Obsessive Interval chart

Columns show enharmonic intervals

Pitch class

{0}

{1}

{2}

{3}

{4}

{5}

{6}

{7}

{8}

{9}

{10}

{11}

{0}

{1}

{2}

{3}

{4}

{5}

{6}

{7}

{8}

{9}

{10}

{11}

{0}

{1}

{2}

{3}

{4}

{5}

{6}

{7}

{8}

{9}

{10}

{11}

{0}

{1}

{2}

{3}

{4}

{5}

{6}

{7}

{8}

{9}

{10}

{11}

{0}

Interval Number

R

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

17

18

19

20

21

22

23

24

25

26

27

28

29

Continues to infinity. I stop here because that is the limit of a guitar with 24 frets

Short name

1st

2nd

3rd

4th

5th

6th

7th

8th

9th

10th

11th

12th

13th

14th

15th

16th

17th

18th

19th

20th

21th

22th

23th

24th

25th

26th

27th

28th

29th

Name

Perfect Unison

Major 2nd

Major 3rd

Perfect 4th

Perfect 5th

Major 6th

Major 7th

Perfect Octave, 8va

Major 9th

Major 10th

Perfect 11th

Perfect 12th

Major 13th

Major 14th

Perfect 15th, 15ma

Further analysis is similar to the pattern to the left, but the obsessive system never uses it past 2 octaves.

symbol

P1

M2

M3

P4

P5

M6

M7

P8

M9

M10

P11

P12

M13

M14

P15

Note root C

C

D

E

F

G

A

B

C

D

E

F

G

A

B

C

D

E

F

G

A

B

C

D

E

F

G

A

B

C

Altered number

b2

b3

b4

b5

b6

b7

b8

b9

b10

b11

b12

b13

b14

b15

Name

Minor 2nd

Minor 3rd

Diminished 4th

Diminished 5th

Minor 6th

Minor 7th

Diminished 8th

Minor 9th

Diminished 10th

Minor 11th

symbol

m2

m3

d4

d5

m6

m7

d8

m9

d10

Note root C

Db

Eb

Fb

Gb

Ab

Bb

Cb

Db

Eb

Fb

Gb

Ab

Bb

Cb

Db

Eb

Fb

Gb

Ab

Bb

Cb

Db

Eb

Fb

Gb

Ab

Bb

Cb

Altered number

#1

#2

#3

#4

#5

#6

#7

#8

#9

#10

#11

#12

#13

#14

Name

Augmented Unison

Augmented 2nd

Augmented 3rd

Augmented 4th

Augmented 5th

Augmented 6th

Augmented 7th

Augmented 8th

Augmented 9th

Augmented 10th

Augmented 11th

Augmented 12th

Augmented 13th

Augmented 14th

symbol

A1

A2

A3

A4

A5

A6

A7

A8

A9

A10

A11

A12

A13

A14

Note root C

C#

D#

E#

F#

G#

A#

B#

C#

D#

E#

F#

G#

A#

B#

C#

D#

E#

F#

G#

A#

B#

C#

D#

E#

F#

G#

A#

B#

Altered number

bb2

bb3

bb4

bb5

bb6

bb7

bb8

bb9

bb10

bb11

bb12

bb13

bb14

bb15

Name

Diminished 2nd

Diminished 3rd

Doubly Diminished 4th

Doubly Diminished 5th

Diminished 6th

Diminished 7th

Doubly Diminished 8th

Diminished 9th

Doubly Diminished 10th

Diminished 11th

symbol

d2

d3

dd4

dd5

d6

d7

dd8

d9

dd10

Note root C

Dbb

Ebb

Fbb

Gbb

Abb

Bbb

Cbb

Dbb

Ebb

Fbb

Gbb

Abb

Bbb

Cbb

Dbb

Ebb

Fbb

Gbb

Abb

Bbb

Cbb

Dbb

Ebb

Fbb

Gbb

Abb

Bbb

Cbb

Altered number

x1

x2

x3

x4

x5

x6

x7

x8

x9

x10

x11

x12

x13

x14

Name

Doubly Augmented Unison

Doubly Augmented 2nd

Doubly Augmented 3rd

Doubly Augmented 4th

Doubly Augmented 5th

Doubly Augmented 6th

Doubly Augmented 7th

Doubly Augmented 8th

Doubly Augmented 9th

Doubly Augmented 10th

Doubly Augmented 11th

Doubly Augmented 12th

Doubly Augmented 13th

Doubly Augmented 14th

symbol

AA1

AA2

AA3

AA4

AA5

AA6

AA7

AA8

AA9

AA10

AA11

AA12

AA13

AA14

Note root C

Cx

Dx

Ex

Fx

Gx

Ax

Bx

Cx

Dx

Ex

Fx

Gx

AAx

Bx

Cx

Dx

Ex

Fx

Gx

AAx

Bx

Cx

Dx

Ex

Fx

Gx

AAx

Altered number

3b3

3b4

3b5

3b6

3b7

3b8

3b9

3b10

3b11

3b12

3b13

3b14

3b15

Name

Doubly Diminished 3rd

(No standard name) 4th

(No standard name) 5th

Doubly Diminished 6th

Doubly Diminished 7th

(No standard name) 8th

Doubly Diminished 9th

(No standard name) 10th

Doubly Diminished 11th

symbol

dd3

(No standard symbol) 4

(No standard symbol) 5

dd6

dd7

(No standard symbol) 8

dd9

(No standard symbol) 10

Note root C

Ebbb

Fbbb

Gbbb

Abbb

Bbbb

Cbbb

Dbbb

Ebbb

Fbbb

Gbbb

Abbb

Bbbb

Cbbb

Dbbb

Ebbb

Fbbb

Gbbb

Abbb

Bbbb

Cbbb

Dbbb

Ebbb

Fbbb

Gbbb

Abbb

Bbbb

Cbbb

Altered number

3#1

3#2

3#3

3#4

3#5

3#6

3#7

3#8

3#9

3#10

3#11

3#12

3#13

3#14

Note root C

Cx#

Dx#

Ex#

Fx#

Gx#

AAx#

Bx#

Cx#

Dx#

Ex#

Fx#

Gx#

AAx#

Bx#

Cx#

Dx#

Ex#

Fx#

Gx#

AAx#

Bx#

Cx#

Dx#

Ex#

Fx#

Gx#

AAx#

Altered number

4b3

4b4

4b5

4b6

4b7

4b8

4b9

4b10

4b11

4b12

4b13

4b14

4b15

Note root C

Ebbbb

Fbbbb

Gbbbb

Abbbb

Bbbbb

Cbbbb

Dbbbb

Ebbbb

Fbbbb

Gbbbb

Abbbb

Bbbbb

Cbbbb

Dbbbb

Ebbbb

Fbbbb

Gbbbb

Abbbb

Bbbbb

Cbbbb

Dbbbb

Ebbbb

Fbbbb

Gbbbb

Abbbb

Bbbbb

Cbbbb

Altered number

4#1

4#2

4#3

4#4

4#5

4#6

4#7

4#8

4#9

4#10

4#11

4#12

4#13

4#14

Note root C

Cxx

Dxx

Exx

Fxx

Gxx

AAxx

Bxx

Cxx

Dxx

Exx

Fxx

Gxx

AAxx

Bxx

Cxx

Dxx

Exx

Fxx

Gxx

AAxx

Bxx

Cxx

Dxx

Exx

Fxx

Gxx

Altered number

5b4

5b5

5b6

5b7

5b8

5b9

5b10

5b11

5b12

5b13

5b14

5b15

Note root C

Fbbbbb

Gbbbbb

Abbbbb

Bbbbbb

Cbbbbb

Dbbbbb

Ebbbbb

Fbbbbb

Gbbbbb

Abbbbb

Bbbbbb

Cbbbbb

Dbbbbb

Ebbbbb

Fbbbbb

Gbbbbb

Abbbbb

Bbbbbb

Cbbbbb

Dbbbbb

Ebbbbb

Fbbbbb

Gbbbbb

Abbbbb

Bbbbbb

Cbbbbb

Altered number

5#1

5#2

5#3

5#4

5#5

5#6

5#7

5#8

5#9

5#10

5#11

5#12

5#13

5#14

Note root C

Cxx#

Dxx#

Exx#

Fxx#

Gxx#

AAxx#

Bxx#

Cxx#

Dxx#

Exx#

Fxx#

Gxx#

AAxx#

Bxx#

Cxx#

Dxx#

Exx#

Fxx#

Gxx#

AAxx#

Bxx#

Cxx#

Dxx#

Exx#

Fxx#

Gxx#

Altered number

6b5

6b6

6b7

6b8

6b9

6b10

6b11

6b12

6b13

6b14

6b15

Note root C

Gbbbbbb

Abbbbbb

Bbbbbbb

Cbbbbbb

Dbbbbbb

Ebbbbbb

Fbbbbbb

Gbbbbbb

Abbbbbb

Bbbbbbb

Cbbbbbb

Dbbbbbb

Ebbbbbb

Fbbbbbb

Gbbbbbb

Abbbbbb

Bbbbbbb

Cbbbbbb

Dbbbbbb

Ebbbbbb

Fbbbbbb

Gbbbbbb

Abbbbbb

Bbbbbbb

Cbbbbbb

Altered number

6#1

6#2

6#3

6#4

6#5

6#6

6#7

6#8

6#9

6#10

6#11

6#12

6#13

6#14

Note root C

Cxxx

Dxxx

Exxx

Fxxx

Gxxx

AAxxx

Bxxx

Cxxx

Dxxx

Exxx

Fxxx

Gxxx

AAxxx

Bxxx

Cxxx

Dxxx

Exxx

Fxxx

Gxxx

AAxxx

Bxxx

Cxxx

Dxxx

Exxx

Fxxx

Altered number

7b5

7b6

7b7

7b8

7b9

7b10

7b11

7b12

7b13

7b14

7b15

Note root C

Gbbbbbbb

Abbbbbbb

Bbbbbbbb

Cbbbbbbb

Dbbbbbbb

Ebbbbbbb

Fbbbbbbb

Gbbbbbbb

Abbbbbbb

Bbbbbbbb

Cbbbbbbb

Dbbbbbbb

Ebbbbbbb

Fbbbbbbb

Gbbbbbbb

Abbbbbbb

Bbbbbbbb

Cbbbbbbb

Dbbbbbbb

Ebbbbbbb

Fbbbbbbb

Gbbbbbbb

Abbbbbbb

Bbbbbbbb

Cbbbbbbb

Altered number

7#1

7#2

7#3

7#4

7#5

7#6

7#7

7#8

7#9

7#10

7#11

7#12

7#13

7#14

Note root C

Cxxx#

Dxxx#

Exxx#

Fxxx#

Gxxx#

AAxxx#

Bxxx#

Cxxx#

Dxxx#

Exxx#

Fxxx#

Gxxx#

AAxxx#

Bxxx#

Cxxx#

Dxxx#

Exxx#

Fxxx#

Gxxx#

AAxxx#

Bxxx#

Cxxx#

Dxxx#

Exxx#

Fxxx#

Altered number

8b6

8b7

8b8

8b9

8b10

8b11

8b12

8b13

8b14

8b15

Note root C

Abbbbbbbb

Bbbbbbbbb

Cbbbbbbbb

Dbbbbbbbb

Ebbbbbbbb

Fbbbbbbbb

Gbbbbbbbb

Abbbbbbbb

Bbbbbbbbb

Cbbbbbbbb

Dbbbbbbbb

Ebbbbbbbb

Fbbbbbbbb

Gbbbbbbbb

Abbbbbbbb

Bbbbbbbbb

Cbbbbbbbb

Dbbbbbbbb

Ebbbbbbbb

Fbbbbbbbb

Gbbbbbbbb

Abbbbbbbb

Bbbbbbbbb

Cbbbbbbbb

Altered number

8#1

8#2

8#3

8#4

8#5

8#6

8#7

8#8

8#9

8#10

8#11

8#12

8#13

8#14

Note root C

Cxxxx

Dxxxx

Exxxx

Fxxxx

Gxxxx

AAxxxx

Bxxxx

Cxxxx

Dxxxx

Exxxx

Fxxxx

Gxxxx

AAxxxx

Bxxxx

Cxxxx

Dxxxx

Exxxx

Fxxxx

Gxxxx

AAxxxx

Bxxxx

Cxxxx

Dxxxx

Exxxx

Altered number

9b6

9b7

9b8

9b9

9b10

9b11

9b12

9b13

9b14

9b15

Note root C

Abbbbbbbbb

Bbbbbbbbbb

Cbbbbbbbbb

Dbbbbbbbbb

Ebbbbbbbbb

Fbbbbbbbbb

Gbbbbbbbbb

Abbbbbbbbb

Bbbbbbbbbb

Cbbbbbbbbb

Dbbbbbbbbb

Ebbbbbbbbb

Fbbbbbbbbb

Gbbbbbbbbb

Abbbbbbbbb

Bbbbbbbbbb

Cbbbbbbbbb

Dbbbbbbbbb

Ebbbbbbbbb

Fbbbbbbbbb

Gbbbbbbbbb

Abbbbbbbbb

Bbbbbbbbbb

Cbbbbbbbbb

Altered number

9#1

9#2

9#3

9#4

9#5

9#6

9#7

9#8

9#9

9#10

9#11

9#12

9#13

9#14

Note root C

Cxxxx#

Dxxxx#

Exxxx#

Fxxxx#

Gxxxx#

AAxxxx#

Bxxxx#

Cxxxx#

Dxxxx#

Exxxx#

Fxxxx#

Gxxxx#

AAxxxx#

Bxxxx#

Cxxxx#

Dxxxx#

Exxxx#

Fxxxx#

Gxxxx#

AAxxxx#

Bxxxx#

Cxxxx#

Dxxxx#

Altered number

10b7

10b8

10b9

10b10

10b11

10b12

10b13

10b14

10b15

Note root C

Bbbbbbbbbbb

Cbbbbbbbbbb

Dbbbbbbbbbb

Ebbbbbbbbbb

Fbbbbbbbbbb

Gbbbbbbbbbb

Abbbbbbbbbb

Bbbbbbbbbbb

Cbbbbbbbbbb

Dbbbbbbbbbb

Ebbbbbbbbbb

Fbbbbbbbbbb

Gbbbbbbbbbb

Abbbbbbbbbb

Bbbbbbbbbbb

Cbbbbbbbbbb

Dbbbbbbbbbb

Ebbbbbbbbbb

Fbbbbbbbbbb

Gbbbbbbbbbb

Abbbbbbbbbb

Bbbbbbbbbbb

Cbbbbbbbbbb

Altered number

10#1

10#2

10#3

10#4

10#5

10#6

10#7

10#8

10#9

10#10

10#11

10#12

10#13

10#14

Note root C

Cxxxxx

Dxxxxx

Exxxxx

Fxxxxx

Gxxxxx

AAxxxxx

Bxxxxx

Cxxxxx

Dxxxxx

Exxxxx

Fxxxxx

Gxxxxx

AAxxxxx

Bxxxxx

Cxxxxx

Dxxxxx

Exxxxx

Fxxxxx

Gxxxxx

AAxxxxx

Bxxxxx

Cxxxxx

Dxxxxx

Altered number

11b7

11b8

11b9

11b10

11b11

11b12

11b13

11b14

11b15

Note root C

Bbbbbbbbbbbb

Cbbbbbbbbbbb

Dbbbbbbbbbbb

Ebbbbbbbbbbb

Fbbbbbbbbbbb

Gbbbbbbbbbbb

Abbbbbbbbbbb

Bbbbbbbbbbbb

Cbbbbbbbbbbb

Dbbbbbbbbbbb

Ebbbbbbbbbbb

Fbbbbbbbbbbb

Gbbbbbbbbbbb

Abbbbbbbbbbb

Bbbbbbbbbbbb

Cbbbbbbbbbbb

Dbbbbbbbbbbb

Ebbbbbbbbbbb

Fbbbbbbbbbbb

Gbbbbbbbbbbb

Abbbbbbbbbbb

Bbbbbbbbbbbb

Cbbbbbbbbbbb

Altered number

11#1

11#2

11#3

11#4

11#5

11#6

11#7

11#8

11#9

11#10

11#11

11#12

11#13

11#14

Note root C

Cxxxxx#

Dxxxxx#

Exxxxx#

Fxxxxx#

Gxxxxx#

AAxxxxx#

Bxxxxx#

Cxxxxx#

Dxxxxx#

Exxxxx#

Fxxxxx#

Gxxxxx#

AAxxxxx#

Bxxxxx#

Cxxxxx#

Dxxxxx#

Exxxxx#

Fxxxxx#

Gxxxxx#

AAxxxxx#

Bxxxxx#

Cxxxxx#

This process of adding sharps or flats could go on infinitely. Clearly these complex  intervals are of little practical use, but they are necessary in calculating the All Possible Scales section.

© Richard Repp 2019 All Rights Reserved