User:Hotcrystal0/Temperaments: Difference between revisions
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Ratio
10763703445887/10737418240000
Factorization
2-34 × 322 × 5-4 × 73
Monzo
[-34 22 -4 3⟩
Size in cents
4.232883¢
Name
Unnamed 159 & 166 & 171 comma
FJS name
[math]\displaystyle{ \text{P1}^{7,7,7}_{5,5,5,5} }[/math]
Special properties
reduced
Tenney norm (log2 nd)
86.579
Weil norm (log2 max(n, d))
86.5825
Wilson norm (sopfr(nd))
175
Comma size
small
Open this interval in xen-calc
Factorization
2-79 × 329 × 713 × 11-1
Monzo
[-79 29 0 13 -1⟩
Size in cents
0.1138668¢
Name
Unnamed difference between 13 64/63 and 27/22
FJS name
[math]\displaystyle{ \text{M3}^{7,7,7,7,7,7,7,7,7,7,7,7,7}_{11} }[/math]
Special properties
reduced
Tenney norm (log2 nd)
164.919
Weil norm (log2 max(n, d))
164.919
Wilson norm (sopfr(nd))
347
Comma size
unnoticeable
Open this interval in xen-calc
Ratio
55788550416/55783203125
Factorization
24 × 320 × 5-9 × 13-4
Monzo
[4 20 -9 0 0 -4⟩
Size in cents
0.1659454¢
Name
Unnamed difference between 4 325/324 and 81/80
FJS name
[math]\displaystyle{ \text{P1}_{5,5,5,5,5,5,5,5,5,13,13,13,13} }[/math]
Special properties
reduced
Tenney norm (log2 nd)
71.3984
Weil norm (log2 max(n, d))
71.3985
Wilson norm (sopfr(nd))
165
Comma size
unnoticeable
Open this interval in xen-calc
Factorization
2-55 × 3-26 × 1326
Monzo
[-55 -26 0 0 0 26⟩
Size in cents
2.889184¢
Name
Unnamed difference between 26 13/12 and 3 octaves
FJS name
[math]\displaystyle{ \text{18d6}^{13,13,13,13,13,13,13,13,13,13,13,13,13,13,13,13,13,13,13,13,13,13,13,13,13,13} }[/math]
Special properties
reduced
Tenney norm (log2 nd)
192.42
Weil norm (log2 max(n, d))
192.423
Wilson norm (sopfr(nd))
526
Comma size
unnoticeable
Open this interval in xen-calc
Hotcrystal0 (talk | contribs) No edit summary |
Hotcrystal0 (talk | contribs) Whoops, inserted commas in the wrong spot |
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This page is for hotcrystal0's temperament research. | This page is for hotcrystal0's temperament research. | ||
==Rank-2== | |||
=== Tridecapyth === | |||
See [[Tridecapyth comma#Tridecapyth]]. | |||
==Rank-3== | |||
===Unnamed 159 & 166 & 171=== | |||
[[Subgroup]]: 2.3.5.7 | |||
[[Comma list]]: 10763703445887/10737418240000 | |||
{{Mapping|legend=1| 1 0 0 | 1 1 0 | 3 1 -3 | 8 -6 -4 }} | |||
[[Optimal tuning]]s: | |||
* [[WE]]: ~2 = 1200.057{{c}}, ~3/2 = 701.806{{c}}, ~20480/15309 = 505.209{{c}} | |||
: [[error map]]: {{val| +0.057 -0.093 +0.036 -0.040 }} | |||
* [[CWE]]: ~2 = 1200.000{{c}}, ~3/2 = 701.777{{c}}, ~20480/15309 = 505.167{{c}} | |||
: error map: {{val| 0.000 -0.178 -0.039 -0.155 }} | |||
{{Optimal ET sequence|legend=1| [to be finished] }} | |||
[[Badness]] (Sintel): [to be finished] | |||
==Commas== | ==Commas== | ||
| Line 28: | Line 54: | ||
|Comma = yes | |Comma = yes | ||
}} | }} | ||
Latest revision as of 00:32, 24 June 2026
This page is for hotcrystal0's temperament research.
Rank-2
Tridecapyth
See Tridecapyth comma#Tridecapyth.
Rank-3
Unnamed 159 & 166 & 171
Subgroup: 2.3.5.7
Comma list: 10763703445887/10737418240000
Mapping: [⟨1 0 0], ⟨1 1 0], ⟨3 1 -3], ⟨8 -6 -4]]
- WE: ~2 = 1200.057 ¢, ~3/2 = 701.806 ¢, ~20480/15309 = 505.209 ¢
- error map: ⟨+0.057 -0.093 +0.036 -0.040]
- CWE: ~2 = 1200.000 ¢, ~3/2 = 701.777 ¢, ~20480/15309 = 505.167 ¢
- error map: ⟨0.000 -0.178 -0.039 -0.155]
Optimal ET sequence: [to be finished]
Badness (Sintel): [to be finished]
Commas
| Interval information |
Audio demonstration
| Interval information |
Audio demonstration
| Interval information |
Audio demonstration
| Interval information |
Audio demonstration