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See [[Tetracot_family#Bunya|Tetracot family]].
{{Infobox regtemp
[[Category:soft_redirect]]
| 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:Marvel temperaments]]
Retrieved from "https://en.xen.wiki/w/Bunya"