone (talk | contribs)
autopatrolled, emailconfirmed
2,289 edits
corrections (missed odd 27 due to manual/non-algorithmic traversal)
Line 61: Line 61:


<syntaxhighlight lang="python">
<syntaxhighlight lang="python">
>>> [k for k in range(15,125,2) if len(fact_int(k))<=4]
>>> odds = [k for k in range(1,125,2) if len(fact_int(k))<=4]
[15, 21, 25, 27, 35, 45, 49, 63, 75, 81, 105]
>>> odds
>>> optimal_edo_sequence({1,3,5,7,9},[edo for edo in range(1,312) if pval(S(15),ed(edo))==0])
[1, 3, 5, 7, 9, 15, 21, 25, 27, 35, 45, 49, 63, 75, 81, 105]
[2, 9, 10, 12, 19, 31, 41, 53, 72, 125, 166]
>>> for i in range(3,len(odds)): # 0th odd is 1, 1st odd is 3, 2nd odd is 5, 3rd odd is 7
>>> optimal_edo_sequence({1,3,5,7,9,15},[edo for edo in range(1,312) if pval(S(15),ed(edo))==0])
...  print('7-limited '+str(odds[i])+'-odd-limit:',optimal_edo_sequence(odds[:i+1],[edo for edo in range(1,312) if pval(S(15),ed(edo))==0]))
[2, 9, 10, 12, 19, 22, 31, 41, 53, 72, 125, 166]
...
>>> optimal_edo_sequence({1,3,5,7,9,15,21},[edo for edo in range(1,312) if pval(S(15),ed(edo))==0])
7-limited 7-odd-limit: [2, 9, 10, 12, 19, 22, 31, 72, 103, 175, 228]
[2, 9, 10, 12, 19, 22, 29, 31, 41, 72, 113, 125, 166, 197]
7-limited 9-odd-limit: [2, 9, 10, 12, 19, 31, 41, 53, 72, 125, 166]
>>> optimal_edo_sequence({1,3,5,7,9,15,21,25},[edo for edo in range(1,312) if pval(S(15),ed(edo))==0])
7-limited 15-odd-limit: [2, 9, 10, 12, 19, 22, 31, 41, 53, 72, 125, 166]
[2, 9, 10, 12, 19, 31, 53, 72, 84, 156, 240]
7-limited 21-odd-limit: [2, 9, 10, 12, 19, 22, 29, 31, 41, 72, 113, 125, 166, 197]
>>> optimal_edo_sequence({1,3,5,7,9,15,21,25,35},[edo for edo in range(1,312) if pval(S(15),ed(edo))==0])
7-limited 25-odd-limit: [2, 9, 10, 12, 19, 31, 53, 72, 84, 156, 240]
[2, 9, 10, 12, 19, 22, 31, 53, 72, 84, 103, 156]
7-limited 27-odd-limit: [2, 9, 10, 12, 19, 31, 41, 53, 72, 125, 197, 281]
>>> optimal_edo_sequence({1,3,5,7,9,15,21,25,35,45},[edo for edo in range(1,312) if pval(S(15),ed(edo))==0])
7-limited 35-odd-limit: [2, 9, 10, 12, 19, 31, 41, 53, 72, 125]
[2, 9, 10, 12, 19, 22, 31, 53, 72, 84, 125, 156, 281]
7-limited 45-odd-limit: [2, 9, 10, 12, 19, 31, 41, 53, 72, 125]
>>> optimal_edo_sequence({1,3,5,7,9,15,21,25,35,45,49},[edo for edo in range(1,312) if pval(S(15),ed(edo))==0])
7-limited 49-odd-limit: [2, 9, 10, 12, 19, 22, 31, 41, 72, 197]
[2, 9, 10, 19, 22, 31, 72, 103, 175, 228] # 49 is bad in 53
7-limited 63-odd-limit: [2, 9, 10, 12, 19, 22, 31, 41, 72, 197]
>>> optimal_edo_sequence({1,3,5,7,9,15,21,25,35,45,49,63},[edo for edo in range(1,312) if pval(S(15),ed(edo))==0])
7-limited 75-odd-limit: [2, 9, 10, 12, 19, 22, 31, 41, 72, 197]
[2, 9, 10, 12, 19, 22, 31, 41, 72, 156, 197] # 63 is not much better
7-limited 81-odd-limit: [2, 9, 10, 12, 19, 31, 41, 53, 72, 113, 166]
>>> optimal_edo_sequence({1,3,5,7,9,15,21,25,35,45,49,63,75},[edo for edo in range(1,312) if pval(S(15),ed(edo))==0])
7-limited 105-odd-limit: [2, 9, 10, 12, 19, 22, 31, 41, 53, 72, 113, 125, 166]
[2, 9, 10, 12, 19, 22, 29, 31, 41, 72, 156, 197, 228] # 75 is okay in 53 so it starts to recover
>>> optimal_edo_sequence({1,3,5,7,9,15,21,25,35,45,49,63,75,81},[edo for edo in range(1,312) if pval(S(15),ed(edo))==0])
[2, 9, 10, 12, 19, 31, 41, 53, 72, 113, 166] # 81 is very good in 53, so it recovers fully here
>>> optimal_edo_sequence({1,3,5,7,9,15,21,25,35,45,49,63,75,81,105},[edo for edo in range(1,312) if pval(S(15),ed(edo))==0])
[2, 9, 10, 12, 19, 22, 31, 41, 53, 72, 113, 125, 166]
</syntaxhighlight>
</syntaxhighlight>
Notice that we haven't put any constraints on over- or undertempering and 53edo still shows up everywhere except the 7-limited 49-, 63- and 75-odd-limit. 31 shows up everywhere simply by absence of good enough smaller competitors. 41edo takes a big enough hit from the overflat 25 that it doesn't recover until the 7-limited 63-odd-limit. By comparison, 125edo recovers faster from the hit from the flat 25. I also want to point out that 240edo is not only obviously way too many notes for marvel but also only appears a single time! I really doubt that 240edo is optimal in any meaningful sense. 197edo at least appears more frequently but still pretty rarely. By contrast, [[156edo]] is apparently overlooked as a large edo marvel tuning, apppearing 5 times (7-limited odd-limits 25 thru 75 except for 49). 125edo and 166edo at least seem to agree with however you derived them being optimal. 84edo isn't so bad either because we know it satisfies the strict requirements, and it appears in the 7-limited 25- thru 45- odd-limits (and more generally, it appears in the <code>optimal_edo_sequence</code> for all full odd-limits 23 thru 51 and appears in the <code>strict_optimal_edo_sequence</code> (meaning identical except instead based on relative error instead of absolute, so that the list is a strict subset) for a lot of those too.
Notice that we haven't put any constraints on tempering or consistency (other than tempering out 225/224 by patent val) and 53edo still shows up everywhere except the 7-limited 49-, 63- and 75-odd-limit. 31 shows up everywhere simply by absence of good enough smaller competitors; same with 41edo though it disappears from the 7-limited 25-odd-limit due to the overflat 25. 72edo is very good as it appears everywhere. I also want to point out that 240edo is not only arguably too many notes for marvel but also only appears a single time! I really doubt that 240edo is optimal in any meaningful sense (except being a nice composite number of notes I guess) because it has 4 inconsistent interval pairs in the 9-odd-limit already (which is almost half of all interval pairs of the 9-odd-limit). By contrast, 166edo and 197edo both appear 5 times so appear to be well justified in terms of absolute error at least. 125edo is even better and interestingly disappears in practically the same places that 53 disappears: in the 49- to 75- 7-limited odd-limits (though 53edo reappears in the 81-odd-limit while 125 appears one later in the 105-odd-limit). 84edo only appears once but it appears in a theoretically notable odd-limit for marvel: the 25-odd-limit, which is notable for being challenging because of marvel's inclination to temper 5 significantly flat (and this is also where 41edo disappears), so IMO isn't so bad either because we know it satisfies the strict requirements and because it appears in the <code>optimal_edo_sequence</code> for all full odd-limits 23 thru 51 and appears in the <code>strict_optimal_edo_sequence</code> (meaning identical except instead based on relative error instead of absolute, so that the list is a strict subset) for a lot of those too, so that it's a natural tuning to consider for high-limit marvel.
--[[User:Godtone|Godtone]] ([[User talk:Godtone|talk]]) 22:30, 15 January 2025 (UTC)
 
--[[User:Godtone|Godtone]] ([[User talk:Godtone|talk]]) 22:52, 15 January 2025 (UTC)
Retrieved from "https://en.xen.wiki/w/Talk:Marvel"
Return to "Marvel" page.