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Hemififths: Difference between revisions

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Line 30: Line 30:
! rowspan="2" | Cents*
! rowspan="2" | Cents*
! colspan="2" | Approximate ratios
! colspan="2" | Approximate ratios
! rowspan="2" | [[Ups and downs notation|Ups and downs<br>notation]]**
|-
|-
! 7-limit
! 7-limit
Line 38: Line 37:
| 0.0
| 0.0
| '''1/1'''
| '''1/1'''
|
|  
| P1
|-
|-
| 1
| 1
Line 45: Line 43:
| 49/40, 60/49
| 49/40, 60/49
| 11/9, '''16/13''', 27/22, 39/32
| 11/9, '''16/13''', 27/22, 39/32
| ~3 = ^m3 = vM3
|-
|-
| 2
| 2
Line 51: Line 48:
| '''3/2'''
| '''3/2'''
|
|
| P5
|-
|-
| 3
| 3
Line 57: Line 53:
| 90/49
| 90/49
| 11/6, 24/13
| 11/6, 24/13
| ~7 = ^m7 = vM7
|-
|-
| 4
| 4
Line 63: Line 58:
| '''9/8'''
| '''9/8'''
|  
|  
| M2
|-
|-
| 5
| 5
Line 69: Line 63:
| 112/81
| 112/81
| '''11/8''', 18/13
| '''11/8''', 18/13
| ~4 = ^4 = vA4
|-
|-
| 6
| 6
Line 75: Line 68:
| 27/16
| 27/16
| 22/13
| 22/13
| M6
|-
|-
| 7
| 7
Line 81: Line 73:
| 28/27
| 28/27
| 33/32, 27/26
| 33/32, 27/26
| ^1 = \m2
|-
|-
| 8
| 8
Line 87: Line 78:
| 80/63, 81/64
| 80/63, 81/64
| 14/11, 33/26
| 14/11, 33/26
| M3
|-
|-
| 9
| 9
Line 93: Line 83:
| 14/9
| 14/9
|  
|  
| ^5 = \m6
|-
|-
| 10
| 10
Line 99: Line 88:
| 40/21
| 40/21
| 21/11
| 21/11
| M7
|-
|-
| 11
| 11
Line 105: Line 93:
| 7/6
| 7/6
|  
|  
| ^M2 = \m3
|-
|-
| 12
| 12
Line 111: Line 98:
| 10/7
| 10/7
|  
|  
| A4 = \~5
|-
|-
| 13
| 13
Line 117: Line 103:
| '''7/4'''
| '''7/4'''
|  
|  
| ^M6 = \m7
|-
|-
| 14
| 14
Line 123: Line 108:
| 15/14
| 15/14
| 14/13
| 14/13
| A1 = \~2
|-
|-
| 15
| 15
Line 129: Line 113:
| '''21/16'''
| '''21/16'''
|  
|  
| ^M3 = \4
|-
|-
| 16
| 16
Line 135: Line 118:
| 45/28
| 45/28
| 21/13
| 21/13
| A5 = \~6
|-
|-
| 17
| 17
Line 141: Line 123:
| 63/32, 160/81
| 63/32, 160/81
| 55/28, 65/33, 77/39
| 55/28, 65/33, 77/39
| ^M7 = \8
|-
|-
| 18
| 18
Line 147: Line 128:
| 98/81, 135/112
| 98/81, 135/112
| 40/33
| 40/33
| A2 = \~3
|-
|-
| 19
| 19
Line 153: Line 133:
| 40/27
| 40/27
|  
|  
| ^A4 = \5
|-
|-
| 20
| 20
Line 159: Line 138:
| 49/27
| 49/27
| 20/11
| 20/11
| A6 = \~7
|-
|-
| 21
| 21
Line 165: Line 143:
| 10/9
| 10/9
|  
|  
| ^A1 = \M2
|-
|-
| 22
| 22
Line 171: Line 148:
| 49/36
| 49/36
| 15/11
| 15/11
| A3 = \~4
|-
|-
| 23
| 23
Line 177: Line 153:
| 5/3
| 5/3
|  
|  
| ^A5 = \M6
|-
|-
| 24
| 24
Line 183: Line 158:
| 49/48, 50/49
| 49/48, 50/49
| 40/39, 45/44, 55/54, 65/64
| 40/39, 45/44, 55/54, 65/64
| A7 - P8 = -d2 = ^\1
|-
|-
| 25
| 25
Line 189: Line 163:
| '''5/4'''
| '''5/4'''
|  
|  
| ^A2 = \M3
|-
|-
| 26
| 26
Line 195: Line 168:
| 49/32
| 49/32
| 20/13
| 20/13
| AA4 = ^\5
|-
|-
| 27
| 27
Line 201: Line 173:
| '''15/8'''
| '''15/8'''
|  
|  
| ^A6 = \M7
|-
|-
| 28
| 28
Line 207: Line 178:
| 147/128
| 147/128
| 15/13
| 15/13
| AA1= ^\2
|-
|-
| 29
| 29
Line 213: Line 183:
| 45/32
| 45/32
|  
|  
| ^A3 = \A4
|}
|}
<nowiki/>* In 7-limit CWE tuning, {{nowrap|generator {{=}} 351.467{{c}} }}, {{nowrap| P5 {{=}} 702.934{{c}} }} and {{nowrap| c {{=}} 2.934{{c}} }}
<nowiki/>* In 7-limit CWE tuning, octave reduced
 
<nowiki/>** Enharmonic equivalences: vvA1 and v\m2. Cents: {{nowrap| ^1 {{=}} 50¢ + 3.5c }} and {{nowrap| /1 {{=}} 50¢ − 8.5c }}


=== As a detemperament of 17et ===
=== As a detemperament of 17et ===
Line 451: Line 418:
| C–Ad
| C–Ad
|}
|}
=== Ups and downs notation ===
In [[Kite's ups and downs notation]], the equivalences are vvA1 and v\m2. Let ''c'' be the amount by which the fifth exceeds 7\12, then {{nowrap| ^1 {{=}} 50{{c}} + 3.5''c'' }} and {{nowrap| /1 {{=}} 50{{c}} − 8.5''c'' }}. For 7-limit CWE tuning, {{nowrap| ''c'' {{=}} 2.934{{c}} }}.
{| class="wikitable center-1 right-2"
|-
! #
! Cents*
! Ups and downs<br>notation
! Associated ratios
|-
| 0
| 0.0
| P1
| 1/1
|-
| 1
| 351.5
| ~3 = ^m3 = vM3
| 11/9~16/13
|-
| 2
| 702.9
| P5
| 3/2
|-
| 3
| 1054.4
| ~7 = ^m7 = vM7
| 11/6~24/13
|-
| 4
| 205.9
| M2
| 9/8
|-
| 5
| 557.3
| ~4 = ^4 = vA4
| 11/8~18/13
|-
| 6
| 908.8
| M6
| 22/13~27/16
|-
| 7
| 60.3
| ^1 = \m2
| 27/26~33/32
|-
| 8
| 411.7
| M3
| 14/11~33/26
|-
| 9
| 763.2
| ^5 = \m6
| 14/9
|-
| 10
| 1114.7
| M7
| 21/11~40/21
|-
| 11
| 266.1
| ^M2 = \m3
| 7/6
|-
| 12
| 617.6
| A4 = \~5
| 10/7
|-
| 13
| 969.1
| ^M6 = \m7
| 7/4
|-
| 14
| 120.5
| A1 = \~2
| 14/13~15/14
|-
| 15
| 472.0
| ^M3 = \4
| 21/16
|-
| 16
| 823.5
| A5 = \~6
| 21/13
|-
| 17
| 1174.9
| ^M7 = \8
| 63/32~160/81
|-
| 18
| 326.4
| A2 = \~3
| 40/33
|-
| 19
| 677.9
| ^A4 = \5
| 40/27
|-
| 20
| 1029.3
| A6 = \~7
| 20/11
|-
| 21
| 180.8
| ^A1 = \M2
| 10/9
|-
| 22
| 532.3
| A3 = \~4
| 15/11
|-
| 23
| 883.7
| ^A5 = \M6
| 5/3
|-
| 24
| 35.2
| A7 - P8 = -d2 = ^\1
| 49/48~50/49
|-
| 25
| 386.7
| ^A2 = \M3
| 5/4
|-
| 26
| 738.1
| AA4 = ^\5
| 20/13
|-
| 27
| 1089.6
| ^A6 = \M7
| 15/8
|-
| 28
| 241.1
| AA1= ^\2
| 15/13
|-
| 29
| 592.5
| ^A3 = \A4
| 45/32
|}
<nowiki/>* In 7-limit CWE tuning, octave reduced


== Chords ==
== Chords ==
Retrieved from "https://en.xen.wiki/w/Hemififths"