User:VIxen/Cemetery: Difference between revisions

(One intermediate revision by one other user not shown)

Line 1:

=== Shaka ===

Two commas that split 2/1 in half, corresponding to convergents to sqrt(2), are the [[1682/1681|''sha''ftesburisma]] [[Square superparticular|S29]]/S41 and the [[9801/9800|''ka''lisma S99]], prompting to temper out {S29, S41, S99}, approximating /29 and /41 [[Primodality|primodal]] chords well.

Subgroup: 2.3.35.11.29.41

Comma list: 841/840, 1189/1188, 1681/1680

Optimal tuning (CTE): ~41/29 = 1\2, ~3/2 = 702.031, ~41/24 = 926.693

[[Support]]ing [[ET]]s: {{EDOs|22, 26, 36, 48, 70, 96, 106, 118, 140, 154, 176, 188, 224, 272, 294, 342}}

Scale: [[Shaka10]]

=== Spog ===

Line 100:

Line 117:

Comma list: 1716/1715, 2080/2079, 17303/17280

~~Mapping:~~ {{~~mapping~~| 2 0 1 2 6 -3 | 0 1 4 0 2 1 | 0 0 -5 2 -3 4 }}

{{Mapping|legend=0| 2 0 1 2 6 -3 | 0 1 4 0 2 1 | 0 0 -5 2 -3 4 }}

{{Optimal ET sequence|legend=1| 22f, 32cf, 54cff, 72, 166, 198, 270, 634, 904, 1174, 1880ef }}

Line 111:

Line 128:

Comma list: 715/714, 1089/1088, 1225/1224, 2025/2023

~~Mapping:~~ {{~~mapping~~| 2 0 1 2 6 -3 0 | 0 1 4 0 2 1 6 | 0 0 -5 2 -3 4 -6 }}

{{Mapping|legend=0| 2 0 1 2 6 -3 0 | 0 1 4 0 2 1 6 | 0 0 -5 2 -3 4 -6 }}

{{Optimal ET sequence|legend=1| 22f, 54cffgg, 72, 166g, 198g, 270, 364, 436, 634g, 706f }}

Line 122:

Line 139:

Comma list: 715/714, 1225/1224, 1540/1539, 2080/2079, 4200/4199

~~Mapping:~~ {{~~mapping~~| 2 0 1 2 6 -3 0 13 | 0 1 4 0 2 1 6 2 | 0 0 -5 2 -3 4 -6 -6 }}

{{Mapping|legend=0| 2 0 1 2 6 -3 0 13 | 0 1 4 0 2 1 6 2 | 0 0 -5 2 -3 4 -6 -6 }}

{{Optimal ET sequence|legend=1| 72, 94, 166g, 198g, 270, 436, 634g, 706f }}

Line 133:

Line 150:

Comma list: 715/714, 1225/1224, 1540/1539, 2080/2079, 2530/2527, 2737/2736

~~Mapping:~~ {{~~mapping~~| 2 0 1 2 6 -3 0 13 19 | 0 1 4 0 2 1 6 2 -2 | 0 0 -5 2 -3 4 -6 -6 -2 }}

{{Mapping|legend=0| 2 0 1 2 6 -3 0 13 19 | 0 1 4 0 2 1 6 2 -2 | 0 0 -5 2 -3 4 -6 -6 -2 }}

{{Optimal ET sequence|legend=1| 72, 94, 166g, 270, 342f, 436, 706fi }}

Line 146:

Line 163:

Comma list: 4225/4224, 9801/9800, 41503/41472

~~Mapping:~~ {{~~mapping~~| 2 0 1 2 6 9 | 0 1 9 -2 5 -6 | 0 0 -10 4 -6 7 }}

{{Mapping|legend=0| 2 0 1 2 6 9 | 0 1 9 -2 5 -6 | 0 0 -10 4 -6 7 }}

: mapping generators: ~99/70, ~3, ~154/65

Line 159:

Line 176:

Comma list: 1089/1088, 1225/1224, 2025/2023, 4225/4224

~~Mapping:~~ {{~~mapping~~| 2 0 1 2 6 9 0 | 0 1 9 -2 5 -6 12 | 0 0 -10 4 -6 7 -12 }}

{{Mapping|legend=0| 2 0 1 2 6 9 0 | 0 1 9 -2 5 -6 12 | 0 0 -10 4 -6 7 -12 }}

{{Optimal ET sequence|legend=1| 44, 50, 94, 144g, 176g, 220g, 270, 364, 414, 634g, 684 }}

Line 170:

Line 187:

Comma list: 1089/1088, 1225/1224, 1729/1728, 2926/2925, 3762/3757

~~Mapping:~~ {{~~mapping~~| 2 0 1 2 6 9 0 1 | 0 1 9 -2 5 -6 12 11 | 0 0 -10 4 -6 7 -12 -11 }}

{{Mapping|legend=0| 2 0 1 2 6 9 0 1 | 0 1 9 -2 5 -6 12 11 | 0 0 -10 4 -6 7 -12 -11 }}

{{Optimal ET sequence|legend=1| 44, 50, 94, 144gh, 176g, 220g, 270, 414h, 590, 634g, 684h }}

Line 181:

Line 198:

Comma list: 897/896, 1089/1088, 1225/1224, 1729/1728, 2737/2736, 2926/2925

~~Mapping:~~ {{~~mapping~~| 2 0 1 2 6 9 0 1 7 | 0 1 9 -2 5 -6 12 11 3 | 0 0 -10 4 -6 7 -12 -11 -3 }}

{{Mapping|legend=0| 2 0 1 2 6 9 0 1 7 | 0 1 9 -2 5 -6 12 11 3 | 0 0 -10 4 -6 7 -12 -11 -3 }}

{{Optimal ET sequence|legend=1| 44, 50, 94, 144gh, 176g, 220g, 226, 270, 320i, 364i, 414hi }}

Line 211:

Line 228:

Comma list: 9801/9800, 10648/10647, 371293/371250

~~Mapping:~~ {{~~mapping~~| 2 0 3 -10 -4 2 | 0 1 2 4 4 3 | 0 0 8 -5 3 7 }}

{{Mapping|legend=0| 2 0 3 -10 -4 2 | 0 1 2 4 4 3 | 0 0 8 -5 3 7 }}

{{Optimal ET sequence|legend=1| 24, 34d, 58, …, 436, 460, 494, 954, 1448, 1506, 2460, 2954, 5414, 6920, 7414, 9874, 12828e }}

[[Badness]]: 0.505 × 10<sup>-3</sup>

@@ Line 1: / Line 1: @@
+=== Shaka ===
+{{See also|Kalismic temperaments}}
+Two commas that split 2/1 in half, corresponding to convergents to sqrt(2), are the [[1682/1681|''sha''ftesburisma]] [[Square superparticular|S29]]/S41 and the [[9801/9800|''ka''lisma S99]], prompting to temper out {S29, S41, S99}, approximating /29 and /41 [[Primodality|primodal]] chords well.
+Subgroup: 2.3.35.11.29.41
+Comma list: 841/840, 1189/1188, 1681/1680
+{{Mapping|legend=2|2 2 6 5 7 8|0 1 1 -1 1 1|0 0 2 2 1 1}}
+Optimal tuning (CTE): ~41/29 = 1\2, ~3/2 = 702.031, ~41/24 = 926.693
+[[Support]]ing [[ET]]s: {{EDOs|22, 26, 36, 48, 70, 96, 106, 118, 140, 154, 176, 188, 224, 272, 294, 342}}
+Scale: [[Shaka10]]
 === Spog ===
@@ Line 100: / Line 117: @@
 Comma list: 1716/1715, 2080/2079, 17303/17280
-Mapping: {{mapping| 2 0 1 2 6 -3 | 0 1 4 0 2 1 | 0 0 -5 2 -3 4 }}
+{{Mapping|legend=0| 2 0 1 2 6 -3 | 0 1 4 0 2 1 | 0 0 -5 2 -3 4 }}
 {{Optimal ET sequence|legend=1| 22f, 32cf, 54cff, 72, 166, 198, 270, 634, 904, 1174, 1880ef }}
@@ Line 111: / Line 128: @@
 Comma list: 715/714, 1089/1088, 1225/1224, 2025/2023
-Mapping: {{mapping| 2 0 1 2 6 -3 0 | 0 1 4 0 2 1 6 | 0 0 -5 2 -3 4 -6 }}
+{{Mapping|legend=0| 2 0 1 2 6 -3 0 | 0 1 4 0 2 1 6 | 0 0 -5 2 -3 4 -6 }}
 {{Optimal ET sequence|legend=1| 22f, 54cffgg, 72, 166g, 198g, 270, 364, 436, 634g, 706f }}
@@ Line 122: / Line 139: @@
 Comma list: 715/714, 1225/1224, 1540/1539, 2080/2079, 4200/4199
-Mapping: {{mapping| 2 0 1 2 6 -3 0 13 | 0 1 4 0 2 1 6 2 | 0 0 -5 2 -3 4 -6 -6 }}
+{{Mapping|legend=0| 2 0 1 2 6 -3 0 13 | 0 1 4 0 2 1 6 2 | 0 0 -5 2 -3 4 -6 -6 }}
 {{Optimal ET sequence|legend=1| 72, 94, 166g, 198g, 270, 436, 634g, 706f }}
@@ Line 133: / Line 150: @@
 Comma list: 715/714, 1225/1224, 1540/1539, 2080/2079, 2530/2527, 2737/2736
-Mapping: {{mapping| 2 0 1 2 6 -3 0 13 19 | 0 1 4 0 2 1 6 2 -2 | 0 0 -5 2 -3 4 -6 -6 -2 }}
+{{Mapping|legend=0| 2 0 1 2 6 -3 0 13 19 | 0 1 4 0 2 1 6 2 -2 | 0 0 -5 2 -3 4 -6 -6 -2 }}
 {{Optimal ET sequence|legend=1| 72, 94, 166g, 270, 342f, 436, 706fi }}
@@ Line 146: / Line 163: @@
 Comma list: 4225/4224, 9801/9800, 41503/41472
-Mapping: {{mapping| 2 0 1 2 6 9 | 0 1 9 -2 5 -6 | 0 0 -10 4 -6 7 }}
+{{Mapping|legend=0| 2 0 1 2 6 9 | 0 1 9 -2 5 -6 | 0 0 -10 4 -6 7 }}
 : mapping generators: ~99/70, ~3, ~154/65
@@ Line 159: / Line 176: @@
 Comma list: 1089/1088, 1225/1224, 2025/2023, 4225/4224
-Mapping: {{mapping| 2 0 1 2 6 9 0 | 0 1 9 -2 5 -6 12 | 0 0 -10 4 -6 7 -12 }}
+{{Mapping|legend=0| 2 0 1 2 6 9 0 | 0 1 9 -2 5 -6 12 | 0 0 -10 4 -6 7 -12 }}
 {{Optimal ET sequence|legend=1| 44, 50, 94, 144g, 176g, 220g, 270, 364, 414, 634g, 684 }}
@@ Line 170: / Line 187: @@
 Comma list: 1089/1088, 1225/1224, 1729/1728, 2926/2925, 3762/3757
-Mapping: {{mapping| 2 0 1 2 6 9 0 1 | 0 1 9 -2 5 -6 12 11 | 0 0 -10 4 -6 7 -12 -11 }}
+{{Mapping|legend=0| 2 0 1 2 6 9 0 1 | 0 1 9 -2 5 -6 12 11 | 0 0 -10 4 -6 7 -12 -11 }}
 {{Optimal ET sequence|legend=1| 44, 50, 94, 144gh, 176g, 220g, 270, 414h, 590, 634g, 684h }}
@@ Line 181: / Line 198: @@
 Comma list: 897/896, 1089/1088, 1225/1224, 1729/1728, 2737/2736, 2926/2925
-Mapping: {{mapping| 2 0 1 2 6 9 0 1 7 | 0 1 9 -2 5 -6 12 11 3 | 0 0 -10 4 -6 7 -12 -11 -3 }}
+{{Mapping|legend=0| 2 0 1 2 6 9 0 1 7 | 0 1 9 -2 5 -6 12 11 3 | 0 0 -10 4 -6 7 -12 -11 -3 }}
 {{Optimal ET sequence|legend=1| 44, 50, 94, 144gh, 176g, 220g, 226, 270, 320i, 364i, 414hi }}
@@ Line 211: / Line 228: @@
 Comma list: 9801/9800, 10648/10647, 371293/371250
-Mapping: {{mapping| 2 0 3 -10 -4 2 | 0 1 2 4 4 3 | 0 0 8 -5 3 7 }}
+{{Mapping|legend=0| 2 0 3 -10 -4 2 | 0 1 2 4 4 3 | 0 0 8 -5 3 7 }}
 {{Optimal ET sequence|legend=1| 24, 34d, 58, …, 436, 460, 494, 954, 1448, 1506, 2460, 2954, 5414, 6920, 7414, 9874, 12828e }}
 [[Badness]]: 0.505 × 10<sup>-3</sup>