The Closest Voice-Leading of All Possible Unique Harmonic Relationships Between a Half-Diminished 7th-chord and One Other (Common) Chord
by Dr. Jody Nagel
 
I. Half-Diminished 7th-chord to Major Triad. (12 Types)
II. Half-Diminished 7th-chord to Minor Triad. (12 Types)
III. Half-Diminished 7th-chord to Major-Minor 7th Chord. (12 Types)
IV. Half-Diminished 7th-chord to Half-Diminished 7th-chord. (6 Types)
V. Half-Diminished 7th-chord to Fully-Diminished 7th-chord. (3 Types)
 
"Spelling in thirds" is not the organizing principle here for spelling half-diminished 7th-chords. Rather, relative to the "key" of the tonic triad specified, a modal-chromatic scale is strictly observed. It is:
1; b2, 2; b3 (or #2), 3; 4, #4; 5; b6, 6; b7, 7; 1.
 
For each progression, the minimum semitone displacement for closest possible 4-part voice-leading is indicated by placing a numeral between the first and second chord (and also between the second and third chord in the case of a tie between two types).
 
Voice-leading involving Common-Tones is indicated with black note-heads.
 
"Augmented-Sixth-Type" voice-leading, when involved, is marked with contrary motion lines.
 
The second chord of each bar is always the same Half-Diminished 7th-chord ! ! !
 

Any relationship between (1) a Half-Diminished 7th-chord and (2) one of the following: [ Major Triad, Minor Triad, Major-Minor 7th-chord, or Fully-Diminished 7th-chord ] is some transposition of one of the relationships given on this page. (Though it may or may not use the closest voice-leading that these models use.)
 
 
Dr. Jody Nagel
March 18, 2005
Computer Music-Notation by Jody Jay Nagel