What is a 7/6 chord?
I am reading James Hober's paper "The 43 Four-Note Qualities", that is based on a Ted Greene paper. You can find it here.
It mentions that there are a total of 43 four-note qualities, nothing more and nothing less (meeting certain criteria, like inversions and homonyms being the same quality). He proves this mathematically in the continuation of that paper here.
At the end of the first paper (page 6, it is not a long paper) he lists the 43 qualities, along with the homonyms (names of the chord) that he considered were "not stretching it too far". On that list there are some chord names that I don't recognize, here is an example:
3) 1 - 2 - 3 - 6 =
C7/11 no R =
Gm7/6 no 5 =
F?9sus no 5 =
Bb6#11 no 3 =
E(7)#9b9b5 no 3,b7 =
Db13#9b5 no R, b7 =
Dm+/9/11 no R
What is a Gm7/6 chord? What is a C7/11 chord? Which notes compose them? Why are they called like that? Where can I find more about them? How do you pronounce them?
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What he's pointing out is that you can use multiple names (homonyms) for the same combination of notes.
For example, with three notes, C-E-G is obviously a C major chord. But you can also describe it as E minor, with the 5th (B) omitted, and a 6th (C) as the bottom note. In his notation, "Em/6 no 5"
I would read this as "E minor over sixth no five".
The notes are described in the first part of the item - "1 - 2 - 3 - 6", with each number describing the number of semitones to the next note. So if you were to start on B (I picked B because it results in no sharps/flats).
B,
B+1 = C
C+2 = D
D+3 = F
F+6 = back to B
What Hober has done is, for each shape, he's picked the "simplest" name for that chord, then applied that to a root note of C, then used the notes in that chord as the basis for picking the root note for naming it other ways.
That's a bit complicated, so let's step through the example.
He's decided that 1-2-3-6 is most simply named as X7/11 no R. That applies no matter what note X is, but he's written C7/11 no R.
That's:
A C major chord - C,E,G
Plus the dominant 7th - C,E,G,Bb
Over the 11th - C,E,F,G,Bb
Minus the root - E,F,G,Bb
... and you can see that it fits the numeric description:
E to F is 1 semitone
F to G is 2 semitones
G to Bb is 3 semitones
Bb back to E is 6 semitones
Then he picks what he considers the next simplest name for the chord: Ym7/6 no 5.
Since he's already picked the notes E,F,G,Bb, in this case Y = G:
G minor - G,Bb,D
Plus the dominant 7th - G,Bb,D,F
Over the 6th - E,G,Bb,D,F
minus the 5th - E,G,Bb,F
... the same notes as C7/11 no R.
Perhaps the easiest example is 2-4-3-3. He treats inversions as equivalent. So 4-3-3-2 is equivalent to 2-4-3-3. Experienced musicians can immediately see that the intervals 4-3-3-2 correspond to the third, fifth, dominant 7th, octave, so that's a X7 chord. If X=C, that's C7: C,E,G,Bb. Or you could call those same four notes F#b9b5 no R.
Chord symbol: Gm13
Chord name: G minor thirteenth
Chord importance: Rarely used
Chord notes: G Bb D F E
Interval structure: R m3 5 m7 13
Comments: minor seventh chord with added 13th (6th). Most of the time
the 5th is left out (3rd note). The 13th = 6th, 13th is used when the
chord is a 7th chord with added 6th, 6th chords are not 7th chords
with added 6th.
Chord belong to these categories: Minor chord ; 7th
chord ; 6th chord ; 13th chord ;
Alternative symbols Gminor13 ;
Gmin13 ; Gm7/13 ; Gm7(add13) ; G-7(add13) ; G-7/13 ; Gmin7/13 ;
Gmin7(add13) ; Gm7/6 ; Gm7(add6) ; G-7(add6) ; G-7/6 ; Gmin7/6 ;
Gmin7(add6) ;
(Note that you can see a minor chord listed as -, min and m.
So Gmin, Gm and G- is the same thing)
via scale-chords.com
C7/11:
Third column, second chord
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