· 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 | 7.21 | 7 | C |
| 2 | 33 | : | 32 | 1.03125 | 53.27 | -39.52 | -40 | C# |
| 3 | 9 | : | 8 | 1.125 | 203.91 | 11.12 | 11 | D |
| 4 | 39 | : | 32 | 1.21875 | 342.48 | 49.69 | 50 | D# |
| 5 | 5 | : | 4 | 1.25 | 386.31 | -6.48 | -6 | E |
| 6 | 21 | : | 16 | 1.3125 | 470.78 | -22.01 | -22 | F |
| 7 | 11 | : | 8 | 1.375 | 551.32 | -41.48 | -41 | F# |
| 8 | 3 | : | 2 | 1.5 | 701.96 | 9.16 | 9 | G |
| 9 | 13 | : | 8 | 1.625 | 840.53 | 47.73 | 48 | G# |
| 10 | 27 | : | 16 | 1.6875 | 905.87 | 13.07 | 13 | A |
| 11 | 7 | : | 4 | 1.75 | 968.83 | -23.97 | -24 | A# |
| 12 | 15 | : | 8 | 1.875 | 1088.27 | -4.52 | -5 | B |
Play heptatonic scale equivalent to harmonics 7-13
Play octatonic scale equivalent to harmonics 8-15
| Largest step size: | 150.64 c | (12:11) |
| Smallest step size: | 43.83 c | (40:39) |
| Number of step sizes: | 10 |
Odd limit 33
HC = 11.8
| Consists of: | |||||
|---|---|---|---|---|---|
| 3 (5) | 5 (2) | 7 (2) | 11 (2) | 13 (2) | |
| Squares | 32 | ||||
| Cubes | 33 | ||||
 | |||||
| Totals | 10 | 2 | 2 | 2 | 2 |
2004 by David J. Finnamore
tuning@elvenminstrel.com