Xenharmonic Wiki

Hemimean family: Difference between revisions

← Older edit
VisualWikitext
Xenllium (talk | contribs)
autopatrolled, emailconfirmed
5,020 edits
Tags: Mobile edit Mobile web edit
Xenllium (talk | contribs)
autopatrolled, emailconfirmed
5,020 edits
Fixed typo
Tags: Mobile edit Mobile web edit
 
(2 intermediate revisions by the same user not shown)
Line 9: Line 9:
[[Subgroup]]: 2.3.5.7
[[Subgroup]]: 2.3.5.7


[[Comma list]]: 3136/3125 (hemimean)
[[Comma list]]: 3136/3125


{{Mapping|legend=1| 1 0 0 -3 | 0 1 0 0 | 0 0 2 5 }}
{{Mapping|legend=1| 1 0 0 -3 | 0 1 0 0 | 0 0 2 5 }}
Line 21: Line 21:
: Angle (28/25, 3/2) = 90 degrees
: Angle (28/25, 3/2) = 90 degrees


[[Optimal tuning]] ([[CTE]]): ~2 = 1\1, ~3/2 = 701.9550, ~28/25 = 193.6499
[[Optimal tuning]]s:
* [[CTE]]: ~2 = 1200.000¢, ~3/2 = 701.955¢, ~28/25 = 193.650¢
* [[CWE]]: ~2 = 1200.000¢, ~3/2 = 702.112¢, ~28/25 = 193.717¢


[[Minimax tuning]]:  
[[Minimax tuning]]:  
Line 47: Line 49:
Sval mapping: {{mapping| 1 0 0 -3 -5 | 0 1 0 0 5 | 0 0 2 5 1 }}
Sval mapping: {{mapping| 1 0 0 -3 -5 | 0 1 0 0 5 | 0 0 2 5 1 }}


Optimal tuning (CTE): ~2 = 1\1, ~3/2 = 702.1960, ~28/25 = 193.6548
Optimal tunings:
* CTE: ~2 = 1200.000¢, ~3/2 = 702.196¢, ~28/25 = 193.655¢
* CWE: ~2 = 1200.000¢, ~3/2 = 702.304¢, ~28/25 = 193.737¢


{{Optimal ET sequence|legend=1| 12, 19g, 31g, …, 87, 99, 217, 229, 316, 328h, 446, 545c, 873cg }}
{{Optimal ET sequence|legend=1| 12, 19g, 31g, …, 87, 99, 217, 229, 316, 328h, 446, 545c, 873cg }}


Badness (Sintel): 0.573
Badness (Sintel): 0.884


==== 2.3.5.7.17.19 subgroup ====
==== 2.3.5.7.17.19 subgroup ====
Line 60: Line 64:
Sval mapping: {{mapping| 1 0 0 -3 -5 -6 | 0 1 0 0 5 5 | 0 0 2 5 1 2 }}
Sval mapping: {{mapping| 1 0 0 -3 -5 -6 | 0 1 0 0 5 5 | 0 0 2 5 1 2 }}


Optimal tuning (CTE): ~2 = 1\1, ~3/2 = 702.132, ~19/17 = 193.647
Optimal tunings:
* CTE: ~2 = 1200.000¢, ~3/2 = 702.132¢, ~19/17 = 193.647¢
* CWE: ~2 = 1200.000¢, ~3/2 = 702.213¢, ~19/17 = 193.716¢


{{Optimal ET sequence|legend=1| 12, 19gh, 31gh, …, 87, 99, 118, 210gh, 217, 229, 328h, 446 }}
{{Optimal ET sequence|legend=0| 12, 19gh, 31gh, …, 87, 99, 118, 210gh, 217, 229, 328h, 446 }}


Badness (Sintel): 0.456
Badness (Sintel): 0.578


=== Semiorion ===
=== Semiorion ===
Line 77: Line 83:
: Sval mapping generators: ~17/12, ~3, ~56/25
: Sval mapping generators: ~17/12, ~3, ~56/25


Optimal tuning (CTE): ~17/12 = 1\2, ~3/2 = 702.3471, ~28/25 = 193.6499
Optimal tunings:
* CTE: ~17/12 = 600.000¢, ~3/2 = 702.347¢, ~28/25 = 193.650¢
* CWE: ~17/12 = 600.000¢, ~3/2 = 702.218¢, ~28/25 = 193.604¢


{{Optimal ET sequence|legend=1| 12, 30d, 38d, 50, 62, 68, 106d, 118, 248g, 316g }}
{{Optimal ET sequence|legend=1| 12, 30d, 38d, 50, 62, 68, 106d, 118, 248g, 316g }}


Badness (Sintel): 1.095
Badness (Sintel): 1.690


==== 2.3.5.7.17.19 subgroup ====
==== 2.3.5.7.17.19 subgroup ====
Line 90: Line 98:
Mapping: {{mapping| 2 0 0 -6 5 3 | 0 1 0 0 1 1 | 0 0 2 5 0 1 }}
Mapping: {{mapping| 2 0 0 -6 5 3 | 0 1 0 0 1 1 | 0 0 2 5 0 1 }}


Optimal tuning (CTE): ~17/12 = 1\2, ~3/2 = 702.509, ~28/25 = 193.669
Optimal tunings:
* CTE: ~17/12 = 600.000¢, ~3/2 = 702.509¢, ~19/17 = 193.669¢
* CWE: ~17/12 = 600.000¢, ~3/2 = 702.279¢, ~19/17 = 193.592¢


{{Optimal ET sequence|legend=1| 12, …, 50, 68, 106d, 118, 248g, 316g }}
{{Optimal ET sequence|legend=0| 12, …, 50, 68, 106d, 118, 248g, 316g }}


Badness (Sintel): 0.569
Badness (Sintel): 0.722


== Belobog ==
== Belobog ==
Line 111: Line 121:
: Angle (28/25, 16/15) = 93.2696
: Angle (28/25, 16/15) = 93.2696


[[Optimal tuning]] ([[CTE]]): ~2 = 1\1, ~3/2 = 701.7205, ~28/25 = 193.5545
[[Optimal tuning]]s:
* [[CTE]]: ~2 = 1200.000¢, ~3/2 = 701.720¢, ~28/25 = 193.554¢
* [[CWE]]: ~2 = 1200.000¢, ~3/2 = 701.714¢, ~28/25 = 193.552¢


[[Minimax tuning]]:  
[[Minimax tuning]]:  
Line 133: Line 145:
Mapping: {{mapping| 1 0 0 -3 -9 15 | 0 1 0 0 2 -2 | 0 0 2 5 8 -7 }}
Mapping: {{mapping| 1 0 0 -3 -9 15 | 0 1 0 0 2 -2 | 0 0 2 5 8 -7 }}


Optimal tuning (CTE): ~2 = 1\1, ~3/2 = 701.8219, ~28/25 = 193.5816
Optimal tunings:
* CTE: ~2 = 1200.000¢, ~3/2 = 701.822¢, ~28/25 = 193.582¢
* CWE: ~2 = 1200.000¢, ~3/2 = 701.835¢, ~28/25 = 193.596¢


{{Optimal ET sequence|legend=1| 31, 43, 56, 74, 87, 118, 130, 217, 248, 347e, 378, 465, 595e }}
{{Optimal ET sequence|legend=0| 31, 43, 56, 74, 87, 118, 130, 217, 248, 347e, 378, 465, 595e }}


Badness (Sintel): 1.034
Badness (Sintel): 1.034
Line 146: Line 160:
Mapping: {{mapping| 1 0 0 -3 -9 -4 | 0 1 0 0 2 -1 | 0 0 2 5 8 8 }}
Mapping: {{mapping| 1 0 0 -3 -9 -4 | 0 1 0 0 2 -1 | 0 0 2 5 8 8 }}


Optimal tuning (CTE): ~2 = 1\1, ~3/2 = 702.5667, ~28/25 = 193.2493
Optimal tunings:
* CTE: ~2 = 1200.000¢, ~3/2 = 702.567¢, ~28/25 = 193.249¢
* CWE: ~2 = 1200.000¢, ~3/2 = 702.634¢, ~28/25 = 193.293¢


{{Optimal ET sequence|legend=1| 12f, 19e, 31, 56, 68e, 87, 118, 186ef, 205d }}
{{Optimal ET sequence|legend=0| 12f, 19e, 31, 56, 68e, 87, 118, 186ef, 205d }}


Badness (Sintel): 1.183
Badness (Sintel): 1.183
Line 161: Line 177:
: Mapping generators: ~2, ~3, ~56/25
: Mapping generators: ~2, ~3, ~56/25


[[Optimal tuning]] ([[CTE]]): ~2 = 1\1, ~3/2 = 701.1636, ~28/25 = 193.8645
[[Optimal tuning]]s:
* [[CTE]]: ~2 = 1200.000¢, ~3/2 = 701.164¢, ~28/25 = 193.865¢
* [[CWE]]: ~2 = 1200.000¢, ~3/2 = 701.723¢, ~28/25 = 193.995¢


[[Minimax tuning]]:  
[[Minimax tuning]]:  
Line 181: Line 199:
: Mapping generators: ~2, ~3, ~18/11
: Mapping generators: ~2, ~3, ~18/11


[[Optimal tuning]] ([[CTE]]): ~2 = 1\1, ~3/2 = 702.2875, ~18/11 = 854.3132
[[Optimal tuning]]s:
* [[CTE]]: ~2 = 1200.000¢, ~3/2 = 702.288¢, ~18/11 = 854.313¢
* [[CWE]]: ~2 = 1200.000¢, ~3/2 = 702.407¢, ~18/11 = 854.350¢


{{Optimal ET sequence|legend=1| 24d, 31, 80, 87, 111, 118, 198, 316, 514c, 545c }}
{{Optimal ET sequence|legend=1| 24d, 31, 80, 87, 111, 118, 198, 316, 514c, 545c }}


[[Badness]] (Sintel): 0.984
[[Badness]] (Sintel): 0.984
=== 13-limit ===
Subgroup: 2.3.5.7.11.13
Comma list: 352/351, 1001/1000, 3025/3024
Mapping: {{Mapping| 1 0 2 2 1 6 | 0 1 2 5 2 -1 | 0 0 -4 -10 -1 -1 }}
Optimal tunings:
* CTE: ~2 = 1200.000¢, ~3/2 = 702.707¢, ~18/11 = 854.537¢
* CWE: ~2 = 1200.000¢, ~3/2 = 702.937¢, ~18/11 = 854.554¢
{{Optimal ET sequence|legend=0| 24d, 31, 80, 87, 111, 118, 198 }}
Badness (Sintel): 1.159


== Semihemimean ==
== Semihemimean ==
Line 218: Line 253:


[[Badness]] (Sintel): 1.550
[[Badness]] (Sintel): 1.550
=== 17-limit ===
Subgroup: 2.3.5.7.11.13.17
Comma list: 289/288, 561/560, 1001/1000, 1632/1625
Mapping: {{Mapping| 2 0 0 -6 -3 15 5 | 0 1 0 0 -2 2 1 | 0 0 2 5 7 -6 0 }}
Optimal tunings:
* CTE: ~17/12 = 600.000¢, ~3/2 = 702.108¢, ~28/25 = 193.723¢
* CWE: ~17/12 = 600.000¢, ~3/2 = 702.269¢, ~28/25 = 193.776¢
{{Optimal ET sequence|legend=0| 12, 50, 68, 80, 118, 130, 198 }}
[[Badness]] (Sintel): 1.743
=== 19-limit ===
Subgroup: 2.3.5.7.11.13.17.19
Comma list: 289/288, 361/360, 456/455, 476/475, 561/560
Mapping: {{Mapping| 2 0 0 -6 -3 15 5 3 | 0 1 0 0 -2 2 1 1 | 0 0 2 5 7 -6 0 1 }}
Optimal tunings:
* CTE: ~17/12 = 600.000¢, ~3/2 = 702.252¢, ~19/17 = 193.758¢
* CWE: ~17/12 = 600.000¢, ~3/2 = 702.355¢, ~19/17 = 193.792¢
{{Optimal ET sequence|legend=0| 12, 50, 68, 80, 118, 130, 198 }}
[[Badness]] (Sintel): 1.318


[[Category:Temperament families]]
[[Category:Temperament families]]
Retrieved from "https://en.xen.wiki/w/Hemimean_family"