Chord Scales

1. Consist entirely of only half steps and whole steps.
2. "Wrap" back to the starting note after exactly one octave.
3. Contain no two consecutive half-steps, even when "wrapping" to the octave above or below.

These rules generate exactly 17 Chord Scales starting on any given note (click here to view source code for a C++ computer program that demonstrates this). They are all conventionally used in jazz harmony. There are 7 modes each of the major and melodic minor scale (7 notes), two diminished scales (8 notes), and one whole tone scale (6 notes):

#	code	construction	name	major mode #	mel. min. mode #
1	85	H W H W H W H W	auxiliary diminished
2	94	H W H W W W W	"altered," diminished whole tone		7
3	110	H W W H W W W	Locrian, half-diminished	7
4	118	H W W W H W W	Phrygian	3
5	122	H W W W W H W	Phrygian +6, Dorian -2		2
6	170	W H W H W H W H	diminished
7	174	W H W H W W W	Locrian #2		6
8	182	W H W W H W W	Aeolian, pure minor	6
9	186	W H W W W H W	Dorian	2
10	188	W H W W W W H	melodic minor		1
11	214	W W H W H W W	Mixolydian -6, "Hindu"		5
12	218	W W H W W H W	Mixolydian	5
13	220	W W H W W W H	Ionian, major	1
14	234	W W W H W H W	Lydian dominant, Mixolydian +4		4
15	236	W W W H W W H	Lydian	4
16	244	W W W W H W H	Lydian +5		3
17	252	W W W W W W	whole tone

The "code" represents the lowest numeric occurrence occurrence (unneccessary LSBs discarded) when the scale's construction is considered an 8-bit binary value with H=0 and W=1.

Funky Extensions

There are a few exceptions to Jim Knapp's concept of jazz chords having four "functions." In this theory, chord extensions replace a normal "function" according to the following:

Function	Substitute tone above	Substitute tone below
root	9th
3rd	11th (sus4)	sus2
5th	13th	11th
7th	15th	6th

From Jim's text: "When a substitute tone is present in a chord, then that tone becomes the chord tone and the original function becomes a passing tone or in-between tone. For example in a (sus4) chord, the 3rd is not a chord tone."

Chords with a "10th" Extension
However, a dominant (sus4) chord sounds good with the 3rd added on top. This does not work if the 3rd is below the 11 since this typcially creates an "illegal -9 interval" (a -9 interval not relative to the bass) which almost always sounds bad. Using Jim's notation, then, the third function is duplicated, and this chord would be called

C7(sus4,add 3)

but this symbol doesn't fully convey the information that the 3 goes on top, like an extension. Dave Peck proposes the following symbol:

C7(sus4,10)

Chords with a "12th" Extension

Dave has devised a similar notation for augmented chords after he noticed that any +5 chord can take a natural 5 as an extension:

C+7(12)     i.e. C, E, G#, Bb, G
Cmaj7(#5,12)     (good chord, but generates invalid chord scale)
Cm(#5,12)     i.e. C, Eb, G#, G

Here the difference with Knapp's system is greater, since Knapp would call the notes of the last example "Cm(-6)," which implies that the G# is performing the 7th function. There is no clear way to specify the 5 as an extension in this case.