Maximally Even

5-35

(02479)
Pentatonic

7-35

(013568t)
Diatonic

8-28

(0134679t)
Diminished (Oct.)

9-12

(01245689t)
Enneatonic

7 Notes

7-35

(013568t)
Diatonic

7-34

(013468t)
Acoustic

7-32

(0134689)
Harmonic Minor

(0135689)
Harmonic Major

7 Notes

7-35

(013568t)
Diatonic

Cluster-free, 7 Notes

7 Notes

7-35

(013568t)
Diatonic

7-34

(013468t)
Acoustic

7-32

(0134689)
Harmonic Minor

(0135689)
Harmonic Major

7-31

(0134679)
Diminished-7

(0235689)
Diminished-7

7-35, (013568t), Diatonic

Set Class

The diatonic scale or major scale refers to the set class (unordered collection of notes) with twelve transpositions of the white keys. This scale is common in many cultures and across styles of music. The seven modes of the diatonic scale include the Ionian or Major mode (Do-Re-Mi-Fa-So-La-Ti-Do), the Natural Minor mode, and more. More

The scale is maximally even, symmetric and related to transpositions of itself by single-semitone voice leadings. In fact, each transposition of the diatonic (major) scale has six scales that are each a semitone voice-leading step away: two other diatonic (major) scales; two acoustic (melodic minor) scales; and one harmonic major and one harmonic minor scale.

See A Diatonic Puzzle for more about what makes the diatonic scale unique, and Staff Notation for more on how the diatonic scale is deeply embedded into standard staff notation. See Diatonic Modes & Chords for more about how the modes and chords fall out of the notes of the major scale.

Less

OPTC equiv: (013568t)

Interval-content vector <254361>

Distance √(4/7)*

the minimum Euclidean distance from this set to any transposition of the perfectly even 7 note chord, in semitones

Ancohemitonic chromatic-cluser-free

Hemitonic set contains one or more semitones

Maximally Even divides the octave maximally evenly (for cardinality of 5, 7, 8 or 9, no set can be perfectly even)

Quartal set can be generated by repeatedly stacking perfect fourths (5 semitones)

Symmetric the involution of this set is the same set

Tritonic set contains one or more tritones

M-related

7-1

(0123456)
Chromatic-7

Complement

5-35

(02479)
Pentatonic

Voice leading distance: 1

7-34

(013468t)
Acoustic

7-32

(0134689)
Harmonic Minor

(0135689)
Harmonic Major

7-30

7-29

8-26

8-23

(0123578t)
Quartal-8

8-22

Has Modes

Aeolian (Natural Minor)

Transpositions

C Major (Diatonic)

D♭ Major (Diatonic)

D Major (Diatonic)

E♭ Major (Diatonic)

E Major (Diatonic)

F Major (Diatonic)

F♯ Major (Diatonic)

G Major (Diatonic)

A♭ Major (Diatonic)

A Major (Diatonic)

B♭ Major (Diatonic)

B Major (Diatonic)

Scale Contains

3-11

3-10

3-9

(027)
sus
Quartal-3

3-8

(026)
X7 no 5
Aug 6

(046)
X7 ♭5 no 3
Aug 6 no ♯4

3-5

(016)
Maj ♯11 no 3

(056)
X7(♯9)noR/no5

3-7

(025)
min 7 no 5

(035)
Maj 6 no R

3-4

(015)
Maj 7 no 5

(045)
Maj 7 no 3

3-6

(024)
Maj add 9 no 5
X9(no3/5)

3-2

(013)
Diatonic-3

(023)
Diatonic-3

4-27

(0258)
min 7 ♭5
min 6

(0368)
Dom 7
Gr. 6

4-26

(0358)
min 7
Maj 6

4-20

4-23

(0257)
X7 sus 4
Quartal-4

4-16

(0157)
X13 noR/no5

(0267)
X7sus4(add3/no5)

4-22

(0247)
Maj add 9
X9sus4(no5)

(0357)
Maj 6/9 no 5
Maj 9 ♯11 no 5

4-Z29

(0137)
All-Interval
X13 no 5

(0467)
All-Interval
XM♯11

4-14

(0237)
XM7♯11(noR)

(0457)
Maj 9 no 3

4-21

(0246)
Dom 9 no 5

4-8

(0156)
XM7♯11(no3)

4-13

(0136)
min Maj 11

(0356)
X7(♭9)no3

4-11

(0135)
Diatonic-4

(0245)
Diatonic-4

4-10

(0235)
Diatonic-4

5-34

(02469)
Dom 9
min ♭13 ♭5

5-29

(01368)
X7sus4(add3)
min 13 no 5

(02578)
min 6/9
Xm11♭5 no 9

5-20

(01568)
Maj 9 ♯11 no 3

(02378)
XM7♯11

5-27

5-25

(02358)
Maj 6 ♯11
min 13 no 11

(03568)
Dom 13 no 9

5-24

(01357)
XM9♯11 no 5
Dom 13 no 5

(02467)
Dom 11 no 5
X9♯11(no♭7)

5-23

(02357)
Diatonic-5

(02457)
Diatonic-5

5-Z12

(01356)
Diatonic-5

6-33

(023579)
Dom 13

(024679)
min 13

6-32

(024579)
Quartal-6

6-Z26

(013578)
Maj 9 ♯11

6-Z25

(013568)
Diatonic-6

(023578)
Diatonic-6