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Jubilismic clan: Difference between revisions

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→Jubilic: rework
m Spell out 1\2 in decimal, note the badness metric being used, and misc. cleanup
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[[Optimal tuning]]s:  
[[Optimal tuning]]s:  
* [[CTE]]: ~7/5 = 1\2, ~5/4 = 379.21
* [[CTE]]: ~7/5 = 600.000, ~5/4 = 379.210
: [[error map]]: {{val| 0.000 -7.104 +10.384 }}
: [[error map]]: {{val| 0.000 -7.104 +10.384 }}
* [[POTE]]: ~7/5 = 1\2, ~5/4 = 380.840
* [[POTE]]: ~7/5 = 600.000, ~5/4 = 380.840
: error map: {{val| 0.000 -5.474 +12.014 }}
: error map: {{val| 0.000 -5.474 +12.014 }}


{{Optimal ET sequence|legend=1| 2, 4, 6, 16, 22, 60d }}
{{Optimal ET sequence|legend=1| 2, 4, 6, 16, 22, 60d }}


[[Badness]]: 0.00190
[[Badness]] (Smith): 0.00190


=== Overview to extensions ===
=== Overview to extensions ===
Line 61: Line 61:


[[Optimal tuning]]s:  
[[Optimal tuning]]s:  
* [[CTE]]: ~7/5 = 1\2, ~8/7 = 232.927
* [[CTE]]: ~7/5 = 600.000, ~8/7 = 232.927
: [[error map]]: {{val| 0.000 -3.175 -19.241 -1.753 }}
: [[error map]]: {{val| 0.000 -3.175 -19.241 -1.753 }}
* [[POTE]]: ~7/5 = 1\2, ~8/7 = 232.089
* [[POTE]]: ~7/5 = 600.000, ~8/7 = 232.089
: error map: {{val| 0.000 -5.689 -18.402 -0.915 }}
: error map: {{val| 0.000 -5.689 -18.402 -0.915 }}


{{Optimal ET sequence|legend=1| 10, 16, 26, 62c }}
{{Optimal ET sequence|legend=1| 10, 16, 26, 62c }}


[[Badness]]: 0.062208
[[Badness]] (Smith): 0.062208


=== 11-limit ===
=== 11-limit ===
Line 78: Line 78:


Optimal tunings:  
Optimal tunings:  
* CTE: ~7/5 = 1\2, ~8/7 = 231.997
* CTE: ~7/5 = 600.000, ~8/7 = 231.997
* POTE: ~7/5 = 1\2, ~8/7 = 230.974
* POTE: ~7/5 = 600.000, ~8/7 = 230.974


{{Optimal ET sequence|legend=0| 10, 16, 26 }}
{{Optimal ET sequence|legend=0| 10, 16, 26 }}


Badness: 0.041563
Badness (Smith): 0.041563


=== 13-limit ===
=== 13-limit ===
Line 93: Line 93:


Optimal tunings:  
Optimal tunings:  
* CTE: ~7/5 = 1\2, ~8/7 = 232.100
* CTE: ~7/5 = 600.000, ~8/7 = 232.100
* POTE: ~7/5 = 1\2, ~8/7 = 230.966
* POTE: ~7/5 = 600.000, ~8/7 = 230.966


{{Optimal ET sequence|legend=0| 10, 16, 26 }}
{{Optimal ET sequence|legend=0| 10, 16, 26 }}


Badness: 0.025477
Badness (Smith): 0.025477


== Astrology ==
== Astrology ==
Line 114: Line 114:


[[Optimal tuning]]s:  
[[Optimal tuning]]s:  
* [[CTE]]: ~7/5 = 1\2, ~8/7 = 380.355
* [[CTE]]: ~7/5 = 600.000, ~8/7 = 380.355
: [[error map]]: {{val| 0.000 -0.180 -5.959 +11.529 }}
: [[error map]]: {{val| 0.000 -0.180 -5.959 +11.529 }}
* [[POTE]]: ~7/5 = 1\2, ~5/4 = 380.578
* [[POTE]]: ~7/5 = 600.000, ~5/4 = 380.578
: error map: {{val| 0.000 +0.937 -5.735 +11.752 }}
: error map: {{val| 0.000 +0.937 -5.735 +11.752 }}


{{Optimal ET sequence|legend=1| 6, 16, 22, 60d }}
{{Optimal ET sequence|legend=1| 6, 16, 22, 60d }}


[[Badness]]: 0.082673
[[Badness]] (Smith): 0.082673


=== 11-limit ===
=== 11-limit ===
Line 131: Line 131:


Optimal tunings:  
Optimal tunings:  
* CTE: ~7/5 = 1\2, ~5/4 = 380.588
* CTE: ~7/5 = 600.000, ~5/4 = 380.588
* POTE: ~7/5 = 1\2, ~5/4 = 380.530
* POTE: ~7/5 = 600.000, ~5/4 = 380.530


{{Optimal ET sequence|legend=0| 6, 16, 22 }}
{{Optimal ET sequence|legend=0| 6, 16, 22 }}


Badness: 0.039151
Badness (Smith): 0.039151


==== 13-limit ====
==== 13-limit ====
Line 146: Line 146:


Optimal tunings:  
Optimal tunings:  
* CTE: ~7/5 = 1\2, ~5/4 = 380.449
* CTE: ~7/5 = 600.000, ~5/4 = 380.449
* POTE: ~7/5 = 1\2, ~5/4 = 379.787
* POTE: ~7/5 = 600.000, ~5/4 = 379.787


{{Optimal ET sequence|legend=0| 6, 16, 22, 38f }}
{{Optimal ET sequence|legend=0| 6, 16, 22, 38f }}


Badness: 0.034376
Badness (Smith): 0.034376


; Music
; Music
Line 164: Line 164:


Optimal tunings:  
Optimal tunings:  
* CTE: ~7/5 = 1\2, ~5/4 = 379.762
* CTE: ~7/5 = 600.000, ~5/4 = 379.762
* POTE: ~7/5 = 1\2, ~5/4 = 379.837
* POTE: ~7/5 = 600.000, ~5/4 = 379.837


{{Optimal ET sequence|legend=0| 16, 22f, 38 }}
{{Optimal ET sequence|legend=0| 16, 22f, 38 }}


Badness: 0.035284
Badness (Smith): 0.035284


== Walid ==
== Walid ==
Line 183: Line 183:


[[Optimal tuning]]s:  
[[Optimal tuning]]s:  
* [[CTE]]: ~7/5 = 1\2, ~3/2 = 754.204
* [[CTE]]: ~7/5 = 600.000, ~3/2 = 754.204
: [[error map]]: {{val| 0.000 +52.249 +59.482 +76.970 }}
: [[error map]]: {{val| 0.000 +52.249 +59.482 +76.970 }}
* [[POTE]]: ~7/5 = 1\2, ~3/2 = 749.415
* [[POTE]]: ~7/5 = 600.000, ~3/2 = 749.415
: error map: {{val| 0.000 +47.460 +64.271 +81.759 }}
: error map: {{val| 0.000 +47.460 +64.271 +81.759 }}


{{Optimal ET sequence|legend=1| 2, 6, 8d }}
{{Optimal ET sequence|legend=1| 2, 6, 8d }}


[[Badness]]: 0.048978
[[Badness]] (Smith): 0.048978


=== 11-limit ===
=== 11-limit ===
Line 200: Line 200:


Optimal tunings:  
Optimal tunings:  
* CTE: ~7/5 = 1\2, ~3/2 = 754.205
* CTE: ~7/5 = 600.000, ~3/2 = 754.205
* POTE: ~7/5 = 1\2, ~3/2 = 749.756
* POTE: ~7/5 = 600.000, ~3/2 = 749.756


{{Optimal ET sequence|legend=0| 2, 6, 8d }}
{{Optimal ET sequence|legend=0| 2, 6, 8d }}


Badness: 0.029193
Badness (Smith): 0.029193


== Antikythera ==
== Antikythera ==
Line 223: Line 223:


[[Optimal tuning]]s:  
[[Optimal tuning]]s:  
* [[CTE]]: ~7/5 = 1\2, ~9/8 = 216.711
* [[CTE]]: ~7/5 = 600.000, ~9/8 = 216.711
: [[error map]]: {{val| 0.000 +12.801 +3.025 +14.463 }}
: [[error map]]: {{val| 0.000 +12.801 +3.025 +14.463 }}
* [[POTE]]: ~7/5 = 1\2, ~9/8 = 214.095
* [[POTE]]: ~7/5 = 600.000, ~9/8 = 214.095
: error map: {{val| 0.000 +10.815 -0.409 +17.079 }}
: error map: {{val| 0.000 +10.815 -0.409 +17.079 }}


Line 232: Line 232:
[[Tp tuning #T2 tuning|RMS error]]: 2.572 cents
[[Tp tuning #T2 tuning|RMS error]]: 2.572 cents


[[Badness]]: 0.00501
[[Badness]] (Smith): 0.00501


== Doublewide ==
== Doublewide ==
Line 247: Line 247:


[[Optimal tuning]]s:  
[[Optimal tuning]]s:  
* [[CTE]]: ~625/432 = 1\2, ~6/5 = 326.170
* [[CTE]]: ~625/432 = 600.000, ~6/5 = 326.170
: [[error map]]: {{val| 0.000 +2.727 -7.802 }}
: [[error map]]: {{val| 0.000 +2.727 -7.802 }}
* [[CWE]]: ~625/432 = 1\2, ~6/5 = 325.815
* [[CWE]]: ~625/432 = 600.000, ~6/5 = 325.815
: error map: {{val| 0.000 +1.304 -8.869 }}
: error map: {{val| 0.000 +1.304 -8.869 }}


Line 270: Line 270:


[[Optimal tuning]]s:  
[[Optimal tuning]]s:  
* [[CTE]]: ~7/5 = 1\2, ~6/5 = 325.769
* [[CTE]]: ~7/5 = 600.000, ~6/5 = 325.769
: [[error map]]: {{val| 0.000 +1.120 -9.007 +8.481 }}
: [[error map]]: {{val| 0.000 +1.120 -9.007 +8.481 }}
* [[POTE]]: ~7/5 = 1\2, ~6/5 = 325.719
* [[POTE]]: ~7/5 = 600.000, ~6/5 = 325.719
: error map: {{val| 0.000 +0.921 -9.156 +8.331 }}
: error map: {{val| 0.000 +0.921 -9.156 +8.331 }}


{{Optimal ET sequence|legend=1| 4, 14bd, 18, 22, 48 }}
{{Optimal ET sequence|legend=1| 4, 14bd, 18, 22, 48 }}


[[Badness]]: 0.043462
[[Badness]] (Smith): 0.043462


=== 11-limit ===
=== 11-limit ===
Line 287: Line 287:


Optimal tunings:  
Optimal tunings:  
* CTE: ~7/5 = 1\2, ~6/5 = 325.719
* CTE: ~7/5 = 600.000, ~6/5 = 325.719
* POTE: ~7/5 = 1\2, ~6/5 = 325.545
* POTE: ~7/5 = 600.000, ~6/5 = 325.545


{{Optimal ET sequence|legend=0| 4, 18, 22, 48 }}
{{Optimal ET sequence|legend=0| 4, 18, 22, 48 }}


Badness: 0.032058
Badness (Smith): 0.032058


=== Fleetwood ===
=== Fleetwood ===
Line 302: Line 302:


Optimal tunings:  
Optimal tunings:  
* CTE: ~7/5 = 1\2, ~6/5 = 326.684
* CTE: ~7/5 = 600.000, ~6/5 = 326.684
* POTE: ~7/5 = 1\2, ~6/5 = 327.038
* POTE: ~7/5 = 600.000, ~6/5 = 327.038


{{Optimal ET sequence|legend=0| 4e, …, 18e, 22 }}
{{Optimal ET sequence|legend=0| 4e, …, 18e, 22 }}


Badness: 0.035202
Badness (Smith): 0.035202


==== 13-limit ====
==== 13-limit ====
Line 317: Line 317:


Optimal tunings:  
Optimal tunings:  
* CTE: ~7/5 = 1\2, ~6/5 = 327.450
* CTE: ~7/5 = 600.000, ~6/5 = 327.450
* POTE: ~7/5 = 1\2, ~6/5 = 327.841
* POTE: ~7/5 = 600.000, ~6/5 = 327.841


{{Optimal ET sequence|legend=0| 4ef, …, 18e, 22 }}
{{Optimal ET sequence|legend=0| 4ef, …, 18e, 22 }}


Badness: 0.031835
Badness (Smith): 0.031835


=== Cavalier ===
=== Cavalier ===
Line 332: Line 332:


Optimal tunings:  
Optimal tunings:  
* CTE: ~7/5 = 1\2, ~6/5 = 324.238
* CTE: ~7/5 = 600.000, ~6/5 = 324.238
* POTE: ~7/5 = 1\2, ~6/5 = 323.427
* POTE: ~7/5 = 600.000, ~6/5 = 323.427


{{Optimal ET sequence|legend=0| 4e, 22e, 26 }}
{{Optimal ET sequence|legend=0| 4e, 22e, 26 }}


Badness: 0.052899
Badness (Smith): 0.052899


==== 13-limit ====
==== 13-limit ====
Line 347: Line 347:


Optimal tunings:  
Optimal tunings:  
* CTE: ~7/5 = 1\2, ~6/5 = 324.187
* CTE: ~7/5 = 600.000, ~6/5 = 324.187
* POTE: ~7/5 = 1\2, ~6/5 = 323.396
* POTE: ~7/5 = 600.000, ~6/5 = 323.396


{{Optimal ET sequence|legend=0| 4ef, 22ef, 26 }}
{{Optimal ET sequence|legend=0| 4ef, 22ef, 26 }}


Badness: 0.035040
Badness (Smith): 0.035040


== Elvis ==
== Elvis ==
Line 368: Line 368:


[[Optimal tuning]]s:  
[[Optimal tuning]]s:  
* [[CTE]]: ~7/5 = 1\2, ~64/45 = 645.313 (~64/63 = 45.313)
* [[CTE]]: ~7/5 = 600.000, ~64/45 = 645.313 (~64/63 = 45.313)
: [[error map]]: {{val| 0.000 -11.329 -12.879 +4.609 }}
: [[error map]]: {{val| 0.000 -11.329 -12.879 +4.609 }}
* [[POTE]]: ~7/5 = 1\2, ~64/45 = 646.279 (~64/63 = 46.279)
* [[POTE]]: ~7/5 = 600.000, ~64/45 = 646.279 (~64/63 = 46.279)
: error map: {{val| 0.000 -9.397 -17.710 -0.222 }}
: error map: {{val| 0.000 -9.397 -17.710 -0.222 }}


{{Optimal ET sequence|legend=1| 2, 24c, 26 }}
{{Optimal ET sequence|legend=1| 2, 24c, 26 }}


[[Badness]]: 0.141473
[[Badness]] (Smith): 0.141473


=== 11-limit ===
=== 11-limit ===
Line 385: Line 385:


Optimal tunings:  
Optimal tunings:  
* CTE: ~7/5 = 1\2, ~16/11 = 645.343 (~56/55 = 45.343)
* CTE: ~7/5 = 600.000, ~16/11 = 645.343 (~56/55 = 45.343)
* POTE: ~7/5 = 1\2, ~16/11 = 646.118 (~56/55 = 46.118)
* POTE: ~7/5 = 600.000, ~16/11 = 646.118 (~56/55 = 46.118)


{{Optimal ET sequence|legend=0| 2, 24c, 26 }}
{{Optimal ET sequence|legend=0| 2, 24c, 26 }}


Badness: 0.063212
Badness (Smith): 0.063212


=== 13-limit ===
=== 13-limit ===
Line 400: Line 400:


Optimal tunings:  
Optimal tunings:  
* CTE: ~7/5 = 1\2, ~16/11 = 645.208 (~56/55 = 45.208)
* CTE: ~7/5 = 600.000, ~16/11 = 645.208 (~56/55 = 45.208)
* POTE: ~7/5 = 1\2, ~16/11 = 646.108 (~56/55 = 46.108)
* POTE: ~7/5 = 600.000, ~16/11 = 646.108 (~56/55 = 46.108)


{{Optimal ET sequence|legend=0| 2f, 24cf, 26 }}
{{Optimal ET sequence|legend=0| 2f, 24cf, 26 }}


Badness: 0.043997
Badness (Smith): 0.043997


== Comic ==
== Comic ==
Line 421: Line 421:


[[Optimal tuning]]s:  
[[Optimal tuning]]s:  
* [[CTE]]: ~7/5 = 1\2, ~40/27 = 653.872 (~28/27 = 53.872)
* [[CTE]]: ~7/5 = 600.000, ~40/27 = 653.872 (~28/27 = 53.872)
: [[error map]]: {{val| 0.000 +5.789 -9.211 +8.277 }}
: [[error map]]: {{val| 0.000 +5.789 -9.211 +8.277 }}
* [[POTE]]: ~7/5 = 1\2, ~40/27 = 654.699 (~28/27 = 54.699)
* [[POTE]]: ~7/5 = 600.000, ~40/27 = 654.699 (~28/27 = 54.699)
: error map: {{val| 0.000 +7.444 -3.417 +14.070 }}
: error map: {{val| 0.000 +7.444 -3.417 +14.070 }}


{{Optimal ET sequence|legend=1| 2cd, …, 20cd, 22 }}
{{Optimal ET sequence|legend=1| 2cd, …, 20cd, 22 }}


[[Badness]]: 0.084395
[[Badness]] (Smith): 0.084395


=== 11-limit ===
=== 11-limit ===
Line 438: Line 438:


Optimal tunings:  
Optimal tunings:  
* CTE: ~7/5 = 1\2, ~22/15 = 654.289 (~28/27 = 54.289)
* CTE: ~7/5 = 600.000, ~22/15 = 654.289 (~28/27 = 54.289)
* POTE: ~7/5 = 1\2, ~22/15 = 655.184 (~28/27 = 55.184)
* POTE: ~7/5 = 600.000, ~22/15 = 655.184 (~28/27 = 55.184)


{{Optimal ET sequence|legend=0| 2cde, …, 20cde, 22 }}
{{Optimal ET sequence|legend=0| 2cde, …, 20cde, 22 }}


Badness: 0.045052
Badness (Smith): 0.045052


=== 13-limit ===
=== 13-limit ===
Line 453: Line 453:


Optimal tunings:  
Optimal tunings:  
* CTE: ~7/5 = 1\2, ~22/15 = 654.547 (~28/27 = 54.547)
* CTE: ~7/5 = 600.000, ~22/15 = 654.547 (~28/27 = 54.547)
* POTE: ~7/5 = 1\2, ~22/15 = 654.435 (~28/27 = 54.435)
* POTE: ~7/5 = 600.000, ~22/15 = 654.435 (~28/27 = 54.435)


{{Optimal ET sequence|legend=0| 2cde, 20cde, 22 }}
{{Optimal ET sequence|legend=0| 2cde, 20cde, 22 }}


Badness: 0.041470
Badness (Smith): 0.041470


== Bipyth ==
== Bipyth ==
Line 474: Line 474:


[[Optimal tuning]]s:  
[[Optimal tuning]]s:  
* [[CTE]]: ~7/5 = 1\2, ~3/2 = 708.695 (~15/14 = 108.695)
* [[CTE]]: ~7/5 = 600.000, ~3/2 = 708.695 (~15/14 = 108.695)
: [[error map]]: {{val| 0.000 +6.740 -8.058 +9.430 }}
: [[error map]]: {{val| 0.000 +6.740 -8.058 +9.430 }}
* [[POTE]]: ~7/5 = 1\2, ~3/2 = 709.437 (~15/14 = 109.437)
* [[POTE]]: ~7/5 = 600.000, ~3/2 = 709.437 (~15/14 = 109.437)
: error map: {{val| 0.000 +7.482 -1.379 +16.109 }}
: error map: {{val| 0.000 +7.482 -1.379 +16.109 }}


{{Optimal ET sequence|legend=1| 10cd, 12cd, 22 }}
{{Optimal ET sequence|legend=1| 10cd, 12cd, 22 }}


[[Badness]]: 0.165033
[[Badness]] (Smith): 0.165033


=== 11-limit ===
=== 11-limit ===
Line 491: Line 491:


Optimal tunings:  
Optimal tunings:  
* CTE: ~7/5 = 1\2, ~3/2 = 708.813 (~15/14 = 108.813)
* CTE: ~7/5 = 600.000, ~3/2 = 708.813 (~15/14 = 108.813)
* POTE: ~7/5 = 1\2, ~3/2 = 709.310 (~15/14 = 109.310)
* POTE: ~7/5 = 600.000, ~3/2 = 709.310 (~15/14 = 109.310)


{{Optimal ET sequence|legend=0| 10cd, 12cde, 22 }}
{{Optimal ET sequence|legend=0| 10cd, 12cde, 22 }}


Badness: 0.070910
Badness (Smith): 0.070910


== Sedecic ==
== Sedecic ==
Line 508: Line 508:


[[Optimal tuning]]s:  
[[Optimal tuning]]s:  
* [[CTE]]: ~128/125 = 1\16, ~3/2 = 701.955 (~525/512 = 26.955)
* [[CTE]]: ~128/125 = 75.000, ~3/2 = 701.955 (~525/512 = 26.955)
: [[error map]]: {{val| 0.000 0.000 -11.314 +6.174 }}
: [[error map]]: {{val| 0.000 0.000 -11.314 +6.174 }}
* [[POTE]]: ~128/125 = 1\16, ~3/2 = 700.554 (~525/512 = 25.554)
* [[POTE]]: ~128/125 = 75.000, ~3/2 = 700.554 (~525/512 = 25.554)
: error map: {{val| 0.000 -1.401 -11.314 +6.174 }}
: error map: {{val| 0.000 -1.401 -11.314 +6.174 }}


{{Optimal ET sequence|legend=1| 16, 32, 48 }}
{{Optimal ET sequence|legend=1| 16, 32, 48 }}


[[Badness]]: 0.265972
[[Badness]] (Smith): 0.265972


=== 11-limit ===
=== 11-limit ===
Line 525: Line 525:


Optimal tunings:  
Optimal tunings:  
* CTE: ~22/21 = 1\16, ~3/2 = 701.844 (~45/44 = 26.844)
* CTE: ~22/21 = 75.000, ~3/2 = 701.844 (~45/44 = 26.844)
* POTE: ~22/21 = 1\16, ~3/2 = 700.331 (~45/44 = 25.331)
* POTE: ~22/21 = 75.000, ~3/2 = 700.331 (~45/44 = 25.331)


{{Optimal ET sequence|legend=0| 16, 32, 48 }}
{{Optimal ET sequence|legend=0| 16, 32, 48 }}


Badness: 0.092774
Badness (Smith): 0.092774


== Notes ==
== Notes ==
Retrieved from "https://en.xen.wiki/w/Jubilismic_clan"