· 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 | -68.05 | -68 | C |
| 2 | 35 | : | 32 | 1.0546875 | 155.14 | -12.91 | -13 | C# |
| 3 | 9 | : | 8 | 1.125 | 203.91 | -64.14 | -64 | D |
| 4 | 5 | : | 4 | 1.25 | 386.31 | 18.26 | 18 | D# |
| 5 | 21 | : | 16 | 1.3125 | 470.78 | 2.73 | 3 | E |
| 6 | 45 | : | 32 | 1.40625 | 590.22 | 22.17 | 22 | F |
| 7 | 3 | : | 2 | 1.5 | 701.96 | 33.90 | 34 | F# |
| 8 | 25 | : | 16 | 1.5625 | 772.63 | 4.57 | 5 | G |
| 9 | 27 | : | 16 | 1.6875 | 905.87 | 37.81 | 38 | G# |
| 10 | 7 | : | 4 | 1.75 | 968.83 | 0.77 | 1 | A |
| 11 | 15 | : | 8 | 1.875 | 1088.27 | 20.21 | 20 | A# |
| 12 | 63 | : | 32 | 1.96875 | 1172.74 | 4.68 | 5 | B |
Play pentatonic scale comprising complete harmonic fragment 5-9
| Largest step size: | 182.40 | (10:9) |
| Smallest step size: | 27.26 | (64:63) |
| Number of step sizes: | 10 |
Odd limit 63. This is the lowest-limit PLOT to have a two-digit odd limit.
HC = 8.5
This tuning makes a 3-D lattice with just a hint of symmetry:
| 25 | |||||||||||
| | | |||||||||||
| 5 | -- | -- | 15 | -- | -- | 45 | |||||
| / | | | | | | | ||||||||
| 35 | 1 | -- | -- | 3 | -- | -- | 9 | -- | -- | 27 | |
| | | / | / | / | ||||||||
| 7 | -- | -- | 21 | -- | -- | 63 |
2004 by David J. Finnamore
tuning@elvenminstrel.com