User:FloraC/Sandbox: Difference between revisions

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! [[Ratio]]<ref>Ratios with more than 9 digits are presented in monzos</ref>
! [[Ratio]]<ref>Ratios with more than 9 digits are presented in monzos</ref>
! Name(s)
! Name(s)
! Comment(s)
|-
|-
| 3
| 3
| <abbr title="36893488147419103232/36472996377170786403">{{monzo| 65 -41 }}</abbr>
| <abbr title="36893488147419103232/36472996377170786403">{{monzo| 65 -41 }}</abbr>
| [[41-comma]]
| [[41-comma]]
|
|-
|-
| 5
| 5
| <abbr title="1953125/1889568">{{Monzo| -5 -10 9 }}</abbr>
| <abbr title="1953125/1889568">{{Monzo| -5 -10 9 }}</abbr>
| [[Shibboleth]]
| [[Shibboleth]]
|
|-
|-
| 5
| 5
| <abbr title="34171875/33554432">{{Monzo| -25 7 6 }}</abbr>
| <abbr title="34171875/33554432">{{Monzo| -25 7 6 }}</abbr>
| [[Ampersand]]
| [[Ampersand]]
|
|-
|-
| 5
| 5
| [[3125/3072]]
| [[3125/3072]]
| Magic comma
| Magic comma
|
|-
|-
| 5
| 5
| <abbr title="20000/19683">{{Monzo| 5 -9 4 }}</abbr>
| <abbr title="20000/19683">{{Monzo| 5 -9 4 }}</abbr>
| [[Tetracot comma]]
| [[Tetracot comma]]
|
|-
|-
| 5
| 5
| <abbr title="131072000/129140163">{{Monzo| 20 -17 3 }}</abbr>
| <abbr title="131072000/129140163">{{Monzo| 20 -17 3 }}</abbr>
| [[Roda]]
| [[Roda]]
|
|-
|-
| 5
| 5
| <abbr title="32805/32768">{{Monzo| -15 8 1 }}</abbr>
| <abbr title="32805/32768">{{Monzo| -15 8 1 }}</abbr>
| [[Schisma]]
| [[Schisma]]
|
|-
|-
| 7
| 7
| <abbr title="15625/15309">{{Monzo| 0 -7 6 -1 }}</abbr>
| <abbr title="15625/15309">{{Monzo| 0 -7 6 -1 }}</abbr>
| [[Great BP diesis]]
| [[Great BP diesis]]
|
|-
|-
| 7
| 7
| <abbr title="854296875/843308032">{{Monzo| -10 7 8 -7 }}</abbr>
| <abbr title="854296875/843308032">{{Monzo| -10 7 8 -7 }}</abbr>
| [[Blackjackisma]]
| [[Blackjackisma]]
|
|-
|-
| 7
| 7
| [[875/864]]
| [[875/864]]
| Keema
| Keema
|
|-
|-
| 7
| 7
| [[3125/3087]]
| [[3125/3087]]
| Gariboh
| Gariboh
|
|-
|-
| 7
| 7
| <abbr title="179200/177147">{{Monzo| 10 -11 2 1 }}</abbr>
| <abbr title="179200/177147">{{Monzo| 10 -11 2 1 }}</abbr>
| [[Tolerma]]
| [[Tolerma]]
|
|-
|-
| 7
| 7
| <abbr title="33075/32768">{{Monzo| -15 3 2 2 }}</abbr>
| <abbr title="33075/32768">{{Monzo| -15 3 2 2 }}</abbr>
| [[Mirwomo comma]]
| [[Mirwomo comma]]
|
|-
|-
| 7
| 7
| [[245/243]]
| [[245/243]]
| Sensamagic
| Sensamagic
|
|-
|-
| 7
| 7
| [[4000/3969]]
| [[4000/3969]]
| Octagar
| Octagar
|
|-
|-
| 7
| 7
| <abbr title="823543/819200">{{Monzo| -15 0 -2 7 }}</abbr>
| <abbr title="823543/819200">{{Monzo| -15 0 -2 7 }}</abbr>
| [[Quince]]
| [[Quince]]
|
|-
|-
| 7
| 7
| [[1029/1024]]
| [[1029/1024]]
| Gamelisma
| Gamelisma
|
|-
|-
| 7
| 7
| [[225/224]]
| [[225/224]]
| Marvel comma
| Marvel comma
|
|-
|-
| 7
| 7
| <abbr title="16875/16807">{{Monzo| 0 3 4 -5 }}</abbr>
| <abbr title="16875/16807">{{Monzo| 0 3 4 -5 }}</abbr>
| [[Mirkwai]]
| [[Mirkwai]]
|
|-
|-
| 7
| 7
| <abbr title="10976/10935">{{Monzo| 5 -7 -1 3 }}</abbr>
| <abbr title="10976/10935">{{Monzo| 5 -7 -1 3 }}</abbr>
| [[Hemimage]]
| [[Hemimage]]
|
|-
|-
| 7
| 7
| [[5120/5103]]
| [[5120/5103]]
| Hemifamity
| Hemifamity
|
|-
|-
| 7
| 7
| <abbr title="33554432/33480783">{{Monzo| 25 -14 0 -1 }}</abbr>
| <abbr title="33554432/33480783">{{Monzo| 25 -14 0 -1 }}</abbr>
| [[Garischisma]]
| [[Garischisma]]
|
|-
|-
| 7
| 7
| [[2401/2400]]
| [[2401/2400]]
| Breedsma
| Breedsma
|
|-
|-
| 11
| 11
| <abbr title="163840/161051">{{Monzo| 15 0 1 0 -5 }}</abbr>
| <abbr title="163840/161051">{{Monzo| 15 0 1 0 -5 }}</abbr>
| [[Thuja comma]]
| [[Thuja comma]]
|
|-
|-
| 11
| 11
| [[245/242]]
| [[245/242]]
| Cassacot
| Cassacot
|
|-
|-
| 11
| 11
| [[100/99]]
| [[100/99]]
| Ptolemisma
| Ptolemisma
|
|-
|-
| 11
| 11
| [[1344/1331]]
| [[1344/1331]]
| Hemimin
| Hemimin
|
|-
|-
| 11
| 11
| [[896/891]]
| [[896/891]]
| Pentacircle
| Pentacircle
|
|-
|-
| 11
| 11
| <abbr title="65536/65219">{{Monzo| 16 0 0 -2 -3 }}</abbr>
| <abbr title="65536/65219">{{Monzo| 16 0 0 -2 -3 }}</abbr>
| [[Orgonisma]]
| [[Orgonisma]]
|
|-
|-
| 11
| 11
| [[243/242]]
| [[243/242]]
| Rastma
| Rastma
|
|-
|-
| 11
| 11
| [[385/384]]
| [[385/384]]
| Keenanisma
| Keenanisma
|
|-
|-
| 11
| 11
| [[441/440]]
| [[441/440]]
| Werckisma
| Werckisma
|
|-
|-
| 11
| 11
| [[1375/1372]]
| [[1375/1372]]
| Moctdel
| Moctdel
|
|-
|-
| 11
| 11
| [[540/539]]
| [[540/539]]
| Swetisma
| Swetisma
|
|-
|-
| 11
| 11
| [[3025/3024]]
| [[3025/3024]]
| Lehmerisma
| Lehmerisma
|
|-
|-
| 11
| 11
| <abbr title="151263/151250">{{Monzo| -1 2 -4 5 -2 }}</abbr>
| <abbr title="151263/151250">{{Monzo| -1 2 -4 5 -2 }}</abbr>
| [[Odiheim]]
| [[Odiheim]]
|
|-
|-
| 13
| 13
| [[343/338]]
| [[343/338]]
|
|  
|  
|-
|-
Line 295: Line 257:
| [[105/104]]
| [[105/104]]
| Animist comma
| Animist comma
|
|-
|-
| 13
| 13
| <abbr title="28672/28431">{{Monzo| 12 -7 0 1 0 -1 }}</abbr>
| <abbr title="28672/28431">{{Monzo| 12 -7 0 1 0 -1 }}</abbr>
| [[Secorian]]
| [[Secorian]]
|
|-
|-
| 13
| 13
| [[275/273]]
| [[275/273]]
| Gassorma
| Gassorma
|
|-
|-
| 13
| 13
| [[144/143]]
| [[144/143]]
| Grossma
| Grossma
|
|-
|-
| 13
| 13
| [[196/195]]
| [[196/195]]
| Mynucuma
| Mynucuma
|
|-
|-
| 13
| 13
| [[640/637]]
| [[640/637]]
| Huntma
| Huntma
|
|-
|-
| 13
| 13
| [[1188/1183]]
| [[1188/1183]]
| Kestrel comma
| Kestrel comma
|
|-
|-
| 13
| 13
| [[325/324]]
| [[325/324]]
| Marveltwin
| Marveltwin
|
|-
|-
| 13
| 13
| [[352/351]]
| [[352/351]]
| Minthma
| Minthma
|
|-
|-
| 13
| 13
| [[364/363]]
| [[364/363]]
| Gentle comma
| Gentle comma
|
|-
|-
| 13
| 13
| [[847/845]]
| [[847/845]]
| Cuthbert
| Cuthbert
|
|-
|-
| 13
| 13
| [[729/728]]
| [[729/728]]
| Squbema
| Squbema
|
|-
|-
| 13
| 13
| [[4096/4095]]
| [[4096/4095]]
| Schismina
| Schismina
|
|-
|-
| 13
| 13
| <abbr title="10648/10647">{{Monzo| 3 -2 0 -1 3 -2 }}</abbr>
| <abbr title="10648/10647">{{Monzo| 3 -2 0 -1 3 -2 }}</abbr>
| [[Harmonisma]]
| [[Harmonisma]]
|
|-
|-
| 17
| 17
| [[2187/2176]]
| [[2187/2176]]
| Septendecimal schisma
| Septendecimal schisma
|
|-
|-
| 17
| 17
| [[256/255]]
| [[256/255]]
| Septendecimal kleisma
| Septendecimal kleisma
|
|-
|-
| 17
| 17
| [[715/714]]
| [[715/714]]
| Septendecimal bridge comma
| Septendecimal bridge comma
|
|-
|-
| 19
| 19
| [[210/209]]
| [[210/209]]
| Spleen comma
| Spleen comma
|
|-
|-
| 19
| 19
| [[361/360]]
| [[361/360]]
| Go comma
| Go comma
|
|-
|-
| 19
| 19
| [[513/512]]
| [[513/512]]
| Undevicesimal comma
| Undevicesimal comma
|
|-
|-
| 19
| 19
| [[1216/1215]]
| [[1216/1215]]
| Eratosthenes' comma
| Eratosthenes' comma
|
|-
|-
| 23
| 23
| [[736/729]]
| [[736/729]]
| Vicesimotertial comma
| Vicesimotertial comma
|
|-
|-
| 29
| 29
| [[145/144]]
| [[145/144]]
| 29th-partial chroma
| 29th-partial chroma
|
|}
|}
<references/>
<references/>

Revision as of 07:20, 19 January 2021

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)
#Gens up Cents [1] Approximate ratios[2]
0 0.00 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
  1. ↑ octave-reduced
  2. ↑ 2.3.5.7, odd limit ≤ 27
Technical data

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

Commas: 81/80, 126/125

7 and 9-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]

Mapping generator: ~3

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[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
  1. ↑ Ratios with more than 9 digits are presented in monzos
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