This really about jazz harmony and chord symbols versus staff and key signatures.
There are many online charts and guides about reading jazz chord symbols.
Of course the issue is how to know the specific quality of the numbered intervals like 7, 9, 6, 5, etc.. Are they major, minor, or diminished?
Other that just memorizing a jazz chord chart a rule of thumb that seems to work is consider the chord as built on a dominant with all the chord tones being diatonic. All the added chord symbols are relative to this basic dominant chord.
If the symbol is C7
, consider that a C dominant seventh chord where the 7th is minor (in terms of key it would be in F major using a B flat.) C9
would be a C dominant ninth chord with a diatonic, major 9th (in the key of F major the 9th above C would be a D natural.)
As you point out, the confusing thing about jazz oriented lead sheets is the main melody may be written on a staff with a key signature, but the chord symbols are NOT written relative to that key signature. The chord symbols are relative to the letter given in the symbol.
To illustrate this point imagine a lead sheet with a melody notated in C major and the chord symbol E9
was used. Rather than being an E minor 7th ♭9 (E,G,B,D,F
all naturals), that should be an E dominant ninth chord where in terms of key it would be the dominant of A major (E,G#,B,D,F#
.) It could also be considered a ninth chord built on the tonic of E mixolydian, but I don't think that makes it easier to understand. We have to do some mental juggling to keep track of the chord and interval qualities and accidentals for different keys.
If you practice in all keys, eventually the intervals of a dominant will 'sink in.' But a quick list might help. Let's switch to a G dominant (the key would be C major.)
INTERVAL ----- QUALITY - LETTER
Root --------- n/a ----- G
13th (6th) --- major --- E
11th (4th) --- perfect - C
9th ---------- major --- A
7th ---------- minor --- F
5th ---------- perfect - D
3rd ---------- major --- B
Root --------- n/a ----- G
All the additional chord symbols are from that diatonic dominant chord reference point.
If the base triad is not major but minor, a symbol is added: Gmin
or Gm
or G-
.
If the seventh is not minor but major, a symbol is added: Gmaj7
or G∆7
Continue from the this diatonic dominant chord for other intervals.
The 5th is normally perfect so b5
is added for a diminished 5th: G7b5
.
The 9th is normally major so b9
could be added for a minor 9th: G7b9
, or #9
for an augmented 9th `G7#9.