Xenharmonic Wiki

Hemimean clan: Difference between revisions

← Older editNewer edit →
VisualWikitext
ET sequence reviewed
Xenllium (talk | contribs)
autopatrolled, emailconfirmed
5,030 edits
mNo edit summary
Line 47: Line 47:
POTE generator: ~26/25 = 64.6086
POTE generator: ~26/25 = 64.6086


Vals: {{val list| 18, 19, 37, 93, 130 }}
Optimal GPV sequence: {{val list| 18, 19, 37, 93, 130 }}


== Hemithirds ==
== Hemithirds ==
Line 64: Line 64:


[[Minimax tuning]]:
[[Minimax tuning]]:
* [[7-odd-limit]]
* [[7-odd-limit]]: ~28/25 = {{monzo| 1/10 -1/20 0 1/20 }}
: [{{monzo| 1 0 0 0 }}, {{monzo| 5/2 3/4 0 -3/4 }}, {{monzo| 11/5 -1/10 0 1/10 }}, {{monzo| 5/2 -1/4 0 1/4 }}]
: [[Eigenmonzo]]s (unchanged intervals): 2, 7/6
* [[9-odd-limit]]
: [{{monzo| 1 0 0 0 }}, {{monzo| 10/7 6/7 0 -3/7 }}, {{monzo| 82/35 -4/35 0 2/35 }}, {{monzo| 20/7 -2/7 0 1/7 }}]
: [[Eigenmonzo]]s (unchanged intervals): 2, 7/6
: [[Eigenmonzo]]s (unchanged intervals): 2, 7/6
* [[9-odd-limit]]: ~28/25 = {{monzo| 6/25 -2/35 0 1/35 }}
: [[Eigenmonzo]]s (unchanged intervals): 2, 9/7


{{Val list|legend=1| 25, 31, 87, 118 }}
{{Val list|legend=1| 25, 31, 87, 118 }}
Line 85: Line 83:


Minimax tuning:
Minimax tuning:
* 11-odd-limit
* 11-odd-limit: ~28/25 = {{monzo| 5/27 0 0 1/27 -1/27 }}
: [{{monzo| 1 0 0 0 0 }}, {{monzo| 11/9 0 0 -5/9 5/9 }}, {{monzo| 64/27 0 0 2/27 -2/27 }}, {{monzo| 79/27 0 0 5/27 -5/27 }}, {{monzo| 79/27 0 0 -22/27 22/27 }}]
: Eigenmonzos (unchanged intervals): 2, 11/7
: Eigenmonzos (unchanged intervals): 2, 11/7


Vals: {{Val list| 25e, 31, 87, 118 }}
Optimal GPV sequence: {{Val list| 25e, 31, 87, 118 }}


Badness: 0.019003
Badness: 0.019003
Line 102: Line 99:
POTE generator: ~28/25 = 193.166
POTE generator: ~28/25 = 193.166


Vals: {{Val list| 31, 56, 87, 118, 205d }}
Optimal GPV sequence: {{Val list| 31, 56, 87, 118, 205d }}


Badness: 0.021738
Badness: 0.021738
Line 132: Line 129:
POTE generator: ~55/36 = 735.125
POTE generator: ~55/36 = 735.125


Vals: {{Val list| 18e, 31, 80, 111, 364cd }}
Optimal GPV sequence: {{Val list| 18e, 31, 80, 111, 364cd }}


Badness: 0.022476
Badness: 0.022476


=== 13-limit ===
==== 13-limit ====
Subgroup: 2.3.5.7.11.13
Subgroup: 2.3.5.7.11.13


Line 145: Line 142:
POTE generator: ~55/36 = 735.126
POTE generator: ~55/36 = 735.126


Vals: {{Val list| 31, 80, 111 }}
Optimal GPV sequence: {{Val list| 31, 80, 111 }}


Badness: 0.025204
Badness: 0.025204


==== 17-limit ====
===== 17-limit =====
Subgroup: 2.3.5.7.11.13.17
Subgroup: 2.3.5.7.11.13.17


Line 158: Line 155:
POTE generator: ~26/17 = 735.125
POTE generator: ~26/17 = 735.125


Vals: {{Val list| 31, 80, 111 }}
Optimal GPV sequence: {{Val list| 31, 80, 111 }}


Badness: 0.019919
Badness: 0.019919


==== 19-limit ====
===== 19-limit =====
Subgroup: 2.3.5.7.11.13.17.19
Subgroup: 2.3.5.7.11.13.17.19


Line 171: Line 168:
POTE generator: ~26/17 = 735.116
POTE generator: ~26/17 = 735.116


Vals: {{Val list| 31, 80, 111 }}
Optimal GPV sequence: {{Val list| 31, 80, 111 }}


Badness: 0.016301
Badness: 0.016301


==== 23-limit ====
===== 23-limit =====
Subgroup: 2.3.5.7.11.13.17.19.23
Subgroup: 2.3.5.7.11.13.17.19.23


Line 188: Line 185:
Badness: 0.014957
Badness: 0.014957


=== Semishly ===
==== Semishly ====
Subgroup: 2.3.5.7.11.13
Subgroup: 2.3.5.7.11.13


Line 197: Line 194:
POTE generator: ~13/10 = 464.980
POTE generator: ~13/10 = 464.980


Vals: {{Val list| 31, 49f, 80f }}
Optimal GPV sequence: {{Val list| 31, 49f, 80f }}


Badness: 0.028408
Badness: 0.028408
Line 229: Line 226:
POTE generator: ~11/8 = 551.765
POTE generator: ~11/8 = 551.765


Vals: {{Val list| 37, 50, 87, 224d, 311d }}
Optimal GPV sequence: {{Val list| 37, 50, 87, 224d, 311d }}


Badness: 0.054744
Badness: 0.054744
Line 242: Line 239:
POTE generator: ~11/8 = 551.758
POTE generator: ~11/8 = 551.758


Vals: {{Val list| 37, 50, 87, 224d, 311d, 398d }}
Optimal GPV sequence: {{Val list| 37, 50, 87, 224d, 311d, 398d }}


Badness: 0.029741
Badness: 0.029741
Line 272: Line 269:
POTE generator: ~75/64 = 278.799
POTE generator: ~75/64 = 278.799


Vals: {{Val list| 13, 43, 56, 99e }}
Optimal GPV sequence: {{Val list| 13, 43, 56, 99e }}


Badness: 0.061413
Badness: 0.061413
Line 285: Line 282:
POTE generator: ~13/11 = 278.802
POTE generator: ~13/11 = 278.802


Vals: {{Val list| 13, 43, 56, 99e }}
Optimal GPV sequence: {{Val list| 13, 43, 56, 99e }}


Badness: 0.047611
Badness: 0.047611
Line 298: Line 295:
POTE generator: ~13/11 = 278.798
POTE generator: ~13/11 = 278.798


Vals: {{Val list| 13, 43, 56, 99e }}
Optimal GPV sequence: {{Val list| 13, 43, 56, 99e }}


Badness: 0.031191
Badness: 0.031191
Line 311: Line 308:
POTE generator: ~13/11 = 278.790
POTE generator: ~13/11 = 278.790


Vals: {{Val list| 13, 43, 56, 99e }}
Optimal GPV sequence: {{Val list| 13, 43, 56, 99e }}


Badness: 0.023899
Badness: 0.023899
Line 324: Line 321:
POTE generator: ~896/825 = 139.403
POTE generator: ~896/825 = 139.403


Vals: {{Val list| 43, 112, 155, 198, 439cd, 637cd }}
Optimal GPV sequence: {{Val list| 43, 112, 155, 198, 439cd, 637cd }}


Badness: 0.092996
Badness: 0.092996
Line 337: Line 334:
POTE generator: ~13/12 = 139.403
POTE generator: ~13/12 = 139.403


Vals: {{Val list| 43, 155, 198, 439cdf, 637cdf }}
Optimal GPV sequence: {{Val list| 43, 155, 198, 439cdf, 637cdf }}


Badness: 0.044328
Badness: 0.044328
Line 367: Line 364:
POTE generator: ~64/63 = 27.663
POTE generator: ~64/63 = 27.663


Vals: {{Val list| 43, 87, 130, 217, 347e, 911cde }}
Optimal GPV sequence: {{Val list| 43, 87, 130, 217, 347e, 911cde }}


Badness: 0.036541
Badness: 0.036541
Line 380: Line 377:
POTE generator: ~64/63 = 27.660
POTE generator: ~64/63 = 27.660


Vals: {{Val list| 43, 87, 130, 217, 347e, 564e }}
Optimal GPV sequence: {{Val list| 43, 87, 130, 217, 347e, 564e }}


Badness: 0.019504
Badness: 0.019504
Line 408: Line 405:
POTE generator: ~99/98 = 24.235
POTE generator: ~99/98 = 24.235


Vals: {{Val list| 49, 50, 99e }}
Optimal GPV sequence: {{Val list| 49, 50, 99e }}


Badness: 0.053828
Badness: 0.053828


=== 13-limit ===
==== 13-limit ====
Subgroup: 2.3.5.7.11.13
Subgroup: 2.3.5.7.11.13


Line 421: Line 418:
POTE generator: ~99/98 = 24.181
POTE generator: ~99/98 = 24.181


Vals: {{Val list| 49, 50, 99e, 149e }}
Optimal GPV sequence: {{Val list| 49, 50, 99e, 149e }}


Badness: 0.053531
Badness: 0.053531


=== Sengage ===
==== Sengage ====
Subgroup: 2.3.5.7.11.13
Subgroup: 2.3.5.7.11.13


Line 434: Line 431:
POTE generator: ~99/98 = 24.234
POTE generator: ~99/98 = 24.234


Vals: {{Val list| 49f, 50, 99ef }}
Optimal GPV sequence: {{Val list| 49f, 50, 99ef }}


Badness: 0.037416
Badness: 0.037416
Line 464: Line 461:
POTE generator: ~56/45 = 378.440
POTE generator: ~56/45 = 378.440


Vals: {{Val list| 19, 111, 130, 241, 371ce, 501cde, 872cde }}
Optimal GPV sequence: {{Val list| 19, 111, 130, 241, 371ce, 501cde, 872cde }}


Badness: 0.045352
Badness: 0.045352
Line 477: Line 474:
POTE generator: ~56/45 = 378.437
POTE generator: ~56/45 = 378.437


Vals: {{Val list| 19, 111, 130, 241, 371ce }}
Optimal GPV sequence: {{Val list| 19, 111, 130, 241, 371ce }}


Badness: 0.023940
Badness: 0.023940
Line 507: Line 504:
POTE generator: ~27/25 = 126.711
POTE generator: ~27/25 = 126.711


Vals: {{Val list| 19, 123de, 142, 161 }}
Optimal GPV sequence: {{Val list| 19, 123de, 142, 161 }}


Badness: 0.094032
Badness: 0.094032
Line 520: Line 517:
POTE generator: ~14/13 = 126.705
POTE generator: ~14/13 = 126.705


Vals: {{Val list| 19, 123def, 142f, 161 }}
Optimal GPV sequence: {{Val list| 19, 123def, 142f, 161 }}


Badness: 0.051571
Badness: 0.051571
Line 533: Line 530:
POTE generator: ~14/13 = 126.703
POTE generator: ~14/13 = 126.703


Vals: {{Val list| 19, 123defg, 142f, 161 }}
Optimal GPV sequence: {{Val list| 19, 123defg, 142f, 161 }}


Badness: 0.041918
Badness: 0.041918
Line 546: Line 543:
POTE generator: ~14/13 = 126.705
POTE generator: ~14/13 = 126.705


Vals: {{Val list| 19, 123defg, 142f, 161 }}
Optimal GPV sequence: {{Val list| 19, 123defg, 142f, 161 }}


Badness: 0.032168
Badness: 0.032168
Line 559: Line 556:
POTE generator: ~14/13 = 126.703
POTE generator: ~14/13 = 126.703


Vals: {{Val list| 19, 123defg, 142f, 161 }}
Optimal GPV sequence: {{Val list| 19, 123defg, 142f, 161 }}


Badness: 0.026117
Badness: 0.026117
Line 572: Line 569:
POTE generator: ~14/13 = 126.704
POTE generator: ~14/13 = 126.704


Vals: {{Val list| 19, 123defg, 142f, 161 }}
Optimal GPV sequence: {{Val list| 19, 123defg, 142f, 161 }}


Badness: 0.021398
Badness: 0.021398
Line 585: Line 582:
POTE generator: ~14/13 = 126.703
POTE generator: ~14/13 = 126.703


Vals: {{Val list| 19, 123defgk, 142fk, 161 }}
Optimal GPV sequence: {{Val list| 19, 123defgk, 142fk, 161 }}


Badness: 0.019331
Badness: 0.019331
Line 615: Line 612:
POTE generator: ~400/363 = 172.912
POTE generator: ~400/363 = 172.912


Vals: {{Val list| 111, 118, 229, 347 }}
Optimal GPV sequence: {{Val list| 111, 118, 229, 347 }}


Badness: 0.043883
Badness: 0.043883
Line 628: Line 625:
POTE generator: ~72/65 = 172.930
POTE generator: ~72/65 = 172.930


Vals: {{Val list| 111, 229f }}
Optimal GPV sequence: {{Val list| 111, 229f }}


Badness: 0.038771
Badness: 0.038771
Line 641: Line 638:
POTE generator: ~400/363 = 172.933
POTE generator: ~400/363 = 172.933


Vals: {{Val list| 111, 229 }}
Optimal GPV sequence: {{Val list| 111, 229 }}


Badness: 0.042744
Badness: 0.042744
Line 658: Line 655:
POTE generator: ~9/8 = 192.9898
POTE generator: ~9/8 = 192.9898


Vals: {{Vals| 6, 19, 25, 31, 56b, 87b }}
Optimal GPV sequence: {{Val list| 6, 19, 25, 31, 56b, 87b }}


=== Tutone ===
=== Tutone ===
Retrieved from "https://en.xen.wiki/w/Hemimean_clan"