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.
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|
|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|
|13||D#||aug mos4th||1155.56||39/20, 35/18|
|14||Ebb||dim mos5th||1244.44||80/39, 72/35|
|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|
The genchain for the nelindic scale is as follows: