Xenharmonic Wiki

Very low accuracy temperaments: Difference between revisions

← Older editNewer edit →
VisualWikitext
Jerdle (talk | contribs)
autopatrolled, emailconfirmed
253 edits
→Codex: As mujannabic has a name, added a reference to it.
Switch to Sintel's badness, WE & CWE tunings (1/2)
Line 14: Line 14:


[[Optimal tuning]]s:  
[[Optimal tuning]]s:  
* [[CTE]]: ~3/2 = 600.000, ~5/4 = 386.314 (~6/5 = 213.686)
* [[WE]]: ~3/2 = 615.125{{c}}, ~5/4 = 321.597{{c}} (~6/5 = 293.528{{c}})
: [[error map]]: {{val| +30.250 -56.581 -4.217 }}
* [[CWE]]: ~3/2 = 600.000{{c}}, ~5/4 = 336.527{{c}} (~6/5 = 263.473{{c}})
: error map: {{val| 0.000 -101.955 -49.787 }}
<!-- * [[CTE]]: ~3/2 = 600.000{{c}}, ~5/4 = 386.314{{c}} (~6/5 = 213.686{{c}})
: [[error map]]: {{val| 0.000 -101.955 0.000 }}
: [[error map]]: {{val| 0.000 -101.955 0.000 }}
* [[POTE]]: ~3/2 = 600.000, ~5/4 = 313.690 (~6/5 = 286.310)
* [[POTE]]: ~3/2 = 600.000{{c}}, ~5/4 = 313.690{{c}} (~6/5 = 286.310{{c}})
: error map: {{val| 0.000 -101.955 -72.624 }}
: error map: {{val| 0.000 -101.955 -72.624 }} -->


{{Optimal ET sequence|legend=1| 2, 4 }}
{{Optimal ET sequence|legend=1| 2, 4 }}


[[Badness]] (Smith): 0.021647
[[Badness]] (Sintel): 0.508


; Music
; Music
Line 34: Line 38:


Optimal tunings:  
Optimal tunings:  
* CTE: ~3/2 = 600.000, ~5/4 = 379.210 (~6/5 = 220.890)
* WE: ~3/2 = 614.759{{c}}, ~7/6 = 309.426{{c}} (~6/5 = 305.334{{c}})
* POTE: ~3/2 = 600.000, ~7/6 = 301.997 (~6/5 = 298.003)
* CWE: ~3/2 = 600.000{{c}}, ~7/6 = 326.047{{c}} (~6/5 = 273.953{{c}})
<!-- * CTE: ~3/2 = 600.000{{c}}, ~5/4 = 379.210{{c}} (~6/5 = 220.890{{c}})
* POTE: ~3/2 = 600.000{{c}}, ~7/6 = 301.997{{c}} (~6/5 = 298.003{{c}}) -->


{{Optimal ET sequence|legend=0| 2, 4 }}
{{Optimal ET sequence|legend=0| 2, 4 }}


Badness (Smith): 0.019373
Badness (Sintel): 0.490


==== 11-limit ====
==== 11-limit ====
Line 49: Line 55:


Optimal tunings:  
Optimal tunings:  
* CTE: ~3/2 = 600.000, ~5/4 = 379.210 (~11/10 = 220.890)
* WE: ~3/2 = 606.293{{c}}, ~5/4 = 343.862{{c}} (~8/7 = 262.431{{c}})
* POTE: ~3/2 = 600.000, ~5/4 = 340.293 (~8/7 = 259.707)
* CWE: ~3/2 = 600.000{{c}}, ~5/4 = 348.102{{c}} (~8/7 = 251.898{{c}})
<!-- * CTE: ~3/2 = 600.000{{c}}, ~5/4 = 379.210{{c}} (~8/7 = 220.890{{c}})
* POTE: ~3/2 = 600.000{{c}}, ~5/4 = 340.293{{c}} (~8/7 = 259.707{{c}}) -->


{{Optimal ET sequence|legend=0| 2, 4 }}
{{Optimal ET sequence|legend=0| 2, 4 }}


Badness (Smith): 0.021810
Badness (Sintel): 0.721


==== Antietam ====
==== Antietam ====
Line 64: Line 72:


Optimal tunings:  
Optimal tunings:  
* CTE: ~3/2 = 600.000, ~5/4 = 415.533 (~12/11 = 184.467)
* WE: ~3/2 = 616.135{{c}}, ~5/4 = 330.741{{c}} (~6/5 = 285.393{{c}})
* POTE: ~3/2 = 600.000, ~7/6 = 322.080 (~6/5 = 277.920)
* CWE: ~3/2 = 600.000{{c}}, ~5/4 = 349.843{{c}} (~8/7 = 250.157{{c}})
<!-- * CTE: ~3/2 = 600.000{{c}}, ~5/4 = 415.533{{c}} (~12/11 = 184.467{{c}})
* POTE: ~3/2 = 600.000{{c}}, ~7/6 = 322.080{{c}} (~6/5 = 277.920{{c}}) -->


{{Optimal ET sequence|legend=0| 2, 4e }}
{{Optimal ET sequence|legend=0| 2, 4e }}


Badness (Smith): 0.018993
Badness (Sintel): 0.628


=== Antaeus ===
=== Antaeus ===
Line 79: Line 89:


Optimal tunings:  
Optimal tunings:  
* CTE: ~3/2 = 600.000, ~5/4 = 323.296 (~7/6 = 276.704)
* WE: ~3/2 = 614.854{{c}}, ~5/4 = 323.784{{c}} (~6/5 = 291.070{{c}})
* POTE: ~3/2 = 600.000, ~5/4 = 315.962 (~7/6 = 284.038)
* CWE: ~3/2 = 600.000{{c}}, ~5/4 = 317.349{{c}} (~6/5 = 282.651{{c}})
<!-- * CTE: ~3/2 = 600.000{{c}}, ~5/4 = 323.296{{c}} (~7/6 = 276.704{{c}})
* POTE: ~3/2 = 600.000{{c}}, ~5/4 = 315.962{{c}} (~7/6 = 284.038{{c}}) -->


{{Optimal ET sequence|legend=0| 2d, 4 }}
{{Optimal ET sequence|legend=0| 2d, 4 }}


Badness (Smith): 0.037537
Badness (Sintel): 0.950


==== 11-limit ====
==== 11-limit ====
Line 94: Line 106:


Optimal tunings:  
Optimal tunings:  
* CTE: ~3/2 = 600.000, ~5/4 = 323.296 (~7/6 = 276.704)
* WE: ~3/2 = 609.311{{c}}, ~5/4 = 323.110{{c}} (~6/5 = 286.200{{c}})
* POTE: ~3/2 = 600.000, ~5/4 = 318.173 (~7/6 = 281.827)
* CWE: ~3/2 = 600.000{{c}}, ~5/4 = 318.904{{c}} (~6/5 = 281.096{{c}})
<!-- * CTE: ~3/2 = 600.000{{c}}, ~5/4 = 323.296{{c}} (~7/6 = 276.704{{c}})
* POTE: ~3/2 = 600.000{{c}}, ~5/4 = 318.173{{c}} (~7/6 = 281.827{{c}}) -->


{{Optimal ET sequence|legend=0| 2d, 4 }}
{{Optimal ET sequence|legend=0| 2d, 4 }}


Badness (Smith): 0.033786
Badness (Sintel): 1.12


== Alteraugment ==
== Alteraugment ==
Line 113: Line 127:


[[Optimal tuning]]s:  
[[Optimal tuning]]s:  
* [[CTE]]: ~4/3 = 400.000, ~5/4 = 386.314 (~16/15 = 13.686)
* [[WE]]: ~4/3 = 389.212{{c}}, ~5/4 = 447.530{{c}} (~10/9 = 58.318{{c}})
: [[error map]]: {{val| -32.364 +44.105 -3.512 }}
* [[CWE]]: ~4/3 = 400.000{{c}}, ~5/4 = 434.191{{c}} (~15/16 = 34.191{{c}})
: error map: {{val| 0.000 +98.045 +47.878 }}
<!-- * [[CTE]]: ~4/3 = 400.000{{c}}, ~5/4 = 386.314{{c}} (~16/15 = 13.686{{c}})
: [[error map]]: {{val| 0.000 +98.045 0.000 }}
: [[error map]]: {{val| 0.000 +98.045 0.000 }}
* [[POTE]]: ~4/3 = 400.000, ~5/4 = 459.935 (~10/9 = 59.935)
* [[POTE]]: ~4/3 = 400.000{{c}}, ~5/4 = 459.935{{c}} (~10/9 = 59.935{{c}})
: error map: {{val| 0.000 +98.045 +73.621 }}
: error map: {{val| 0.000 +98.045 +73.621 }} -->


{{Optimal ET sequence|legend=1| 3, 12bcc, 15bbcc }}
{{Optimal ET sequence|legend=1| 3, 12bcc, 15bbcc }}


[[Badness]] (Smith): 0.078042
[[Badness]] (Sintel): 1.83


== Yo (2c &amp; 3)  ==
== Yo (2c & 3)  ==
This temperament family is characterized by the [[color notation|yo 2nd]] [[10/9]] being tempering out.
This temperament family is characterized by the [[color notation|yo 2nd]] [[10/9]] being tempering out.


Line 132: Line 150:


[[Optimal tuning]]s:  
[[Optimal tuning]]s:  
* [[CTE]]: ~2 = 1200.000, ~3/2 = 761.310
* [[WE]]: ~2 = 1187.236{{c}}, ~3/2 = 767.716{{c}}
: [[error map]]: {{val| -12.764 +52.997 -63.645 }}
* [[CWE]]: ~2 = 1200.000{{c}}, ~3/2 = 767.718{{c}}
: error map: {{val| 0.000 +65.763 -50.877 }}
<!-- * [[CTE]]: ~2 = 1200.000{{c}}, ~3/2 = 761.310{{c}}
: [[error map]]: {{val| 0.000 +74.015 -34.374 }}
: [[error map]]: {{val| 0.000 +74.015 -34.374 }}
* [[POTE]]: ~2 = 1200.000, ~3/2 = 775.970
* [[POTE]]: ~2 = 1200.000{{c}}, ~3/2 = 775.970{{c}}
: error map: {{val| 0.000 +65.763 -50.878 }}
: error map: {{val| 0.000 +65.763 -50.878 }} -->


{{Optimal ET sequence|legend=1| 3, 11bc, 14bc, 17bb }}
{{Optimal ET sequence|legend=1| 2c, 3 }}


[[Badness]] (Smith): 0.016712
[[Badness]] (Sintel): 0.392


=== Brutus ===
=== Brutus ===
Line 149: Line 171:


Optimal tunings:  
Optimal tunings:  
* CTE: ~2 = 1200.000, ~3/2 = 813.116
* WE: ~2 = 1158.982{{c}}, ~3/2 = 819.228{{c}}
* POTE: ~2 = 1200.000, ~3/2 = 848.221
* CWE: ~2 = 1200.000{{c}}, ~3/2 = 831.346{{c}}
<!-- * CTE: ~2 = 1200.000{{c}}, ~3/2 = 813.116{{c}}
* POTE: ~2 = 1200.000{{c}}, ~3/2 = 848.221{{c}} -->


{{Optimal ET sequence|legend=0| 3, 7bc }}
{{Optimal ET sequence|legend=0| 3, 7bc }}


Badness (Smith): 0.053389
Badness (Sintel): 1.35


=== Phlegyas ===
=== Phlegyas ===
Line 164: Line 188:


Optimal tunings:  
Optimal tunings:  
* CTE: ~2 = 1200.000, ~3/2 = 747.225
* WE: ~2 = 1206.510{{c}}, ~3/2 = 747.166{{c}}
* POTE: ~2 = 1200.000, ~3/2 = 743.135
* CWE: ~2 = 1200.000{{c}}, ~3/2 = 743.797{{c}}
<!-- * CTE: ~2 = 1200.000{{c}}, ~3/2 = 747.225{{c}}
* POTE: ~2 = 1200.000{{c}}, ~3/2 = 743.135{{c}} -->


{{Optimal ET sequence|legend=0| 3, 5c, 8c }}
{{Optimal ET sequence|legend=0| 3, 5c, 8c }}


Badness (Smith): 0.051293
Badness (Sintel): 1.30


=== Charon ===
=== Charon ===
Line 179: Line 205:


Optimal tunings:  
Optimal tunings:  
* CTE: ~7/5 = 600.000, ~3/2 = 768.427 (~15/14 = 168.427)
* WE: ~7/5 = 593.832{{c}}, ~3/2 = 774.559{{c}} (~15/14 = 180.726{{c}})
* POTE: ~7/5 = 600.000, ~3/2 = 782.604 (~15/14 = 182.604)
* CWE: ~7/5 = 600.000{{c}}, ~3/2 = 774.466{{c}} (~15/14 = 174.466{{c}})
<!-- * CTE: ~7/5 = 600.000{{c}}, ~3/2 = 768.427{{c}} (~15/14 = 168.427{{c}})
* POTE: ~7/5 = 600.000{{c}}, ~3/2 = 782.604{{c}} (~15/14 = 182.604{{c}}) -->


{{Optimal ET sequence|legend=0| 4bcd, 6 }}
{{Optimal ET sequence|legend=0| 4bcd, 6 }}


Badness (Smith): 0.056404
Badness (Sintel): 1.43


=== Nessus ===
=== Nessus ===
Line 198: Line 226:


Optimal tunings:  
Optimal tunings:  
* CTE: ~2 = 1200.000, ~7/4 = 980.335
* WE: ~2 = 1189.201{{c}}, ~3/2 = 978.002{{c}}
* POTE: ~2 = 1200.000, ~7/4 = 986.883
* CWE: ~2 = 1200.000{{c}}, ~3/2 = 983.918{{c}}
<!-- * CTE: ~2 = 1200.000{{c}}, ~7/4 = 980.335{{c}}
* POTE: ~2 = 1200.000{{c}}, ~7/4 = 986.883{{c}} -->


{{Optimal ET sequence|legend=0| 5c, 6 }}
{{Optimal ET sequence|legend=0| 5c, 6 }}


Badness (Smith): 0.059070
Badness (Sintel): 1.49


== Ternary ==
== Ternary ==
Line 217: Line 247:


[[Optimal tuning]]s:  
[[Optimal tuning]]s:  
* [[CTE]]: ~5/4 = 400.000, ~7/4 = 968.826 (~28/25 = 168.826)
* [[WE]]: ~5/4 = 391.796{{c}}, ~7/4 = 1012.806{{c}} (~15/14 = 162.582{{c}})
: [[error map]]: {{val| -24.612 +57.026 -43.741 -5.243 }}
* [[CWE]]: ~5/4 = 400.000{{c}}, ~7/4 = 1016.378{{c}} (~8/7 = 183.622{{c}})
: error map: {{val| 0.000 +98.045 +13.686 +47.552 }}
<!-- * [[CTE]]: ~5/4 = 400.000{{c}}, ~7/4 = 968.826{{c}} (~28/25 = 168.826{{c}})
: [[error map]]: {{val| 0.000 +98.045 +13.686 0.000 }}
: [[error map]]: {{val| 0.000 +98.045 +13.686 0.000 }}
* [[POTE]]: ~5/4 = 400.000, ~7/4 = 1034.013 (~15/14 = 165.987)
* [[POTE]]: ~5/4 = 400.000{{c}}, ~7/4 = 1034.013{{c}} (~15/14 = 165.987{{c}})
: error map: {{val| 0.000 +98.045 +13.686 +65.187 }}
: error map: {{val| 0.000 +98.045 +13.686 +65.187 }} -->


{{Optimal ET sequence|legend=1| 3d, 6, 9bd }}
{{Optimal ET sequence|legend=1| 3d, 6, 9bd }}


[[Badness]] (Smith): 0.028673
[[Badness]] (Sintel): 0.726


=== 11-limit ===
=== 11-limit ===
Line 234: Line 268:


Optimal tunings:  
Optimal tunings:  
* CTE: ~5/4 = 400.000, ~7/4 = 961.874 (~11/10 = 161.874)
* WE: ~5/4 = 391.788{{c}}, ~7/4 = 1011.942{{c}} (~12/11 = 163.422{{c}})
* POTE: ~5/4 = 400.000, ~7/4 = 1033.153 (~12/11 = 166.847)
* CWE: ~5/4 = 400.000{{c}}, ~7/4 = 1013.973{{c}} (~12/11 = 186.027{{c}})
<!-- * CTE: ~5/4 = 400.000{{c}}, ~7/4 = 961.874{{c}} (~11/10 = 161.874{{c}})
* POTE: ~5/4 = 400.000{{c}}, ~7/4 = 1033.153{{c}} (~12/11 = 166.847{{c}}) -->


{{Optimal ET sequence|legend=0| 3de, 6 }}
{{Optimal ET sequence|legend=0| 3de, 6 }}


Badness (Smith): 0.025592
Badness (Sintel): 0.846


== Geryon ==
== Geryon ==
Retrieved from "https://en.xen.wiki/w/Very_low_accuracy_temperaments"