# User:Sintel/sandbox

testing lua stuff

 ← 11edo Sintel/sandbox 13edo →
Prime factorization 22 × 3
Step size 100¢ (by definition)
Fifth 7\12 (700¢)
(convergent)
Semitones (A1:m2) 1:1 (100¢ : 100¢)
Consistency limit 9
Distinct consistency limit 5
Special properties

17 equal divisions of the octave (abbreviated 17edo or 17ed2), also called 17-tone equal temperament (17tet) or 17 equal temperament (17et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 17 equal parts of about 70.6 ¢ each. Each step represents a frequency ratio of 21/17, or the 17th root of 2.

Approximation of odd harmonics in 17edo
Harmonic 3 5 7 9 11 13 15 17 19 21 23
Error Absolute (¢) +3.9 -33.4 +19.4 +7.9 +13.4 +6.5 -29.4 -34.4 -15.2 +23.3 +7.0
Relative (%) +5.6 -47.3 +27.5 +11.1 +19.0 +9.3 -41.7 -48.7 -21.5 +33.1 +9.9
Steps
(reduced)
27
(10)
39
(5)
48
(14)
54
(3)
59
(8)
63
(12)
66
(15)
69
(1)
72
(4)
75
(7)
77
(9)
 Ratio 13/8 Subgroup monzo 2.13 [-3 1⟩ Size in cents 840.52766¢ Name (lesser) tridecimal neutral sixth Color name 3o6, tho 6th FJS name $\text{m6}^{13}$ Special properties reduced,reduced harmonic Tenney height (log2 nd) 6.70044 Weil height (log2 max(n, d)) 7.40088 Wilson height (sopfr (nd)) 19 Harmonic entropy(Shannon, $\sqrt{nd}$) ~4.23596 bits https://en.xen.wiki/w/File:Jid_13_8_pluck_adu_dr220.mp3[sound info] open this interval in xen-calc

## Uniform maps

13-limit uniform maps between 16.5 and 17.5
Min. size Max. size Wart notation Map
16.5000 16.5636 17bccdddeeefff 17 26 38 46 57 61]
16.5636 16.5810 17bccdeeefff 17 26 38 47 57 61]
16.5810 16.6196 17bdeeefff 17 26 39 47 57 61]
16.6196 16.6212 17bdeeef 17 26 39 47 57 62]
16.6212 16.7196 17bdef 17 26 39 47 58 62]
16.7196 16.8899 17def 17 27 39 47 58 62]
16.8899 16.9103 17de 17 27 39 47 58 63]
16.9103 16.9198 17d 17 27 39 47 59 63]
16.9198 17.0117 17 17 27 39 48 59 63]
17.0117 17.1601 17c 17 27 40 48 59 63]
17.1601 17.1994 17cff 17 27 40 48 59 64]
17.1994 17.2760 17ceeff 17 27 40 48 60 64]
17.2760 17.3506 17cddeeff 17 27 40 49 60 64]
17.3506 17.4304 17bbcddeeff 17 28 40 49 60 64]
17.4304 17.4424 17bbcddeeffff 17 28 40 49 60 65]
17.4424 17.4884 17bbcccddeeffff 17 28 41 49 60 65]
17.4884 17.5000 17bbcccddeeeeffff 17 28 41 49 61 65]

#### Mapping matrix markup

Using the pre tag:

      2 3 5
2 [ 1 1 0]
3/2 [ 0 1 4]


Latex:

$\begin{array}{c c} & \begin{array}{c c c} 2 & 3 & 5 \\ \end{array} \\ \begin{array}{c c c}2 \\ 3/2 \end{array} & \left[ \begin{array}{c c c} 1 & 1 & 0 \\ 0 & 1 & 4 \end{array} \right] \end{array}$

CSS pre and ptt:

2 3 5 2 [ 1 1 0] 3/2 [ 0 1 4]