Bunya: Difference between revisions

From Xenharmonic Wiki
Jump to navigation Jump to search
← Older edit
VisualWikitext
Xenwolf (talk | contribs)
autopatrolled, Bureaucrats, confirmaccount-notify, Interface administrators, Sysops
8,705 edits
m recat
+ link to data page
 
(5 intermediate revisions by 2 users not shown)
Line 1: Line 1:
#redirect [[Tetracot family #Bunya]]
{{Infobox regtemp
| Title = Bunya
| Subgroups = 2.3.5.7, 2.3.5.7.11, 2.3.5.7.11.13
| Comma basis = [[225/224]], [[15625/15309]] (7-limit);<br>[[100/99]], [[225/224]], [[243/242]] (11-limit)<br>[[100/99]], [[144/143]], [[225/224]], [[243/242]]<br>(13-limit)
| Edo join 1 = 34d | Edo join 2 = 41
| Mapping = 1; 4 9 26 10 -2
| Generators = 10/9
| Generators tuning = 175.9
| Optimization method = CWE
| MOS scales = [[6L 1s]], [[7L 6s]], [[7L 13s]], [[7L 20s]]
| Odd limit 1 = 9 | Mistuning 1 = 6.58 | Complexity 1 = 27
| Odd limit 2 = 13 | Mistuning 2 = 10.9 | Complexity 2 = 34
}}
The '''bunya''' [[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]], bunya tempers out [[225/224]], making it a [[marvel temperaments|marvel temperament]]. This means the [[~]][[15/8]], at 13 generator steps, is equated with ~[[28/15]], and ~[[7/4]] is found as twice of that interval.
Additionally, the generator can be taken to represent [[21/19]], which gives us an extension for prime 19 at +29 generator steps.
See [[Tetracot family #Bunya]] for technical data.
== Interval chain ==
In the following tables, odd harmonics 1–13 and their inverses are in '''bold'''.
{| class="wikitable center-1 right-2"
|-
! #
! Cents*
! Approximate ratios
|-
| 0
| 0.0
| '''1/1'''
|-
| 1
| 175.9
| 10/9, 11/10
|-
| 2
| 351.7
| 11/9, '''16/13'''
|-
| 3
| 527.6
| 15/11
|-
| 4
| 703.4
| '''3/2'''
|-
| 5
| 879.3
| 5/3
|-
| 6
| 1055.1
| 11/6, 24/13
|-
| 7
| 31.0
| 40/39, 45/44, 55/54, 56/55
|-
| 8
| 206.8
| '''9/8'''
|-
| 9
| 382.7
| '''5/4'''
|-
| 10
| 558.5
| '''11/8''', 18/13
|-
| 11
| 734.4
| 20/13
|-
| 12
| 910.2
| 22/13
|-
| 13
| 1086.1
| 15/8, 28/15
|-
| 14
| 61.9
| 25/24, 27/26, 28/27, 33/32
|-
| 15
| 237.8
| 15/13
|-
| 16
| 413.6
| 14/11
|-
| 17
| 589.5
| 7/5
|-
| 18
| 765.3
| 14/9
|-
| 19
| 941.2
| 45/26
|-
| 20
| 1117.1
| 21/11
|-
| 21
| 92.9
| 21/20
|-
| 22
| 268.8
| 7/6
|-
| 23
| 444.6
| 35/27
|-
| 24
| 620.5
| 56/39, 63/44
|-
| 25
| 796.3
| 63/40
|-
| 26
| 972.2
| '''7/4'''
|-
| 27
| 1148.0
| 35/18
|}
<nowiki/>* In 13-limit CWE tuning, octave reduced
== Tunings ==
=== Tuning spectrum ===
{| class="wikitable center-all left-4"
|-
! Edo<br>generator
! [[Eigenmonzo|Eigenmonzo<br>(unchanged-interval)]]
! Generator (¢)
! Comments
|-
|
| 11/10
| 165.004
|
|-
| 1\7
|
| 171.429
| 7d val
|-
|
| 11/9
| 173.704
|
|-
|
| 12/11
| 174.894
|
|-
| 7\48
|
| 175.000
| 48d val, lower bound of 7- to 13-odd-limit diamond monotone
|-
|
| 11/8
| 175.132
|
|-
|
| 15/14
| 175.427
|
|-
|
| 7/5
| 175.442
| 11-odd-limit minimax
|-
|
| 3/2
| 175.489
|
|-
| 6\41
|
| 175.610
| Lower bound of 15-odd-limit diamond monotone
|-
|
| 7/4
| 175.724
|
|-
|
| 7/6
| 175.767
| 7-odd-limit minimax
|-
|
| 9/7
| 175.829
| 9-odd-limit minimax
|-
|
| 13/11
| 175.899
| 13- and 15-odd-limit minimax
|-
| 11\75
|
| 176.000
|
|-
|
| 13/7
| 176.011
|
|-
|
| 15/8
| 176.021
|
|-
|
| 11/7
| 176.094
|
|-
|
| 5/4
| 176.257
| 5-odd-limit minimax
|-
|
| 13/9
| 176.338
|
|-
| 5\34
|
| 176.471
| 34d val, upper bound of 7- to 15-odd-limit diamond monotone
|-
|
| 15/13
| 176.516
|
|-
|
| 5/3
| 176.872
|
|-
|
| 13/10
| 176.890
|
|-
|
| 13/12
| 176.905
|
|-
| 4\27
|
| 177.778
| 27dde val
|-
|
| 15/11
| 178.984
|
|-
|
| 13/8
| 179.736
|
|-
| 3\20
|
| 180.000
| 20cddde val
|-
|
| 9/5
| 182.404
|
|}
[[Category:Bunya| ]] <!-- main article -->
[[Category:Rank-2 temperaments]]
[[Category:Tetracot family]]
[[Category:Tetracot family]]
{{IoT}}
[[Category:Marvel temperaments]]

Latest revision as of 10:38, 30 May 2026

Bunya
Subgroups 2.3.5.7, 2.3.5.7.11, 2.3.5.7.11.13
Comma basis 225/224, 15625/15309 (7-limit);
100/99, 225/224, 243/242 (11-limit)
100/99, 144/143, 225/224, 243/242
(13-limit)
Reduced mapping ⟨1; 4 9 26 10 -2]
ET join 34d & 41
Generators (CWE) ~10/9 = 175.9 ¢
MOS scales 6L 1s, 7L 6s, 7L 13s, 7L 20s
Ploidacot tetracot
Minimax error 9-odd-limit: 6.58 ¢;
13-odd-limit: 10.9 ¢
Target scale size 9-odd-limit: 27 notes;
13-odd-limit: 34 notes

The bunya 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, bunya tempers out 225/224, making it a marvel temperament. This means the ~15/8, at 13 generator steps, is equated with ~28/15, and ~7/4 is found as twice of that interval.

Additionally, the generator can be taken to represent 21/19, which gives us an extension for prime 19 at +29 generator steps.

See Tetracot family #Bunya for technical data.

Interval chain

In the following tables, odd harmonics 1–13 and their inverses are in bold.

# Cents* Approximate ratios
0 0.0 1/1
1 175.9 10/9, 11/10
2 351.7 11/9, 16/13
3 527.6 15/11
4 703.4 3/2
5 879.3 5/3
6 1055.1 11/6, 24/13
7 31.0 40/39, 45/44, 55/54, 56/55
8 206.8 9/8
9 382.7 5/4
10 558.5 11/8, 18/13
11 734.4 20/13
12 910.2 22/13
13 1086.1 15/8, 28/15
14 61.9 25/24, 27/26, 28/27, 33/32
15 237.8 15/13
16 413.6 14/11
17 589.5 7/5
18 765.3 14/9
19 941.2 45/26
20 1117.1 21/11
21 92.9 21/20
22 268.8 7/6
23 444.6 35/27
24 620.5 56/39, 63/44
25 796.3 63/40
26 972.2 7/4
27 1148.0 35/18

* 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
12/11 174.894
7\48 175.000 48d val, lower bound of 7- to 13-odd-limit diamond monotone
11/8 175.132
15/14 175.427
7/5 175.442 11-odd-limit minimax
3/2 175.489
6\41 175.610 Lower bound of 15-odd-limit diamond monotone
7/4 175.724
7/6 175.767 7-odd-limit minimax
9/7 175.829 9-odd-limit minimax
13/11 175.899 13- and 15-odd-limit minimax
11\75 176.000
13/7 176.011
15/8 176.021
11/7 176.094
5/4 176.257 5-odd-limit minimax
13/9 176.338
5\34 176.471 34d val, upper bound of 7- to 15-odd-limit diamond monotone
15/13 176.516
5/3 176.872
13/10 176.890
13/12 176.905
4\27 177.778 27dde val
15/11 178.984
13/8 179.736
3\20 180.000 20cddde val
9/5 182.404
Retrieved from "https://en.xen.wiki/index.php?title=Bunya&oldid=231330"