User:Sintel/sandbox

[math]\displaystyle{ \def\hs{\hspace{-3px}} \def\vsp{{}\mkern-5.5mu}{} \def\llangle{\left\langle\vsp\left\langle} \def\lllangle{\left\langle\vsp\left\langle\vsp\left\langle} \def\llllangle{\left\langle\vsp\left\langle\vsp\left\langle\vsp\left\langle} \def\llbrack{\left[\left[} \def\lllbrack{\left[\left[\left[} \def\llllbrack{\left[\left[\left[\left[} \def\llvert{\left\vert\left\vert} \def\lllvert{\left\vert\left\vert\left\vert} \def\llllvert{\left\vert\left\vert\left\vert\left\vert} \def\rrangle{\right\rangle\vsp\right\rangle} \def\rrrangle{\right\rangle\vsp\right\rangle\vsp\right\rangle} \def\rrrrangle{\right\rangle\vsp\right\rangle\vsp\right\rangle\vsp\right\rangle} \def\rrbrack{\right]\right]} \def\rrrbrack{\right]\right]\right]} \def\rrrrbrack{\right]\right]\right]\right]} \def\rrvert{\right\vert\right\vert} \def\rrrvert{\right\vert\right\vert\right\vert} \def\rrrrvert{\right\vert\right\vert\right\vert\right\vert} }[/math][math]\displaystyle{ \def\abs#1{\left|{#1}\right|} \def\norm#1{\left\|{#1}\right\|} \def\floor#1{\left\lfloor{#1}\right\rfloor} \def\ceil#1{\left\lceil{#1}\right\rceil} \def\round#1{\left\lceil{#1}\right\rfloor} \def\rround#1{\left\lfloor{#1}\right\rceil} }[/math]

Backslashes

\\\\\\\\

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Texops

[math]\displaystyle{ \rround{x + y} }[/math]

Uniform maps

7-limit uniform maps between 11.8 and 12.2

Min. size	Max. size	Wart notation	Map
11.6722	11.8436	12cd	⟨12 19 27 33]
11.8436	11.9329	12d	⟨12 19 28 33]
11.9329	12.2743	12	⟨12 19 28 34]

7-limit uniform maps between 14.8 and 15.2

Min. size	Max. size	Wart notation	Map
14.7826	14.8268	15bc	⟨15 23 34 42]
14.8268	14.8583	15c	⟨15 24 34 42]
14.8583	15.1388	15	⟨15 24 35 42]
15.1388	15.2890	15d	⟨15 24 35 43]

5-limit uniform maps between 14.5 and 15.5

Min. size	Max. size	Wart notation	Map
14.5000	14.8268	15bc	⟨15 23 34]
14.8268	14.8583	15c	⟨15 24 34]
14.8583	15.2890	15	⟨15 24 35]
15.2890	15.4578	15cc	⟨15 24 36]
15.4578	15.5000	15bbcc	⟨15 25 36]

Bravura

C C

testing lua stuff

← 11edo

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 (%)	+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)

Interval information

Ratio	13/8
Subgroup monzo	2.13 [-3 1⟩
Size in cents	840.5277¢
Name	(lesser) tridecimal neutral sixth
Color name	3o6, tho 6th
FJS name	[math]\displaystyle{ \text{m6}^{13} }[/math]
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, [math]\displaystyle{ \sqrt{nd} }[/math])	~4.23596 bits
[sound info]
Open this interval in xen-calc

Mapping matrix markup

Using the pre tag:

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

Latex:

[math]\displaystyle{ \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]