Gamelismic clan: Difference between revisions
Cmloegcmluin (talk | contribs) adding parenthetical "(unchanged intervals)" to eigenmonzo lists |
|||
| Line 46: | Line 46: | ||
* [[7-odd-limit|7-]] and [[9-odd-limit]]: ~8/7 = {{monzo| 2/9 0 1/18 -1/18 }} | * [[7-odd-limit|7-]] and [[9-odd-limit]]: ~8/7 = {{monzo| 2/9 0 1/18 -1/18 }} | ||
: [{{monzo| 1 0 0 0 }}, {{monzo| 5/3 0 1/6 -1/6 }}, {{monzo| 25/9 0 17/18 -17/18 }}, {{monzo| 25/9 0 -1/18 1/18 }}] | : [{{monzo| 1 0 0 0 }}, {{monzo| 5/3 0 1/6 -1/6 }}, {{monzo| 25/9 0 17/18 -17/18 }}, {{monzo| 25/9 0 -1/18 1/18 }}] | ||
: [[Eigenmonzo]]s: 2, 7/5 | : [[Eigenmonzo]]s (unchanged intervals): 2, 7/5 | ||
[[Algebraic generator]]: larger root of 20''x''<sup>2</sup> - 36''x'' + 15, or (9 + √6)/10. | [[Algebraic generator]]: larger root of 20''x''<sup>2</sup> - 36''x'' + 15, or (9 + √6)/10. | ||
| Line 68: | Line 68: | ||
* [[11-odd-limit]]: ~8/7 = {{monzo| 4/19 2/19 0 0 -1/19 }} | * [[11-odd-limit]]: ~8/7 = {{monzo| 4/19 2/19 0 0 -1/19 }} | ||
: [{{monzo| 1 0 0 0 0 }}, {{monzo| 31/19 6/19 0 0 -3/19 }}, {{monzo| 49/19 34/19 0 0 -17/19 }}, {{monzo| 53/19 -2/19 0 0 1/19 }}, {{monzo| 62/19 -26/19 0 0 13/19 }}] | : [{{monzo| 1 0 0 0 0 }}, {{monzo| 31/19 6/19 0 0 -3/19 }}, {{monzo| 49/19 34/19 0 0 -17/19 }}, {{monzo| 53/19 -2/19 0 0 1/19 }}, {{monzo| 62/19 -26/19 0 0 13/19 }}] | ||
: Eigenmonzos: 2, 11/9 | : Eigenmonzos (unchanged intervals): 2, 11/9 | ||
Algebraic generator: [[Algebraic number|positive root]] of ''x''<sup>2</sup> + 16''x'' - 31, or √95 - 8. | Algebraic generator: [[Algebraic number|positive root]] of ''x''<sup>2</sup> + 16''x'' - 31, or √95 - 8. | ||
| Line 89: | Line 89: | ||
Minimax tuning: | Minimax tuning: | ||
* 13- and 15-odd-limit: ~8/7 = {{monzo| 3/14 1/14 0 0 0 -1/28 }} | * 13- and 15-odd-limit: ~8/7 = {{monzo| 3/14 1/14 0 0 0 -1/28 }} | ||
: Eigenmonzos: 2, 13/9 | : Eigenmonzos (unchanged intervals): 2, 13/9 | ||
Algebraic generator: Gatetone, positive root of 4''x''<sup>6</sup> - 7''x'' - 1. Recurrence converges slowly. | Algebraic generator: Gatetone, positive root of 4''x''<sup>6</sup> - 7''x'' - 1. Recurrence converges slowly. | ||
| Line 110: | Line 110: | ||
Minimax tuning: | Minimax tuning: | ||
* 17-odd-limit: ~8/7 = {{monzo| 3/13 1/13 0 0 0 0 -1/26 }} | * 17-odd-limit: ~8/7 = {{monzo| 3/13 1/13 0 0 0 0 -1/26 }} | ||
: Eigenmonzos: 2, 18/17 | : Eigenmonzos (unchanged intervals): 2, 18/17 | ||
Vals: {{Val list| 41, 46, 87, 220dg, 307dgg }} | Vals: {{Val list| 41, 46, 87, 220dg, 307dgg }} | ||
| Line 195: | Line 195: | ||
* [[7-odd-limit|7-]] and [[9-odd-limit]]: ~8/7 = {{monzo| 7/24 0 -1/24 }} | * [[7-odd-limit|7-]] and [[9-odd-limit]]: ~8/7 = {{monzo| 7/24 0 -1/24 }} | ||
: [{{monzo| 1 0 0 0 }}, {{monzo| 15/8 0 -1/8 0 }}, {{monzo| 0 0 1 0 }}, {{monzo| 65/24 0 1/24 0 }}] | : [{{monzo| 1 0 0 0 }}, {{monzo| 15/8 0 -1/8 0 }}, {{monzo| 0 0 1 0 }}, {{monzo| 65/24 0 1/24 0 }}] | ||
: [[Eigenmonzo]]s: 2, 5 | : [[Eigenmonzo]]s (unchanged intervals): 2, 5 | ||
{{Val list|legend=1| 36, 41, 77, 118, 277d }} | {{Val list|legend=1| 36, 41, 77, 118, 277d }} | ||
| Line 215: | Line 215: | ||
* [[11-odd-limit]]: ~8/7 = {{monzo| 7/24 0 -1/24 }} | * [[11-odd-limit]]: ~8/7 = {{monzo| 7/24 0 -1/24 }} | ||
: [{{monzo| 1 0 0 0 0 }}, {{monzo| 15/8 0 -1/8 0 0 }}, {{monzo| 0 0 1 0 0 }}, {{monzo| 65/24 0 1/24 0 0 }}, {{monzo| 37/6 0 -7/6 0 0 }}] | : [{{monzo| 1 0 0 0 0 }}, {{monzo| 15/8 0 -1/8 0 0 }}, {{monzo| 0 0 1 0 0 }}, {{monzo| 65/24 0 1/24 0 0 }}, {{monzo| 37/6 0 -7/6 0 0 }}] | ||
: Eigenmonzos: 2, 5 | : Eigenmonzos (unchanged intervals): 2, 5 | ||
Vals: {{Val list| 36e, 41, 77, 118, 159, 277d }} | Vals: {{Val list| 36e, 41, 77, 118, 159, 277d }} | ||
| Line 403: | Line 403: | ||
* [[7-odd-limit]]: ~15/14 = {{monzo| 2/13 1/13 -1/13 }} | * [[7-odd-limit]]: ~15/14 = {{monzo| 2/13 1/13 -1/13 }} | ||
: [{{monzo| 1 0 0 0 }}, {{monzo| 25/13 6/13 -6/13 0 }}, {{monzo| 25/13 -7/13 7/13 0 }}, {{monzo| 35/13 -2/13 2/13 0 }}] | : [{{monzo| 1 0 0 0 }}, {{monzo| 25/13 6/13 -6/13 0 }}, {{monzo| 25/13 -7/13 7/13 0 }}, {{monzo| 35/13 -2/13 2/13 0 }}] | ||
: [[Eigenmonzo]]s: 2, 6/5 | : [[Eigenmonzo]]s (unchanged intervals): 2, 6/5 | ||
* [[9-odd-limit]]: ~15/14 = {{monzo| 1/19 2/19 -1/19 }} | * [[9-odd-limit]]: ~15/14 = {{monzo| 1/19 2/19 -1/19 }} | ||
: [{{monzo| 1 0 0 0 }}, {{monzo| 25/19 12/19 -6/19 0 }}, {{monzo| 50/19 -14/19 7/19 0 }}, {{monzo| 55/19 -4/19 2/19 0 }}] | : [{{monzo| 1 0 0 0 }}, {{monzo| 25/19 12/19 -6/19 0 }}, {{monzo| 50/19 -14/19 7/19 0 }}, {{monzo| 55/19 -4/19 2/19 0 }}] | ||
: [[Eigenmonzo]]s: 2, 10/9 | : [[Eigenmonzo]]s (unchanged intervals): 2, 10/9 | ||
[[Tuning ranges]]: | [[Tuning ranges]]: | ||
| Line 435: | Line 435: | ||
* [[11-odd-limit]]: ~15/14 = {{monzo| 1/19 2/19 -1/19 }} | * [[11-odd-limit]]: ~15/14 = {{monzo| 1/19 2/19 -1/19 }} | ||
: [{{monzo| 1 0 0 0 0 }}, {{monzo| 25/19 12/19 -6/19 0 0 }}, {{monzo| 50/19 -14/19 7/19 0 0 }}, {{monzo| 55/19 -4/19 2/19 0 0 }}, {{monzo| 53/19 30/19 -15/19 0 0 }}] | : [{{monzo| 1 0 0 0 0 }}, {{monzo| 25/19 12/19 -6/19 0 0 }}, {{monzo| 50/19 -14/19 7/19 0 0 }}, {{monzo| 55/19 -4/19 2/19 0 0 }}, {{monzo| 53/19 30/19 -15/19 0 0 }}] | ||
: Eigenmonzos: 2, 10/9 | : Eigenmonzos (unchanged intervals): 2, 10/9 | ||
Tuning ranges: | Tuning ranges: | ||
| Line 782: | Line 782: | ||
* [[7-odd-limit]]: ~10/9 = {{monzo| 3/26 0 -1/13 1/13 }} | * [[7-odd-limit]]: ~10/9 = {{monzo| 3/26 0 -1/13 1/13 }} | ||
: [{{monzo| 1 0 0 0 }}, {{monzo| 47/26 0 6/13 -6/13 }}, {{monzo| 71/26 0 11/13 -11/13 }}, {{monzo| 71/26 0 -2/13 2/13 }}] | : [{{monzo| 1 0 0 0 }}, {{monzo| 47/26 0 6/13 -6/13 }}, {{monzo| 71/26 0 11/13 -11/13 }}, {{monzo| 71/26 0 -2/13 2/13 }}] | ||
: [[Eigenmonzo]]s: 2, 7/5 | : [[Eigenmonzo]]s (unchanged intervals): 2, 7/5 | ||
* [[9-odd-limit]]: ~10/9 = {{monzo| 5/28 -1/7 0 1/14 }} | * [[9-odd-limit]]: ~10/9 = {{monzo| 5/28 -1/7 0 1/14 }} | ||
: [{{monzo| 1 0 0 0 }}, {{monzo| 10/7 6/7 0 -3/7 }}, {{monzo| 57/28 11/7 0 -11/14 }}, {{monzo| 20/7 -2/7 0 1/7 }}] | : [{{monzo| 1 0 0 0 }}, {{monzo| 10/7 6/7 0 -3/7 }}, {{monzo| 57/28 11/7 0 -11/14 }}, {{monzo| 20/7 -2/7 0 1/7 }}] | ||
: [[Eigenmonzo]]s: 2, 9/7 | : [[Eigenmonzo]]s (unchanged intervals): 2, 9/7 | ||
{{Val list|legend=1| 26, 46, 72, 118, 190 }} | {{Val list|legend=1| 26, 46, 72, 118, 190 }} | ||
| Line 805: | Line 805: | ||
* [[11-odd-limit]]: ~10/9 = {{monzo| 5/28 -1/7 0 1/14 }} | * [[11-odd-limit]]: ~10/9 = {{monzo| 5/28 -1/7 0 1/14 }} | ||
: [{{monzo| 1 0 0 0 0 }}, {{monzo| 10/7 6/7 0 -3/7 0 }}, {{monzo| 57/28 11/7 0 -11/14 0 }}, {{monzo| 20/7 -2/7 0 1/7 0 }}, {{monzo| 99/28 -3/7 0 3/14 0 }}] | : [{{monzo| 1 0 0 0 0 }}, {{monzo| 10/7 6/7 0 -3/7 0 }}, {{monzo| 57/28 11/7 0 -11/14 0 }}, {{monzo| 20/7 -2/7 0 1/7 0 }}, {{monzo| 99/28 -3/7 0 3/14 0 }}] | ||
: Eigenmonzos: 2, 9/7 | : Eigenmonzos (unchanged intervals): 2, 9/7 | ||
Vals: {{Val list| 26, 46, 72, 118, 190 }} | Vals: {{Val list| 26, 46, 72, 118, 190 }} | ||