User:Godtone/optimal edo sequences: Difference between revisions

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In the below I detail the <code>optimal_edo_sequence</code>s for a large range of odd-limits (19 thru 123). However, the formatting requires some explanation. I was originally specifically interested in how [[fifth-chroma temperaments]] {{nowrap| {{EDOs| 77, 80, 84(, 87, 94) }} }} fare relative to each-other, to get a sense of what their relative strengths and weaknesses are. Therefore I list which of those five [[edo]]s appear in the sequence separately, followed by what ~~[[edo]]s~~ appear after them (to get a sense of what the smallest edos that are improvements are). However, this excludes edos smaller than 94 (other than 77, 80, 84 and 87 ofc), so I later did a sequence for smaller edos (in the 1 to 94 range) for completeness. A notable edo appearing frequently in ~~this list~~ (which is excluded in the first lists for being < 94) is [[89edo]], which interestingly splits 25/24 either into 4 or 6 depending on if you use the flat or sharp mapping of 5/4 (respectively), so that it's almost like it's approximately fifth-chroma in resolution. I also only calculate with pure-octave and patent vals, but since I know the correct high-limit val for 80edo (one of my favourite tuning systems), I use that val for it instead.

In the below I detail the <code>optimal_edo_sequence</code>s for a large range of odd-limits (19 thru 123). However, the formatting requires some explanation. I was originally specifically interested in how [[fifth-chroma temperaments]] {{nowrap| {{EDOs| 77, 80, 84(, 87, 94) }} }} fare relative to each-other, to get a sense of what their relative strengths and weaknesses are. Therefore I list which of those five [[edo]]s appear in the sequence separately, followed by what edos appear after them (to get a sense of what the smallest edos that are improvements are). However, this excludes edos smaller than 94 (other than 77, 80, 84 and 87 ofc), so I later did a sequence for smaller edos (in the 1 to 94 range) for completeness. A notable edo appearing frequently in these sequences (which is excluded in the first lists for being < 94) is [[89edo]], which interestingly splits 25/24 either into 4 or 6 depending on if you use the flat or sharp mapping of 5/4 (respectively), so that it's almost like it's approximately fifth-chroma in resolution. This is also notable because other than [[82edo]], it's the only edo to appear relatively frequently which is in the 77 to 94 range other than 77, 80, 84, 87, 94. I also only calculate with pure-octave and patent vals, but [[User:Godtone#RINGER_80|since I know]] the correct high-limit val for 80edo (as it's one of my favourite tuning systems), I use that val for it instead.

<~~pre~~>

patent_vals[80] = val(lim(255),ed(80),'koprsuvBC')

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# I separated it into two calculations because beyond the 51-odd-limit the usefulness is more dubious beyond just general sources of opportunistic concordance.

for ol in range(51,124,2):

for ol in range(53,124,2): # (Also because these calculations took significantly longer.)

result = optimal_edo_sequence(odd_lim(ol,complements=False))

print(str(ol)+'-odd-limit:',[ x for x in result if x in [77,80,84,87,94] ],'\n & additionally:',[ x for x in result if x > 94 ])

~~51-odd-limit: [77, 80, 84, 87, 94]~~

~~& additionally: [118, 125, 130, 140, 171, 202, 224, 248, 260, 265, 270, 296, 311]~~

53-odd-limit: [77, 84, 94]

& additionally: [111, 113, 118, 125, 130, 140, 171, 193, 202, 224, 253, 265, 270, 296, 301]

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& additionally: [106, 109, 111, 113, 118, 128, 130, 137, 140, 152, 159, 161, 181, 202, 207, 217, 224, 239, 248, 270, 277, 296, 301, 311]

~~125-odd-limit: [80, 87]~~

# SMALLER EDOS (up to 94):

~~& additionally: [106, 109, 111, 115, 118, 130, 137, 140, 152, 159, 161, 181, 183, 202, 217, 224, 239, 248, 270, 277, 289, 301, 311]~~

~~LOWER LISTS~~:

19-odd-limit: [1, 2, 3, 4, 5, 7, 9, 12, 15, 16, 19, 20, 22, 24, 36, 41, 43, 44, 50, 56, 62, 68, 72, 80, 94]

21-odd-limit: [1, 2, 3, 4, 5, 7, 9, 10, 12, 15, 16, 20, 24, 26, 31, 33, 36, 41, 43, 50, 53, 56, 62, 68, 72, 89, 94]

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121-odd-limit: [1, 2, 3, 4, 5, 7, 9, 10, 12, 14, 15, 17, 19, 22, 24, 26, 27, 29, 31, 36, 41, 43, 46, 53, 58, 63, 65, 72, 77, 84, 87, 94]

123-odd-limit: [1, 2, 3, 4, 5, 7, 9, 10, 12, 14, 15, 17, 19, 22, 24, 26, 27, 29, 31, 36, 41, 46, 53, 58, 63, 65, 72, 77, 84, 87, 94]

</~~pre~~>

</syntaxhighlight>

@@ Line 1: / Line 1: @@
-In the below I detail the <code>optimal_edo_sequence</code>s for a large range of odd-limits (19 thru 123). However, the formatting requires some explanation. I was originally specifically interested in how [[fifth-chroma temperaments]] {{nowrap| {{EDOs| 77, 80, 84(, 87, 94) }} }} fare relative to each-other, to get a sense of what their relative strengths and weaknesses are. Therefore I list which of those five [[edo]]s appear in the sequence separately, followed by what [[edo]]s appear after them (to get a sense of what the smallest edos that are improvements are). However, this excludes edos smaller than 94 (other than 77, 80, 84 and 87 ofc), so I later did a sequence for smaller edos (in the 1 to 94 range) for completeness. A notable edo appearing frequently in this list (which is excluded in the first lists for being < 94) is [[89edo]], which interestingly splits 25/24 either into 4 or 6 depending on if you use the flat or sharp mapping of 5/4 (respectively), so that it's almost like it's approximately fifth-chroma in resolution. I also only calculate with pure-octave and patent vals, but since I know the correct high-limit val for 80edo (one of my favourite tuning systems), I use that val for it instead.
+In the below I detail the <code>optimal_edo_sequence</code>s for a large range of odd-limits (19 thru 123). However, the formatting requires some explanation. I was originally specifically interested in how [[fifth-chroma temperaments]] {{nowrap| {{EDOs| 77, 80, 84(, 87, 94) }} }} fare relative to each-other, to get a sense of what their relative strengths and weaknesses are. Therefore I list which of those five [[edo]]s appear in the sequence separately, followed by what edos appear after them (to get a sense of what the smallest edos that are improvements are). However, this excludes edos smaller than 94 (other than 77, 80, 84 and 87 ofc), so I later did a sequence for smaller edos (in the 1 to 94 range) for completeness. A notable edo appearing frequently in these sequences (which is excluded in the first lists for being < 94) is [[89edo]], which interestingly splits 25/24 either into 4 or 6 depending on if you use the flat or sharp mapping of 5/4 (respectively), so that it's almost like it's approximately fifth-chroma in resolution. This is also notable because other than [[82edo]], it's the only edo to appear relatively frequently which is in the 77 to 94 range other than 77, 80, 84, 87, 94. I also only calculate with pure-octave and patent vals, but [[User:Godtone#RINGER_80|since I know]] the correct high-limit val for 80edo (as it's one of my favourite tuning systems), I use that val for it instead.
-<pre>
+<syntaxhighlight lang="python">
 patent_vals[80] = val(lim(255),ed(80),'koprsuvBC')
@@ Line 44: / Line 44: @@
 # I separated it into two calculations because beyond the 51-odd-limit the usefulness is more dubious beyond just general sources of opportunistic concordance.
-for ol in range(51,124,2):
+for ol in range(53,124,2): # (Also because these calculations took significantly longer.)
    result = optimal_edo_sequence(odd_lim(ol,complements=False))
    print(str(ol)+'-odd-limit:',[ x for x in result if x in [77,80,84,87,94] ],'\n  & additionally:',[ x for x in result if x > 94 ])
--odd-limit: [77, 80, 84, 87, 94]
-  & additionally: [118, 125, 130, 140, 171, 202, 224, 248, 260, 265, 270, 296, 311]
 -odd-limit: [77, 84, 94]
    & additionally: [111, 113, 118, 125, 130, 140, 171, 193, 202, 224, 253, 265, 270, 296, 301]
@@ Line 123: / Line 121: @@
    & additionally: [106, 109, 111, 113, 118, 128, 130, 137, 140, 152, 159, 161, 181, 202, 207, 217, 224, 239, 248, 270, 277, 296, 301, 311]
--odd-limit: [80, 87]
+# SMALLER EDOS (up to 94):
-  & additionally: [106, 109, 111, 115, 118, 130, 137, 140, 152, 159, 161, 181, 183, 202, 217, 224, 239, 248, 270, 277, 289, 301, 311]
-LOWER LISTS:
 -odd-limit: [1, 2, 3, 4, 5, 7, 9, 12, 15, 16, 19, 20, 22, 24, 36, 41, 43, 44, 50, 56, 62, 68, 72, 80, 94]
 -odd-limit: [1, 2, 3, 4, 5, 7, 9, 10, 12, 15, 16, 20, 24, 26, 31, 33, 36, 41, 43, 50, 53, 56, 62, 68, 72, 89, 94]
@@ Line 184: / Line 175: @@
 -odd-limit: [1, 2, 3, 4, 5, 7, 9, 10, 12, 14, 15, 17, 19, 22, 24, 26, 27, 29, 31, 36, 41, 43, 46, 53, 58, 63, 65, 72, 77, 84, 87, 94]
 -odd-limit: [1, 2, 3, 4, 5, 7, 9, 10, 12, 14, 15, 17, 19, 22, 24, 26, 27, 29, 31, 36, 41, 46, 53, 58, 63, 65, 72, 77, 84, 87, 94]
-</pre>
+</syntaxhighlight>