The Quartercache: Difference between revisions

Line 16:

[[Optimal tuning]] ([[CTE]]): ~2 = 1\1, ~3/2 = 701.9742, ~5/4 = 386.3137, ~33/32 = 53.3683

{{~~Val list~~|legend=1| 21, 22, 43, 46, 65d, 68, 89, 111, 159, 202, 224, 270, 494, 742, 764, 966, 1236, 1506, 2159, 2653, 3125, 3395, 7060, 7554, 10949e, 14614e, 15850ee, 22168bdee, 23404bcdee, 26799bcdeee, 34353bcdeeee }}

{{Optimal ET sequence|legend=1| 21, 22, 43, 46, 65d, 68, 89, 111, 159, 202, 224, 270, 494, 742, 764, 966, 1236, 1506, 2159, 2653, 3125, 3395, 7060, 7554, 10949e, 14614e, 15850ee, 22168bdee, 23404bcdee, 26799bcdeee, 34353bcdeeee }}

[[Badness]]: 0.274 × 10-6

Line 32:

[[POTE generator]]s: ~3/2 = 701.9826, ~33/32 = 53.3748

{{~~Val list~~|legend=1| 21, 22, 24, 43, 46, 89, 135, 359, 494, 629, 742, 877, 1012, 1506, 2248, 2383, 2518, 7419, 8431e, 10949e, 13467e }}

{{Optimal ET sequence|legend=1| 21, 22, 24, 43, 46, 89, 135, 359, 494, 629, 742, 877, 1012, 1506, 2248, 2383, 2518, 7419, 8431e, 10949e, 13467e }}

The following unnamed rank-2 quartismic temperament MOS scales have been found

Line 63:

[[POTE generator]]s: ~3/2 = 701.7299, ~33/32 = 53.3889

{{~~Val list~~|legend=1| 24, 46c, 65d, 89, 135, 159, 224, 383, 472, 696, 1168, 1327, 1551, 2023e }}

{{Optimal ET sequence|legend=1| 24, 46c, 65d, 89, 135, 159, 224, 383, 472, 696, 1168, 1327, 1551, 2023e }}

[[Badness]]: 4.563 × 10-3

Line 91:

[[POTE generator]]s: ~3/2 = 697.3325, ~33/32 = 54.1064

[[Badness]]: 15.125 × 10-3

Line 107:

[[POTE generator]]s: ~5/4 = 380.3623, ~9/7 = 433.3120

[[Badness]]: 70.470 × 10-3

Line 123:

[[POTE generator]]s: ~33/32 = 55.3538

{{~~Val list~~|legend=1| 21, 22, 43, 65d, 521d, 543, 564, 586, 629c, 651 }}

{{Optimal ET sequence|legend=1| 21, 22, 43, 65d, 521d, 543, 564, 586, 629c, 651 }}

[[Badness]]: 64.233 × 10-3

Line 139:

[[Mapping]]: [{{val| 2 0 11 2 10 }}, {{val| 0 1 -2 1 -1 }}, {{val| 0 0 0 5 1 }}]

[[Badness]]: 23.250 × 10-3

Line 161:

[[POTE generator]]s: ~6/5 = 317.0291, ~68/55 = 370.2940

[[Badness]]: 26.882 × 10-3

Line 177:

[[POTE generator]]s: ~425/384 = 175.9566, ~33/32 = 52.9708

[[Badness]]: 81.083 × 10-3

Line 192:

[[POTE generator]]: ~160/121 = 483.0098

[[Badness]]: 0.154578

Line 207:

[[Optimal tuning]] ([[CTE]]): ~33/32 = 53.366

=== 13-limit ===

Line 218:

Optimal tuning (CTE): ~33/32 = 53.366

Optimal ~~GPV~~ sequence~~: {{val list~~| 832, 1619 }}

== Prequartismic ==

@@ Line 16: / Line 16: @@
 [[Optimal tuning]] ([[CTE]]): ~2 = 1\1, ~3/2 = 701.9742, ~5/4 = 386.3137, ~33/32 = 53.3683
-{{Val list|legend=1| 21, 22, 43, 46, 65d, 68, 89, 111, 159, 202, 224, 270, 494, 742, 764, 966, 1236, 1506, 2159, 2653, 3125, 3395, 7060, 7554, 10949e, 14614e, 15850ee, 22168bdee, 23404bcdee, 26799bcdeee, 34353bcdeeee }}
+{{Optimal ET sequence|legend=1| 21, 22, 43, 46, 65d, 68, 89, 111, 159, 202, 224, 270, 494, 742, 764, 966, 1236, 1506, 2159, 2653, 3125, 3395, 7060, 7554, 10949e, 14614e, 15850ee, 22168bdee, 23404bcdee, 26799bcdeee, 34353bcdeeee }}
 [[Badness]]: 0.274 × 10<sup>-6</sup>
@@ Line 32: / Line 32: @@
 [[POTE generator]]s: ~3/2 = 701.9826, ~33/32 = 53.3748
-{{Val list|legend=1| 21, 22, 24, 43, 46, 89, 135, 359, 494, 629, 742, 877, 1012, 1506, 2248, 2383, 2518, 7419, 8431e, 10949e, 13467e }}
+{{Optimal ET sequence|legend=1| 21, 22, 24, 43, 46, 89, 135, 359, 494, 629, 742, 877, 1012, 1506, 2248, 2383, 2518, 7419, 8431e, 10949e, 13467e }}
 The following unnamed rank-2 quartismic temperament MOS scales have been found
@@ Line 63: / Line 63: @@
 [[POTE generator]]s: ~3/2 = 701.7299, ~33/32 = 53.3889
-{{Val list|legend=1| 24, 46c, 65d, 89, 135, 159, 224, 383, 472, 696, 1168, 1327, 1551, 2023e }}
+{{Optimal ET sequence|legend=1| 24, 46c, 65d, 89, 135, 159, 224, 383, 472, 696, 1168, 1327, 1551, 2023e }}
 [[Badness]]: 4.563 × 10<sup>-3</sup>
@@ Line 91: / Line 91: @@
 [[POTE generator]]s: ~3/2 = 697.3325, ~33/32 = 54.1064
-{{Val list|legend=1| 24, 43, 67, 110c }}
+{{Optimal ET sequence|legend=1| 24, 43, 67, 110c }}
 [[Badness]]: 15.125 × 10<sup>-3</sup>
@@ Line 107: / Line 107: @@
 [[POTE generator]]s: ~5/4 = 380.3623, ~9/7 = 433.3120
-{{Val list|legend=1| 19d, 22 }}
+{{Optimal ET sequence|legend=1| 19d, 22 }}
 [[Badness]]: 70.470 × 10<sup>-3</sup>
@@ Line 123: / Line 123: @@
 [[POTE generator]]s: ~33/32 = 55.3538
-{{Val list|legend=1| 21, 22, 43, 65d, 521d, 543, 564, 586, 629c, 651 }}
+{{Optimal ET sequence|legend=1| 21, 22, 43, 65d, 521d, 543, 564, 586, 629c, 651 }}
 [[Badness]]: 64.233 × 10<sup>-3</sup>
@@ Line 139: / Line 139: @@
 [[Mapping]]: [{{val| 2 0 11 2 10 }}, {{val| 0 1 -2 1 -1 }}, {{val| 0 0 0 5 1 }}]
-{{Val list|legend=1| 22, 46, 68, 114 }}
+{{Optimal ET sequence|legend=1| 22, 46, 68, 114 }}
 [[Badness]]: 23.250 × 10<sup>-3</sup>
@@ Line 161: / Line 161: @@
 [[POTE generator]]s: ~6/5 = 317.0291, ~68/55 = 370.2940
-{{Val list|legend=1| 68, 91, 159, 246, 337, 405 }}
+{{Optimal ET sequence|legend=1| 68, 91, 159, 246, 337, 405 }}
 [[Badness]]: 26.882 × 10<sup>-3</sup>
@@ Line 177: / Line 177: @@
 [[POTE generator]]s: ~425/384 = 175.9566, ~33/32 = 52.9708
-{{Val list|legend=1| 48d, 68, 116d, 157c, 225 }}
+{{Optimal ET sequence|legend=1| 48d, 68, 116d, 157c, 225 }}
 [[Badness]]: 81.083 × 10<sup>-3</sup>
@@ Line 192: / Line 192: @@
 [[POTE generator]]: ~160/121 = 483.0098
-{{Val list|legend=1| 159, 559d, 718, 877 }}
+{{Optimal ET sequence|legend=1| 159, 559d, 718, 877 }}
 [[Badness]]: 0.154578
@@ Line 207: / Line 207: @@
 [[Optimal tuning]] ([[CTE]]): ~33/32 = 53.366
-{{Val list|legend=1| 832, 1619 }}
+{{Optimal ET sequence|legend=1| 832, 1619 }}
 === 13-limit ===
@@ Line 218: / Line 218: @@
 Optimal tuning (CTE): ~33/32 = 53.366
-Optimal GPV sequence: {{val list| 832, 1619 }}
+{{Optimal ET sequence|legend=1| 832, 1619 }}
 == Prequartismic ==