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Hemififths: Difference between revisions

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Hemififths was named by [[Gene Ward Smith]] in 2004<ref>[https://yahootuninggroupsultimatebackup.github.io/tuning-math/topicId_10541.html Yahoo! Tuning Group (Archive) | ''Names for important high-complexity temperaments'']</ref>.  
Hemififths was named by [[Gene Ward Smith]] in 2004<ref>[https://yahootuninggroupsultimatebackup.github.io/tuning-math/topicId_10541.html Yahoo! Tuning Group (Archive) | ''Names for important high-complexity temperaments'']</ref>.  


See [[Breedsmic temperaments #Hemififths]] and [[No-fives_subgroup_temperaments#Hemif]] for more technical data.
See [[Breedsmic temperaments #Hemififths]] and [[No-fives subgroup temperaments#Hemif]] for more technical data.


== Interval chain ==
== Interval chain ==
In the following table, odd harmonics 1–21 are labeled in '''bold'''.  
In the following table, odd harmonics 1–21 are labeled in '''bold'''.  
{| class="wikitable center-1 right-2"
{| class="wikitable center-1 right-2"
|-
! rowspan="2" | &#35;
! rowspan="2" | &#35;
! rowspan="2" | Cents*
! rowspan="2" | Cents*
Line 21: Line 22:
| '''1/1'''
| '''1/1'''
|
|
|P1
| P1
|-
|-
| 1
| 1
Line 27: Line 28:
| 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
| ~3 = ^m3 = vM3
|-
|-
| 2
| 2
Line 33: Line 34:
| '''3/2'''
| '''3/2'''
|
|
|P5
| P5
|-
|-
| 3
| 3
Line 39: Line 40:
| 90/49
| 90/49
| 11/6, 24/13
| 11/6, 24/13
|~7 = ^m7 = vM7
| ~7 = ^m7 = vM7
|-
|-
| 4
| 4
Line 45: Line 46:
| '''9/8'''
| '''9/8'''
|  
|  
|M2
| M2
|-
|-
| 5
| 5
Line 51: Line 52:
| 112/81
| 112/81
| '''11/8''', 18/13
| '''11/8''', 18/13
|~4 = ^4 = vA4
| ~4 = ^4 = vA4
|-
|-
| 6
| 6
Line 57: Line 58:
| 27/16
| 27/16
| 22/13
| 22/13
|M6
| M6
|-
|-
| 7
| 7
Line 63: Line 64:
| 28/27
| 28/27
| 33/32, 27/26
| 33/32, 27/26
|^1 = \m2
| ^1 = \m2
|-
|-
| 8
| 8
Line 69: Line 70:
| 80/63, 81/64
| 80/63, 81/64
| 14/11, 33/26
| 14/11, 33/26
|M3
| M3
|-
|-
| 9
| 9
Line 75: Line 76:
| 14/9
| 14/9
|  
|  
|^5 = \m6
| ^5 = \m6
|-
|-
| 10
| 10
Line 81: Line 82:
| 40/21
| 40/21
| 21/11
| 21/11
|M7
| M7
|-
|-
| 11
| 11
Line 87: Line 88:
| 7/6
| 7/6
|  
|  
|^M2 = \m3
| ^M2 = \m3
|-
|-
| 12
| 12
Line 93: Line 94:
| 10/7
| 10/7
|  
|  
|A4 = \~5
| A4 = \~5
|-
|-
| 13
| 13
Line 99: Line 100:
| '''7/4'''
| '''7/4'''
|  
|  
|^M6 = \m7
| ^M6 = \m7
|-
|-
| 14
| 14
Line 105: Line 106:
| 15/14
| 15/14
| 14/13
| 14/13
|A1 = \~2
| A1 = \~2
|-
|-
| 15
| 15
Line 111: Line 112:
| '''21/16'''
| '''21/16'''
|  
|  
|^M3 = \4
| ^M3 = \4
|-
|-
| 16
| 16
Line 117: Line 118:
| 45/28
| 45/28
| 21/13
| 21/13
|A5 = \~6
| A5 = \~6
|-
|-
| 17
| 17
Line 123: Line 124:
| 63/32, 160/81
| 63/32, 160/81
|
|
|^M7 = \8
| ^M7 = \8
|-
|-
| 18
| 18
Line 129: Line 130:
| 98/81, 135/112
| 98/81, 135/112
| 40/33
| 40/33
|A2 = \~3
| A2 = \~3
|-
|-
| 19
| 19
Line 135: Line 136:
| 40/27
| 40/27
|  
|  
|^A4 = \5
| ^A4 = \5
|-
|-
| 20
| 20
Line 141: Line 142:
| 49/27
| 49/27
| 20/11
| 20/11
|A6 = \~7
| A6 = \~7
|-
|-
| 21
| 21
Line 147: Line 148:
| 10/9
| 10/9
|  
|  
|^A1 = \M2
| ^A1 = \M2
|-
|-
| 22
| 22
Line 153: Line 154:
| 49/36
| 49/36
| 15/11
| 15/11
|A3 = \~4
| A3 = \~4
|-
|-
| 23
| 23
Line 159: Line 160:
| 5/3
| 5/3
|  
|  
|^A5 = \M6
| ^A5 = \M6
|-
|-
| 24
| 24
Line 165: Line 166:
| 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
| A7 - P8 = -d2 = ^\1
|-
|-
| 25
| 25
Line 171: Line 172:
| '''5/4'''
| '''5/4'''
|  
|  
|^A2 = \M3
| ^A2 = \M3
|-
|-
| 26
| 26
Line 177: Line 178:
| 49/32
| 49/32
| 20/13
| 20/13
|AA4 = ^\5
| AA4 = ^\5
|-
|-
| 27
| 27
Line 183: Line 184:
| '''15/8'''
| '''15/8'''
|  
|  
|^A6 = \M7
| ^A6 = \M7
|-
|-
| 28
| 28
Line 189: Line 190:
| 147/128
| 147/128
| 15/13
| 15/13
|AA1= ^\2
| AA1= ^\2
|-
|-
| 29
| 29
Line 195: Line 196:
| 45/32
| 45/32
|  
|  
|^A3 = \A4
| ^A3 = \A4
|}
|}
<nowiki>*</nowiki> In 7-limit CTE tuning, generator = 351.445¢, P5 = 702.89¢, c = 2.89¢
<nowiki />* In 7-limit CTE tuning, {{nowrap|generator {{=}} 351.445¢,|P5 {{=}} 702.89¢|and c {{=}} 2.89¢}}


<nowiki>**</nowiki> Enharmonic equivalences: vvA1 and v\m2. Cents: ^1 = 50¢ + 3.5c and /1 = 50¢ - 8.5c
<nowiki />** Enharmonic equivalences: vvA1 and v\m2. Cents: {{nowrap|^1 {{=}} 50¢ + 3.5c}} and {{nowrap|/1 {{=}} 50¢ &minus; 8.5c}}


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