User:R-4981/Redbull: Difference between revisions

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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.]]

[[File:Redbull Scale's Theory.png|thumb|An illustration of the structure of the Redbull scale.]]

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.

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.

== 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 C7. Applying this property, the scale that is created as a result of recursively dividing those intervals furthermore twice is ~~redbull~~.

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 C7. Applying this property, the scale that is created as a result of recursively dividing those intervals furthermore 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, 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.

== Intervals ==

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== Properties and trivia ==

[[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 [[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.

* The [[pentad]] obtained by stacking 3-steps from the tonic approximates 5:6:7:8:9.

* 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.

* 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"~~, proposed by [[User:R-4981|R-4981]], comes from the {{w|Red Bull|energy drink brand from Austria}}.

* The name ''Redbull'', proposed by [[User:R-4981|R-4981]], comes from the {{w|Red Bull|energy drink brand from Austria}}.

== Scala file ==

@@ Line 1: / Line 1: @@
-[[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.]]
+[[File:Redbull Scale's Theory.png|thumb|An illustration of the structure of the Redbull scale.]]
-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.
+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.
 == Theory ==
-{{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 C7. Applying this property, the scale that is created as a result of recursively dividing those intervals furthermore twice is redbull.
+{{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 C7. Applying this property, the scale that is created as a result of recursively dividing those intervals furthermore 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, 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.
 == Intervals ==
@@ Line 88: / Line 88: @@
 == Properties and trivia ==
-[[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 [[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.
 * The [[pentad]] obtained by stacking 3-steps from the tonic approximates 5:6:7:8:9.
-* 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.
+* 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", proposed by [[User:R-4981|R-4981]], comes from the {{w|Red Bull|energy drink brand from Austria}}.
+* The name ''Redbull'', proposed by [[User:R-4981|R-4981]], comes from the {{w|Red Bull|energy drink brand from Austria}}.
 == Scala file ==