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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.  
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.  


{{Todo|inline=1|expand}}
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, it is a [[parapyth]] temperament, as it tempers out [[352/351]], [[364/363]], and [[896/891]].
 
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 ==
== Interval chain ==
In the following tables, odd harmonics 1–13 and their inverses are in '''bold'''.  
In the following tables, odd harmonics 1–13 and their inverses are in '''bold'''.  


{| class="wikitable right-1 right-2"
{| class="wikitable center-1 right-2"
|-
|-
! #
! #
Line 26: Line 30:
|-
|-
| 0
| 0
| 0.00
| 0.0
| '''1/1'''
| '''1/1'''
|-
|-
| 1
| 1
| 175.89
| 175.9
| 10/9, 11/10
| 10/9, 11/10
|-
|-
| 2
| 2
| 351.77
| 351.7
| 11/9, '''16/13'''
| 11/9, '''16/13'''
|-
|-
| 3
| 3
| 527.66
| 527.6
| 15/11
| 15/11
|-
|-
| 4
| 4
| 703.54
| 703.4
| '''3/2'''
| '''3/2'''
|-
|-
| 5
| 5
| 879.43
| 879.3
| 5/3
| 5/3
|-
|-
| 6
| 6
| 1055.31
| 1055.1
| 11/6, 24/13
| 11/6, 24/13
|-
|-
| 7
| 7
| 31.20
| 31.0
| 40/39, 45/44, 55/54, 56/55
| 40/39, 45/44, 55/54, 56/55
|-
|-
| 8
| 8
| 207.09
| 206.8
| '''9/8'''
| '''9/8'''
|-
|-
| 9
| 9
| 382.97
| 382.7
| '''5/4'''
| '''5/4'''
|-
|-
| 10
| 10
| 558.86
| 558.5
| '''11/8''', 18/13
| '''11/8''', 18/13
|-
|-
| 11
| 11
| 734.74
| 734.4
| 20/13
| 20/13
|-
|-
| 12
| 12
| 910.63
| 910.2
| 22/13
| 22/13
|-
|-
| 13
| 13
| 1086.52
| 1086.1
| 15/8, 28/15
| 15/8, 28/15
|-
|-
| 14
| 14
| 62.40
| 61.9
| 25/24, 27/26, 28/27, 33/32
| 25/24, 27/26, 28/27, 33/32
|-
|-
| 15
| 15
| 238.29
| 237.8
| 15/13
| 15/13
|-
|-
| 16
| 16
| 414.17
| 413.6
| 14/11
| 14/11
|-
|-
| 17
| 17
| 590.06
| 589.5
| 7/5
| 7/5
|-
|-
| 18
| 18
| 765.94
| 765.3
| 14/9
| 14/9
|-
|-
| 19
| 19
| 941.83
| 941.2
|  
| 45/26
|-
|-
| 20
| 20
| 1117.72
| 1117.1
| 21/11
| 21/11
|-
|-
| 21
| 21
| 93.60
| 92.9
| 21/20
| 21/20
|-
|-
| 22
| 22
| 269.49
| 268.8
| 7/6
| 7/6
|-
|-
| 23
| 23
| 445.37
| 444.6
|  
| 35/27
|-
|-
| 24
| 24
| 621.26
| 620.5
|  
| 56/39, 63/44
|-
|-
| 25
| 25
| 797.15
| 796.3
|  
| 63/40
|-
|-
| 26
| 26
| 973.03
| 972.2
| '''7/4'''
| '''7/4'''
|-
|-
| 27
| 27
| 1148.92
| 1148.0
| 35/18
| 35/18
|-
| 28
| 124.80
| 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
| 12/11
| 174.894
| 174.894
|  
|  
|-
|-
| 7\48
|
| 175.000
| 48d val, lower bound of 7- to 13-odd-limit diamond monotone
|-
|
| 11/8
| 11/8
| 175.132
| 175.132
|  
|  
|-
|-
|
| 15/14
| 15/14
| 175.427
| 175.427
|  
|  
|-
|-
|
| 7/5
| 7/5
| 175.442
| 175.442
| 11-odd-limit minimax
| 11-odd-limit minimax
|-
|-
| 4/3
|  
| 3/2
| 175.489
| 175.489
|  
|  
|-
|-
| 8/7
| 6\41
|
| 175.610
| Lower bound of 15-odd-limit diamond monotone
|-
|
| 7/4
| 175.724
| 175.724
|  
|  
|-
|-
|
| 7/6
| 7/6
| 175.767
| 175.767
| 7-odd-limit minimax
| 7-odd-limit minimax
|-
|-
|
| 9/7
| 9/7
| 175.829
| 175.829
| 9-odd-limit minimax
| 9-odd-limit minimax
|-
|-
|
| 13/11
| 13/11
| 175.899
| 175.899
| 13- and 15-odd-limit minimax
| 13- and 15-odd-limit minimax
|-
|-
| 14/13
| 11\75
|
| 176.000
|
|-
|
| 13/7
| 176.011
| 176.011
|  
|  
|-
|-
| 16/15
|  
| 15/8
| 176.021
| 176.021
|  
|  
|-
|-
| 14/11
|  
| 11/7
| 176.094
| 176.094
|  
|  
|-
|-
|
| 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
| 34d val, upper bound of 7- to 15-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
|  
|  
|-
|-
| 4\27
|
| 177.778
| 27dde val
|-
|
| 15/11
| 15/11
| 178.984
| 178.984
|  
|  
|-
|-
| 16/13
|  
| 13/8
| 179.736
| 179.736
|  
|  
|-
|-
| 10/9
| 3\20
|
| 180.000
| 20cddde val
|-
|
| 9/5
| 182.404
| 182.404
|  
|  
Retrieved from "https://en.xen.wiki/w/Bunya"