· Prime Limit
· Octave RepeatingThis is the lowest-limit PLOT to offer a complete harmonic fragment as an octave-equivalent pentatonic scale: 5-9.
| Scale Degree | Num | : | Den | Quotient | Cents | Tuning Table | Rounded Tuning Table | Note Name |
|---|---|---|---|---|---|---|---|---|
| 1 | 1 | : | 1 | 1 | 0.00 | 12.04 | 12 | C |
| 2 | 135 | : | 128 | 1.0546875 | 92.18 | 4.22 | 4 | C# |
| 3 | 9 | : | 8 | 1.125 | 203.91 | 15.95 | 16 | D |
| 4 | 75 | : | 64 | 1.171875 | 274.58 | -13.38 | -13 | D# |
| 5 | 5 | : | 4 | 1.25 | 386.31 | -1.65 | -2 | E |
| 6 | 21 | : | 16 | 1.3125 | 470.78 | -17.18 | -17 | F |
| 7 | 45 | : | 32 | 1.40625 | 590.22 | 2.26 | 2 | F# |
| 8 | 3 | : | 2 | 1.5 | 701.96 | 13.99 | 14 | G |
| 9 | 25 | : | 16 | 1.5625 | 772.63 | -15.33 | -15 | G# |
| 10 | 27 | : | 16 | 1.6875 | 905.87 | 17.90 | 18 | A |
| 11 | 7 | : | 4 | 1.75 | 968.83 | -19.14 | -19 | A# |
| 12 | 15 | : | 8 | 1.875 | 1088.27 | 0.31 | 0 | B |
Play pentatonic scale comprising complete harmonic fragment 5-9
| Largest step size: | 133.24 c | (27:25) |
| Smallest step size: | 62.96 c | (28:27) |
| Number of step sizes: | 7 |
Odd limit 135
HC = 8.5
This tuning makes a slightly asymmetrical 3-D lattice, like a T that
fell over and broke its right arm:
| 25 | -- | 75 | |||||
| | | | | ||||||
| 5 | -- | 15 | -- | 45 | -- | 135 | |
| | | | | | | | | ||||
| 1 | -- | 3 | -- | 9 | -- | 27 | |
| / | / | ||||||
| 7 | -- | 21 |
2004 by David J. Finnamore
tuning@elvenminstrel.com