· Prime Limit
· Octave RepeatingStarting on degree 9, this tuning is the complete harmonic fragment 12 through 23. It makes the full series 1-24 available. From here on up, the odd limit is the same as the prime limit.
| Scale Degree | Num | : | Den | Quotient | Cents | Tuning Table | Rounded Tuning Table | Note Name |
|---|---|---|---|---|---|---|---|---|
| 1 | 1 | : | 1 | 1 | 0.00 | 29.78 | 30 | C |
| 2 | 17 | : | 16 | 1.0625 | 104.96 | 34.74 | 35 | C# |
| 3 | 9 | : | 8 | 1.125 | 203.91 | 33.69 | 34 | D |
| 4 | 19 | : | 16 | 1.1875 | 297.51 | 27.29 | 27 | D# |
| 5 | 5 | : | 4 | 1.25 | 386.31 | 16.09 | 16 | E |
| 6 | 21 | : | 16 | 1.3125 | 470.78 | 0.56 | 1 | F |
| 7 | 11 | : | 8 | 1.375 | 551.32 | -18.90 | -19 | F# |
| 8 | 23 | : | 16 | 1.4375 | 628.27 | -41.95 | -42 | G |
| 9 | 3 | : | 2 | 1.5 | 701.96 | -68.27 | -68 | G# |
| 10 | 13 | : | 8 | 1.625 | 840.53 | -29.69 | -30 | A |
| 11 | 7 | : | 4 | 1.75 | 968.83 | -1.39 | -1 | A# |
| 12 | 15 | : | 8 | 1.875 | 1088.27 | 18.05 | 18 | B |
Play Tuning
| Largest step size: | 138.57 c | (13:12) |
| Smallest step size: | 73.68 c | (24:23} |
| Number of step sizes: | 12 |
HC = 19.6
| Consists of: | ||||||||
|---|---|---|---|---|---|---|---|---|
| 3 (3) | 5 (2) | 7 (2) | 11 | 13 | 17 | 19 | 23 | |
| Squares | 32 | |||||||
 | ||||||||
| Totals | 5 | 2 | 2 | 1 | 1 | 1 | 1 | 1 |
2004 by David J. Finnamore
tuning@elvenminstrel.com