The five theorems
Every claim here was computed and then checked against an independent implementation. Each one has a button, because a claim you can hear beats a claim you can read.
Theorem 1
Only the 4th and the 7th can go
The major scale contains exactly one tritone: F–B. Remove either member of it — and only those two — and nothing dissonant is left. Every other removal keeps it.
| −C | D E F G A B | 1 tritone | 6-33 |
| −D | C E F G A B | 1 tritone | — |
| −E | C D F G A B | 1 tritone | 6-33 |
| −F | C D E G A B | 0 tritones | 6-32 |
| −G | C D E F A B | 1 tritone | — |
| −A | C D E F G B | 1 tritone | — |
| −B | C D E F G A | 0 tritones | 6-32 |
Theorem 2
Your major and minor hexatonics are the same six notes
C major without its 4th, A minor without its ♭6, and the hexachord Guido d’Arezzo taught sight-singing with are one pitch-class set in three rotations. So the app stores one scale and rotates it — never two.
C D E G A B
A B C D E G
G A B C D E
One caution worth keeping: do not say music had six notes before it had seven. The seven letters came first and underlie the hexachord — the six syllables were a way of learning to sing, not a claim about how many notes existed.
Ionian/Lydian Hexatonic
C D E G A B
1 2 3 5 6 7
Sus Hexatonic
D E G A B C
1 2 4 5 6 b7
Phrygian Hexatonic
E G A B C D
1 b3 4 5 b6 b7
Ionian/Mixolydian Hexatonic
G A B C D E
1 2 3 4 5 6
Dorian/Aeolian Hexatonic
A B C D E G
1 2 b3 4 5 b7
Locrian Hexatonic
B C D E G A
1 b2 b3 4 b6 b7
Theorem 3
The scale is a chord
Stack all six notes in thirds and nothing is left over. From C you get maj13 without the 11th; from A you get m11. Every note is a chord tone — because the note that wasn’t is the one we removed.
A caveat the honest version needs: the “avoid note” idea is about harmony — the 4th is kept out of voicings and long notes, not banned from being played at all. And over a minor chord, whether the ♭6 counts as an avoid note is genuinely disputed. The tritone argument above does not depend on any of that, which is why it leads.
Theorem 4
The harmony is tiny, and that is the feature
Four triads. Three four-note sets, two of which carry a second, equally correct name. There is no D minor and no B diminished, because both needed the F.
Theorem 5
You cannot practise it in thirds
Step two degrees through a six-note scale and you do not get thirds. You get two major thirds, two minor thirds and two perfect fourths — the fourths appearing exactly where the removed note left a gap.
C–E (M3) D–G (P4) E–A (P4) G–B (M3) A–C (m3) B–D (m3)
Now step three degrees. Every single one is a perfect fourth or a perfect fifth. Six for six. The seven-note scale cannot do this — F–B comes out an augmented fourth and breaks the chain, and the note that breaks it is the note we removed.
six notes
C–G (P5) D–A (P5) E–B (P5) G–C (P4) A–D (P4) B–E (P4)
seven notes
C–F (P4) D–G (P4) E–A (P4) F–B (A4) G–C (P4) A–D (P4) B–E (P4)
And the consequence
Six resolves faster than seven
Group the scale in fives against 4/4 and the accent phases against the barline. The phrase resolves when the tonic and the accent land on a downbeat together.
Six shares factors with almost everything. Seven shares factors with nothing. That is the whole reason a six-note scale is the right one to teach grouping on — and the reason a room full of players can land a cycle together.
What was removed
The concept is subtractive, so the app draws the absence. Red is the note that is gone; gold is the note sounding; cream is the rest of the scale.