User:FloraC/Sandbox: Difference between revisions
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: [[Eigenmonzo]]s: 2, 5 | : [[Eigenmonzo]]s: 2, 5 | ||
[[ | [[Tuning ranges]]: | ||
* Valid range: [694.737, 700.000] (19 to 12) | * Valid range: [694.737, 700.000] (19 to 12) | ||
* Nice range: [694.786, 701.955] | * Nice range: [694.786, 701.955] | ||
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Algebraic generator: Cybozem, the real root of 15''x''<sup>3</sup> - 10''x''<sup>2</sup> - 18, which comes to 503.4257 cents. The recurrence converges quickly. | Algebraic generator: Cybozem, the real root of 15''x''<sup>3</sup> - 10''x''<sup>2</sup> - 18, which comes to 503.4257 cents. The recurrence converges quickly. | ||
{{EDOs|legend=1| 12, 19, 31, 81, 112b, 143b }} | |||
[[Badness]]: 0.0137 | [[Badness]]: 0.0137 | ||
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# Comma list shows the simplest commas sufficient to define the temperament. This must be stated somewhere in this wiki. | # Comma list shows the simplest commas sufficient to define the temperament. This must be stated somewhere in this wiki. | ||
# Mapping generators should show all the ratios as used in the mapping, including the period. | # Mapping generators should show all the ratios as used in the mapping, including the period. | ||
# Minimax tuning are based on tonality diamond, so it should explicitly state the ''odd'' limit, or a diamond function of ratios. | # Minimax tuning are based on tonality diamond, so it should explicitly state the ''odd'' limit, or a diamond function of ratios. | ||
# EDO template. It shows "EDOs" currently but we might switch to "Vals" later by changing the template. | |||
== Commas == | == Commas == |
Revision as of 06:52, 3 February 2021
Test User:FloraC/Temperament data
Comma list: 81/80, 126/125
- 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
Comment: doesn't actually look great
Test User:FloraC/Collapsed box
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
User:FloraC/Collapsed box User:FloraC/Collapsed box
Comment: This provides much more freedom. Looks great to me by this very formatting.
Note:
- Order: comma list, mapping, mapping generators (or simply "generators", this is the same thing), wedgie, minimax tuning, tuning ranges, algebraic generator, vals, badness, complexity spectrum.
- Comma list shows the simplest commas sufficient to define the temperament. This must be stated somewhere in this wiki.
- Mapping generators should show all the ratios as used in the mapping, including the period.
- Minimax tuning are based on tonality diamond, so it should explicitly state the odd limit, or a diamond function of ratios.
- EDO template. It shows "EDOs" currently but we might switch to "Vals" later by changing the template.
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[1] | 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 |
- ↑ Ratios with more than 9 digits are presented in monzos