Talk:Marvel: Difference between revisions

Line 57:

--[[User:Godtone|Godtone]] ([[User talk:Godtone|talk]]) 21:57, 15 January 2025 (UTC)

Because the consistency argument may not be sufficiently convincing, here is <code>optimal_edo_sequence</code>s (minimising the mean square cent error on the tonality diamond, with cent error deviations weighted by the square-root of the odd-limit of each interval, which is the most forgiving tuning fidelity that can be reasonable) for edos tempering out [[225/224|S15]]:

>>> [k for k in range(15,125,2) if len(fact_int(k))<=4]

[15, 21, 25, 27, 35, 45, 49, 63, 75, 81, 105]

>>> optimal_edo_sequence({1,3,5,7,9},[edo for edo in range(1,312) if pval(S(15),ed(edo))==0])

[2, 9, 10, 12, 19, 31, 41, 53, 72, 125, 166]

>>> optimal_edo_sequence({1,3,5,7,9,15},[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])

[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},[edo for edo in range(1,312) if pval(S(15),ed(edo))==0])

[2, 9, 10, 12, 19, 31, 53, 72, 84, 156, 240]

>>> 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])

[2, 9, 10, 12, 19, 22, 31, 53, 72, 84, 103, 156]

>>> 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])

[2, 9, 10, 12, 19, 22, 31, 53, 72, 84, 125, 156, 281]

>>> 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])

[2, 9, 10, 19, 22, 31, 72, 103, 175, 228] # 49 is bad in 53

>>> 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])

[2, 9, 10, 12, 19, 22, 31, 41, 72, 156, 197] # 63 is not much better

>>> 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])

[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>

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.

--[[User:Godtone|Godtone]] ([[User talk:Godtone|talk]]) 22:30, 15 January 2025 (UTC)

@@ Line 57: / Line 57: @@
 --[[User:Godtone|Godtone]] ([[User talk:Godtone|talk]]) 21:57, 15 January 2025 (UTC)
+Because the consistency argument may not be sufficiently convincing, here is <code>optimal_edo_sequence</code>s (minimising the mean square cent error on the tonality diamond, with cent error deviations weighted by the square-root of the odd-limit of each interval, which is the most forgiving tuning fidelity that can be reasonable) for edos tempering out [[225/224|S15]]:
+<syntaxhighlight lang="python">
+>>> [k for k in range(15,125,2) if len(fact_int(k))<=4]
+[15, 21, 25, 27, 35, 45, 49, 63, 75, 81, 105]
+>>> optimal_edo_sequence({1,3,5,7,9},[edo for edo in range(1,312) if pval(S(15),ed(edo))==0])
+[2, 9, 10, 12, 19, 31, 41, 53, 72, 125, 166]
+>>> optimal_edo_sequence({1,3,5,7,9,15},[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])
+[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},[edo for edo in range(1,312) if pval(S(15),ed(edo))==0])
+[2, 9, 10, 12, 19, 31, 53, 72, 84, 156, 240]
+>>> 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])
+[2, 9, 10, 12, 19, 22, 31, 53, 72, 84, 103, 156]
+>>> 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])
+[2, 9, 10, 12, 19, 22, 31, 53, 72, 84, 125, 156, 281]
+>>> 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])
+[2, 9, 10, 19, 22, 31, 72, 103, 175, 228] # 49 is bad in 53
+>>> 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])
+[2, 9, 10, 12, 19, 22, 31, 41, 72, 156, 197] # 63 is not much better
+>>> 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])
+[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>
+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.
+--[[User:Godtone|Godtone]] ([[User talk:Godtone|talk]]) 22:30, 15 January 2025 (UTC)