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The 94 equal temperament, often abbreviated 94-tET, 94-[[EDO|EDO]], or 94-ET, is the scale derived by dividing the [[Octave|octave]] into 94 equally-sized steps, where each step represents a frequency ratio of 12.766 [[cent|cent]]s. It is a remarkable all-around utility temperament, good from low prime limit to very high prime limit situations. It is the first equal temperament to be[[consistent| consistent]] though the [[23-limit|23-limit]], and no other equal temperament is so consistent until 282 and 311 make their appearance.
The '''94 equal temperament''', often abbreviated '''94-tET''', '''94-[[EDO]]''', or '''94-ET''', is the scale derived by dividing the [[octave]] into 94 equally-sized steps, where each step represents a frequency ratio of 12.766 [[cent]]s. It is a remarkable all-around utility temperament, good from low prime limit to very high prime limit situations. It is the first equal temperament to be [[consistent]] though the [[23-limit]], and no other equal temperament is so consistent until 282 and 311 make their appearance.


The list of 23-limit commas it tempers out is huge, but it's worth noting that it tempers out 32805/32768 and is thus a schismatic system, that it tempers out 225/224 and 385/384 and so is a marvel system, and that it also tempers out 3125/3087, 4000/3969, 5120/5103 and 540/539. It provides the optimal patent val for the rank five temperament tempering out 275/273, and for a number of other temperaments, such as [[Marvel_family#Isis|isis]].
The list of 23-limit commas it tempers out is huge, but it's worth noting that it tempers out 32805/32768 and is thus a schismatic system, that it tempers out 225/224 and 385/384 and so is a marvel system, and that it also tempers out 3125/3087, 4000/3969, 5120/5103 and 540/539. It provides the optimal patent val for the rank five temperament tempering out 275/273, and for a number of other temperaments, such as [[isis]].


Also, see the [[Table of 94edo intervals]].
Also, see the [[Table of 94edo intervals]].




{| class="wikitable" style="text-align:center;"
{| class="wikitable center-all"
!
!
!prime 2
! prime 2
!prime 3
! prime 3
!prime 5
! prime 5
!prime 7
! prime 7
!prime 11
! prime 11
!prime 13
! prime 13
!prime 17
! prime 17
!prime 19
! prime 19
!prime 23
! prime 23
!prime 29
! prime 29
!prime 31
! prime 31
|-
|-
!error
! error
|0.0¢
| 0.0¢
| +0.17¢
| +0.17¢
| -3.33¢
| -3.33¢
Line 35: Line 35:




=Rank two temperaments=
== Rank two temperaments ==


{| class="wikitable"
{| class="wikitable right-all center-4 left-5"
! Periods <br> per <br> octave
! Generator
! Cents
! Associated <br> ratio
! Temperament
|-
|-
! | Periods
| 1
 
| 3\94
per
| 38.298
 
| 49/48
octave
| [[Slender]]
! | Generator
! | Cents
! | Associated
 
ratio
! | Temperament
|-
|-
| style="text-align:right;" | 1
| 1
| style="text-align:right;" | 3\94
| 5\94
| style="text-align:right;" | 38.298
| 63.830
| style="text-align:center;" | 49/48
| 25/24
| | [[Slender|Slender]]
| [[Sycamore]] / [[betic]]
|-
|-
| style="text-align:right;" | 1
| 1
| style="text-align:right;" | 5\94
| 11\94
| style="text-align:right;" | 63.830
| 140.426
| style="text-align:center;" | 25/24
| 243/224 <br> 13/12
| | [[Sycamore|Sycamore]]/[[betic|betic]]
| [[Tsaharuk]] <br> [[Quanic]]
|-
|-
| style="text-align:right;" | 1
| 1
| style="text-align:right;" | 11\94
| 19\94
| style="text-align:right;" | 140.426
| 242.553
| style="text-align:center;" | 243/224
| 147/128
 
| [[Septiquarter]]
13/12
| | [[Tsaharuk|Tsaharuk]]
 
[[Quanic|Quanic]]
|-
|-
| style="text-align:right;" | 1
| 1
| style="text-align:right;" | 19\94
| 39\94
| style="text-align:right;" | 242.553
| 497.872
| style="text-align:center;" | 147/128
| 4/3
| | [[Septiquarter|Septiquarter]]
| [[Schismatic]] / [[Garibaldi]]
|-
|-
| style="text-align:right;" | 1
| 2
| style="text-align:right;" | 39\94
| 2\94
| style="text-align:right;" | 497.872
| 25.532
| style="text-align:center;" | 4/3
| 64/63
| | [[Schismatic|Schismatic]]/[[Garibaldi|garibaldi]]
| [[Ketchup]]
|-
|-
| style="text-align:right;" | 2
| 2
| style="text-align:right;" | 2\94
| 43\94
| style="text-align:right;" | 25.532
| 548.936
| style="text-align:center;" | 64/63
| 11/8
| | [[Ketchup|Ketchup]]
| [[Kleischismic]]
|-
|-
| style="text-align:right;" | 2
| 2
| style="text-align:right;" | 43\94
| 11\94
| style="text-align:right;" | 548.936
| 140.426
| style="text-align:center;" | 11/8
| 27/25
| | [[Kleischismic|Kleischismic]]
| [[Fifive]]
|-
|-
| style="text-align:right;" | 2
| 2
| style="text-align:right;" | 11\94
| 34\94
| style="text-align:right;" | 140.426
| 434.043
| style="text-align:center;" | 27/25
| 9/7
| | [[Fifive|Fifive]]
| [[Pogo]] / [[supers]]
|-
|-
| style="text-align:right;" | 2
| 2
| style="text-align:right;" | 34\94
| 30\94
| style="text-align:right;" | 434.043
| 382.979
| style="text-align:center;" | 9/7
| 5/4
| | [[Pogo|Pogo]], [[supers|supers]]
| [[Wizard]] / [[gizzard]]
|-
| style="text-align:right;" | 2
| style="text-align:right;" | 30\94
| style="text-align:right;" | 382.979
| style="text-align:center;" | 5/4
| | [[wizard|Wizard]]/[[gizzard|gizzard]]
|}
|}


Below are some 23-limit temperaments supported by 94et. It might be noted that 94, a very good tuning for [[Garibaldi_temperament|garibaldi temperament]], shows us how to extend it to the 23-limit.
Below are some 23-limit temperaments supported by 94et. It might be noted that 94, a very good tuning for [[Garibaldi_temperament|garibaldi temperament]], shows us how to extend it to the 23-limit.


46&amp;94 &lt;&lt;8 30 -18 -4 -28 8 -24 2 ... ||
* 46&amp;94 &lt;&lt;8 30 -18 -4 -28 8 -24 2 ... ||
 
* 68&amp;94 &lt;&lt;20 28 2 -10 24 20 34 52 ... ||
68&amp;94 &lt;&lt;20 28 2 -10 24 20 34 52 ... ||
* 53&amp;94 &lt;&lt;1 -8 -14 23 20 -46 -3 -35 ... || (one garibaldi)
 
* 41&amp;94 &lt;&lt;1 -8 -14 23 20 48 -3 -35 ... || (another garibaldi, only differing in the mappings of 17 and 23)
53&amp;94 &lt;&lt;1 -8 -14 23 20 -46 -3 -35 ... || (one garibaldi)
* 135&amp;94 &lt;&lt;1 -8 -14 23 20 48 -3 59 ... || (another garibaldi)
 
* 130&amp;94 &lt;&lt;6 -48 10 -50 26 6 -18 -22 ... || (a pogo extension)
41&amp;94 &lt;&lt;1 -8 -14 23 20 48 -3 -35 ... || (another garibaldi, only differing in the mappings of 17 and 23)
* 58&amp;94 &lt;&lt;6 46 10 44 26 6 -18 -22 ... || (a supers extension)
 
* 50&amp;94 &lt;&lt;24 -4 40 -12 10 24 22 6 ... ||
135&amp;94 &lt;&lt;1 -8 -14 23 20 48 -3 59 ... || (another garibaldi)
* 72&amp;94 &lt;&lt;12 -2 20 -6 52 12 -36 -44 ... || (a gizzard extension)
 
* 80&amp;94 &lt;&lt;18 44 30 38 -16 18 40 28 ... ||
130&amp;94 &lt;&lt;6 -48 10 -50 26 6 -18 -22 ... || (a pogo extension)
* 94 solo &lt;&lt;12 -2 20 -6 -42 12 -36 -44 ... || (a rank one temperament!)
 
58&amp;94 &lt;&lt;6 46 10 44 26 6 -18 -22 ... || (a supers extension)
 
50&amp;94 &lt;&lt;24 -4 40 -12 10 24 22 6 ... ||
 
72&amp;94 &lt;&lt;12 -2 20 -6 52 12 -36 -44 ... || (a gizzard extension)
 
80&amp;94 &lt;&lt;18 44 30 38 -16 18 40 28 ... ||
 
94 solo &lt;&lt;12 -2 20 -6 -42 12 -36 -44 ... || (a rank one temperament!)


Temperaments for which 94 is a [[MOS|MOS]]:
Temperaments for which 94 is a [[MOS|MOS]]:


311&amp;94 &lt;&lt;3 70 -42 69 -34 50 85 83...||
* 311&amp;94 &lt;&lt;3 70 -42 69 -34 50 85 83...||
 
* 422&amp;94 &lt;&lt;8 124 -18 90 -28 102 164 96 ... ||
422&amp;94 &lt;&lt;8 124 -18 90 -28 102 164 96 ... ||


=Scales=
== Scales ==


[[garibaldi12|garibaldi12]]
* [[garibaldi12]]
* [[garibaldi17]]


[[garibaldi17|garibaldi17]]      [[Category:94edo]]
[[Category:94edo]]
[[Category:edo]]
[[Category:Edo]]
[[Category:garibaldi]]
[[Category:Garibaldi]]
[[Category:marvel]]
[[Category:Marvel]]
[[Category:theory]]
[[Category:Theory]]
Retrieved from "https://en.xen.wiki/w/94edo"