Scale library
Every family in every key, spelled the way it should be written — one letter per degree, no enharmonic shortcuts.
C Ionian/Lydian Hexatonic
C D E G A BRefuses to commit to 4 or ♯4 — which is exactly why it sits on both maj7 and maj7♯11. Stack all six in thirds and you get maj13(no 11): every note is a chord tone.
also called: major hexatonic (no 4) · major pentatonic + 7
degrees
1 2 3 5 6 7
set class
6-32
interval vector
<143250>
tritones
0
Tertian harmony inside it — 7 distinct sets
Interval cycles — what happens when you sequence it
in thirdsC–E D–G E–A G–B A–C B–D2× M3, 2× P4, 2× m3
in fourthsC–G D–A E–B G–C A–D B–E3× P5, 3× P4 — all perfect
in fifthsC–A D–B E–C G–D A–E B–G2× M6, 2× m6, 2× P5
in sixthsC–B D–C E–D G–E A–G B–A1× M7, 4× m7, 1× M6
The same family in every key
No repeated letters, no triple accidentals, in any of them. That is what the letter-and-alteration model buys you.