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Bunya: Difference between revisions

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Complete intro and interval table
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m Separate the comma groups with ";", as elsewhere in the field and on other regtemp pages
 
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| Title = Bunya
| Title = Bunya
| Subgroups = 2.3.5.7, 2.3.5.7.11, 2.3.5.7.11.13
| 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)
| 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
| Edo join 1 = 34d | Edo join 2 = 41
| Mapping = 1; 4 9 26 10 -2
| Mapping = 1; 4 9 26 10 -2
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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.  


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.  
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.  
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"
|-
|-
! #
! #
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== 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
|  
|  
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