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'''Amity''' is a temperament for the 5, 7, 11, and 13 [[Harmonic limit|prime limits]]. EDOs that support amity include [[46edo]], [[53edo]], [[99edo]], [[152edo]], and [[205edo]].
'''Amity''' is a temperament for the 5, 7, 11, and 13 [[Harmonic limit|prime limits]]. EDOs that support amity include [[46edo]], [[53edo]], [[99edo]], [[152edo]], and [[205edo]].


See [[Ragismic_microtemperaments#Amity|Ragismic microtemperaments]] for more information.
See [[Amity family]] or [[Ragismic microtemperaments #Amity]] for more information.


=Interval chain=
== Interval chain ==
{| class="wikitable"
{| class="wikitable center-all right-2"
|-
|-
! rowspan="2"| Generators
! rowspan="2"| Generators
Line 10: Line 10:
! colspan="2"| Approximate ratios
! colspan="2"| Approximate ratios
|-
|-
! | Amity <br>(53&amp;205)
! Amity <br>(53&amp;205)
! | Hitchcock <br>(46&amp;53)
! Hitchcock <br>(46&amp;53)
|-
|-
| | 0
| 0
| style="text-align:right;" | 0.000
| 0.000
| colspan="2"| 1/1
| colspan="2"| 1/1
|-
|-
| | 1
| 1
| style="text-align:right;" | 339.43
| 339.43
| |  
|  
| | 11/9
| 11/9
|-
|-
| | 2
| 2
| style="text-align:right;" | 678.86
| 678.86
| colspan="2"| 40/27
| colspan="2"| 40/27
|-
|-
| | 3
| 3
| style="text-align:right;" | 1018.30
| 1018.30
| colspan="2"| 9/5
| colspan="2"| 9/5
|-
|-
| | 4
| 4
| style="text-align:right;" | 157.73
| 157.73
| | 35/32
| 35/32
| | 12/11~35/32~11/10
| 12/11~35/32~11/10
|-
|-
| | 5
| | 5
| style="text-align:right;" | 497.16
| 497.16
| colspan="2"| 4/3
| colspan="2"| 4/3
|-
|-
| | 6
| 6
| style="text-align:right;" | 836.59
| 836.59
| |  
|  
| | 21/13~13/8
| 21/13~13/8
|-
|-
| | 7
| 7
| style="text-align:right;" | 1176.03
| 1176.03
| | 65/33, 77/39~160/81
| 65/33, 77/39~160/81
| | 63/32~128/65~65/33, <br>77/39~160/81
| 63/32~128/65~65/33, <br>77/39~160/81
|-
|-
| | 8
| 8
| style="text-align:right;" | 315.46
| 315.46
| colspan="2"| 6/5
| colspan="2"| 6/5
|-
|-
| | 9
| 9
| style="text-align:right;" | 654.89
| 654.89
| |  
|  
| | 16/11~22/15
| 16/11~22/15
|-
|-
| | 10
| 10
| style="text-align:right;" | 994.32
| 994.32
| colspan="2"| 16/9
| colspan="2"| 16/9
|-
|-
| | 11
| 11
| style="text-align:right;" | 133.75
| 133.75
| | 27/25
| 27/25
| | 14/13~27/25~13/12
| 14/13~27/25~13/12
|-
|-
| | 12
| 12
| style="text-align:right;" | 473.19
| 473.19
| colspan="2"| 21/16
| colspan="2"| 21/16
|-
|-
| | 13
| 13
| style="text-align:right;" | 812.62
| 812.62
| colspan="2"| 8/5
| colspan="2"| 8/5
|-
|-
| | 14
| 14
| style="text-align:right;" | 1152.05
| 1152.05
| | 35/18
| 35/18
| | 64/33~35/18
| 64/33~35/18
|-
|-
| | 15
| 15
| style="text-align:right;" | 291.48
| 291.48
| colspan="2"| 13/11~32/27
| colspan="2"| 13/11~32/27
|-
|-
| | 16
| 16
| style="text-align:right;" | 630.92
| 630.92
| |  
|  
| | 13/9
| 13/9
|-
|-
| | 17
| 17
| style="text-align:right;" | 970.35
| 970.35
| colspan="2"| 7/4
| colspan="2"| 7/4
|-
|-
| | 18
| 18
| style="text-align:right;" | 109.78
| 109.78
| colspan="2"| 16/15
| colspan="2"| 16/15
|-
|-
| | 19
| 19
| style="text-align:right;" | 449.21
| 449.21
| |  
|  
| | 13/10
| 13/10
|-
|-
| | 20
| 20
| style="text-align:right;" | 788.64
| 788.64
| |  
|  
| |  
|  
|-
|-
| | 21
| 21
| style="text-align:right;" | 1128.08
| 1128.08
| | 48/25~25/13
| 48/25~25/13
| | 21/11~48/25
| 21/11~48/25
|-
|-
| | 22
| 22
| style="text-align:right;" | 267.51
| 267.51
| colspan="2"| 7/6
| colspan="2"| 7/6
|-
|-
| | 23
| 23
| style="text-align:right;" | 606.94
| 606.94
| |  
|  
| |  
|  
|-
|-
| | 24
| 24
| style="text-align:right;" | 946.37
| 946.37
| |  
|  
| | 26/15
| 26/15
|-
|-
| | 25
| 25
| style="text-align:right;" | 85.81
| 85.81
| colspan="2"| 21/20
| colspan="2"| 21/20
|-
|-
| | 26
| 26
| style="text-align:right;" | 425.24
| 425.24
| | 32/25
| 32/25
| | 14/11~32/25
| 14/11~32/25
|-
|-
| | 27
| 27
| style="text-align:right;" | 764.67
| 764.67
| colspan="2"| 14/9
| colspan="2"| 14/9
|-
|-
| | 28
| 28
| style="text-align:right;" | 1104.10
| 1104.10
| |  
|  
| |  
|  
|-
|-
| | 29
| 29
| style="text-align:right;" | 243.53
| 243.53
| | 15/13
| 15/13
| |  
|  
|-
|-
| | 30
| 30
| style="text-align:right;" | 582.97
| 582.97
| colspan="2"| 7/5
| colspan="2"| 7/5
|-
|-
| | 31
| 31
| style="text-align:right;" | 922.40
| 922.40
| |  
|  
| |  
|  
|-
|-
| | 32
| 32
| style="text-align:right;" | 61.83
| 61.83
| | 28/27~27/26
| 28/27~27/26
| | 28/27
| 28/27
|-
|-
| | 33
| 33
| style="text-align:right;" | 401.26
| 401.26
| |  
|  
| |  
|  
|-
|-
| | 34
| 34
| style="text-align:right;" | 740.69
| 740.69
| | 20/13
| 20/13
| |  
|  
|-
|-
| | 35
| 35
| style="text-align:right;" | 1080.13
| 1080.13
| colspan="2"| 28/15
| colspan="2"| 28/15
|-
|-
| | 36
| 36
| style="text-align:right;" | 219.56
| 219.56
| | 25/22
| 25/22
| |  
|  
|-
|-
| | 37
| 37
| style="text-align:right;" | 558.99
| 558.99
| | 18/13
| 18/13
| |  
|  
|}
|}
<span style="font-family: Arial,Helvetica,sans-serif;">*in 7-limit POTE tuning</span>
<nowiki>*</nowiki> in 7-limit POTE tuning


=Tuning Spectra=
== Tuning Spectra ==
==Spectrum of Amity Tunings (53&amp;205)==
=== Spectrum of Amity Tunings (53&amp;205) ===


13-limit commas: 352/351, 540/539, 625/624, 729/728
13-limit commas: 352/351, 540/539, 625/624, 729/728
{| class="wikitable"
{| class="wikitable center-all left-3"
|-
|-
! | Eigenmonzo
! Eigenmonzo
! | Generator
! Generator
! Comment
|-
|-
| | 10/9
| 10/9
| | 339.199
| 339.199
|
|-
|-
| | 13/11
| 13/11
| | 339.281
| 339.281
|
|-
|-
| | 8/7
| 8/7
| | 339.343
| 339.343
|
|-
|-
| | 7/6
| 7/6
| | 339.403
| 339.403
|
|-
|-
| | 7/5
| 7/5
| | 339.417 (7 limit minimax)
| 339.417
| 7 limit minimax
|-
|-
| | 9/7
| 9/7
| | 339.441 (9 limit minimax)
| 339.441
| 9 limit minimax
|-
|-
| | 15/14
| 15/14
| | 339.444
| 339.444
|
|-
|-
| | 6/5
| 6/5
| | 339.455
| 339.455
|
|-
|-
| | 14/11
| 14/11
| | 339.462 (11 limit minimax)
| 339.462
| 11 limit minimax
|-
|-
| | 11/9
| 11/9
| | 339.473
| 339.473
|
|-
|-
| | 15/11
| 15/11
| | 339.476
| 339.476
|
|-
|-
| | 12/11
| 12/11
| | 339.485
| 339.485
|
|-
|-
| | 11/10
| 11/10
| | 339.490
| 339.490
|
|-
|-
| | 11/8
| 11/8
| | 339.495 (13, 15 limit minimax)
| 339.495
| 13, 15 limit minimax
|-
|-
| | 14/13
| 14/13
| | 339.505
| 339.505
|
|-
|-
| | 5/4
| 5/4
| | 339.514 (5 limit minimax)
| 339.514
| 5 limit minimax
|-
|-
| | 16/15
| 16/15
| | 339.541
| 339.541
|
|-
|-
| | 18/13
| 18/13
| | 339.551
| 339.551
|
|-
|-
| | 13/12
| 13/12
| | 339.558
| 339.558
|
|-
|-
| | 16/13
| 16/13
| | 339.563
| 339.563
|
|-
|-
| | 15/13
| 15/13
| | 339.577
| 339.577
|
|-
|-
| | 13/10
| 13/10
| | 339.582
| 339.582
|
|-
|-
| | 4/3
| 4/3
| | 339.609
| 339.609
|
|}
|}


==Spectrum of Hitchcock Tunings (46&amp;53)==
=== Spectrum of Hitchcock Tunings (46&amp;53) ===


13-limit commas: 121/120, 169/168, 176/175, 325/324
13-limit commas: 121/120, 169/168, 176/175, 325/324
{| class="wikitable"
{| class="wikitable center-all left-3"
|-
|-
! | Eigenmonzo
! Eigenmonzo
! | Generator
! Generator
! Comment
|-
|-
| | 12/11
| 12/11
| | 337.659
| 337.659
|
|-
|-
| | 11/8
| 11/8
| | 338.742
| 338.742
|
|-
|-
| | 14/13
| 14/13
| | 338.936
| 338.936
|
|-
|-
| | 14/11
| 14/11
| | 339.135
| 339.135
|
|-
|-
| | 10/9
| 10/9
| | 339.199
| 339.199
|
|-
|-
| | 13/11
| 13/11
| | 339.281
| 339.281
|
|-
|-
| | 8/7
| 8/7
| | 339.343
| 339.343
|
|-
|-
| | 7/6
| 7/6
| | 339.403
| 339.403
|
|-
|-
| | 7/5
| 7/5
| | 339.417 (7 limit minimax)
| 339.417
| 7 limit minimax
|-
|-
| | 9/7
| 9/7
| | 339.441 (9, 11, 13 limit minimax)
| 339.441
| 9, 11, 13 limit minimax
|-
|-
| | 15/14
| 15/14
| | 339.444 (15 limit minimax)
| 339.444
| 15 limit minimax
|-
|-
| | 6/5
| 6/5
| | 339.455
| 339.455
|
|-
|-
| | 5/4
| 5/4
| | 339.514 (5 limit minimax)
| 339.514
| 5 limit minimax
|-
|-
| | 16/15
| 16/15
| | 339.541
| 339.541
|
|-
|-
| | 4/3
| 4/3
| | 339.609
| 339.609
|
|-
|-
| | 15/13
| 15/13
| | 339.677
| 339.677
|
|-
|-
| | 13/10
| 13/10
| | 339.695
| 339.695
|
|-
|-
| | 18/13
| 18/13
| | 339.789
| 339.789
|
|-
|-
| | 13/12
| 13/12
| | 339.870
| 339.870
|
|-
|-
| | 16/13
| 16/13
| | 340.088
| 340.088
|
|-
|-
| | 15/11
| 15/11
| | 340.339
| 340.339
|
|-
|-
| | 11/10
| 11/10
| | 341.251
| 341.251
|
|-
|-
| | 11/9
| 11/9
| | 347.408
| 347.408
|
|}
|}


[[Category:Amity]]
[[Category:Amity |Amity ]]
[[Category:Temperament]]
[[Category:Temperament]]

Revision as of 05:56, 1 October 2020

Amity is a temperament for the 5, 7, 11, and 13 prime limits. EDOs that support amity include 46edo, 53edo, 99edo, 152edo, and 205edo.

See Amity family or Ragismic microtemperaments #Amity for more information.

Interval chain

Generators Cents*
(octave-reduced) 		Approximate ratios
Amity
(53&205) 		Hitchcock
(46&53)
0 0.000 1/1
1 339.43 11/9
2 678.86 40/27
3 1018.30 9/5
4 157.73 35/32 12/11~35/32~11/10
5 497.16 4/3
6 836.59 21/13~13/8
7 1176.03 65/33, 77/39~160/81 63/32~128/65~65/33,
77/39~160/81
8 315.46 6/5
9 654.89 16/11~22/15
10 994.32 16/9
11 133.75 27/25 14/13~27/25~13/12
12 473.19 21/16
13 812.62 8/5
14 1152.05 35/18 64/33~35/18
15 291.48 13/11~32/27
16 630.92 13/9
17 970.35 7/4
18 109.78 16/15
19 449.21 13/10
20 788.64
21 1128.08 48/25~25/13 21/11~48/25
22 267.51 7/6
23 606.94
24 946.37 26/15
25 85.81 21/20
26 425.24 32/25 14/11~32/25
27 764.67 14/9
28 1104.10
29 243.53 15/13
30 582.97 7/5
31 922.40
32 61.83 28/27~27/26 28/27
33 401.26
34 740.69 20/13
35 1080.13 28/15
36 219.56 25/22
37 558.99 18/13

* in 7-limit POTE tuning

Tuning Spectra

Spectrum of Amity Tunings (53&205)

13-limit commas: 352/351, 540/539, 625/624, 729/728

Eigenmonzo Generator Comment
10/9 339.199
13/11 339.281
8/7 339.343
7/6 339.403
7/5 339.417 7 limit minimax
9/7 339.441 9 limit minimax
15/14 339.444
6/5 339.455
14/11 339.462 11 limit minimax
11/9 339.473
15/11 339.476
12/11 339.485
11/10 339.490
11/8 339.495 13, 15 limit minimax
14/13 339.505
5/4 339.514 5 limit minimax
16/15 339.541
18/13 339.551
13/12 339.558
16/13 339.563
15/13 339.577
13/10 339.582
4/3 339.609

Spectrum of Hitchcock Tunings (46&53)

13-limit commas: 121/120, 169/168, 176/175, 325/324

Eigenmonzo Generator Comment
12/11 337.659
11/8 338.742
14/13 338.936
14/11 339.135
10/9 339.199
13/11 339.281
8/7 339.343
7/6 339.403
7/5 339.417 7 limit minimax
9/7 339.441 9, 11, 13 limit minimax
15/14 339.444 15 limit minimax
6/5 339.455
5/4 339.514 5 limit minimax
16/15 339.541
4/3 339.609
15/13 339.677
13/10 339.695
18/13 339.789
13/12 339.870
16/13 340.088
15/11 340.339
11/10 341.251
11/9 347.408
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