C7(b13) Chord on Guitar
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Major chords [chords based on a major triad]
CC(add9)C6C6/9Cmaj7Cmaj7(9)Cmaj7(13)Cmaj7(#11)Cmaj7(#5)C7C7(9)C7(13)C7(b9)C7(#9)C7(13,b9)C7(b13)C7(#5)C7(b9,b13)C7(#11)C7(b5)Minor chords [chords based on a minor triad]
CmCm6Cm6/9Cm(add9)Cm7Cm7(9)Cm7(11)Cm7(13)Cm7(b13)Cmmaj7Cm7(b5)Cm7(11,b5)Sus chords [3rd suspended and replaced by a 4th or 2nd]
Csus4Csus2C7sus4C7sus4(9)C7sus4(b9)C7sus4(13)Augmented chords [major chords with augmented 5th (#5) ]
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The C7(b13) belongs to the category of altered dominant 7th chords (general: V7alt). These are dominant 7th chords with one ore more of the altered tensions b9, #9, b13 or #11 (which is a special case, since it rather comes along with the natural tensions 9 and 13. Please look up the description for a 7(#11) chord. The altered tensions b9, #9 and b13 mainly occur, when the V7 chord resolves from V to I, like from the C7 to Fmaj7 or Fm7. You may sometimes also stumble across the universal notation C7alt for a C altered chord, saying that the player can decide by himself which altered tensions he/she wants to use. An experienced guitar player will normally decide by himself anyway and for example just play a 7(b9) or 7(#9) chord where 7(b13) is written or the other way round.
C7(b13) theoretically consists of the tones C (1), E (3), G (5), Bb (7) and Ab (b13), but the 5th will practically always be abandoned for the b13, that on the guitar is located just one fret higher.
The b13 is located a minor 6th above a root, but it has to be written as b13 in the chord symbol and not as b6, because it is a chord extension. A 6th can only be written when there's no 7th. And a b6 is nearly inexistent in chord symbols, because those chords will mostly be reinterpreted as inversion of a related chord and then often be notated as slash chord.
moveable
You can transpose these chord shapes to any different key just by moving the whole chord shape along the guitar fretboard until the squared spot represents the new root.
