Xenharmonic Wiki

Hemifamity family: Difference between revisions

← Older editNewer edit →
VisualWikitext
Xenwolf (talk | contribs)
autopatrolled, Bureaucrats, confirmaccount-notify, Interface administrators, Sysops
8,705 edits
m →Music: format as single list
Cmloegcmluin (talk | contribs)
autopatrolled, emailconfirmed
5,160 edits
adding parenthetical "(unchanged intervals)" to eigenmonzo lists
Line 19: Line 19:
* [[7-odd-limit]]: 3 and 7 1/7c sharp, 5 just
* [[7-odd-limit]]: 3 and 7 1/7c sharp, 5 just
: [{{monzo| 1 0 0 0 }}, {{monzo| 10/7 1/7 1/7 -1/7 }}, {{monzo| 0 0 1 0 }}, {{monzo| 10/7 -6/7 1/7 6/7 }}]
: [{{monzo| 1 0 0 0 }}, {{monzo| 10/7 1/7 1/7 -1/7 }}, {{monzo| 0 0 1 0 }}, {{monzo| 10/7 -6/7 1/7 6/7 }}]
: [[Eigenmonzo]]s: 2, 5/4, 7/6
: [[Eigenmonzo]]s (unchanged intervals): 2, 5/4, 7/6
* [[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| 1 0 0 0 }}, {{monzo| 5/4 1/4 1/8 -1/8 }}, {{monzo| 0 0 1 0 }}, {{monzo| 5/2 -3/2 1/4 3/4 }}]
: [{{monzo| 1 0 0 0 }}, {{monzo| 5/4 1/4 1/8 -1/8 }}, {{monzo| 0 0 1 0 }}, {{monzo| 5/2 -3/2 1/4 3/4 }}]
: [[Eigenmonzo]]s: 2, 5/4, 9/7
: [[Eigenmonzo]]s (unchanged intervals): 2, 5/4, 9/7


{{Val list|legend=1| 99, 239, 292, 391, 881bd }}
{{Val list|legend=1| 99, 239, 292, 391, 881bd }}
Line 69: Line 69:


Minimax tuning:  
Minimax tuning:  
* 13-odd-limit eigenmonzos: 2, 10/9, 13/10
* 13-odd-limit eigenmonzos (unchanged intervals): 2, 10/9, 13/10
* 15-odd-limit eigenmonzos: 2, 15/13, 6/5
* 15-odd-limit eigenmonzos (unchanged intervals): 2, 15/13, 6/5


Vals: {{Val list| 29, 41, 46, 58, 87, 145, 232, 377cef }}
Vals: {{Val list| 29, 41, 46, 58, 87, 145, 232, 377cef }}
Line 86: Line 86:
* [[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]]s: 2, 5/4, 14/11
: [[Eigenmonzo]]s (unchanged intervals): 2, 5/4, 14/11


{{Val list|legend=1| 41, 53, 58, 94, 99e, 152, 555dee, 707ddee, 859bddee }}
{{Val list|legend=1| 41, 53, 58, 94, 99e, 152, 555dee, 707ddee, 859bddee }}
Line 100: Line 100:
* 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 }}]
: [[Eigenmonzo]]s: 2, 11/8, 14/13
: [[Eigenmonzo]]s (unchanged intervals): 2, 11/8, 14/13


=== 17-limit  ===
=== 17-limit  ===
Line 112: Line 112:
* 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 }}]
: [[Eigenmonzo]]s: 2, 11/8, 14/13
: [[Eigenmonzo]]s (unchanged intervals): 2, 11/8, 14/13


Vals: {{Val list| 58, 94, 111, 152f, 205 }}
Vals: {{Val list| 58, 94, 111, 152f, 205 }}
Line 128: Line 128:
* [[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]]s: ~2, ~14/11, ~7/5
: [[Eigenmonzo]]s (unchanged intervals): ~2, ~14/11, ~7/5


{{Val list|legend=1| 34, 41, 53, 87, 140, 181, 321 }}
{{Val list|legend=1| 34, 41, 53, 87, 140, 181, 321 }}
Line 144: Line 144:
* 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 }}]
: Eigenmonzos: 2, 14/11, 7/5
: Eigenmonzos (unchanged intervals): 2, 14/11, 7/5


Lattice basis:  
Lattice basis:  
Line 170: Line 170:
* [[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]]s: 2, 11/9, 9/7
: [[Eigenmonzo]]s (unchanged intervals): 2, 11/9, 9/7


{{Val list|legend=1| 41, 87, 111, 152, 239, 391 }}
{{Val list|legend=1| 41, 87, 111, 152, 239, 391 }}
Retrieved from "https://en.xen.wiki/w/Hemifamity_family"