· Prime Limit
· Octave RepeatingThis is effectively the same as its otonal counterpart. It simply covers a different box on the harmonic matrix.
| Scale Degree | Num | : | Den | Quotient | Cents | Tuning Table | Rounded Tuning Table | Note Name |
|---|---|---|---|---|---|---|---|---|
| 1 | 1 | : | 1 | 1 | 0.00 | -10.75 | -11 | C |
| 2 | 16 | : | 15 | 1.066666667 | 111.73 | 0.98 | 1 | C# |
| 3 | 256 | : | 225 | 1.137777778 | 223.46 | 12.71 | 13 | D |
| 4 | 32 | : | 27 | 1.185185185 | 294.13 | -16.62 | -17 | D# |
| 5 | 32 | : | 25 | 1.28 | 427.37 | 16.62 | 17 | E |
| 6 | 4 | : | 3 | 1.333333333 | 498.04 | -12.71 | -13 | F |
| 7 | 64 | : | 45 | 1.422222222 | 609.78 | -0.98 | -1 | F# |
| 8 | 1024 | : | 675 | 1.517037037 | 721.51 | 10.75 | 11 | G |
| 9 | 8 | : | 5 | 1.6 | 813.69 | 2.93 | 3 | G# |
| 10 | 128 | : | 75 | 1.706666667 | 925.42 | 14.66 | 15 | A |
| 11 | 16 | : | 9 | 1.777777778 | 996.09 | -14.66 | -15 | A# |
| 12 | 256 | : | 135 | 1.896296296 | 1107.82 | -2.93 | -3 | B |
Play Tuning
| Largest step size: | 133.24 c | (27:25) |
| Smallest step size: | 70.67 c | (25:24) |
| Number of step sizes: | 4 |
Odd limit 675
HC = 6.5
This tuning makes a nice little 2-D periodicity block:
| 1 | -- | 3 | -- | 9 | -- | 27 |
| | | | | | | | | |||
| 5 | -- | 15 | -- | 45 | -- | 135 |
| | | | | | | | | |||
| 25 | -- | 75 | -- | 225 | -- | 675 |
2004 by David J. Finnamore
tuning@elvenminstrel.com