MET-24 is a "three-dimensional" or "rank-3" temperament with three generators: the 2/1 octave, a fifth at 703.711 cents (1201 steps of 2048-ed2), and a spacing between chains of fifths at 57.422 cents (98 steps of 2048-ed2).
This post includes two lattice diagrams using a very simple form of mixed sagittal notation equivalent to a kind of keyboard tablature.
In the first lattice, the 1/1 is D on the lower chain of fifths, with notes on the upper chain of fifths shown by a /|\ sign. This sign can stand for 33/32 (e.g. G-G/|\ as 4/3-11/8); 28/27 (e.g. E-E/|\ as 9/8-7/6); and also 91/88 (e.g. F-F/|\ as 13/11-11/9) or 121/117 (e.g. Bb-Bb/|\ as 11/7-13/8).
Since MET-24 tempers out 352/351 (e.g. 32/27 vs. 13/11), 364/363 (e.g. 13/11 vs. 33/28), and also their sum (896/891, e.g. 28/27 vs. 33/32) and minute difference (10648/10647, e.g. 121/117 vs. 91/88), these diverse interpretations of the spacing generator are not so surprising.
Lattice for MET-24, 1/1 = D (on lower 12-note chain of fifths) +0.3 +2.1 -1.1 +0.6 +2.4 -0.6 -3.8 -2.0 -0.3 +1.5 +3.2 +0.1 138.9 842.6 346.3 1050.0 553.7 57.4 761.1 264.8 968.6 472.3 1176.0 679.7 Eb/|\ Bb/|\ F/|\ C/|\ G/|\ D/|\ A/|\ E/|\ B/|\ F#/|\ C#/|\ G#/|\ 13/12--13/8---11/9---11/6---11/8---91/88--14/9---7/6---7/4---21/16--63/32--77/52 / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / 22/21--11/7---13/11--16/9----4/3---1/1---3/2----9/8---22/13--14/11--21/11--63/44 Eb Bb F C G D A E B F# C# G# 81.4 785.2 288.9 992.6 496.3 0 703.7 207.4 911.1 414.8 1118.6 622.3 +0.9 +2.7 -0.3 -3.5 -1.8 +1.8 +3.5 +0.3 -2.7 -0.9 +0.8 Horizontal lines = tempered 3:2 (703.711 cents) Vertical lines = tempered 7:6 (264.844 cents) Quadrangles from lower left = tempered 12:14:18:21 Two adjacent quadrangles = tempered 1-3-7-9 hexany Generators of MET-24 temperament: (2/1, 703.711, 57.422) ! met24c_d.scl ! Canonical version of MET-24 in 2048-ed2, 1/1=D (lower chain) 24 ! 57.42187 81.44531 138.86718 207.42187 264.84375 288.86718 346.28906 414.84375 472.26562 496.28906 553.71093 622.26562 679.68750 703.71093 761.13281 785.15624 842.57812 911.13281 968.55468 992.57812 1050.00000 1118.55468 1175.97656 2/1
In this second lattice, the 1/1 is C on the upper chain of fifths, so that notes on the lower chain are marked with a \|/ sign to show that they are lower by a spacing generator of 57.422 cents. This placement of the 1/1 at C on the upper chain of fifths is one possible choice for an Arab Rast, for example.
Lattice for MET-24, 1/1 = C (on upper 12-note chain of fifths) Eb Bb F C G D A E B F# C# G# +0.9 +2.7 -0.3 -3.5 -1.8 +3.5 -0.3 -2.7 +0.3 +0.8 -2.3 =0.6 288.9 992.6 496.3 0 703.7 207.4 911.1 414.8 1118.6 622.3 126.0 829.7 13/11--16/9--4/3---1/1---3/2----9/8--22/13-14/11--21/11--63/44--14/13--21/13 / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / 8/7--12/7---9/7--176/91-16/11-12/11--18/11--16/13--24/13--18/13--27/26--264/169 Eb\|/ Bb\|/ F\|/ C\|/ G\|/ D\|/ A\|/ E\|/ B\|/ F#\|/ C#\|/ G#\|/ 231.4 935.2 438.9 1142.6 646.3 150.0 853.7 357.4 1061.1 564.8 68.6 772.3 +0.3 +2.0 +3.8 +0.6 -2.4 -0.6 +1.1 -2.1 -0.3 +1.5 +3.2 +0.05 ! met24c_cup.scl ! MET-24 (2048-ed2), (2/1, 703.711, 57.422), 1/1=C on upper chain 24 ! 68.55468 125.97656 150.00000 207.42187 231.44531 288.86718 357.42187 414.84375 438.86718 496.28906 564.84375 622.26562 646.28906 703.71093 772.26562 829.68750 853.71093 911.13281 935.15624 992.57812 1061.13281 1118.55468 1142.57812 2/1Dialogue on other options is most welcome: for example, making a more thorough use of Sagittal symbols, or indicating some notes as comma variations of others.