Hemifamity family: Difference between revisions
No edit summary |
m Text replacement - "Category:Temperament families" to "Category:Temperament families Category:Pages with mostly numerical content" |
||
| (One intermediate revision by the same user not shown) | |||
| Line 24: | Line 24: | ||
* [[7-odd-limit]]: 3 and 7 1/7c sharp, 5 just | * [[7-odd-limit]]: 3 and 7 1/7c sharp, 5 just | ||
: {{monzo list| 1 0 0 0 | 10/7 1/7 1/7 -1/7 | 0 0 1 0 | 10/7 -6/7 1/7 6/7 }} | : {{monzo list| 1 0 0 0 | 10/7 1/7 1/7 -1/7 | 0 0 1 0 | 10/7 -6/7 1/7 6/7 }} | ||
: [[Eigenmonzo basis| | : [[Eigenmonzo basis|unchanged-interval (eigenmonzo) basis]]: 2.5.7/3 | ||
* [[9-odd-limit]]: 3 1/8c sharp, 5 just, 7 1/4c sharp | * [[9-odd-limit]]: 3 1/8c sharp, 5 just, 7 1/4c sharp | ||
: {{monzo list| 1 0 0 0 | 5/4 1/4 1/8 -1/8 | 0 0 1 0 | 5/2 -3/2 1/4 3/4 }} | : {{monzo list| 1 0 0 0 | 5/4 1/4 1/8 -1/8 | 0 0 1 0 | 5/2 -3/2 1/4 3/4 }} | ||
: [[Eigenmonzo basis| | : [[Eigenmonzo basis|unchanged-interval (eigenmonzo) basis]]: 2.5.9/7 | ||
{{Optimal ET sequence|legend=1| 41, 53, 87, 94, 99, 239, 251, 292, 391, 881bd, 1272bcdd }} | {{Optimal ET sequence|legend=1| 41, 53, 87, 94, 99, 239, 251, 292, 391, 881bd, 1272bcdd }} | ||
| Line 86: | Line 86: | ||
* [[11-odd-limit]] | * [[11-odd-limit]] | ||
: [{{monzo| 1 0 0 0 0 }}, {{monzo| 17/10 0 1/10 0 -1/10 }}, {{monzo| 17/5 -2 6/5 0 -1/5 }}, {{monzo| 16/5 -2 3/5 0 2/5 }}, {{monzo| 17/5 -2 1/5 0 4/5 }}] | : [{{monzo| 1 0 0 0 0 }}, {{monzo| 17/10 0 1/10 0 -1/10 }}, {{monzo| 17/5 -2 6/5 0 -1/5 }}, {{monzo| 16/5 -2 3/5 0 2/5 }}, {{monzo| 17/5 -2 1/5 0 4/5 }}] | ||
: [[Eigenmonzo basis| | : [[Eigenmonzo basis|unchanged-interval (eigenmonzo) basis]]: 2.9/5.11/9 | ||
{{Optimal ET sequence|legend=1| 29, 41, 58, 87, 99e, 145, 186e }} | {{Optimal ET sequence|legend=1| 29, 41, 58, 87, 99e, 145, 186e }} | ||
| Line 104: | Line 104: | ||
Minimax tuning: | Minimax tuning: | ||
* 13-odd-limit | * 13-odd-limit unchanged-interval (eigenmonzo) basis: 2.9/5.13/9 | ||
* 15-odd-limit | * 15-odd-limit unchanged-interval (eigenmonzo) basis: 2.5/3.13/9 | ||
{{Optimal ET sequence|legend=0| 29, 41, 46, 58, 87, 145, 232 }} | {{Optimal ET sequence|legend=0| 29, 41, 46, 58, 87, 145, 232 }} | ||
| Line 147: | Line 147: | ||
* [[11-odd-limit]] | * [[11-odd-limit]] | ||
: [{{monzo| 1 0 0 0 0 }}, {{monzo| 4/3 0 2/21 -1/21 1/21 }}, {{monzo| 0 0 1 0 0 }}, {{monzo| 2 0 3/7 2/7 -2/7 }}, {{monzo| 2 0 3/7 -5/7 5/7 }}] | : [{{monzo| 1 0 0 0 0 }}, {{monzo| 4/3 0 2/21 -1/21 1/21 }}, {{monzo| 0 0 1 0 0 }}, {{monzo| 2 0 3/7 2/7 -2/7 }}, {{monzo| 2 0 3/7 -5/7 5/7 }}] | ||
: [[Eigenmonzo basis| | : [[Eigenmonzo basis|unchanged-interval (eigenmonzo) basis]]: 2.5.11/7 | ||
{{Optimal ET sequence|legend=1| 41, 53, 58, 94, 99e, 152, 497de, 555dee, 707ddee, 859bddee }} | {{Optimal ET sequence|legend=1| 41, 53, 58, 94, 99e, 152, 497de, 555dee, 707ddee, 859bddee }} | ||
| Line 167: | Line 167: | ||
* 13- and 15-odd-limit | * 13- and 15-odd-limit | ||
: [{{monzo| 1 0 0 0 0 0 }}, {{monzo| 13/8 -1/2 1/8 0 0 1/8 }}, {{monzo| 13/4 -3 5/4 0 0 1/4 }}, {{monzo| 7/2 0 1/2 0 0 -1/2 }}, {{monzo| 25/8 -9/2 5/8 0 0 13/8 }}, {{monzo| 13/4 -3 1/4 0 0 5/4 }}] | : [{{monzo| 1 0 0 0 0 0 }}, {{monzo| 13/8 -1/2 1/8 0 0 1/8 }}, {{monzo| 13/4 -3 5/4 0 0 1/4 }}, {{monzo| 7/2 0 1/2 0 0 -1/2 }}, {{monzo| 25/8 -9/2 5/8 0 0 13/8 }}, {{monzo| 13/4 -3 1/4 0 0 5/4 }}] | ||
: | : unchanged-interval (eigenmonzo) basis: 2.11.13/7 | ||
{{Optimal ET sequence|legend=0| 41, 53, 58, 94, 111, 152f, 415dff }}* | {{Optimal ET sequence|legend=0| 41, 53, 58, 94, 111, 152f, 415dff }}* | ||
| Line 200: | Line 200: | ||
* 17-odd-limit | * 17-odd-limit | ||
: [{{monzo| 1 0 0 0 0 0 0 }}, {{monzo| 13/12 0 0 1/12 1/6 -1/12 0 }}, {{monzo| -7/4 0 0 5/4 3/2 -5/4 0 }}, {{monzo| 7/4 0 0 3/4 1/2 -3/4 0 }}, {{monzo| 0 0 0 0 1 0 0 }}, {{monzo| 7/4 0 0 -1/4 1/2 1/4 0 }}, {{monzo| 35/12 0 0 23/12 5/6 -23/12 0 }}] | : [{{monzo| 1 0 0 0 0 0 0 }}, {{monzo| 13/12 0 0 1/12 1/6 -1/12 0 }}, {{monzo| -7/4 0 0 5/4 3/2 -5/4 0 }}, {{monzo| 7/4 0 0 3/4 1/2 -3/4 0 }}, {{monzo| 0 0 0 0 1 0 0 }}, {{monzo| 7/4 0 0 -1/4 1/2 1/4 0 }}, {{monzo| 35/12 0 0 23/12 5/6 -23/12 0 }}] | ||
: | : unchanged-interval (eigenmonzo) basis: 2.11.13/7 | ||
{{Optimal ET sequence|legend=0| 58, 94, 111, 152f, 205, 263df }} | {{Optimal ET sequence|legend=0| 58, 94, 111, 152f, 205, 263df }} | ||
| Line 221: | Line 221: | ||
* [[11-odd-limit]] | * [[11-odd-limit]] | ||
: [{{monzo| 1 0 0 0 0 }}, {{monzo| 5/3 0 1/6 -1/6 0 }}, {{monzo| 26/9 0 13/18 -7/18 -1/3 }}, {{monzo| 26/9 0 -5/18 11/18 -1/3 }}, {{monzo| 26/9 0 -5/18 -7/18 2/3 }}] | : [{{monzo| 1 0 0 0 0 }}, {{monzo| 5/3 0 1/6 -1/6 0 }}, {{monzo| 26/9 0 13/18 -7/18 -1/3 }}, {{monzo| 26/9 0 -5/18 11/18 -1/3 }}, {{monzo| 26/9 0 -5/18 -7/18 2/3 }}] | ||
: [[Eigenmonzo basis| | : [[Eigenmonzo basis|unchanged-interval (eigenmonzo) basis]]: 2.7/5.11/5 | ||
{{Optimal ET sequence|legend=1| 34, 41, 53, 87, 140, 181, 321 }} | {{Optimal ET sequence|legend=1| 34, 41, 53, 87, 140, 181, 321 }} | ||
| Line 245: | Line 245: | ||
* 13- and 15-odd-limit | * 13- and 15-odd-limit | ||
: [{{monzo| 1 0 0 0 0 0 }}, {{monzo| 5/3 0 1/6 -1/6 0 0 }}, {{monzo| 26/9 0 13/18 -7/18 -1/3 0 }}, {{monzo| 26/9 0 -5/18 11/18 -1/3 0 }}, {{monzo| 26/9 0 -5/18 -7/18 2/3 0 }}, {{monzo| 26/9 0 -7/9 1/9 2/3 0 }}] | : [{{monzo| 1 0 0 0 0 0 }}, {{monzo| 5/3 0 1/6 -1/6 0 0 }}, {{monzo| 26/9 0 13/18 -7/18 -1/3 0 }}, {{monzo| 26/9 0 -5/18 11/18 -1/3 0 }}, {{monzo| 26/9 0 -5/18 -7/18 2/3 0 }}, {{monzo| 26/9 0 -7/9 1/9 2/3 0 }}] | ||
: | : unchanged-interval (eigenmonzo) basis: 2.7/5.11/5 | ||
{{Optimal ET sequence|legend=0| 34, 41, 46, 53, 87, 140, 321, 461e }} | {{Optimal ET sequence|legend=0| 34, 41, 46, 53, 87, 140, 321, 461e }} | ||
| Line 293: | Line 293: | ||
* [[11-odd-limit]]: | * [[11-odd-limit]]: | ||
: [{{monzo| 1 0 0 0 0 }}, {{monzo| 8/5 2/5 0 -1/15 -2/15 }}, {{monzo| 14/5 6/5 0 7/15 -16/15 }}, {{monzo| 16/5 -6/5 0 13/15 -4/15 }}, {{monzo| 16/5 -6/5 0 -2/15 11/15 }}] | : [{{monzo| 1 0 0 0 0 }}, {{monzo| 8/5 2/5 0 -1/15 -2/15 }}, {{monzo| 14/5 6/5 0 7/15 -16/15 }}, {{monzo| 16/5 -6/5 0 13/15 -4/15 }}, {{monzo| 16/5 -6/5 0 -2/15 11/15 }}] | ||
: [[Eigenmonzo basis| | : [[Eigenmonzo basis|unchanged-interval (eigenmonzo) basis]]: 2.9/7.11/9 | ||
{{Optimal ET sequence|legend=1| 41, 87, 111, 152, 239, 391 }} | {{Optimal ET sequence|legend=1| 41, 87, 111, 152, 239, 391 }} | ||
| Line 330: | Line 330: | ||
[[Category:Temperament families]] | [[Category:Temperament families]] | ||
[[Category:Pages with mostly numerical content]] | |||
[[Category:Hemifamity family| ]] <!-- main article --> | [[Category:Hemifamity family| ]] <!-- main article --> | ||
[[Category:Hemifamity| ]] <!-- key article --> | [[Category:Hemifamity| ]] <!-- key article --> | ||
[[Category:Rank 3]] | [[Category:Rank 3]] | ||
[[Category:Listen]] | [[Category:Listen]] | ||