· Prime Limit
· Octave RepeatingThis is the lowest-limit PLOT to offer a heptatonic octave-equivalent scale comprising a complete harmonic fragment: 7-13. It also yields the octatonic fragment 8-15.
| Scale Degree | Num | : | Den | Quotient | Cents | Tuning Table | Rounded Tuning Table | Note Name |
|---|---|---|---|---|---|---|---|---|
| 1 | 1 | : | 1 | 1 | 0.00 | -28.64 | -29 | C |
| 2 | 33 | : | 32 | 1.03125 | 53.27 | -75.37 | -75 | C# |
| 3 | 9 | : | 8 | 1.125 | 203.91 | -24.73 | -25 | D |
| 4 | 5 | : | 4 | 1.25 | 386.31 | 57.67 | 58 | D# |
| 5 | 21 | : | 16 | 1.3125 | 470.78 | 42.14 | 42 | E |
| 6 | 11 | : | 8 | 1.375 | 551.32 | 22.68 | 23 | F |
| 7 | 3 | : | 2 | 1.5 | 701.96 | 73.32 | 73 | F# |
| 8 | 25 | : | 16 | 1.5625 | 772.63 | 43.99 | 44 | G |
| 9 | 13 | : | 8 | 1.625 | 840.53 | 11.89 | 12 | G# |
| 10 | 27 | : | 16 | 1.6875 | 905.87 | -22.77 | -23 | A |
| 11 | 7 | : | 4 | 1.75 | 968.83 | -59.81 | -60 | A# |
| 12 | 15 | : | 8 | 1.875 | 1088.27 | -40.37 | -40 | B |
Play heptatonic scale equivalent to harmonics 7-13
Play octatonic scale equivalent to harmonics 8-15
| Largest step size: | 182.40 c | (10:9) |
| Smallest step size: | 53.27 c | (33:32) |
| Number of step sizes: | 11 |
Odd limit 39
HC = 13.4
| Consists of: | |||||
|---|---|---|---|---|---|
| 3 (4) | 5 (2) | 7 (2) | 11 (2) | 13 | |
| Squares | 32 | 52 | |||
| Cubes | 33 | ||||
 | |||||
| Totals | 9 | 4 | 2 | 2 | 1 |
2004 by David J. Finnamore
tuning@elvenminstrel.com