User:R-4981/Redbull: Difference between revisions

[[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.]]

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.

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.

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.

| 8/7

| 25/18, 7/5

[[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.

* 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|famous energy drink from Austria}}.