27ed4
Lua error: Internal error: The interpreter has terminated with signal "24". 27ed4 is an equal tuning that divides the 4/1 ratio (double-octave, tetratave, fifteenth) into steps of 888/9 cents.
It serves as a good first approximation to nelindic temperament, and is in many respects a "3n+1 cousin" of 5-limit 12et (even though it takes every other step of the dissimilar 27et), with relatively high error but low complexity, similar step size, and even sharing a common comma (128/125). Note the latter means that 27ed4 divides 4/1 into three approximate 8/5's, just as 12ed2 divides 2/1 into three 5/4's, and thus it has a 5/2 equally sharp of rational as the 5/4 in 12ed2. Its 7 and 13 approximations are a bit sharp themselves, and overall it lends itself well to IoE compression: the TE tuning gives one of 2395.819236 cents.
Intervals
The following table of intervals uses the 7-note (6L 1s) MOS scale of nelindic for the naturals, using a simple A-G notation and standard sharps/flats for the chroma. Extended to the 13-note (7L 6s) scale, these would include all of the sharps except for F#. Due to the L/s ratio of 3:1, in the 13-note case, most former diminished intervals become minor, most former minor intervals become augmented, and most former augmented intervals become major.
| Steps | Note | Interval name | Cents | ~ Ratios |
|---|---|---|---|---|
| 0 | A | unison | 0.00 | 1/1 |
| 1 | A# | aug unison | 88.89 | 21/20 |
| 2 | Bbb | ddim mos2nd | 177.78 | 10/9 |
| 3 | Bb | dim mos2nd | 266.67 | 7/6 |
| 4 | B | perf mos2nd | 355.56 | 16/13 |
| 5 | B# | aug mos2nd | 444.44 | 13/10, 9/7 |
| 6 | Cbb | dim mos3rd | 533.33 | 27/20, 19/14 |
| 7 | Cb | min mos3rd | 622.22 | 10/7, 13/9 |
| 8 | C | maj mos3rd | 711.11 | 3/2 |
| 9 | C# | aug mos3rd | 800.00 | 8/5 |
| 10 | Dbb | dim mos4th | 888.89 | 5/3 |
| 11 | Db | min mos4th | 977.78 | 7/4 |
| 12 | D | maj mos4th | 1066.67 | 13/7 |
| 13 | D# | aug mos4th | 1155.56 | 39/20, 35/18 |
| 14 | Ebb | dim mos5th | 1244.44 | 80/39, 72/35 |
| 15 | Eb | min mos5th | 1333.33 | 28/13 |
| 16 | E | maj mos5th | 1422.22 | 16/7 |
| 17 | E# | aug mos5th | 1511.11 | 12/5 |
| 18 | Fbb | dim mos6th | 1600.00 | 5/2 |
| 19 | Fb | min mos6th | 1688.89 | 8/3 |
| 20 | F | maj mos6th | 1777.78 | 14/5, 36/13 |
| 21 | F# | aug mos6th | 1866.67 | 80/27, 38/13 |
| 22 | Gb | dim mos7th | 1955.56 | 40/13, 28/9 |
| 23 | G | perf mos7th | 2044.44 | 13/4 |
| 24 | G# | aug mos7th | 2133.33 | 24/7 |
| 25 | Abb | ddim tetratave | 2222.22 | 18/5 |
| 26 | Ab | dim tetratave | 2311.11 | 80/21 |
| 27 | A | tetratave | 2400.00 | 4/1 |
The genchain for the nelindic scale is as follows:
| Abb | Bbb | Cbb | Dbb | Ebb | Fbb | Gb | Ab | Bb | Cb | Db | Eb | Fb | G | A | B | C | D | E | F | G# | A# | B# | C# | D# | E# | F# |
| dd1 | dd2 | d3 | d4 | d5 | d6 | d7 | d1 | d2 | m3 | m4 | m5 | m6 | P7 | P1 | P2 | M3 | M4 | M5 | M6 | A7 | A1 | A2 | A3 | A4 | A5 | A6 |