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Topic: Math and music
Replies: 44   Last Post: Oct 20, 2004 7:38 AM

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Allen L. Barker

Posts: 6
Registered: 12/8/04
Re: Math and music
Posted: Oct 16, 2004 12:27 AM
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A few more examples... The chromatic scale diagrams are useful in
a general sense, because they don't depend on any particular scale,
key, or collection of notes.

----------------------------------------------------

Chromatic scale (notes numbered in base 12)

0---4---8---0---4---8---0---4---8---0---4---8---0---4---8---0---4---8---0---4
| /| /| /| /| /| /| /| /| /| /| /| /| /| /| /| /| /| /| /|
| / | / | / | / | / | / | / | / | / | / | / | / | / | / | / | / | / | / | / |
|/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |
9---1---5---9---1---5---9---1---5---9---1---5---9---1---5---9---1---5---9---1
| /| /| /| /| /| /| /| /| /| /| /| /| /| /| /| /| /| /| /|
| / | / | / | / | / | / | / | / | / | / | / | / | / | / | / | / | / | / | / |
|/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |
6---a---2---6---a---2---6---a---2---6---a---2---6---a---2---6---a---2---6---a
| /| /| /| /| /| /| /| /| /| /| /| /| /| /| /| /| /| /| /|
| / | / | / | / | / | / | / | / | / | / | / | / | / | / | / | / | / | / | / |
|/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |
3---7---b---3---7---b---3---7---b---3---7---b---3---7---b---3---7---b---3---7
| /| /| /| /| /| /| /| /| /| /| /| /| /| /| /| /| /| /| /|
| / | / | / | / | / | / | / | / | / | / | / | / | / | / | / | / | / | / | / |
|/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |
0---4---8---0---4---8---0---4---8---0---4---8---0---4---8---0---4---8---0---4
| /| /| /| /| /| /| /| /| /| /| /| /| /| /| /| /| /| /| /|
| / | / | / | / | / | / | / | / | / | / | / | / | / | / | / | / | / | / | / |
|/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |
9---1---5---9---1---5---9---1---5---9---1---5---9---1---5---9---1---5---9---1
| /| /| /| /| /| /| /| /| /| /| /| /| /| /| /| /| /| /| /|
| / | / | / | / | / | / | / | / | / | / | / | / | / | / | / | / | / | / | / |
|/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |
6---a---2---6---a---2---6---a---2---6---a---2---6---a---2---6---a---2---6---a
| /| /| /| /| /| /| /| /| /| /| /| /| /| /| /| /| /| /| /|
| / | / | / | / | / | / | / | / | / | / | / | / | / | / | / | / | / | / | / |
|/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |
3---7---b---3---7---b---3---7---b---3---7---b---3---7---b---3---7---b---3---7
| /| /| /| /| /| /| /| /| /| /| /| /| /| /| /| /| /| /| /|
| / | / | / | / | / | / | / | / | / | / | / | / | / | / | / | / | / | / | / |
|/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |
0---4---8---0---4---8---0---4---8---0---4---8---0---4---8---0---4---8---0---4
| /| /| /| /| /| /| /| /| /| /| /| /| /| /| /| /| /| /| /|
| / | / | / | / | / | / | / | / | / | / | / | / | / | / | / | / | / | / | / |
|/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |
9---1---5---9---1---5---9---1---5---9---1---5---9---1---5---9---1---5---9---1
| /| /| /| /| /| /| /| /| /| /| /| /| /| /| /| /| /| /| /|
| / | / | / | / | / | / | / | / | / | / | / | / | / | / | / | / | / | / | / |
|/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |
6---a---2---6---a---2---6---a---2---6---a---2---6---a---2---6---a---2---6---a
| /| /| /| /| /| /| /| /| /| /| /| /| /| /| /| /| /| /| /|
| / | / | / | / | / | / | / | / | / | / | / | / | / | / | / | / | / | / | / |
|/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |
3---7---b---3---7---b---3---7---b---3---7---b---3---7---b---3---7---b---3---7
| /| /| /| /| /| /| /| /| /| /| /| /| /| /| /| /| /| /| /|
| / | / | / | / | / | / | / | / | / | / | / | / | / | / | / | / | / | / | / |
|/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |
0---4---8---0---4---8---0---4---8---0---4---8---0---4---8---0---4---8---0---4


Chords with root 0 (the pattern is the same for all chords):

9th=7th+add9
3rd 3--7 5th 7 5th 7th a 2 add9 9 7th 0--4--7
| / /| | / (-3rd=sus2) |
|/ / | |/ | augmented
0 0--4 3rd 7--b maj7 6
root root /| |
/ | |
minor major 0--4 3
/| |
/ | |
sus4 5 9 0
(-3rd) 6th
diminished

Note the cycle of 5ths along the / diagonals; counting along the \ diagonals.
Note guitar/bass fretboard pattern (minus "guitar bump") along alternate \ diags.
Standard note convention: 0=B 1=C 2=C# 3=D 4=D# 5=E 6=F 7=F# 8=G 9=G# a=A b=A#

----------------------------------------------------

Melodic minor scale in the key of 0 (notes numbered in base 12)

0 4 8 0 4 8 0 4 8 0 4 8 0 4 8 0 4 8 0 4
| /| /| /| /| /| /|
| / | / | / | / | / | / |
| / | / | / | / | / | / |
9 1 5---9 1 5---9 1 5---9 1 5---9 1 5---9 1 5---9 1
| / | / | / | / | / | /
| / | / | / | / | / | /
|/ |/ |/ |/ |/ |/
6 a 2 6 a 2 6 a 2 6 a 2 6 a 2 6 a 2 6 a
/| /| /| /| /| /|
/ | / | / | / | / | / |
/ | / | / | / | / | / |
3---7---b---3---7---b---3---7---b---3---7---b---3---7---b---3---7---b---3---7
| / | / | / | / | / | / | /
| / | / | / | / | / | / | /
|/ |/ |/ |/ |/ |/ |/
0 4 8 0 4 8 0 4 8 0 4 8 0 4 8 0 4 8 0 4
| /| /| /| /| /| /|
| / | / | / | / | / | / |
| / | / | / | / | / | / |
9 1 5---9 1 5---9 1 5---9 1 5---9 1 5---9 1 5---9 1
| / | / | / | / | / | /
| / | / | / | / | / | /
|/ |/ |/ |/ |/ |/
6 a 2 6 a 2 6 a 2 6 a 2 6 a 2 6 a 2 6 a
/| /| /| /| /| /|
/ | / | / | / | / | / |
/ | / | / | / | / | / |
3---7---b---3---7---b---3---7---b---3---7---b---3---7---b---3---7---b---3---7
| / | / | / | / | / | / | /
| / | / | / | / | / | / | /
|/ |/ |/ |/ |/ |/ |/
0 4 8 0 4 8 0 4 8 0 4 8 0 4 8 0 4 8 0 4
| /| /| /| /| /| /|
| / | / | / | / | / | / |
| / | / | / | / | / | / |
9 1 5---9 1 5---9 1 5---9 1 5---9 1 5---9 1 5---9 1
| / | / | / | / | / | /
| / | / | / | / | / | /
|/ |/ |/ |/ |/ |/
6 a 2 6 a 2 6 a 2 6 a 2 6 a 2 6 a 2 6 a
/| /| /| /| /| /|
/ | / | / | / | / | / |
/ | / | / | / | / | / |
3---7---b---3---7---b---3---7---b---3---7---b---3---7---b---3---7---b---3---7
| / | / | / | / | / | / | /
| / | / | / | / | / | / | /
|/ |/ |/ |/ |/ |/ |/
0 4 8 0 4 8 0 4 8 0 4 8 0 4 8 0 4 8 0 4


Chords with root 0 (the pattern is the same for all chords):

9th=7th+add9
3rd 3--7 5th 7 5th 7th a 2 add9 9 7th 0--4--7
| / /| | / (-3rd=sus2) |
|/ / | |/ | augmented
0 0--4 3rd 7--b maj7 6
root root /| |
/ | |
minor major 0--4 3
/| |
/ | |
sus4 5 9 0
(-3rd) 6th
diminished

Note the cycle of 5ths along the / diagonals; counting along the \ diagonals.
Note guitar/bass fretboard pattern (minus "guitar bump") along alternate \ diags.
Standard note convention: 0=B 1=C 2=C# 3=D 4=D# 5=E 6=F 7=F# 8=G 9=G# a=A b=A#

----------------------------------------------------

Chromatic scale with standard note names (using flats)

B---Eb--G---B---Eb--G---B---Eb--G---B---Eb--G---B---Eb--G---B---Eb--G---B---Eb
| /| /| /| /| /| /| /| /| /| /| /| /| /| /| /| /| /| /| /|
| / | / | / | / | / | / | / | / | / | / | / | / | / | / | / | / | / | / | / |
|/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |
Ab--C---E---Ab--C---E---Ab--C---E---Ab--C---E---Ab--C---E---Ab--C---E---Ab--C
| /| /| /| /| /| /| /| /| /| /| /| /| /| /| /| /| /| /| /|
| / | / | / | / | / | / | / | / | / | / | / | / | / | / | / | / | / | / | / |
|/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |
F---A---Db--F---A---Db--F---A---Db--F---A---Db--F---A---Db--F---A---Db--F---A
| /| /| /| /| /| /| /| /| /| /| /| /| /| /| /| /| /| /| /|
| / | / | / | / | / | / | / | / | / | / | / | / | / | / | / | / | / | / | / |
|/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |
D---Gb--Bb--D---Gb--Bb--D---Gb--Bb--D---Gb--Bb--D---Gb--Bb--D---Gb--Bb--D---Gb
| /| /| /| /| /| /| /| /| /| /| /| /| /| /| /| /| /| /| /|
| / | / | / | / | / | / | / | / | / | / | / | / | / | / | / | / | / | / | / |
|/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |
B---Eb--G---B---Eb--G---B---Eb--G---B---Eb--G---B---Eb--G---B---Eb--G---B---Eb
| /| /| /| /| /| /| /| /| /| /| /| /| /| /| /| /| /| /| /|
| / | / | / | / | / | / | / | / | / | / | / | / | / | / | / | / | / | / | / |
|/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |
Ab--C---E---Ab--C---E---Ab--C---E---Ab--C---E---Ab--C---E---Ab--C---E---Ab--C
| /| /| /| /| /| /| /| /| /| /| /| /| /| /| /| /| /| /| /|
| / | / | / | / | / | / | / | / | / | / | / | / | / | / | / | / | / | / | / |
|/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |
F---A---Db--F---A---Db--F---A---Db--F---A---Db--F---A---Db--F---A---Db--F---A
| /| /| /| /| /| /| /| /| /| /| /| /| /| /| /| /| /| /| /|
| / | / | / | / | / | / | / | / | / | / | / | / | / | / | / | / | / | / | / |
|/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |
D---Gb--Bb--D---Gb--Bb--D---Gb--Bb--D---Gb--Bb--D---Gb--Bb--D---Gb--Bb--D---Gb
| /| /| /| /| /| /| /| /| /| /| /| /| /| /| /| /| /| /| /|
| / | / | / | / | / | / | / | / | / | / | / | / | / | / | / | / | / | / | / |
|/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |
B---Eb--G---B---Eb--G---B---Eb--G---B---Eb--G---B---Eb--G---B---Eb--G---B---Eb
| /| /| /| /| /| /| /| /| /| /| /| /| /| /| /| /| /| /| /|
| / | / | / | / | / | / | / | / | / | / | / | / | / | / | / | / | / | / | / |
|/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |
Ab--C---E---Ab--C---E---Ab--C---E---Ab--C---E---Ab--C---E---Ab--C---E---Ab--C
| /| /| /| /| /| /| /| /| /| /| /| /| /| /| /| /| /| /| /|
| / | / | / | / | / | / | / | / | / | / | / | / | / | / | / | / | / | / | / |
|/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |
F---A---Db--F---A---Db--F---A---Db--F---A---Db--F---A---Db--F---A---Db--F---A
| /| /| /| /| /| /| /| /| /| /| /| /| /| /| /| /| /| /| /|
| / | / | / | / | / | / | / | / | / | / | / | / | / | / | / | / | / | / | / |
|/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |
D---Gb--Bb--D---Gb--Bb--D---Gb--Bb--D---Gb--Bb--D---Gb--Bb--D---Gb--Bb--D---Gb
| /| /| /| /| /| /| /| /| /| /| /| /| /| /| /| /| /| /| /|
| / | / | / | / | / | / | / | / | / | / | / | / | / | / | / | / | / | / | / |
|/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |
B---Eb--G---B---Eb--G---B---Eb--G---B---Eb--G---B---Eb--G---B---Eb--G---B---Eb


Chords with root 0 (the pattern is the same for all chords):

9th=7th+add9
3rd 3--7 5th 7 5th 7th a 2 add9 9 7th 0--4--7
| / /| | / (-3rd=sus2) |
|/ / | |/ | augmented
0 0--4 3rd 7--b maj7 6
root root /| |
/ | |
minor major 0--4 3
/| |
/ | |
sus4 5 9 0
(-3rd) 6th
diminished

Note the cycle of 5ths along the / diagonals; counting along the \ diagonals.
Note guitar/bass fretboard pattern (minus "guitar bump") along alternate \ diags.
Standard note convention: 0=B 1=C 2=C# 3=D 4=D# 5=E 6=F 7=F# 8=G 9=G# a=A b=A#

----------------------------------------------------



Date Subject Author
10/13/04
Read Math and music
David Dalton
10/13/04
Read Re: Math and music
Timothy Murphy
10/14/04
Read Re: Math and music
Thomas Mautsch
10/13/04
Read Re: Math and music
Bob Pease
10/14/04
Read Re: Math and music
hs
10/14/04
Read Re: Math and music
Bob Pease
10/13/04
Read Re: Math and music
Dave Schutt
10/13/04
Read Re: Math and music
Matthew Fields
10/13/04
Read Re: Math and music
Jon Slaughter
10/14/04
Read Re: Math and music
David Webber
10/14/04
Read Re: Math and music
Phil Carmody
10/14/04
Read Re: Math and music
David Webber
10/14/04
Read Re: Math and music
Jon Slaughter
10/14/04
Read Re: Math and music
David Webber
10/14/04
Read Re: Math and music
Martin Penderis
10/15/04
Read Re: Math and music
lutonomy
10/15/04
Read Re: Math and music
Robert Israel
10/15/04
Read Re: Math and music
David Webber
10/15/04
Read Re: Math and music
paramucho
10/15/04
Read Re: Math and music
lutonomy
10/15/04
Read Re: Math and music
Chan-Ho Suh
10/15/04
Read Re: Math and music
Matthew Fields
10/15/04
Read Re: Math and music
Bob Pease
10/15/04
Read Re: Math and music
Matthew Fields
10/15/04
Read Re: Math and music
Bob Pease
10/15/04
Read Re: Math and music
Gerry Myerson
10/15/04
Read Re: Math and music
Jon Slaughter
10/14/04
Read Re: Math and music
Bob Pease
10/14/04
Read Re: Math and music
George Cox
10/14/04
Read Re: Math and music
David Webber
10/13/04
Read Re: Math and music
Gerry Myerson
10/14/04
Read Re: Math and music
Bob Pease
10/15/04
Read Re: Math and music
John M. Gamble
10/15/04
Read Re: Math and music
Allen L. Barker
10/16/04
Read Re: Math and music
Allen L. Barker
10/16/04
Read Re: Math and music
David Webber
10/16/04
Read Re: Math and music
Matthew Fields
10/16/04
Read Re: Math and music
Graham Breed
10/16/04
Read Re: Math and music
David Webber
10/16/04
Read Re: Math and music
Matthew Fields
10/16/04
Read Re: Math and music
Graham Breed
10/16/04
Read Re: Math and music
Matthew Fields
10/16/04
Read Re: Math and music
Matthew Fields
10/19/04
Read Re: Math and music
K. E. Pledger
10/20/04
Read Re: Math and music
Eckard Blumschein

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