Xenharmonic Wiki

Pentacircle clan: Difference between revisions

← Older editNewer edit →
VisualWikitext
Xenllium (talk | contribs)
autopatrolled, emailconfirmed
5,031 edits
No edit summary
Tags: Mobile edit Mobile web edit
Line 25: Line 25:
{{Optimal ET sequence|legend=1| 12, 17, 36, 41, 58, 63, 104, 225e, 266e, 370bee, 699bbdeee }}
{{Optimal ET sequence|legend=1| 12, 17, 36, 41, 58, 63, 104, 225e, 266e, 370bee, 699bbdeee }}


[[Badness]]: 0.0205 × 10<sup>-3</sup>
[[Badness]] (Sintel): 0.299


=== Overview to extensions ===
=== Overview to extensions ===
Line 65: Line 65:
Optimal ET sequence: {{Optimal ET sequence| 12f, 17, 41, 46, 58, 87, 104, 266ef, 329bef, 370beef, 474beef, 595bdeeeff, 699bbdeeeff }}
Optimal ET sequence: {{Optimal ET sequence| 12f, 17, 41, 46, 58, 87, 104, 266ef, 329bef, 370beef, 474beef, 595bdeeeff, 699bbdeeeff }}


Badness: 0.101 × 10<sup>-3</sup>
Badness (Sintel): 0.266


==== Etypyth ====
==== Etypyth ====
Line 80: Line 80:
Optimal ET sequence: {{Optimal ET sequence| 12f, 17g, 29g, 41g, 46, 58, 75e, 104, 121, 225e }}
Optimal ET sequence: {{Optimal ET sequence| 12f, 17g, 29g, 41g, 46, 58, 75e, 104, 121, 225e }}


Badness: 0.325 × 10<sup>-3</sup>
Badness (Sintel): 0.536


== Terrapyth ==
== Terrapyth ==
Line 101: Line 101:
{{Optimal ET sequence|legend=1| 17c, 29, 46, 92de, 121, 167, 288be }}
{{Optimal ET sequence|legend=1| 17c, 29, 46, 92de, 121, 167, 288be }}


[[Badness]]: 5.35 × 10<sup>-3</sup>
[[Badness]] (Sintel): 6.432


=== 13-limit ===
=== 13-limit ===
Line 116: Line 116:
Optimal ET sequence: {{Optimal ET sequence| 17c, 29, 46, 75e, 92def, 121, 167, 288be }}
Optimal ET sequence: {{Optimal ET sequence| 17c, 29, 46, 75e, 92def, 121, 167, 288be }}


Badness: 2.48 × 10<sup>-3</sup>
Badness (Sintel): 2.319


=== 17-limit ===
=== 17-limit ===
Line 131: Line 131:
Optimal ET sequence: {{Optimal ET sequence| 17cg, 29g, 46, 75e, 92defg, 121, 167, 288beg }}
Optimal ET sequence: {{Optimal ET sequence| 17cg, 29g, 46, 75e, 92defg, 121, 167, 288beg }}


Badness: 1.52 × 10<sup>-3</sup>
Badness (Sintel): 1.449


== Pentafrost ==
== Pentafrost ==
Line 149: Line 149:
* [[CWE]]: ~2 = 1200.000, ~3/2 = 701.903, ~7/4 = 964.614
* [[CWE]]: ~2 = 1200.000, ~3/2 = 701.903, ~7/4 = 964.614
: error map: {{val| 0.000 -0.052 -1.541 -4.212 +5.683 }}
: error map: {{val| 0.000 -0.052 -1.541 -4.212 +5.683 }}
* [[CE]]: ~2 = 1200.000, ~3/2 = 702.006, ~7/4 = 964.085
* [[CEE]]: ~2 = 1200.000, ~3/2 = 702.006, ~7/4 = 964.085
: error map: {{val| 0.000 +0.051 -2.364 -4.741 +4.741 }}
: error map: {{val| 0.000 +0.051 -2.364 -4.741 +4.741 }}


{{Optimal ET sequence|legend=1| 12, 24, 29, 36, 41, 106d }}
{{Optimal ET sequence|legend=1| 12, 24, 29, 36, 41, 106d }}


[[Badness]]: 1.58 × 10<sup>-3</sup>
[[Badness]] (Sintel): 1.903


=== 13-limit ===
=== 13-limit ===
Line 168: Line 168:
* CTE: ~2 = 1200.000, ~3/2 = 702.106, ~7/4 = 962.655
* CTE: ~2 = 1200.000, ~3/2 = 702.106, ~7/4 = 962.655
* CWE: ~2 = 1200.000, ~3/2 = 702.145, ~7/4 = 962.175
* CWE: ~2 = 1200.000, ~3/2 = 702.145, ~7/4 = 962.175
* CE: ~2 = 1200.000, ~3/2 = 702.360, ~7/4 = 962.210
* CEE: ~2 = 1200.000, ~3/2 = 702.360, ~7/4 = 962.210


Optimal ET sequence: {{Optimal ET sequence| 12f, 24, 29, 41 }}
Optimal ET sequence: {{Optimal ET sequence| 12f, 24, 29, 41 }}


Badness: 1.59 × 10<sup>-3</sup>
Badness (Sintel): 1.487


=== Permafrost ===
=== Permafrost ===
Line 186: Line 186:
* CTE: 2 = 1200.000, ~3/2 = 701.783, ~7/4 = 966.113
* CTE: 2 = 1200.000, ~3/2 = 701.783, ~7/4 = 966.113
* CWE: 2 = 1200.000, ~3/2 = 701.753, ~7/4 = 966.445
* CWE: 2 = 1200.000, ~3/2 = 701.753, ~7/4 = 966.445
* CE: 2 = 1200.000, ~3/2 = 701.770, ~7/4 = 965.771
* CEE: 2 = 1200.000, ~3/2 = 701.770, ~7/4 = 965.771


Optimal ET sequence: {{Optimal ET sequence| 12, 17, 24, 36, 41, 77e }}
Optimal ET sequence: {{Optimal ET sequence| 12, 17, 24, 36, 41, 77e }}


Badness: 2.62 × 10<sup>-3</sup>
Badness (Sintel): 2.450


== Tolerant ==
== Tolerant ==
=== 7-limit ===
: ''For the 7-limit version of this temperament, see [[Miscellaneous 7-limit temperaments #Tolerant]].''
[[Subgroup]]: 2.3.5.7


[[Comma list]]: 179200/177147
{{Mapping|legend=1| 1 0 0 -10 | 0 1 0 11 | 0 0 1 -2 }}
: mapping generators: ~2, ~3, ~5
[[Optimal tuning]]s:
* [[CTE]]: ~2 = 1200.000, ~3/2 = 703.608, ~5/4 = 385.669
: [[error map]]: {{val| 0.000 +1.653 -0.645 -0.472 }}
* [[POTE]]: ~2 = 1200.000, ~3/2 = 703.957, ~5/4 = 386.886
: error map: {{val| 0.000 +2.002 +0.573 +0.930 }}
{{Optimal ET sequence|legend=1| 34d, 39d, 41, 80, 87, 121, 167, 208, 329b, 375b, 496bd }}
[[Badness]]: 0.165 × 10<sup>-3</sup>
=== 11-limit ===
[[Subgroup]]: 2.3.5.7.11
[[Subgroup]]: 2.3.5.7.11


Line 218: Line 200:


{{Mapping|legend=1| 1 0 0 -10 -3 | 0 1 0 11 7 | 0 0 1 -2 -2 }}
{{Mapping|legend=1| 1 0 0 -10 -3 | 0 1 0 11 7 | 0 0 1 -2 -2 }}
: mapping generators: ~2, ~3, ~5


[[Optimal tuning]]s:
[[Optimal tuning]]s:
Line 227: Line 211:
{{Optimal ET sequence|legend=1| 34d, 39d, 41, 80, 87, 121, 167, 208, 288be, 375be }}
{{Optimal ET sequence|legend=1| 34d, 39d, 41, 80, 87, 121, 167, 208, 288be, 375be }}


[[Badness]]: 1.039 × 10<sup>-3</sup>
[[Badness]] (Sintel): 1.249


=== 13-limit ===
=== 13-limit ===
Line 242: Line 226:
Optimal ET sequence: {{Optimal ET sequence| 34d, 41, 46, 75e, 80, 87, 121, 167, 208, 375be }}
Optimal ET sequence: {{Optimal ET sequence| 34d, 41, 46, 75e, 80, 87, 121, 167, 208, 375be }}


Badness: 1.02 × 10<sup>-3</sup>
Badness (Sintel): 0.955


=== 17-limit ===
=== 17-limit ===
Line 257: Line 241:
Optimal ET sequence: {{Optimal ET sequence| 34d, 41, 46, 75e, 80, 87, 121, 167, 288beg, 496bdeefggg }}
Optimal ET sequence: {{Optimal ET sequence| 34d, 41, 46, 75e, 80, 87, 121, 167, 288beg, 496bdeefggg }}


Badness: 0.982 × 10<sup>-3</sup>
Badness (Sintel): 0.934


== Kujuku ==
== Kujuku ==
Line 278: Line 262:
{{Optimal ET sequence|legend=1| 24, 29, 34d, 53d, 58, 87, 121, 145, 179e, 208, 266e }}
{{Optimal ET sequence|legend=1| 24, 29, 34d, 53d, 58, 87, 121, 145, 179e, 208, 266e }}


[[Badness]]: 2.26 × 10<sup>-3</sup>
[[Badness]] (Sintel): 2.719


=== 13-limit ===
=== 13-limit ===
Line 293: Line 277:
Optimal ET sequence: {{Optimal ET sequence| 24, 29, 34d, 53d, 58, 87, 121, 179ef, 208, 266ef, 474beef }}
Optimal ET sequence: {{Optimal ET sequence| 24, 29, 34d, 53d, 58, 87, 121, 179ef, 208, 266ef, 474beef }}


Badness: 1.06 × 10<sup>-3</sup>
Badness (Sintel): 0.991


Complexity spectrum: 15/13, 4/3, 13/10, 9/8, 13/11, 15/11, 12/11, 11/9, 11/8, 14/11, 16/13, 16/15, 11/10, 13/12, 9/7, 5/4, 18/13, 7/6, 6/5, 8/7, 10/9, 14/13, 15/14, 7/5
Complexity spectrum: 15/13, 4/3, 13/10, 9/8, 13/11, 15/11, 12/11, 11/9, 11/8, 14/11, 16/13, 16/15, 11/10, 13/12, 9/7, 5/4, 18/13, 7/6, 6/5, 8/7, 10/9, 14/13, 15/14, 7/5
Line 310: Line 294:
Optimal ET sequence: {{Optimal ET sequence| 24, 34d, 58, 87, 121, 179ef, 208g, 266efg }}
Optimal ET sequence: {{Optimal ET sequence| 24, 34d, 58, 87, 121, 179ef, 208g, 266efg }}


Badness: 1.24 × 10<sup>-3</sup>
Badness (Sintel): 1.181


== Trienparapyth ==
== Trienparapyth ==
Line 333: Line 317:
{{Optimal ET sequence|legend=1| 7d, 14e, 15d, 22, 51, 58, 80, 87, 145, 167, 312ce, 479bce }}
{{Optimal ET sequence|legend=1| 7d, 14e, 15d, 22, 51, 58, 80, 87, 145, 167, 312ce, 479bce }}


[[Badness]]: 1.26 × 10<sup>-3</sup>
[[Badness]] (Sintel): 1.515


=== 13-limit ===
=== 13-limit ===
Line 350: Line 334:
Optimal ET sequence: {{Optimal ET sequence| 7d, 22, 29, 51f, 51cde, 58, 80, 87, 145, 167, 225ce, 254, 312ce }}
Optimal ET sequence: {{Optimal ET sequence| 7d, 22, 29, 51f, 51cde, 58, 80, 87, 145, 167, 225ce, 254, 312ce }}


Badness: 1.23 × 10<sup>-3</sup>
Badness (Sintel): 1.154


=== 2.3.5.7.11.13.19 subgroup ===
=== 2.3.5.7.11.13.19 subgroup ===
Line 369: Line 353:
Optimal ET sequence: {{Optimal ET sequence| 7d, 22, 29, 51fh, 51cde, 58h, 80, 87, 138cdeh, 167h }}
Optimal ET sequence: {{Optimal ET sequence| 7d, 22, 29, 51fh, 51cde, 58h, 80, 87, 138cdeh, 167h }}


Badness: 1.22 × 10<sup>-3</sup>
Badness (Sintel): 1.198


=== 2.3.5.7.11.13.19.23 subgroup ===
=== 2.3.5.7.11.13.19.23 subgroup ===
Line 386: Line 370:
Optimal ET sequence: {{Optimal ET sequence| 22i, 29, 51fhi, 51cde, 58hi, 80, 87, 109, 138cdehi, 167hi }}
Optimal ET sequence: {{Optimal ET sequence| 22i, 29, 51fhi, 51cde, 58hi, 80, 87, 109, 138cdehi, 167hi }}


Badness: 1.04 × 10<sup>-3</sup>
Badness (Sintel): 1.136


[[Category:Temperament clans]]
[[Category:Temperament clans]]
Retrieved from "https://en.xen.wiki/w/Pentacircle_clan"