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Adopt CWE tuning. Misc. improvements
 
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{{Infobox regtemp
| Title = Mystery
| Subgroups = 2.3.5.7, 2.3.5.7.11, 2.3.5.7.11.13
| Comma basis = [[5120/5103]], [[50421/50000]] (7-limit); <br>[[441/440]], [[896/891]], [[3388/3375]] (11-limit); <br>[[196/195]], [[352/351]], [[364/363]], [[676/675]] (13-limit)
| Edo join 1 = 29 | Edo join 2 = 58
| Mapping = 29; 0 1 1 1 1
| Generators = 5/4
| Generators tuning = 387.9
| Optimization method = CWE
| MOS scales = [[29L&nbsp;29s]], [[58L&nbsp;29s]]
| Pergen = (P8/29, ^1)
| Color name = Quadsawati
| Odd limit 1 = 9 | Mistuning 1 = 3.20 | Complexity 1 = 58
| Odd limit 2 = 13-limit 21 | Mistuning 2 = 4.69 | Complexity 2 = 58
}}
'''Mystery''' is a [[regular temperament]] which takes [[29edo|1\29]] [[period]] and adds a single [[generator]] to correct the [[harmonic]]s [[5/1|5]], [[7/1|7]], [[11/1|11]], and [[13/1|13]] to almost just qualities. It [[tempering out|tempers out]] the [[29-comma]] in the 5-limit, [[5120/5103]] in the 7-limit, [[441/440]], [[896/891]], [[3388/3375]], and [[4000/3993]] in the 11-limit, [[196/195]], [[352/351]], [[364/363]], [[676/675]], and [[847/845]] in the 13-limit.  
'''Mystery''' is a [[regular temperament]] which takes [[29edo|1\29]] [[period]] and adds a single [[generator]] to correct the [[harmonic]]s [[5/1|5]], [[7/1|7]], [[11/1|11]], and [[13/1|13]] to almost just qualities. It [[tempering out|tempers out]] the [[29-comma]] in the 5-limit, [[5120/5103]] in the 7-limit, [[441/440]], [[896/891]], [[3388/3375]], and [[4000/3993]] in the 11-limit, [[196/195]], [[352/351]], [[364/363]], [[676/675]], and [[847/845]] in the 13-limit.  


See [[Hemifamity temperaments #Mystery]] for technical details.  
See [[Hemifamity temperaments #Mystery]] for technical details.  
 
__TOC__
{{Clear}}
== Interval chain ==
== Interval chain ==
In the following table, odd harmonics 1–21 are in '''bold'''.  
In the following table, odd harmonics 1–21 are in '''bold'''.  
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<nowiki>*</nowiki> in 13-limit CWE tuning
<nowiki>*</nowiki> in 13-limit CWE tuning


[[Category:Temperaments]]
== Scales ==
* [[Mystery58]]
 
== Tunings ==
=== Norm-based tunings ===
{| class="wikitable mw-collapsible mw-collapsed"
|+ style="font-size: 105%; white-space: nowrap;" | 7-limit norm-based tunings
|-
! rowspan="2" |
! colspan="3" | Euclidean
|-
! Constrained
! Constrained & skewed
! Destretched
|-
! Tenney
| CTE: ~5/4 = 387.6143{{c}}
| CWE: ~5/4 = 388.3030{{c}}
| POTE: ~5/4 = 388.6457{{c}}
|}
 
{| class="wikitable mw-collapsible mw-collapsed"
|+ style="font-size: 105%; white-space: nowrap;" | 13-limit norm-based tunings
|-
! rowspan="2" |
! colspan="3" | Euclidean
|-
! Constrained
! Constrained & skewed
! Destretched
|-
! Tenney
| CTE: ~5/4 = 386.9394{{c}}
| CWE: ~5/4 = 387.9017{{c}}
| POTE: ~5/4 = 388.3541{{c}}
|}
 
=== Tuning spectrum ===
{| class="wikitable center-all left-4"
|-
! Edo<br>generator
! [[Eigenmonzo|Unchanged interval<br>(eigenmonzo)]]*
! Generator (¢)
! Comments
|-
| 9\29
|
| 372.414
| Lower bound of 7- to 15-odd-limit, <br>and 13-limit 21-odd-limit diamond monotone
|-
|
| 15/8
| 384.820
|
|-
|
| 13/8
| 385.355
|
|-
|
| 11/8
| 385.801
|
|-
| 28\87
|
| 386.207
|
|-
|
| 5/4
| 386.314
|
|-
|
| 13/12
| 386.849
|
|-
|
| 11/6
| 387.294
|
|-
|
| 5/3
| 387.807
|
|-
|
| 13/9
| 388.342
|
|-
|
| 21/16
| 388.022
|
|-
|
| 11/9
| 388.787
|
|-
| 47\145
|
| 388.966
|
|-
|
| 9/5
| 389.300
|
|-
|
| 7/4
| 389.516
|
|-
|
| 7/6
| 391.009
|
|-
|
| 9/7
| 392.502
|
|-
| 19\58
|
| 393.103
| Upper bound of 13- and 15-odd-limit, <br>and 13-limit 21-odd-limit diamond monotone
|-
| 10\29
|
| 413.793
| 29cdef val, upper bound of 7- to 11-odd-limit diamond monotone
|}
<nowiki/>* Besides the octave
 
[[Category:Mystery| ]] <!-- main article -->
[[Category:Mystery| ]] <!-- main article -->
[[Category:Hemifamity temperaments]]
[[Category:Rank-2 temperaments]]
[[Category:Aberschismic temperaments]]
Retrieved from "https://en.xen.wiki/w/Mystery"