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[[File:Redbull Cromatic Scale.mp3|thumb|A chromatic redbull scale on C.]]
[[File:Redbull Cromatic Scale.mp3|thumb|A chromatic redbull scale on C.]]
[[File:Redbull Scale's Theory.png|thumb|An illustration of the structure of the redbull scale.]]


'''Redbull''' is an "irregularly" tempered [[scale]] obtained by recursively dividing one [[octave]] on the logarithmic scale (1200 [[cent|¢]]) by 1:√3 into 16 tones. This is not a [[regular temperament]], and it is impossible to approximate it with them, but on the other hand it has very systematic and unique properties that are completely different from them.
The '''redbull scale'''{{idiosyncratic}} is a 16-tone [[fractal scale]] obtained by recursively dividing one [[octave]] on the logarithmic scale (1200{{cent}}) with a 1:√3 ratio.


[[File:Redbull Scale's Theory.png|thumb|An easy-to-understand (not accurate) illustration of the theory of the Redbull Scale.]]
== Theory ==
400{{cent}} is the most commonly used approximation to [[5/4]], mainly due to its use in [[12edo]]. This interval is also expressed as [[3edo|1\3]], and its square root on the logarithmic scale, ≈692.82{{cent}} (hereinafter expressed as 1\√3 for convenience), functions as an approximation of [[3/2]]. Furthermore, the interval divided into √3 equal parts with 1\√3 as the center{{clarify}} is ≈985.641¢, which works as an approximation of [[7/4]] or [[9/5]], and the [[tetrad]] that combines these is 4:5:6:7, the so-called It will be the minor 7th{{clarify}}. Applying this property, the scale that is created as a result of recursively dividing those intervals furthermore twice is redbull.


As we all know, 400¢ is the most commonly used approximation to [[5/4]]. This interval is also expressed as [[3edo|1\3]], but its square root on the logarithmic axis, 692.82¢ (hereinafter expressed as 1\√3 for convenience), functions as an approximation of [[3/2]]. Furthermore, the interval divided into √3 equal parts with 1\√3 as the center is 985.64¢, which works as an approximation of [[7/4]] or [[9/5]], and the tetrachord that combines these is 4:5:6:7, the so-called It will be the minor 7th. Applying this property, the scale that is created as a result of recursively dividing those intervals futhermore twice is Redbull.
Most of the notes on this scale are irrational numbers in both cent and frequency units, so redbull cannot be reproduced with an [[edo]]. Also, since there is no interval that can be called a generator, it is also impossible to approximate redbull with a [[mos scale]]. Also, since there is no interval that can be called a generator, and it varies even by one step­{{clarify}}, there are many intervals within redbull that approximate [[just intonation]], just like [[afdo]]s.
 
Most of the notes on this scale are irrational numbers in both cent and frequency units, so redbull cannot be reproduced with an [[edo]]. Also, since there is no interval that can be called a generator, so it is also impossible to approximate redbull with a [[mos scale]]. Therefore, as mentioned at the beginning, redbull is very special and irregularly tempered scale. Also, since there is no interval that can be called a generator, and it varies even by one step, there are many intervals within Redbull that approximate [[just intonation]], just like [[afdo]]s.


== Intervals ==
== Intervals ==
If you need exact cent values, please refer to the Scala file below.
For more precise cent values, refer to the [[#Scala file|Scala file]] below.


{| class="wikitable center-all"
{| class="wikitable center-all"
Line 16: Line 16:
! Degree
! Degree
! Cents
! Cents
! Approximate Ratios
! Approximate ratios
|-
|-
| 0
| 0
Line 23: Line 23:
|-
|-
| 1
| 1
| 133.33
| 133.333
| 14/13, 13/12, 12/11
| 14/13, 13/12, 12/11
|-
|-
| 2
| 2
| 230.94
| 230.940
| 8/7
| 8/7
|-
|-
| 3
| 3
| 328.55
| 328.547
| 6/5
| 6/5
|-
|-
Line 39: Line 39:
|-
|-
| 5
| 5
| 497.6
| 497.607
| 4/3
| 4/3
|-
|-
| 6
| 6
| 569.06
| 569.060
| 25/18, 7/5
| 25/18, 7/5
|-
|-
| 7
| 7
| 640.51
| 640.513
| 10/7, 13/9, 16/11
| 10/7, 13/9, 16/11
|-
|-
| 8
| 8
| 692.82
| 692.820
| 3/2
| 3/2
|-
|-
| 9
| 9
| 790.43
| 790.427
| 11/7
| 11/7
|-
|-
| 10
| 10
| 861.88
| 861.880
| 13/8, 18/11, 5/3
| 13/8, 18/11, 5/3
|-
|-
| 11
| 11
| 933.33
| 933.333
| 12/7
| 12/7
|-
|-
| 12
| 12
| 985.64
| 985.641
| 7/4, 9/5
| 7/4, 9/5
|-
|-
| 13
| 13
| 1057.09
| 1057.094
| 11/6, 24/13, 13/7
| 11/6, 24/13, 13/7
|-
|-
| 14
| 14
| 1109.40
| 1109.401
| 15/8, 17/9, 28/15
| 15/8, 17/9, 28/15
|-
|-
| 15
| 15
| 1161.71
| 1161.708
| 33/17, 64/33
| 33/17, 64/33
|-
|-
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[[File:Redbull Pentic.mp3|thumb|A pentatonic redbull scale on C.]]
[[File:Redbull Pentic.mp3|thumb|A pentatonic redbull scale on C.]]


* As mentioned above, the 4-step chord in Redbull is similar to the seventh in [[12edo]], but since 4 is a divisor of 16, there are only 4 types of these chords, and the others are only inversions.
* As mentioned above, the [[tetrad]] obtained by stacking 4-steps from the tonic (i.e. starting on degree 0) is similar to the seventh tetrad in [[12edo]], approximating 4:5:6:7. Since 4 is a divisor of 16, there are only 4 types of 4-step tetrads, the others being only inversions, and the other types of 4-step tetrads do not approximate 4:5:6:7.
* in Redbull, a chord obtained by estimating three steps can be approximated in only one way by just intonation: 5:6:7:8:9.{{clarify}}
* The [[pentad]] obtained by stacking 3-steps from the tonic approximates 5:6:7:8:9.
* Furthermore, Redbull has a pentatonic, which is similar to [[2L 3s]], and the constituent notes of that scale can be approximated as 9:12:13:16:17 in just intonation.
* Furthermore, redbull has a pentatonic subset which is similar to [[2L 3s]]{{clarify}}, and the constituent notes of that scale can be approximated as 9:12:13:16:17 in just intonation.
* The name "Redbull" comes from a {{w|Red Bull|famous energy drink from Austria}}. This drink is popular all over the world due to its fruity taste and reasonable price.
* The name "redbull", proposed by [[User:R-4981|R-4981]], comes from the {{w|Red Bull|famous energy drink from Austria}}.


== Scala file ==
== Scala file ==
<pre>
<pre>
! redbull.scl
! redbull.scl
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230.94010768
230.94010768
328.54688202
328.54688202
400
400.
497.60677434
497.60677434
569.05989232
569.05989232
Line 118: Line 117:
1109.40107676
1109.40107676
1161.70838948
1161.70838948
1200
1200.
</pre>
</pre>


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