Wollemia: Difference between revisions

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Expand a little bit: add the additional 7-limit comma
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The '''wollemia''' [[regular temperament|temperament]] is one of the [[7-limit]] [[extension]]s of [[tetracot]], the [[5-limit]] temperament [[tempering out]] the [[tetracot comma]] (20000/19683), and is naturally a full [[13-limit]] temperament.
The '''wollemia''' [[regular temperament|temperament]] is one of the [[7-limit]] [[extension]]s of [[tetracot]], the [[5-limit]] temperament [[tempering out]] the [[tetracot comma]] (20000/19683), and is naturally a full [[13-limit]] temperament.


In addition to the tetracot comma, wollemia tempers out [[126/125]], making it a [[starling_temperaments|starling temperament]].
In addition to the tetracot comma, wollemia tempers out [[126/125]], making it a [[starling temperaments|starling temperament]].
 
See [[Tetracot family #Wollemia]] for technical data.  


{{Todo|inline=1|expand}}
{{Todo|inline=1|expand}}
Line 26: Line 28:
|-
|-
| 0
| 0
| 0.00
| 0.0
| '''1/1'''
| '''1/1'''
|-
|-
| 1
| 1
| 177.23
| 177.1
| 10/9, 11/10
| 10/9, 11/10
|-
|-
| 2
| 2
| 354.46
| 354.2
| 11/9, '''16/13'''
| 11/9, '''16/13'''
|-
|-
| 3
| 3
| 531.69
| 531.3
| 15/11
| 15/11
|-
|-
| 4
| 4
| 708.92
| 708.4
| '''3/2'''
| '''3/2'''
|-
|-
| 5
| 5
| 886.16
| 885.5
| 5/3
| 5/3
|-
|-
| 6
| 6
| 1063.39
| 1062.6
| 11/6, 24/13, 28/15
| 11/6, 24/13, 28/15
|-
|-
| 7
| 7
| 40.62
| 39.7
| 40/39, 45/44, 55/54
| 40/39, 45/44, 55/54
|-
|-
| 8
| 8
| 217.85
| 216.8
| '''9/8'''
| '''9/8'''
|-
|-
| 9
| 9
| 395.08
| 393.9
| '''5/4''', 14/11
| '''5/4''', 14/11
|-
|-
| 10
| 10
| 572.31
| 570.9
| 7/5, '''11/8''', 18/13
| 7/5, '''11/8''', 18/13
|-
|-
| 11
| 11
| 749.54
| 748.0
| 14/9, 20/13
| 14/9, 20/13
|-
|-
| 12
| 12
| 926.77
| 925.1
| 22/13
| 22/13
|-
|-
| 13
| 13
| 1104.01
| 1102.2
| 15/8
| 15/8, 21/11
|-
|-
| 14
| 14
| 81.24
| 79.3
| 25/24, 27/26
| 21/20, 25/24, 27/26
|-
|-
| 15
| 15
| 258.47
| 256.4
| 7/6, 15/13
| 7/6, 15/13
|-
|-
| 16
| 16
| 435.70
| 433.5
|  
| 33/26, 35/27
|-
|-
| 17
| 17
| 612.93
| 610.6
|  
| 45/32, 63/44
|-
|-
| 18
| 18
| 790.16
| 787.7
|  
| 25/16
|-
|-
| 19
| 19
| 967.39
| 964.8
| '''7/4'''
| '''7/4'''
|-
|-
| 20
| 20
| 1144.62
| 1141.9
|  
| 35/18, 49/25
|-
| 21
| 121.86
| 14/13
|}
|}
<nowiki/>* In 13-limit POTE tuning, octave reduced
<nowiki/>* In 13-limit CWE tuning, octave reduced


== Tunings ==
== Tunings ==
=== Tuning spectrum ===
=== Tuning spectrum ===
{| class="wikitable center-all left-3"
{| class="wikitable center-all left-4"
|-
|-
! Edo<br>generator
! [[Eigenmonzo|Eigenmonzo<br>(Unchanged-interval)]]
! [[Eigenmonzo|Eigenmonzo<br>(Unchanged-interval)]]
! Generator (¢)
! Generator (¢)
! Comments
! Comments
|-
|-
|
| 11/10
| 11/10
| 165.004
| 165.004
|  
|  
|-
|-
| 1\7
|
| 171.429
| 7d val
|-
|
| 11/9
| 11/9
| 173.704
| 173.704
|  
|  
|-
|-
| 12/11
|  
| 11/6
| 174.894
| 174.894
|  
|  
|-
|-
|
| 11/8
| 11/8
| 175.132
| 175.132
|  
|  
|-
|-
| 4/3
|  
| 3/2
| 175.489
| 175.489
|  
|  
|-
|-
|
| 13/11
| 13/11
| 175.899
| 175.899
|  
|  
|-
|-
| 16/15
|  
| 15/8
| 176.021
| 176.021
|  
|  
|-
|-
|
| 5/4
| 5/4
| 176.257
| 176.257
| 5-odd-limit minimax
| 5-odd-limit minimax
|-
|-
| 18/13
|  
| 13/9
| 176.338
| 176.338
|  
|  
|-
|-
| 5\34
|
| 176.471
| Lower bound of 7- to 13-odd-limit diamond monotone
|-
|
| 15/13
| 15/13
| 176.516
| 176.516
|  
|  
|-
|-
| 6/5
|  
| 5/3
| 176.872
| 176.872
|  
|  
|-
|-
|
| 13/10
| 13/10
| 176.890
| 176.890
|  
|  
|-
|-
|
| 13/12
| 13/12
| 176.905
| 176.905
|  
|  
|-
|-
| 8/7
|  
| 7/4
| 177.307
| 177.307
| 7-, 9-, 11-, 13- and 15-odd-limit minimax
| 7-, 9-, 11-, 13- and 15-odd-limit minimax
|-
|-
| 14/13
|  
| 13/7
| 177.538
| 177.538
|  
|  
|-
|-
| 4\27
|
| 177.777
| 27e val, upper bound of 9- to 13-odd-limit diamond monotone<br>15-odd-limit diamond monotone (singleton)
|-
|
| 7/6
| 7/6
| 177.791
| 177.791
|  
|  
|-
|-
|
| 7/5
| 7/5
| 178.251
| 178.251
|  
|  
|-
|-
|
| 9/7
| 9/7
| 178.629
| 178.629
|  
|  
|-
|-
|
| 15/11
| 15/11
| 178.984
| 178.984
|  
|  
|-
|-
| 14/11
|  
| 11/7
| 179.723
| 179.723
|  
|  
|-
|-
| 16/13
|  
| 13/8
| 179.736
| 179.736
|  
|  
|-
|-
| 3\20
|
| 180.000
| 20cde val, upper bound of 7-odd-limit diamond monotone
|-
|
| 15/14
| 15/14
| 180.093
| 180.093
|  
|  
|-
|-
| 10/9
|  
| 9/5
| 182.404
| 182.404
|  
|  

Latest revision as of 10:40, 30 May 2026

Wollemia
Subgroups 2.3.5.7, 2.3.5.7.11, 2.3.5.7.11.13
Comma basis 126/125, 2240/2187 (7-limit);
56/55, 100/99, 243/242 (11-limit)
56/55, 91/90, 100/99, 243/242
(13-limit)
Reduced mapping ⟨1; 4 9 19 10 -2]
ET join 27e & 34
Generators (CWE) ~10/9 = 177.1 ¢
MOS scales 6L 1s, 7L 6s, 7L 13s, 7L 20s
Ploidacot tetracot
Minimax error 9-odd-limit: 14.5 ¢;
13-odd-limit: 21.7 ¢
Target scale size 9-odd-limit: 20 notes;
13-odd-limit: 27 notes

The wollemia temperament is one of the 7-limit extensions of tetracot, the 5-limit temperament tempering out the tetracot comma (20000/19683), and is naturally a full 13-limit temperament.

In addition to the tetracot comma, wollemia tempers out 126/125, making it a starling temperament.

See Tetracot family #Wollemia for technical data.

Todo: expand

Interval chain

# Cents* Approximate ratios
0 0.0 1/1
1 177.1 10/9, 11/10
2 354.2 11/9, 16/13
3 531.3 15/11
4 708.4 3/2
5 885.5 5/3
6 1062.6 11/6, 24/13, 28/15
7 39.7 40/39, 45/44, 55/54
8 216.8 9/8
9 393.9 5/4, 14/11
10 570.9 7/5, 11/8, 18/13
11 748.0 14/9, 20/13
12 925.1 22/13
13 1102.2 15/8, 21/11
14 79.3 21/20, 25/24, 27/26
15 256.4 7/6, 15/13
16 433.5 33/26, 35/27
17 610.6 45/32, 63/44
18 787.7 25/16
19 964.8 7/4
20 1141.9 35/18, 49/25

* In 13-limit CWE tuning, octave reduced

Tunings

Tuning spectrum

Edo
generator 		Eigenmonzo
(Unchanged-interval) 		Generator (¢) Comments
11/10 165.004
1\7 171.429 7d val
11/9 173.704
11/6 174.894
11/8 175.132
3/2 175.489
13/11 175.899
15/8 176.021
5/4 176.257 5-odd-limit minimax
13/9 176.338
5\34 176.471 Lower bound of 7- to 13-odd-limit diamond monotone
15/13 176.516
5/3 176.872
13/10 176.890
13/12 176.905
7/4 177.307 7-, 9-, 11-, 13- and 15-odd-limit minimax
13/7 177.538
4\27 177.777 27e val, upper bound of 9- to 13-odd-limit diamond monotone
15-odd-limit diamond monotone (singleton)
7/6 177.791
7/5 178.251
9/7 178.629
15/11 178.984
11/7 179.723
13/8 179.736
3\20 180.000 20cde val, upper bound of 7-odd-limit diamond monotone
15/14 180.093
9/5 182.404
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