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is it possible to make something like a 3x3 magic square that contains notes instead of numbers and all rows, columns, and diagonals form chords?

well, sort of. i used a computer to search for a solution. there are none using just major chords, none using minor chords, or a mix of the two.

maj is (C E G)

min is (C D# G).

if you add on diminished and augmented chords, a solution is found! but it turns out major and minor are unused, and there are no solutions where the diagonals are counted.

dim is (C D# F#)

aug is (C E G#)

there is basically just one solution, considering rotations, mirror images, and transposition of pitch. the rows are all diminished chords and the columns are all augmented chords.

C D# F#

E G A#

G# B D

by adding sus4 and flat5, you can find squares including the diagonals

sus4 (C F G)

b5 (C E F#)

the computer found four unique solutions:

rows: dim sus4 b5 cols: b5 min maj diags: b5 maj

C D# A

G# F# C#

D A# E

rows: maj min b5 cols: dim sus4 b5 diags: maj b5

C E G

F# A C#

D# B F

rows: b5 min maj cols: b5 sus4 dim diags: maj b5

C F# A#

G# E C#

D B G

rows: b5 sus4 dim cols: maj min b5 diags: b5 maj

C F# A#

A D E

F B G#

note that in the solutions found, none use aug, but all the rest of the chord types are used!

using this magic square

C D# A

G# F# C#

D A# E

i created a sequence of rows, cols, and diagonals, such that each is used only once, and such that each chord has one common note with the next one. and, among many possibilities, i used one such sequence to form this progression:

C F# E (diagonal NW-SE)

A F# D (diagonal NE-SW)

D A# E (bottom row)

C G# D (left column)

C D# A (top row)

D# F# A# (middle column)

G# F# C# (middle row)

A C# E (right column)

and the last chord leads nicely to the beginning chord

well, sort of. i used a computer to search for a solution. there are none using just major chords, none using minor chords, or a mix of the two.

maj is (C E G)

min is (C D# G).

if you add on diminished and augmented chords, a solution is found! but it turns out major and minor are unused, and there are no solutions where the diagonals are counted.

dim is (C D# F#)

aug is (C E G#)

there is basically just one solution, considering rotations, mirror images, and transposition of pitch. the rows are all diminished chords and the columns are all augmented chords.

C D# F#

E G A#

G# B D

by adding sus4 and flat5, you can find squares including the diagonals

sus4 (C F G)

b5 (C E F#)

the computer found four unique solutions:

rows: dim sus4 b5 cols: b5 min maj diags: b5 maj

C D# A

G# F# C#

D A# E

rows: maj min b5 cols: dim sus4 b5 diags: maj b5

C E G

F# A C#

D# B F

rows: b5 min maj cols: b5 sus4 dim diags: maj b5

C F# A#

G# E C#

D B G

rows: b5 sus4 dim cols: maj min b5 diags: b5 maj

C F# A#

A D E

F B G#

note that in the solutions found, none use aug, but all the rest of the chord types are used!

using this magic square

C D# A

G# F# C#

D A# E

i created a sequence of rows, cols, and diagonals, such that each is used only once, and such that each chord has one common note with the next one. and, among many possibilities, i used one such sequence to form this progression:

C F# E (diagonal NW-SE)

A F# D (diagonal NE-SW)

D A# E (bottom row)

C G# D (left column)

C D# A (top row)

D# F# A# (middle column)

G# F# C# (middle row)

A C# E (right column)

and the last chord leads nicely to the beginning chord

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richard13

Well, that's ONE way to spend your timeActually Bill, it reminds me a bit of Eduard's experiment of changing one note each time in a 4 chord progression (I think).