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	highly composite zeta peak zeta peak integer zeta integral zeta gap

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 2^1/17, 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 (%)	+6	-47	+27	+11	+19	+9	-42	-49	-21	+33	+10
Steps (reduced)		27 (10)	39 (5)	48 (14)	54 (3)	59 (8)	63 (12)	66 (15)	69 (1)	72 (4)	75 (7)	77 (9)

Interval information

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	[math]\text{m6}^{13}[/math]
Special properties	reduced
Tenney height (log2 nd)	6.70044
Weil height (log2 max(n, d))	7.40088
Wilson height (sopfr (nd))	19
Harmonic entropy (Shannon, [math]\sqrt{n\cdot d}[/math])	~4.58259 bits
[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:

[math] \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} [/math]

CSS pre and ptt:

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