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'''Mystery''' is the [[regular temperament]] which takes [[29edo|1\29]] [[period]] and adds a single [[generator]] to correct the harmonic 5, 7, 11, and 13 to almost just versions. It 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.  
{{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.  


See [[Hemifamity temperaments #Mystery]] for technical details.
__TOC__
{{Clear}}
== Interval chain ==
== Interval chain ==
In the following table, odd harmonics 1–21 are in '''bold'''.
{| class="wikitable center-1 right-2 right-4"
{| class="wikitable center-1 right-2 right-4"
! rowspan="2" |Period
! rowspan="2" | Period
! colspan="2" |Generator 0
! colspan="2" | Generator 0
! colspan="2" |Generator 1
! colspan="2" | Generator 1
|-
|-
! Cents
! Cents
! Approx. Ratios
! Approx. ratios
! Cents
! Cents
! Approx. Ratios
! Approx. ratios
|-
|-
| 0
| 0
| 0.00
| 0.00
| 1/1
| '''1/1'''
| 15.94
| 15.49
| 91/90, 100/99, 105/104, 121/120
| 91/90, 100/99, 105/104, 121/120
|-
|-
Line 21: Line 41:
| 41.38
| 41.38
| 40/39, 45/44, 50/49
| 40/39, 45/44, 50/49
| 57.32
| 56.87
| 28/27, 33/32
| 28/27, 33/32
|-
|-
| 2
| 2
| 82.76
| 82.76
| 21/20
| 21/20, 22/21
| 98.70
| 98.25
| 35/33
| 35/33
|-
|-
Line 33: Line 53:
| 124.14
| 124.14
| 14/13, 15/14
| 14/13, 15/14
| 140.08
| 139.63
| 13/12
| 13/12
|-
|-
Line 39: Line 59:
| 165.52
| 165.52
| 11/10
| 11/10
| 181.46
| 181.01
| 10/9
| 10/9
|-
|-
| 5
| 5
| 206.90
| 206.90
| 9/8
| '''9/8'''
| 222.84
| 222.38
| 25/22
| 25/22
|-
|-
Line 51: Line 71:
| 248.28
| 248.28
| 15/13
| 15/13
| 264.22
| 263.76
| 7/6
| 7/6
|-
|-
Line 57: Line 77:
| 289.66
| 289.66
| 13/11, 32/27, 33/28
| 13/11, 32/27, 33/28
| 305.60
| 305.14
| 25/21
| 25/21
|-
|-
Line 63: Line 83:
| 331.03
| 331.03
| 40/33
| 40/33
| 346.97
| 346.52
| 11/9, 39/32
| 11/9, 39/32
|-
|-
Line 69: Line 89:
| 372.41
| 372.41
| 26/21
| 26/21
| 388.35
| 387.90
| '''5/4'''
| '''5/4'''
|-
|-
Line 75: Line 95:
| 413.79
| 413.79
| 14/11, 33/26, 80/63
| 14/11, 33/26, 80/63
| 429.73
| 429.28
|  
| 77/60
|-
|-
| 11
| 11
| 455.17
| 455.17
| 13/10
| 13/10
| 471.11
| 470.66
| 21/16
| '''21/16'''
|-
|-
| 12
| 12
| 496.55
| 496.55
| '''4/3'''
| 4/3
| 512.49
| 512.04
| 35/26, 75/56
| 35/26, 75/56
|-
|-
Line 93: Line 113:
| 537.93
| 537.93
| 15/11
| 15/11
| 553.87
| 553.42
| '''11/8'''
| '''11/8'''
|-
|-
Line 99: Line 119:
| 579.31
| 579.31
| 7/5
| 7/5
| 595.25
| 594.80
| 45/32
| 45/32
|-
|-
Line 105: Line 125:
| 620.69
| 620.69
| 10/7
| 10/7
| 636.63
| 636.18
| 13/9
| 13/9
|-
|-
Line 111: Line 131:
| 662.07
| 662.07
| 22/15
| 22/15
| 678.01
| 677.56
| 40/27
| 40/27
|-
|-
Line 117: Line 137:
| 703.45
| 703.45
| '''3/2'''
| '''3/2'''
| 719.39
| 718.94
| 50/33
| 50/33
|-
|-
Line 123: Line 143:
| 744.83
| 744.83
| 20/13
| 20/13
| 760.77
| 760.32
| 14/9
| 14/9
|-
|-
Line 129: Line 149:
| 786.21
| 786.21
| 11/7, 52/33, 63/40
| 11/7, 52/33, 63/40
| 802.15
| 801.69
| 35/22
| 35/22
|-
|-
| 20
| 20
| 827.59
| 827.59
| 33/20
| 21/13
| 843.53
| 843.07
| '''13/8''', 27/22
| '''13/8''', 44/27
|-
|-
| 21
| 21
| 868.97
| 868.97
| 21/13
| 33/20
| 884.91
| 884.45
| 5/3
| 5/3
|-
|-
Line 147: Line 167:
| 910.34
| 910.34
| 22/13, 27/16, 56/33
| 22/13, 27/16, 56/33
| 926.29
| 925.83
|  
| 77/45
|-
|-
| 23
| 23
| 951.72
| 951.72
| 26/15
| 26/15
| 967.66
| 967.21
| '''7/4'''
| '''7/4'''
|-
|-
Line 159: Line 179:
| 993.10
| 993.10
| 16/9
| 16/9
| 1009.04
| 1008.59
| 25/14, 70/39
| 25/14, 70/39
|-
|-
Line 165: Line 185:
| 1034.48
| 1034.48
| 20/11
| 20/11
| 1050.42
| 1049.97
| 11/6
| 11/6
|-
|-
Line 171: Line 191:
| 1075.86
| 1075.86
| 13/7, 28/15
| 13/7, 28/15
| 1090.80
| 1091.35
| 15/8
| '''15/8'''
|-
|-
| 27
| 27
| 1117.24
| 1117.24
| 40/21
| 21/11, 40/21
| 1133.18
| 1133.73
| 25/13, 52/27
| 25/13, 52/27
|-
|-
Line 183: Line 203:
| 1158.62
| 1158.62
| 39/20, 49/25, 88/45
| 39/20, 49/25, 88/45
| 1174.56
| 1174.11
| 63/32, 65/33, 77/39, 160/81
| 63/32, 65/33, 77/39, 160/81
|-
|-
| 29
| 29
| 1200.00
| 1200.00
| 2/1
| '''2/1'''
|
|
|}
<nowiki>*</nowiki> in 13-limit CWE tuning
 
== 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>*</nowiki> in 13-limit POTE tuning
<nowiki/>* Besides the octave


[[Category:Temperament]]
[[Category:Mystery| ]] <!-- main article -->
[[Category:Mystery| ]] <!-- main article -->
[[Category:Hemifamity]]
[[Category:Rank-2 temperaments]]
[[Category:Hemifamity temperaments]]
Retrieved from "https://en.xen.wiki/w/Mystery"