User:R-4981/Pepsi: Difference between revisions

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[[File:Pepsi Plot.png|thumb|A graphical expression of the interval chain of the Pepsi.]]

The '''Pepsi'''{{idiosyncratic}}~~, one of "irregular" temperament,~~ is ~~constructed by~~ the ~~repetition of power of √3 starting from~~ [[3/2]] (701.955¢)~~. It can also be regarded as a~~ [[~~Regular temperament~~]] ~~on the logarithmic axis, i.e., a sequence of intervals with double exponentiational increment (<math>702\cdot3^{n/2}</math>¢)~~.

The '''Pepsi'''{{idiosyncratic}} (name proposed by [[User:R-4981|R-4981]]) [[tuning system]] is the [[geometric pitch sequence]] (GPS) where the initial interval is [[3/2]] (701.955¢) and each subsequent interval has its pitch [[Interval size measure|measure]] multiplied by √3.

~~at first glance this temperament exhibits characteristics similar to [[Redbull]],~~ the ~~direction~~ of ~~its potential use value is fundamentally different because of the different construction methods. Also~~, ~~since the double index is not a tetration~~ (~~obvious~~)~~, this scale cannot be expressed~~ in [[~~EDSO~~]] ~~or [[Super-pitch]]ies.~~

The formula for the ''n''th interval of this tuning, where ''p''(''n'') is pitch in [[cent]]s, is:

~~== Interval chains ==~~

:<math>p(n) \approx 701.955~¢ \cdot 3^{n/2}</math>,

or in its exact form:

:<math>p(n) = \left(1200 \log_2 \left(\frac{3}{2}\right) \right)¢ \cdot 3^{n/2}</math>.

At first glance, this tuning exhibits characteristics similar to [[Redbull]], namely its common use of √3, but the direction of its potential use value is fundamentally different because of the different construction methods. Also, since the double index is not a tetration (obvious), this scale cannot be expressed in [[EDSO]] or [[super-pitch]].

== Interval chain ==

In this table, the intervals are [[octave-reduced]]. Except 3/2 which is just by construction, every ratio given in the second row is approximated by the corresponding pitch of the tuning.

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~~== See also ==~~

[[Category:Tuning]]

* [[Redbull]]

* [[Super-pitch]]

* [[EDSO]]

~~[[Category:Temperaments]]~~

[[Category:~~Pages with Scala files~~]]

~~{{Stub}}~~

@@ Line 1: / Line 1: @@
 [[File:Pepsi Plot.png|thumb|A graphical expression of the interval chain of the Pepsi.]]
-The '''Pepsi'''{{idiosyncratic}}, one of "irregular" temperament, is constructed by the repetition of power of √3 starting from [[3/2]] (701.955¢). It can also be regarded as a [[Regular temperament]] on the logarithmic axis, i.e., a sequence of intervals with double exponentiational increment (<math>702\cdot3^{n/2}</math>¢).
+The '''Pepsi'''{{idiosyncratic}} (name proposed by [[User:R-4981|R-4981]]) [[tuning system]] is the [[geometric pitch sequence]] (GPS) where the initial interval is [[3/2]] (701.955¢) and each subsequent interval has its pitch [[Interval size measure|measure]] multiplied by √3.
-at first glance this temperament exhibits characteristics similar to [[Redbull]], the direction of its potential use value is fundamentally different because of the different construction methods.  Also, since the double index is not a tetration (obvious), this scale cannot be expressed in [[EDSO]] or [[Super-pitch]]ies.
+The formula for the ''n''th interval of this tuning, where ''p''(''n'') is pitch in [[cent]]s, is:
-== Interval chains ==
+:<math>p(n) \approx 701.955~¢ \cdot 3^{n/2}</math>,
+or in its exact form:
+:<math>p(n) = \left(1200 \log_2 \left(\frac{3}{2}\right) \right)¢ \cdot 3^{n/2}</math>.
+At first glance, this tuning exhibits characteristics similar to [[Redbull]], namely its common use of √3, but the direction of its potential use value is fundamentally different because of the different construction methods. Also, since the double index is not a tetration (obvious), this scale cannot be expressed in [[EDSO]] or [[super-pitch]].
+== Interval chain ==
+In this table, the intervals are [[octave-reduced]]. Except 3/2 which is just by construction, every ratio given in the second row is approximated by the corresponding pitch of the tuning.
 {| class="wikitable"
 |-
@@ Line 50: / Line 58: @@
 |}
-== See also ==
+[[Category:Tuning]]
-* [[Redbull]]
-* [[Super-pitch]]
-* [[EDSO]]
-[[Category:Temperaments]]
-[[Category:Pages with Scala files]]
-{{Stub}}