Wollemia: Difference between revisions

From Xenharmonic Wiki
Jump to navigation Jump to search
← Older editNewer edit →
VisualWikitext
mNo edit summary
Birth
Tag: Removed redirect
Line 1: Line 1:
#redirect [[Tetracot family #Wollemia]]
{{Infobox regtemp
| Title = 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);<br>[[56/55]], [[100/99]], [[243/242]] (11-limit)<br>[[56/55]], [[91/90]], [[100/99]], [[243/242]]<br>(13-limit)
| Edo join 1 = 27e | Edo join 2 = 34
| Mapping = 1; 4 9 19 10 -2
| Generators = 10/9
| Generators tuning = 177.1
| Optimization method = CWE
| MOS scales = [[6L 1s]], [[7L 6s]], [[7L 13s]], [[7L 20s]]
| Odd limit 1 = 9 | Mistuning 1 = 14.5 | Complexity 1 = 27
| Odd limit 2 = 13 | Mistuning 2 = 21.7 | Complexity 2 = 34
}}
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.


{{Todo|inline=1|expand}}
== Interval chain ==
{| class="wikitable right-1 right-2"
|-
! #
! Cents*
! Approximate ratios
|-
| 0
| 0.00
| '''1/1'''
|-
| 1
| 177.23
| 10/9, 11/10
|-
| 2
| 354.46
| 11/9, '''16/13'''
|-
| 3
| 531.69
| 15/11
|-
| 4
| 708.92
| '''3/2'''
|-
| 5
| 886.16
| 5/3
|-
| 6
| 1063.39
| 11/6, 24/13, 28/15
|-
| 7
| 40.62
| 40/39, 45/44, 55/54
|-
| 8
| 217.85
| '''9/8'''
|-
| 9
| 395.08
| '''5/4''', 14/11
|-
| 10
| 572.31
| 7/5, '''11/8''', 18/13
|-
| 11
| 749.54
| 14/9, 20/13
|-
| 12
| 926.77
| 22/13
|-
| 13
| 1104.01
| 15/8
|-
| 14
| 81.24
| 25/24, 27/26
|-
| 15
| 258.47
| 7/6, 15/13
|-
| 16
| 435.70
|
|-
| 17
| 612.93
|
|-
| 18
| 790.16
|
|-
| 19
| 967.39
| '''7/4'''
|-
| 20
| 1144.62
|
|-
| 21
| 121.86
| 14/13
|}
<nowiki/>* In 13-limit POTE tuning, octave reduced
== Tunings ==
=== Tuning spectrum ===
{| class="wikitable center-all left-3"
|-
! [[Eigenmonzo|Eigenmonzo<br>(Unchanged-interval)]]
! Generator (¢)
! Comments
|-
| 11/10
| 165.004
|
|-
| 11/9
| 173.704
|
|-
| 12/11
| 174.894
|
|-
| 11/8
| 175.132
|
|-
| 4/3
| 175.489
|
|-
| 13/11
| 175.899
|
|-
| 16/15
| 176.021
|
|-
| 5/4
| 176.257
| 5-odd-limit minimax
|-
| 18/13
| 176.338
|
|-
| 15/13
| 176.516
|
|-
| 6/5
| 176.872
|
|-
| 13/10
| 176.890
|
|-
| 13/12
| 176.905
|
|-
| 8/7
| 177.307
| 7-, 9-, 11-, 13- and 15-odd-limit minimax
|-
| 14/13
| 177.538
|
|-
| 7/6
| 177.791
|
|-
| 7/5
| 178.251
|
|-
| 9/7
| 178.629
|
|-
| 15/11
| 178.984
|
|-
| 14/11
| 179.723
|
|-
| 16/13
| 179.736
|
|-
| 15/14
| 180.093
|
|-
| 10/9
| 182.404
|
|}
[[Category:Wollemia| ]] <!-- main article -->
[[Category:Rank-2 temperaments]]
[[Category:Rank-2 temperaments]]
[[Category:Tetracot family]]
[[Category:Tetracot family]]
[[Category:Starling temperaments]]
[[Category:Starling temperaments]]

Revision as of 18:35, 15 April 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: 27 notes;
13-odd-limit: 34 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.

Todo: expand

Interval chain

# Cents* Approximate ratios
0 0.00 1/1
1 177.23 10/9, 11/10
2 354.46 11/9, 16/13
3 531.69 15/11
4 708.92 3/2
5 886.16 5/3
6 1063.39 11/6, 24/13, 28/15
7 40.62 40/39, 45/44, 55/54
8 217.85 9/8
9 395.08 5/4, 14/11
10 572.31 7/5, 11/8, 18/13
11 749.54 14/9, 20/13
12 926.77 22/13
13 1104.01 15/8
14 81.24 25/24, 27/26
15 258.47 7/6, 15/13
16 435.70
17 612.93
18 790.16
19 967.39 7/4
20 1144.62
21 121.86 14/13

* In 13-limit POTE tuning, octave reduced

Tunings

Tuning spectrum

Eigenmonzo
(Unchanged-interval) 		Generator (¢) Comments
11/10 165.004
11/9 173.704
12/11 174.894
11/8 175.132
4/3 175.489
13/11 175.899
16/15 176.021
5/4 176.257 5-odd-limit minimax
18/13 176.338
15/13 176.516
6/5 176.872
13/10 176.890
13/12 176.905
8/7 177.307 7-, 9-, 11-, 13- and 15-odd-limit minimax
14/13 177.538
7/6 177.791
7/5 178.251
9/7 178.629
15/11 178.984
14/11 179.723
16/13 179.736
15/14 180.093
10/9 182.404
Retrieved from "https://en.xen.wiki/index.php?title=Wollemia&oldid=227888"