Golden magic
Golden magic is a tuning of magic temperament where the 19 tone, 22 tone and 41 tone MOS's have step size ratios equal to the golden ratio. It is very closely approximated by 104edo and 167edo. The generator of golden magic is roughly 380.819 cents.
Scale
Golden magic approximates simple intervals in the 2.3.7.11 subgroup very closely and 5 somewhat less closely (in fact 5 has the highest error of any identity in the 11 limit). Here's the 41 tone MOS with a JI detempering in the 2.3.7.11 subgroup:
| Scale Degree | Ratio | Golden Magic | Detempered | Error | Color Notation |
| 0 | 1/1 | 0.000 | 0.000 | 0.000 | w1 |
| 1 | 49/48 | 35.563 | 35.697 | -0.134 | zz2 |
| 2 | 33/32 | 57.543 | 53.273 | 4.270 | 1o1 |
| 3 | 81/77 | 93.106 | 87.676 | 5.430 | 1ur1 |
| 4 | 77/72 | 115.085 | 116.234 | -1.149 | 1oz2 |
| 5 | 12/11 | 150.649 | 150.637 | 0.012 | 1u2 |
| 6 | 54/49 | 172.628 | 168.213 | 4.415 | rr1 |
| 7 | 9/8 | 208.191 | 203.910 | 4.281 | w2 |
| 8 | 8/7 | 230.171 | 231.174 | -1.004 | r2 |
| 9 | 7/6 | 265.734 | 266.871 | -1.137 | z3 |
| 10 | 33/28 | 287.713 | 284.447 | 3.266 | 1or2 |
| 11 | 77/64 | 323.276 | 320.144 | 3.133 | 1oz3 |
| 12 | 11/9 | 345.256 | 347.408 | -2.152 | 1o3 |
| 13 | 96/77 | 380.819 | 381.811 | -0.992 | 1ur3 |
| 14 | 14/11 | 416.382 | 417.508 | -1.126 | 1uz4 |
| 15 | 9/7 | 438.362 | 435.084 | 3.278 | r3 |
| 16 | 21/16 | 473.925 | 470.781 | 3.144 | z4 |
| 17 | 4/3 | 495.904 | 498.045 | -2.141 | w4 |
| 18 | 49/36 | 531.468 | 533.742 | -2.274 | zz5 |
| 19 | 11/8 | 553.447 | 551.318 | 2.129 | 1o4 |
| 20 | 108/77 | 589.010 | 585.721 | 3.289 | 1ur4 |
| 21 | 77/54 | 610.990 | 614.279 | -3.289 | 1oz5 |
| 22 | 16/11 | 646.553 | 648.682 | -2.129 | 1u5 |
| 23 | 72/49 | 668.532 | 666.258 | 2.274 | rr4 |
| 24 | 3/2 | 704.096 | 701.955 | 2.141 | w5 |
| 25 | 32/21 | 726.075 | 729.219 | -3.144 | r5 |
| 26 | 14/9 | 761.638 | 764.916 | -3.278 | z6 |
| 27 | 11/7 | 783.618 | 782.492 | 1.126 | 1or5 |
| 28 | 77/48 | 819.181 | 818.189 | 0.992 | 1oz6 |
| 29 | 18/11 | 854.744 | 852.592 | 2.152 | 1u6 |
| 30 | 128/77 | 876.724 | 879.856 | -3.133 | 1ur6 |
| 31 | 56/33 | 912.287 | 915.553 | -3.266 | 1uz7 |
| 32 | 12/7 | 934.266 | 933.129 | 1.137 | r6 |
| 33 | 7/4 | 969.829 | 968.826 | 1.004 | z7 |
| 34 | 16/9 | 991.809 | 996.090 | -4.281 | w7 |
| 35 | 49/27 | 1027.372 | 1031.787 | -4.415 | zz8 |
| 36 | 11/6 | 1049.351 | 1049.363 | -0.012 | 1o7 |
| 37 | 144/77 | 1084.915 | 1083.766 | 1.149 | 1ur7 |
| 38 | 154/81 | 1106.894 | 1112.324 | -5.430 | 1oz8 |
| 39 | 64/33 | 1142.457 | 1146.727 | -4.270 | 1u8 |
| 40 | 96/49 | 1164.437 | 1164.303 | 0.134 | rr7 |
| 41 | 2/1 | 1200.000 | 1200.000 | 0.000 | w8 |
The highest error of any interval in the 1,3,7,9,11 tonality diamond is 9/8, which is 4.281 cents sharp, and the lowest error is 0.012 cents, for 11/6. Golden magic tempers out the Saluzo comma as well as the Saquinzo comma. Furthermore, five generators of golden magic equal the perfect fifth in Peppermint-24, and golden magic can be construed as a close rank 2 approximation of Peppermint, with the quasi-diesis being 57.543 cents.
The extension of golden magic to the full 11 limit also tempers out the Laquinyo comma, the Ruyoyo comma, the Zozoyo comma, and the Zotriyo comma.
Golden magic can be extended to the 13 limit by tempering out the Tholuluzo comma and the Thoquadzo comma. The 63 tone golden magic MOS has a copy of the 9 tone praveensmic MOS as well as the 18 tone 3-MOS.
Golden Kite Guitar
A guitar fretting very similar to the Kite guitar is possible with the 41 tone golden magic MOS -- frets can be set to every other note of the 41 tone MOS. To make 11 limit chord fingerings more ergonomic across the neck (since 11 limit intervals require relatively huge stretches near the nut on a Kite guitar), one can fret the guitar to the full 41 tone MOS up to the twelfth fret and transition to 2\41 increments beyond that.
A tuning that consists of alternating downmajor thirds at 380.819c and upmajor thirds at 438.362c is recommended as it makes the stretches needed to play 11 limit chords on a Kite guitar more manageable.