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Amity: Difference between revisions

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The resource I found says Gene, not Paul
m Text replacement - "Eigenmonzo<br>(unchanged-interval)" to "Unchanged interval<br>(eigenmonzo)"
 
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== Interval chain ==
== Interval chain ==
In the following table, odd harmonics 1–21 and their inversions are labeled in '''bold'''.
{| class="wikitable center-1 right-2"
{| class="wikitable center-1 right-2"
|-
|-
! rowspan="2" | #
! rowspan="3" | #
! rowspan="2" | Cents*  
! rowspan="3" | Cents*  
! colspan="3" | Approximate ratios
! colspan="3" | Approximate ratios
|-
|-
! 7-limit
! rowspan="2" | 7-limit
! 13-limit extensions, <br>amity mapping ({{nowrap| 53 & 152 }})
! colspan="2" | 13-limit extensions
! 13-limit extensions, <br>hitchcock mapping ({{nowrap| 46 & 53 }})
|-
! Amity ({{nowrap| 53 & 152 }})
! Hitchcock ({{nowrap| 46 & 53 }})
|-
|-
| 0
| 0
| 0.00
| 0.00
| 1/1
| '''1/1'''
|
|
|
|
Line 31: Line 35:
|-
|-
| 2
| 2
| 678.86
| 678.87
| 40/27
| 40/27
|
|
Line 43: Line 47:
|-
|-
| 4
| 4
| 157.73
| 157.74
| 35/32
| 35/32
|
|
Line 49: Line 53:
|-
|-
| 5
| 5
| 497.16
| 497.17
| '''4/3'''
| '''4/3'''
|
|
Line 55: Line 59:
|-
|-
| 6
| 6
| 836.59
| 836.61
| 81/50
| 81/50
|
|
Line 61: Line 65:
|-
|-
| 7
| 7
| 1176.03
| 1176.04
| 63/32, 160/81
| 63/32, 160/81
| 65/33, 77/39
| 65/33, 77/39
Line 67: Line 71:
|-
|-
| 8
| 8
| 315.46
| 315.48
| 6/5
| 6/5
|
|
Line 73: Line 77:
|-
|-
| 9
| 9
| 654.89
| 654.91
| 35/24
| 35/24
|
|
Line 79: Line 83:
|-
|-
| 10
| 10
| 994.32
| 994.35
| 16/9
| '''16/9'''
|
|
| 39/22
| 39/22
|-
|-
| 11
| 11
| 133.75
| 133.78
| 27/25
| 27/25
|
|
Line 91: Line 95:
|-
|-
| 12
| 12
| 473.19
| 473.22
| 21/16
| '''21/16'''
|
|
|
|
|-
|-
| 13
| 13
| 812.62
| 812.65
| '''8/5'''
| '''8/5'''
|
|
Line 103: Line 107:
|-
|-
| 14
| 14
| 1152.05
| 1152.09
| 35/18
| 35/18
|
|
Line 109: Line 113:
|-
|-
| 15
| 15
| 291.48
| 291.52
| 32/27
| 32/27
| 13/11
| 13/11
Line 115: Line 119:
|-
|-
| 16
| 16
| 630.92
| 630.96
| 36/25
| 36/25
|
|
Line 121: Line 125:
|-
|-
| 17
| 17
| 970.35
| 970.39
| '''7/4'''
| '''7/4'''
|
|
Line 127: Line 131:
|-
|-
| 18
| 18
| 109.78
| 109.83
| 16/15
| '''16/15'''
|
|
|
|
|-
|-
| 19
| 19
| 449.21
| 449.26
| 35/27
| 35/27
|
|
Line 139: Line 143:
|-
|-
| 20
| 20
| 788.64
| 788.70
| 63/40
| 63/40
|
|
Line 145: Line 149:
|-
|-
| 21
| 21
| 1128.08
| 1128.13
| 48/25
| 48/25
| 25/13
| 25/13
Line 151: Line 155:
|-
|-
| 22
| 22
| 267.51
| 267.57
| 7/6
| 7/6
|
|
Line 157: Line 161:
|-
|-
| 23
| 23
| 606.94
| 607.00
| 64/45
| 64/45
|
|
Line 163: Line 167:
|-
|-
| 24
| 24
| 946.37
| 946.44
| 81/70
| 81/70
|
|
Line 169: Line 173:
|-
|-
| 25
| 25
| 85.81
| 85.87
| 21/20
| 21/20
|
|
Line 175: Line 179:
|-
|-
| 26
| 26
| 425.24
| 425.31
| 32/25
| 32/25
|
|
Line 181: Line 185:
|-
|-
| 27
| 27
| 764.67
| 764.74
| 14/9
| 14/9
|
|
Line 187: Line 191:
|-
|-
| 28
| 28
| 1104.10
| 1104.18
| 256/135
| 256/135
|
|
Line 193: Line 197:
|-
|-
| 29
| 29
| 243.53
| 243.61
| 147/128
| 147/128
| 15/13
| 15/13
Line 199: Line 203:
|-
|-
| 30
| 30
| 582.97
| 583.05
| 7/5
| 7/5
|
|
Line 205: Line 209:
|-
|-
| 31
| 31
| 922.40
| 922.48
| 128/75
| 128/75
|
|
Line 211: Line 215:
|-
|-
| 32
| 32
| 61.83
| 61.92
| 28/27
| 28/27
| 27/26
| 27/26
Line 217: Line 221:
|-
|-
| 33
| 33
| 401.26
| 401.35
| 63/50
| 63/50
|
|
Line 223: Line 227:
|-
|-
| 34
| 34
| 740.69
| 740.79
| 49/32
| 49/32
| 20/13
| 20/13
Line 229: Line 233:
|-
|-
| 35
| 35
| 1080.13
| 1080.22
| 28/15
| 28/15
|
|
Line 235: Line 239:
|-
|-
| 36
| 36
| 219.56
| 219.66
| 256/225
| 256/225
| 25/22
| 25/22
Line 241: Line 245:
|-
|-
| 37
| 37
| 558.99
| 559.09
| 112/81
| 112/81
| 18/13
| 18/13
Line 247: Line 251:
|-
|-
| 38
| 38
| 898.42
| 898.53
| 42/25
| 42/25
|
|
Line 253: Line 257:
|-
|-
| 39
| 39
| 37.86
| 37.96
| 49/48
| 49/48
| 40/39, 45/44
| 40/39, 45/44
|
|
|}
|}
<nowiki />* In 7-limit POTE tuning, octave reduced
<nowiki/>* In 7-limit CWE tuning, octave reduced


== Tunings ==
== Tunings ==
=== Tunings spectra ===
=== Tunings spectra ===
==== Amity ====
==== Amity ====
{| class="wikitable center-all left-3"
{| class="wikitable center-all left-4"
|-
|-
! [[Eigenmonzo|Eigenmonzo<br>(unchanged-interval)]]*
! Edo<br>generator
! [[Eigenmonzo|Unchanged interval<br>(eigenmonzo)]]*
! Generator (¢)
! Generator (¢)
! Comments
! Comments
|-
|-
| 11\39
|
| 338.462
| 39ee… val, lower bound of 7- and 9-odd-limit diamond monotone
|-
| 13\46
|
| 339.130
| 46ef val
|-
|
| 9/5
| 9/5
| 339.199
| 339.199
|  
|  
|-
|-
|
| 13/11
| 13/11
| 339.281
| 339.281
|  
|  
|-
|-
|
| 7/4
| 7/4
| 339.343
| 339.343
|  
|  
|-
|-
| 28\99
|
| 339.394
| 99ef val, lower bound of 11-, 13-, 15-, and 13-limit 21-odd-limit diamond monotone
|-
|
| 7/6
| 7/6
| 339.403
| 339.403
|  
|  
|-
|-
|
| 7/5
| 7/5
| 339.417
| 339.417
| 7-odd-limit minimax
| 7-odd-limit minimax
|-
|-
|
| 9/7
| 9/7
| 339.441
| 339.441
| 9-odd-limit minimax
| 9-odd-limit minimax
|-
|-
|
| 15/14
| 15/14
| 339.444
| 339.444
|  
|  
|-
|-
|
| 5/3
| 5/3
| 339.455
| 339.455
|  
|  
|-
|-
|
| 11/7
| 11/7
| 339.462
| 339.462
| 11-odd-limit minimax
| 11-odd-limit minimax
|-
|-
|
| 11/9
| 11/9
| 339.473
| 339.473
|  
|  
|-
|-
| 43\152
|
| 339.474
| 152f val
|-
|
| 15/11
| 15/11
| 339.476
| 339.476
|  
|  
|-
|-
|
| 11/6
| 11/6
| 339.485
| 339.485
|  
|  
|-
|-
|
| 11/10
| 11/10
| 339.490
| 339.490
|  
|  
|-
|-
|
| 11/8
| 11/8
| 339.495
| 339.495
| 13- and 15-odd-limit minimax
| 13- and 15-odd-limit minimax
|-
|-
|
| 13/7
| 13/7
| 339.505
| 339.505
|  
|  
|-
|-
| 58\205
|
| 339.512
|
|-
|
| 5/4
| 5/4
| 339.514
| 339.514
| 5-odd-limit minimax
| 5-odd-limit minimax
|-
|-
|
| 15/8
| 15/8
| 339.541
| 339.541
|  
|  
|-
|-
|
| 13/9
| 13/9
| 339.551
| 339.551
|  
|  
|-
|-
|
| 13/12
| 13/12
| 339.558
| 339.558
|  
|  
|-
|-
|
| 13/8
| 13/8
| 339.563
| 339.563
|  
|  
|-
|-
|
| 15/13
| 15/13
| 339.577
| 339.577
|  
|  
|-
|-
|
| 13/10
| 13/10
| 339.582
| 339.582
|  
|  
|-
|-
|
| 3/2
| 3/2
| 339.609
| 339.609
|  
|  
|-
| 15\53
|
| 339.623
| Upper bound of 11-, 13-, 15-odd-limit and 13-limit 21-odd-limit diamond monotone
|-
| 17\60
|
| 340.000
| 60deee… val, upper bound of 7- and 9-odd-limit diamond monotone
|}
|}


==== Hitchcock ====
==== Hitchcock ====
{| class="wikitable center-all left-3"
{| class="wikitable center-all left-4"
|-
|-
! Eigenmonzo<br>(unchanged-interval)*
! Edo<br>generator
! Unchanged interval<br>(eigenmonzo)*
! Generator (¢)
! Generator (¢)
! Comments
! Comments
|-
|-
|
| 11/6
| 11/6
| 337.659
| 337.659
|  
|  
|-
|-
| 11\39
|
| 338.462
| Lower bound of 7-, 9, and 11-odd-limit diamond monotone
|-
|
| 11/8
| 11/8
| 338.742
| 338.742
|  
|  
|-
|-
|
| 13/7
| 13/7
| 338.936
| 338.936
|  
|  
|-
|-
| 13\46
|
| 339.130
| Lower bound of 13-, 15-odd-limit and 13-limit 21-odd-limit diamond monotone
|-
|
| 11/7
| 11/7
| 339.135
| 339.135
|  
|  
|-
|-
|
| 9/5
| 9/5
| 339.199
| 339.199
|  
|  
|-
|-
|
| 13/11
| 13/11
| 339.281
| 339.281
|  
|  
|-
|-
|
| 7/4
| 7/4
| 339.343
| 339.343
|  
|  
|-
|-
| 28\99
|
| 339.394
|
|-
|
| 7/6
| 7/6
| 339.403
| 339.403
|  
|  
|-
|-
|
| 7/5
| 7/5
| 339.417
| 339.417
| 7-odd-limit minimax
| 7-odd-limit minimax
|-
|-
|
| 9/7
| 9/7
| 339.441
| 339.441
| 9-, 11-, and 13-odd-limit minimax
| 9-, 11-, and 13-odd-limit minimax
|-
|-
|
| 15/14
| 15/14
| 339.444
| 339.444
| 15-odd-limit minimax
| 15-odd-limit minimax
|-
|-
|
| 5/3
| 5/3
| 339.455
| 339.455
|  
|  
|-
|-
|
| 5/4
| 5/4
| 339.514
| 339.514
| 5-odd-limit minimax
| 5-odd-limit minimax
|-
|-
|
| 15/8
| 15/8
| 339.541
| 339.541
|  
|  
|-
|-
|
| 3/2
| 3/2
| 339.609
| 339.609
|  
|  
|-
|-
| 15\53
|
| 339.623
| Upper bound of 11-, 13-, 15-odd-limit and 13-limit 21-odd-limit diamond monotone
|-
|
| 15/13
| 15/13
| 339.677
| 339.677
|  
|  
|-
|-
|
| 13/10
| 13/10
| 339.695
| 339.695
|  
|  
|-
|-
|
| 13/9
| 13/9
| 339.789
| 339.789
|  
|  
|-
|-
|
| 13/12
| 13/12
| 339.870
| 339.870
|  
|  
|-
|-
| 17\60
|
| 340.000
| 60de val, upper bound of 7- and 9-odd-limit diamond monotone
|-
|
| 13/8
| 13/8
| 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
Line 465: Line 577:
== Music ==
== Music ==
; [[User:Francium|Francium]]
; [[User:Francium|Francium]]
* [https://youtu.be/AsDaJXCBd_w?si=6BfHt5gYpCPD1oxq ''For Amity''] (2023) &ndash; amity in 463edo tuning
* [https://www.youtube.com/watch?v=AsDaJXCBd_w ''For Amity''] (2023) – in 463edo tuning
 
== Notes ==


[[Category:Amity| ]] <!-- main article -->
[[Category:Amity| ]] <!-- main article -->
Retrieved from "https://en.xen.wiki/w/Amity"