Mystery: Difference between revisions

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See [[Hemifamity temperaments #Mystery]].
'''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.
[[Category:soft redirect]]
 
== Interval chain ==
{| class="wikitable center-1 right-2 right-4"
! rowspan="2" |Period
! colspan="2" |Generator 0
! colspan="2" |Generator 1
|-
! Cents
! Approx. Ratios
! Cents
! Approx. Ratios
|-
| 0
| 0.00
| 1/1
| 15.94
| 91/90, 100/99, 105/104, 121/120
|-
| 1
| 41.38
| 40/39, 45/44, 50/49
| 57.32
| 28/27, 33/32
|-
| 2
| 82.76
| 21/20
| 98.70
| 35/33
|-
| 3
| 124.14
| 14/13, 15/14
| 140.08
| 13/12
|-
| 4
| 165.52
| 11/10
| 181.46
| 10/9
|-
| 5
| 206.90
| 9/8
| 222.84
| 25/22
|-
| 6
| 248.28
| 15/13
| 264.22
| 7/6
|-
| 7
| 289.66
| 13/11, 32/27, 33/28
| 305.60
| 25/21
|-
| 8
| 331.03
| 40/33
| 346.97
| 11/9, 39/32
|-
| 9
| 372.41
| 26/21
| 388.35
| '''5/4'''
|-
| 10
| 413.79
| 14/11, 33/26, 80/63
| 429.73
|
|-
| 11
| 455.17
| 13/10
| 471.11
| 21/16
|-
| 12
| 496.55
| '''4/3'''
| 512.49
| 35/26, 75/56
|-
| 13
| 537.93
| 15/11
| 553.87
| '''11/8'''
|-
| 14
| 579.31
| 7/5
| 595.25
| 45/32
|-
| 15
| 620.69
| 10/7
| 636.63
| 13/9
|-
| 16
| 662.07
| 22/15
| 678.01
| 40/27
|-
| 17
| 703.45
| '''3/2'''
| 719.39
| 50/33
|-
| 18
| 744.83
| 20/13
| 760.77
| 14/9
|-
| 19
| 786.21
| 11/7, 52/33, 63/40
| 802.15
| 35/22
|-
| 20
| 827.59
| 33/20
| 843.53
| '''13/8''', 27/22
|-
| 21
| 868.97
| 21/13
| 884.91
| 5/3
|-
| 22
| 910.34
| 22/13, 27/16, 56/33
| 926.29
|
|-
| 23
| 951.72
| 26/15
| 967.66
| '''7/4'''
|-
| 24
| 993.10
| 16/9
| 1009.04
| 25/14, 70/39
|-
| 25
| 1034.48
| 20/11
| 1050.42
| 11/6
|-
| 26
| 1075.86
| 13/7, 28/15
| 1090.80
| 15/8
|-
| 27
| 1117.24
| 40/21
| 1133.18
| 25/13, 52/27
|-
| 28
| 1158.62
| 39/20, 49/25, 88/45
| 1174.56
| 63/32, 65/33, 77/39, 160/81
|-
| 29
| 1200.00
| 2/1
|
|
|}
<nowiki>*</nowiki> in 13-limit POTE tuning
 
[[Category:Temperament]]
[[Category:Mystery| ]] <!-- main article -->
[[Category:Hemifamity]]

Revision as of 12:58, 23 April 2021

Mystery is the regular temperament which takes 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.

Interval chain

Period Generator 0 Generator 1
Cents Approx. Ratios Cents Approx. Ratios
0 0.00 1/1 15.94 91/90, 100/99, 105/104, 121/120
1 41.38 40/39, 45/44, 50/49 57.32 28/27, 33/32
2 82.76 21/20 98.70 35/33
3 124.14 14/13, 15/14 140.08 13/12
4 165.52 11/10 181.46 10/9
5 206.90 9/8 222.84 25/22
6 248.28 15/13 264.22 7/6
7 289.66 13/11, 32/27, 33/28 305.60 25/21
8 331.03 40/33 346.97 11/9, 39/32
9 372.41 26/21 388.35 5/4
10 413.79 14/11, 33/26, 80/63 429.73
11 455.17 13/10 471.11 21/16
12 496.55 4/3 512.49 35/26, 75/56
13 537.93 15/11 553.87 11/8
14 579.31 7/5 595.25 45/32
15 620.69 10/7 636.63 13/9
16 662.07 22/15 678.01 40/27
17 703.45 3/2 719.39 50/33
18 744.83 20/13 760.77 14/9
19 786.21 11/7, 52/33, 63/40 802.15 35/22
20 827.59 33/20 843.53 13/8, 27/22
21 868.97 21/13 884.91 5/3
22 910.34 22/13, 27/16, 56/33 926.29
23 951.72 26/15 967.66 7/4
24 993.10 16/9 1009.04 25/14, 70/39
25 1034.48 20/11 1050.42 11/6
26 1075.86 13/7, 28/15 1090.80 15/8
27 1117.24 40/21 1133.18 25/13, 52/27
28 1158.62 39/20, 49/25, 88/45 1174.56 63/32, 65/33, 77/39, 160/81
29 1200.00 2/1

* in 13-limit POTE tuning

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