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94edo: Difference between revisions

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m Standardize format Sagittal
→Regular temperament properties: + link to slithy and dhaivatic. - glacier (subgroup temp already covered by tsaharuk and quanic). - all the unnamed rank-2's. Formatting
Line 967: Line 967:
|-
|-
| 2.3
| 2.3
| {{monzo| 149 -94 }}
| {{Monzo| 149 -94 }}
| {{mapping| 94 149 }}
| {{Mapping| 94 149 }}
| −0.054
| −0.054
| 0.054
| 0.054
Line 975: Line 975:
| 2.3.5
| 2.3.5
| 32805/32768, 9765625/9565938
| 32805/32768, 9765625/9565938
| {{mapping| 94 149 218 }}
| {{Mapping| 94 149 218 }}
| +0.442
| +0.442
| 0.704
| 0.704
Line 982: Line 982:
| 2.3.5.7
| 2.3.5.7
| 225/224, 3125/3087, 118098/117649
| 225/224, 3125/3087, 118098/117649
| {{mapping| 94 149 218 264 }}
| {{Mapping| 94 149 218 264 }}
| +0.208
| +0.208
| 0.732
| 0.732
Line 989: Line 989:
| 2.3.5.7.11
| 2.3.5.7.11
| 225/224, 385/384, 1331/1323, 2200/2187
| 225/224, 385/384, 1331/1323, 2200/2187
| {{mapping| 94 149 218 264 325 }}
| {{Mapping| 94 149 218 264 325 }}
| +0.304
| +0.304
| 0.683
| 0.683
Line 996: Line 996:
| 2.3.5.7.11.13
| 2.3.5.7.11.13
| 225/224, 275/273, 325/324, 385/384, 1331/1323
| 225/224, 275/273, 325/324, 385/384, 1331/1323
| {{mapping| 94 149 218 264 325 348 }}
| {{Mapping| 94 149 218 264 325 348 }}
| +0.162
| +0.162
| 0.699
| 0.699
Line 1,003: Line 1,003:
| 2.3.5.7.11.13.17
| 2.3.5.7.11.13.17
| 170/169, 225/224, 275/273, 289/288, 325/324, 385/384
| 170/169, 225/224, 275/273, 289/288, 325/324, 385/384
| {{mapping| 94 149 218 264 325 348 384 }}
| {{Mapping| 94 149 218 264 325 348 384 }}
| +0.238
| +0.238
| 0.674
| 0.674
Line 1,010: Line 1,010:
| 2.3.5.7.11.13.17.19
| 2.3.5.7.11.13.17.19
| 170/169, 190/189, 225/224, 275/273, 289/288, 325/324, 385/384
| 170/169, 190/189, 225/224, 275/273, 289/288, 325/324, 385/384
| {{mapping| 94 149 218 264 325 348 384 399 }}
| {{Mapping| 94 149 218 264 325 348 384 399 }}
| +0.323
| +0.323
| 0.669
| 0.669
Line 1,017: Line 1,017:
| 2.3.5.7.11.13.17.19.23
| 2.3.5.7.11.13.17.19.23
| 170/169, 190/189, 209/208, 225/224, 275/273, 289/288, 300/299, 323/322
| 170/169, 190/189, 209/208, 225/224, 275/273, 289/288, 300/299, 323/322
| {{mapping| 94 149 218 264 325 348 384 399 425 }}
| {{Mapping| 94 149 218 264 325 348 384 399 425 }}
| +0.354
| +0.354
| 0.637
| 0.637
Line 1,045: Line 1,045:
| 25/24
| 25/24
| [[Betic]]
| [[Betic]]
|-
| 1
| 7\94
| 89.36
| 21/20
| [[Slithy]]
|-
|-
| 1
| 1
Line 1,050: Line 1,056:
| 140.43
| 140.43
| 13/12
| 13/12
| [[Tsaharuk]] / [[quanic]] / [[glacier]]
| [[Tsaharuk]] / [[quanic]]
|-
|-
| 1
| 1
Line 1,063: Line 1,069:
| 147/128
| 147/128
| [[Septiquarter]]
| [[Septiquarter]]
|-
| 1
| 25\94
| 319.15
| 6/5
| [[Dhaivatic]]
|-
|-
| 1
| 1
Line 1,100: Line 1,112:
| [[Kleischismic]]
| [[Kleischismic]]
|}
|}
<nowiki/>* [[Normal lists|Octave-reduced form]], reduced to the first half-octave, and [[Normal lists|minimal form]] in parentheses if distinct
<nowiki/>* [[Normal forms|Octave-reduced form]], reduced to the first half-octave, and [[normal froms|minimal form]] in parentheses if distinct
 
Below are some 23-limit temperaments supported by 94et. It might be noted that 94, a very good tuning for [[garibaldi temperament]], shows us how to extend it to the 23-limit.
 
* {{nowrap|46 &amp; 94}}
* {{nowrap|68 &amp; 94}}
* {{nowrap|53 &amp; 94}}  (one garibaldi)
* {{nowrap|41 &amp; 94}}  (another garibaldi, only differing in the mappings of 17 and 23)
* {{nowrap|135 &amp; 94}}  (another garibaldi)
* {{nowrap|130 &amp; 94}}  (a pogo extension)
* {{nowrap|58 &amp; 94}}  (a supers extension)
* {{nowrap|50 &amp; 94}}
* {{nowrap|72 &amp; 94}}  (a gizzard extension)
* {{nowrap|80 &amp; 94}}
* 94 solo (a rank one temperament!)


Temperaments to which 94et can be detempered:  
Temperaments to which 94et can be detempered:  
* [[Satin]] ({{nowrap|94 & 217}})  
* [[Satin]] ({{nowrap|94 & 217}})  
* [[Gariwizmic]] (94 & 176)  
* [[Gariwizmic]] (94 & 176)  
Line 1,125: Line 1,122:
94et [[Tempering out|tempers out]] the following [[Comma|commas]] using its patent [[val]], ⟨94 149 218 264 325 348 384 399 425].
94et [[Tempering out|tempers out]] the following [[Comma|commas]] using its patent [[val]], ⟨94 149 218 264 325 348 384 399 425].
{| class="commatable wikitable center-1 center-2 right-3 center-6"
{| class="commatable wikitable center-1 center-2 right-3 center-6"
![[Harmonic limit|Prime]]
! [[Harmonic limit|Prime<br>mit]]
[[Harmonic limit|limit]]
! [[Ratio]]<ref>Ratios with more than 8 digits are presented by placeholders with informative hints</ref>
![[Ratio]]<ref>Ratios with more than 8 digits are presented by placeholders with informative hints</ref>
! [[Cents]]
![[Cents]]
! [[Monzo]]
![[Monzo]]
! colspan="2" | [[Kite's color notation|Color name]]
! colspan="2" |[[Color name]]
! Name(s)
!Name(s)
|-
|-
|3
| 3
|<abbr title="36893488147419103232/36472996377170786403">(90 digits)</abbr>
| <abbr title="36893488147419103232/36472996377170786403">(90 digits)</abbr>
|16.22
| 16.22
|{{monzo|149 -94}}
| {{monzo| 149 -94 }}
|Wa-94
| Wa-94
|94-edo
| 94-edo
|[[94-comma]]
| [[94-comma]]
|-
|-
|5
| 5
|[[32805/32768|(10 digits)]]
| [[32805/32768|(10 digits)]]
|1.95
| 1.95
|{{monzo|-15 8 1}}
| {{Monzo| -15 8 1 }}
|Layo
| Layo
|Ly
| Ly
|[[Schisma]]
| [[Schisma]]
|-
|-
|7
| 7
|[[3125/3087]]
| [[3125/3087]]
|21.18
| 21.18
|{{monzo|0 -2 5 -3}}
| {{Monzo| 0 -2 5 -3 }}
|Triru-aquinyo
| Triru-aquinyo
|r<sup>3</sup>y<sup>5</sup>
| r<sup>3</sup>y<sup>5</sup>
|Gariboh comma
| Gariboh comma
|-
|-
|7
| 7
|[[4000/3969]]
| [[4000/3969]]
|13.47
| 13.47
|{{monzo|5 -4 3 -2}}
| {{Monzo| 5 -4 3 -2 }}
|Rurutriyo
| Rurutriyo
|rry<sup>3</sup>
| rry<sup>3</sup>
|Octagar comma
| Octagar comma
|-
|-
|7
| 7
|[[225/224]]
| [[225/224]]
|7.71
| 7.71
|{{monzo|-5 2 2 -1}}
| {{monzo| -5 2 2 -1 }}
|Ruyoyo
| Ruyoyo
|ryy
| ryy
|Marvel comma
| Marvel comma
|-
|-
|7
| 7
|<abbr title="36893488147419103232/36472996377170786403">(12 digits)</abbr>
| <abbr title="36893488147419103232/36472996377170786403">(12 digits)</abbr>
|6.59
| 6.59
|[1 10 0 -6⟩
| {{monzo| 1 10 0 -6 }}
|Latribiru
| Latribiru
|L6r
| L6r
|Stearnsma
| Stearnsma
|-
|-
|7
| 7
|[[5120/5103]]
| [[5120/5103]]
|5.76
| 5.76
|{{monzo|10 -6 1 -1}}
| {{monzo| 10 -6 1 -1 }}
|Saruyo
| Saruyo
|sry
| sry
|Hemifamity comma
| Hemifamity comma
|-
|-
|7
| 7
|[[33554432/33480783|(16 digits)]]
| [[33554432/33480783|(16 digits)]]
|3.80
| 3.80
|{{monzo|25 -14 0 -1}}
| {{Monzo| 25 -14 0 -1 }}
|Sasaru
| Sasaru
|ssr
| ssr
|[[Garischisma]]
| [[Garischisma]]
|-
|-
|11
| 11
|[[385/384]]
| [[385/384]]
|4.50
| 4.50
|{{monzo|-7 -1 1 1 1}}
| {{Monzo| -7 -1 1 1 1 }}
|Lozoyo
| Lozoyo
|1ozg
| 1ozg
|Keenanisma
| Keenanisma
|-
|-
|11
| 11
|[[540/539]]
| [[540/539]]
|3.21
| 3.21
|{{monzo|2 3 1 -2 -1}}
| {{Monzo| 2 3 1 -2 -1 }}
|Lururuyo
| Lururuyo
|1urry
| 1urry
|Swetisma
| Swetisma
|-
|-
|11
| 11
|[[4225/4224]]
| [[4225/4224]]
|0.41
| 0.41
|[-7 -1 2 0 -1 2⟩
| {{Monzo| -7 -1 2 0 -1 2 }}
|Thotholuyoyo
| Thotholuyoyo
|3oo1uyy
| 3oo1uyy
|Leprechaun comma
| Leprechaun comma
|-
|-
|11
| 11
|[[9801/9800]]
| [[9801/9800]]
|0.17
| 0.17
|[-3 4 -2 -2 2⟩
| {{Monzo| -3 4 -2 -2 2 }}
|Bilorugu
| Bilorugu
|1oorrgg-2
| 1oorrgg-2
|Kalisma
| Kalisma
|-
|-
|13
| 13
|[[275/273]]
| [[275/273]]
|12.64
| 12.64
|{{monzo|0 -1 2 -1 1 -1}}
| {{Monzo| 0 -1 2 -1 1 -1 }}
|Thuloruyoyo
| Thuloruyoyo
|3u1oryy
| 3u1oryy
|Gassorma
| Gassorma
|-
|-
|13
| 13
|[[640/637]]
| [[640/637]]
|8.13
| 8.13
|{{monzo|7 0 1 -2 0 -1}}
| {{Monzo| 7 0 1 -2 0 -1 }}
|Thururuyo
| Thururuyo
|3urry
| 3urry
|Huntma
| Huntma
|-
|-
|13
| 13
|[[1188/1183]]
| [[1188/1183]]
|7.30
| 7.30
|{{monzo|2 3 0 -1 1 -2}}
| {{Monzo| 2 3 0 -1 1 -2 }}
|Thuthuloru
| Thuthuloru
|3uu1or
| 3uu1or
|Kestrel comma
| Kestrel comma
|-
|-
|13
| 13
|[[325/324]]
| [[325/324]]
|5.34
| 5.34
|{{monzo|-2 -4 2 0 0 1}}
| {{Monzo| -2 -4 2 0 0 1 }}
|Thoyoyo
| Thoyoyo
|3oyy
| 3oyy
|Marveltwin comma
| Marveltwin comma
|-
|-
|13
| 13
|[[352/351]]
| [[352/351]]
|4.93
| 4.93
|{{monzo|5 -3 0 0 1 -1}}
| {{Monzo| 5 -3 0 0 1 -1 }}
|Thulo
| Thulo
|3u1o
| 3u1o
|Major minthma
| Major minthma
|-
|-
|13
| 13
|[[847/845]]
| [[847/845]]
|4.09
| 4.09
|{{monzo|0 0 -1 1 2 -2}}
| {{Monzo| 0 0 -1 1 2 -2 }}
|Thuthulolozogu
| Thuthulolozogu
|3uu1oozg
| 3uu1oozg
|Cuthbert comma
| Cuthbert comma
|-
|-
|13
| 13
|[[729/728]]
| [[729/728]]
|2.38
| 2.38
|{{monzo|-3 6 0 -1 0 -1}}
| {{Monzo| -3 6 0 -1 0 -1 }}
|Lathuru
| Lathuru
|L3ur
| L3ur
|Squbema
| Squbema
|-
|-
|13
| 13
|[[2080/2079]]
| [[2080/2079]]
|0.83
| 0.83
|{{monzo|5 -3 1 -1 -1 1}}
| {{Monzo| 5 -3 1 -1 -1 1 }}
|Tholuruyo
| Tholuruyo
|3o1ury
| 3o1ury
|Ibnsinma, sinaisma
| Ibnsinma, sinaisma
|-
|-
|13
| 13
|[[4096/4095]]
| [[4096/4095]]
|0.42
| 0.42
|{{monzo|12 -2 -1 -1 0 -1}}
| {{Monzo| 12 -2 -1 -1 0 -1 }}
|Sathurugu
| Sathurugu
|s3urg
| s3urg
|Minisma
| Minisma
|-
|-
|17
| 17
|[[289/288]]
| [[289/288]]
|6.00
| 6.00
|[5 -2 0 0 0 0 2&#x27E9;
| {{Monzo| 5 -2 0 0 0 0 2 }}
|Soso
| Soso
|17oo
| 17oo
|Semitonisma
| Semitonisma
|-
|-
|17
| 17
|[[715/714]]
| [[715/714]]
|2.42
| 2.42
|{{monzo|-1 -1 1 -1 1 1 -1}}
| {{Monzo| -1 -1 1 -1 1 1 -1 }}
|Sutholoruyo
| Sutholoruyo
|17u3o1ory
| 17u3o1ory
|Septendecimal bridge comma
| Septendecimal bridge comma
|-
|-
|19
| 19
|[[361/360]]
| [[361/360]]
|4.80
| 4.80
|{{monzo|-3 -2 -1 0 0 0 0 2}}
| {{Monzo| -3 -2 -1 0 0 0 0 2 }}
|Nonogu
| Nonogu
|19oog2
| 19oog2
|Go comma
| Go comma
|-
|-
|19
| 19
|[[513/512]]
| [[513/512]]
|3.38
| 3.38
|{{monzo|-9 3 0 0 0 0 0 1}}
| {{Monzo| -9 3 0 0 0 0 0 1 }}
|Lano
| Lano
|L19o
| L19o
|Boethius' comma
| Boethius' comma
|-
|-
|19
| 19
|[[1216/1215]]
| [[1216/1215]]
|1.42
| 1.42
|{{monzo|6 -5 -1 0 0 0 0 1}}
| {{Monzo| 6 -5 -1 0 0 0 0 1 }}
|Sanogu
| Sanogu
|s19og
| s19og
|Eratosthenes' comma
| Eratosthenes' comma
|}
|}


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