User:Hotcrystal0/Temperaments

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]]

Optimal tunings:

• 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

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
Audio demonstration
Open this interval in xen-calc

Interval information

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
Audio demonstration
Open this interval in xen-calc

Interval information

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
Audio demonstration
Open this interval in xen-calc

Interval information

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
Audio demonstration
Open this interval in xen-calc