User:FloraC/Sandbox

Test User:FloraC/Temperament data

Subgroup: missing ^? 

Comma list: 81/80, 126/125

Mapping: missing ^? 

mapping generators: ~2, ~3

Wedgie: ⟨⟨ 1 4 10 4 13 12 ]]

Minimax tuning: 7- and 9-odd-limit:

[[1 0 0 0⟩, [1 0 1/4 0⟩, [0 0 1 0⟩, [-3 0 5/2 0⟩]

Eigenmonzos: 2, 5

Tuning ranges: Valid range: [694.737, 700.000] (19 to 12)

Nice range: [694.786, 701.955]

Strict range: [694.786, 700.000]

Algebraic generator: Cybozem, the real root of 15x³ - 10x² - 18, which comes to 503.4257 cents. The recurrence converges quickly.

Badness: 0.0137

Septimal meantone

Period: 1\1

Optimal (POTE) generator: ~3/2 = 696.495

EDO generators: 7\12, 11\19, 18\31, 25\43, 29\50

Scales: Meantone5, Meantone7, Meantone12

Interval table (12-note MOS, 2.3.5.7 POTE tuning)

#	Cents	Approximate ratios
0	0.0	1/1
1	696.5	3/2
2	193.0	9/8, 10/9
3	889.5	5/3
4	386.0	5/4
5	1082.5	15/8, 28/15
6	579.0	7/5
7	75.5	21/20, 25/24, 28/27
8	772.0	14/9, 25/16
9	268.5	7/6
10	965.0	7/4
11	461.4	21/16

Technical data

Commas: 81/80, 126/125

Period-generator mapping: [⟨1 0 -4 -13], ⟨0 1 4 10]]

Mapping generator: ~3

7- and 9-odd-limit minimax

[[1 0 0 0⟩, [1 0 1/4 0⟩, [0 0 1 0⟩, [-3 0 5/2 0⟩]

Eigenmonzos: 2, 5

Valid range: [694.737, 700.000] (19 to 12)

Nice range: [694.786, 701.955]

Strict range: [694.786, 700.000]

Algebraic generator: Cybozem, the real root of 15x³ - 10x² - 18, which comes to 503.4257 cents. The recurrence converges quickly.

Wedgie: ⟨⟨1 4 10 4 13 12]]

Vals: 5, 7, 12, 19, 26, 31, 43, 45, 50, 55, 67, 69, 74, 81, 88, 98, 105, 117, 131b, 212bb, 293bb

Badness: 0.0137

Commas

41edo tempers out the following commas using its patent val, ⟨41 65 95 115 142 152 168 174 185 199 203].

Prime limit	Ratio	Name(s)
3	[65 -41⟩	41-comma
5	[-5 -10 9⟩	Shibboleth
5	[-25 7 6⟩	Ampersand
5	3125/3072	Magic comma
5	[5 -9 4⟩	Tetracot comma
5	[20 -17 3⟩	Roda
5	[-15 8 1⟩	Schisma
7	[0 -7 6 -1⟩	Great BP diesis
7	[-10 7 8 -7⟩	Blackjackisma
7	875/864	Keema
7	3125/3087	Gariboh
7	[10 -11 2 1⟩	Tolerma
7	[-15 3 2 2⟩	Mirwomo comma
7	245/243	Sensamagic
7	4000/3969	Octagar
7	[-15 0 -2 7⟩	Quince
7	1029/1024	Gamelisma
7	225/224	Marvel comma
7	[0 3 4 -5⟩	Mirkwai
7	[5 -7 -1 3⟩	Hemimage
7	5120/5103	Hemifamity
7	[25 -14 0 -1⟩	Garischisma
7	2401/2400	Breedsma
11	[15 0 1 0 -5⟩	Thuja comma
11	245/242	Cassacot
11	100/99	Ptolemisma
11	1344/1331	Hemimin
11	896/891	Pentacircle
11	[16 0 0 -2 -3⟩	Orgonisma
11	243/242	Rastma
11	385/384	Keenanisma
11	441/440	Werckisma
11	1375/1372	Moctdel
11	540/539	Swetisma
11	3025/3024	Lehmerisma
11	[-1 2 -4 5 -2⟩	Odiheim
13	343/338
13	105/104	Animist comma
13	[12 -7 0 1 0 -1⟩	Secorian
13	275/273	Gassorma
13	144/143	Grossma
13	196/195	Mynucuma
13	640/637	Huntma
13	1188/1183	Kestrel comma
13	325/324	Marveltwin
13	352/351	Minthma
13	364/363	Gentle comma
13	847/845	Cuthbert
13	729/728	Squbema
13	4096/4095	Schismina
13	[3 -2 0 -1 3 -2⟩	Harmonisma
17	2187/2176	Septendecimal schisma
17	256/255	Septendecimal kleisma
17	715/714	Septendecimal bridge comma
19	210/209	Spleen comma
19	361/360	Go comma
19	513/512	Undevicesimal comma
19	1216/1215	Eratosthenes' comma
23	736/729	Vicesimotertial comma
29	145/144	29th-partial chroma