Pepsi
The Pepsi[idiosyncratic term] (name proposed by 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 measure multiplied by √3.
The formula for the nth interval of this tuning, where p(n) is pitch in cents, is:
- [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.
| 701.955 | 15.822 | 905.865 | 47.465 | 317.595 | 142.396 | 952.785 | 427.187 | 458.355 | 81.56 | 175.065 | 244.679 | 525.196 | 734.038 | 375.587 | 1002.115 | 1126.761 | 606.345 | ... |
| 3/2 | 64/63 | 27/16 | 36/35 | 6/5 | 13/12 | 19/11 | 9/7 | 13/10 | 21/20 | 35/32 | 15/13 | 35/26 | 50/33 | 56/45 | 9/5 | 21/11 | 45/32 | ... |