Here's all the fractions up to 72-edo:Dave Keenan wrote: ↑Tue Dec 03, 2019 12:01 pmI call it "group number" because many EDOs (but not all) have a whole-number value for this, like the element groups on the chemistry periodic table.

Group number EDOs Colour ------------------------------------------------- 0 1Most of the non-integer groups are in fifths or sevenths, which was kind of to be expected. (Halves, thirds, and quarters also show up occasionally.) The integer groups also often happen to fall on important EDOs—groups I through XX are all the fifths of these EDOs in order: 6, 8, 23b, 5, 37, 22, 17, 29, 65, 12, 67, 31, 19, 26, 47, 7, 37b, 16, 9, and 11.BlackI 3, 6GoldII 8Gold2.5 13Gold2.8 18GoldIII 23bGold- fifth = 14\23 - 13\23 is group 17.5 IV 5, 10, 15, 20, 25, 30Gold4.86 42Gold- group = 4 + 6/7 V 37Gold5.2 32Gold5.33 59Green- group = 5 + 1/3 - formerly Gold 5.5 27, 54Green5.71 49Green- group = 5 + 5/7 5.8 71GreenVI 22, 44, 66Green6.25 61Green6.4 39Blue6.57 56Blue- group = 6 + 4/7 VII 17, 34, 51, 68Blue7.43 63Blue- group = 7 + 3/7 7.6 46BlueVIII 29, 58Magenta8.29 70Magenta- group = 8 + 2/7 8.5 41Grey8.8 53Grey- actual 2:3 fifth is group X where X is the number of apotomes in a 9:16 minor seventh IX 65GreyX 12, 24, 36, 48, 60, 72OrangeXI 67Yellow11.2 55Yellow11.5 43YellowXII 31, 62Cyan12.4 50Cyan12.57 69Cyan- group = 12 + 4/7 XIII 19, 38, 57Cyan13.43 64Purple- group = 13 + 3/7 13.6 45PurpleXIV 26, 52Purple14.5 33Rose14.8 40RoseXV 47RoseXVI 7, 14, 21, 28, 35RoseXVII 37bRose- fifth = 21\37 - 22\37 is group V 17.5 23RoseXVIII 16RoseXIX 9RoseXX 11RoseXXI 17bWhite- fifth = 9\17 - 10\17 is group VII XXII 2, 4WhiteXXIII 7bbWhite- fifth = 3\7 - 4\7 is group XVI - 5\7 (7b) is group 4/7 = 0.57 XXIV 1bWhite- 0¢ fifth

The function's derivative is actually continuous at 700¢ (it's 0.72 groups per cent on both sides).

(also why is the fact that the exact color boundaries were never specified—even Trojan's was, after some searching—bothering me so much)

59 and 61 also overlap.