User:FloraC/Sandbox: Difference between revisions

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Comment: doesn't actually look great
Comment: doesn't actually look great


== Test [[User:FloraC/Collapsed box]] ==
== Septimal meantone ==
<span style="display: block; text-align: right;">[[:de:septimal-mitteltönig|Deutsch]]</span>
 
{{main| Meantone }}
{{see also| Wikipedia: Septimal meantone temperament }}
 
The [[7/4]] of septimal meantone is the augmented sixth, C-A#, and other septimal intervals are [[7/6]], C-D#, the augmented second, [[7/5]], C-F#, the tritone, and [[21/16]], C-E#, the augmented third. Septimal meantone also tempers out the common 7-limit comma [[225/224]] and is in fact can be defined as the 7-limit temperament that tempers out 81/80 and 225/224.
 
Period: 1\1
Period: 1\1


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EDO generators: [[12edo|7\12]], [[19edo|11\19]], [[31edo|18\31]], [[43edo|25\43]], [[50edo|29\50]]
EDO generators: [[12edo|7\12]], [[19edo|11\19]], [[31edo|18\31]], [[43edo|25\43]], [[50edo|29\50]]


Scales: [[Meantone5]], [[Meantone7]], [[Meantone12]]
Scales (Scala files): [[Meantone5]], [[Meantone7]], [[Meantone12]]
 
<div class="toccolours mw-collapsible mw-collapsed" style="width:600px; overflow:auto;">
<div style="line-height:1.6;">Interval table (12-note MOS, 2.3.5.7 POTE tuning)</div>
<div class="mw-collapsible-content">


{{User:FloraC/Collapsed box
| title = Interval table (12-note MOS, 2.3.5.7 POTE tuning)
| text =
{| class="wikitable right-1 right-2 sortable"
{| class="wikitable right-1 right-2 sortable"
|+
|-
|-
! #
! #
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| 21/16
| 21/16
|}
|}
<references/>
<references/></div></div>
}}
 
{{User:FloraC/Collapsed box|title = Technical data |text =  
<div class="toccolours mw-collapsible mw-collapsed" style="width:600px; overflow:auto;">
<div style="line-height:1.6;">Technical data</div>
<div class="mw-collapsible-content">
 
Subgroup: 2.3.5.7


Comma list: 81/80, 126/125
[[Comma]] list: 81/80, 126/125


[[Mapping]]: [{{val| 1 0 -4 -13 }}, {{val| 0 1 4 10 }}]
[[Mapping]]: [{{val|1 0 -4 -13}}, {{val|0 1 4 10}}]


Mapping generators: ~2, ~3
Mapping generators: ~2, ~3
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[[Minimax tuning]]:  
[[Minimax tuning]]:  
* 7- and [[9-odd-limit]]
* 7- and [[9-odd-limit]]
: [{{Monzo| 1 0 0 0 }}, {{Monzo| 1 0 1/4 0 }}, {{Monzo| 0 0 1 0 }}, {{Monzo| -3 0 5/2 0 }}]
: [{{Monzo| 1 0 0 0 }}, {{Monzo| 1 0 1/4 0 }}, {{Monzo| 0 0 1 0 }}, {{Monzo| -3 0 5/2 0 }}]
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[[Tuning ranges]]:  
[[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]
* Strict range: [694.786, 700.000]
* strict range: [694.786, 700.000]


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.
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[[Badness]]: 0.0137
[[Badness]]: 0.0137
}}
 
</div></div>


Comment: This provides much more freedom. Looks great to me by this very formatting.  
Comment: This provides much more freedom. Looks great to me by this very formatting.  


Note:  
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.  
# Order: subgroup, 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.  
# 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.  

Revision as of 12:56, 9 February 2021

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

Comment: doesn't actually look great

Septimal meantone

Deutsch

Main article: Meantone
See also: Wikipedia: Septimal meantone temperament

The 7/4 of septimal meantone is the augmented sixth, C-A#, and other septimal intervals are 7/6, C-D#, the augmented second, 7/5, C-F#, the tritone, and 21/16, C-E#, the augmented third. Septimal meantone also tempers out the common 7-limit comma 225/224 and is in fact can be defined as the 7-limit temperament that tempers out 81/80 and 225/224.

Period: 1\1

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

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

Scales (Scala files): Meantone5, Meantone7, Meantone12

Interval table (12-note MOS, 2.3.5.7 POTE tuning)
# Cents[1] Approximate ratios[2]
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
  1. ↑ octave-reduced
  2. ↑ 2.3.5.7, odd limit ≤ 27
Technical data

Subgroup: 2.3.5.7

Comma list: 81/80, 126/125

Mapping: [⟨1 0 -4 -13], ⟨0 1 4 10]]

Mapping generators: ~2, ~3

Wedgie: ⟨⟨1 4 10 4 13 12]]

Minimax tuning:

[[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.

Optimal ET sequence: 12, 19, 31, 81, 112b, 143b

Badness: 0.0137

Comment: This provides much more freedom. Looks great to me by this very formatting.

Note:

  1. Order: subgroup, comma list, mapping, mapping generators (or simply "generators", this is the same thing), wedgie, minimax tuning, tuning ranges, algebraic generator, vals, badness, complexity spectrum.
  2. Comma list shows the simplest commas sufficient to define the temperament. This must be stated somewhere in this wiki.
  3. Mapping generators should show all the ratios as used in the mapping, including the period.
  4. Minimax tuning are based on tonality diamond, so it should explicitly state the odd limit, or a diamond function of ratios.
  5. Use Template:Vals.

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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