Mystery: Difference between revisions
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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 29s]], [[58L 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 | ||
== Scales == | |||
* [[Mystery58]] | |||
== Tunings == | == 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 === | === Tuning spectrum === | ||
{| class="wikitable center-all left-4" | {| class="wikitable center-all left-4" | ||
|- | |- | ||
! Edo<br>generator | ! Edo<br>generator | ||
! [[Eigenmonzo| | ! [[Eigenmonzo|Unchanged interval<br>(eigenmonzo)]]* | ||
! Generator (¢) | ! Generator (¢) | ||
! Comments | ! Comments | ||
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<nowiki/>* Besides the octave | <nowiki/>* Besides the octave | ||
[[Category:Mystery| ]] <!-- main article --> | [[Category:Mystery| ]] <!-- main article --> | ||
[[Category:Rank-2 temperaments]] | [[Category:Rank-2 temperaments]] | ||
[[Category:Hemifamity temperaments]] | [[Category:Hemifamity temperaments]] | ||