Cdimmaj7b13 guitar chord — root mapping, fingerings, arpeggios, triads, pentatonic, scales

The whole-half diminished scale is an eight-note symmetric scale used over diminished 7th chords. Degrees I, bIII, bV and VI form the dim7 chord, while the remaining notes pass between them and support long symmetric lines. The fingering repeats every minor 3rd, so only three distinct pitch collections exist. The scale is used over passing dim7 chords, leading-tone diminished chords and chromatic connections.

Diminished Whole-Half is a symmetrical eight-note scale alternating whole steps and half steps: W–H–W–H–W–H–W–H. Its central sonority is the fully diminished seventh chord 1 b3 b5 bb7; in the commonly used scale formula, the diminished 7th is written enharmonically as the natural 6. The remaining degrees—2, 4, #5, and 7—form a second fully diminished seventh chord. Because of its symmetry, the scale does not establish a stable major or minor center by itself: the root is defined by the diminished chord, bass, and subsequent resolution. Its defining sound is the interaction of two interlocking diminished seventh chords separated by a whole step.

The functions of the degrees are defined relative to the selected root of the fully diminished seventh chord. Because of the scale’s symmetry, one pitch collection can be heard from several different centers.

1 — chord root: the scale center and the root of the diminished triad and fully diminished dim7 chord.

2 — major 2nd / 9th: not part of the primary dim7; it lies a whole step above the root and belongs to the second diminished seventh chord, 2 4 #5 7.

b3—minor 3rd: a chord tone of the primary diminished triad and the seventh chord 1 b3 b5 bb7.

4 — perfect 4th / 11th: not part of the primary dim7; it belongs to the second diminished seventh chord and lies a semitone below b5.

b5—diminished 5th: the principal structural tone of the diminished chord. It forms a tritone with the root and may be labeled #4 under a different chordal interpretation.

#5 — augmented 5th / minor 6th: not part of the primary dim7; it belongs to the second diminished seventh chord and lies a semitone below 6.

6 — major 6th / diminished 7th: written as 6 in the scale formula, but functionally spelled bb7 as a member of the fully diminished seventh chord. It is the fourth chord tone of dim7.

7 — major 7th / leading tone: belongs to the second diminished seventh chord, lies a semitone below the root, and may resolve upward to 1.

Diminished Whole-Half contains eight degrees and is not a diatonic scale, so it has no conventional sequence of seven major, minor, and diminished chords. Stacking every other scale degree from each note produces diminished triads:

1–b3–b5;

2–4–#5;

b3–b5–6;

4–#5–7;

b5–6–1;

#5–7–2;

6–1–b3;

7–2–4.

Adding one more scale 3rd produces fully diminished seventh chords. Because of the symmetry, they reduce to two distinct pitch collections:

1 b3 b5 6 — strictly spelled 1 b3 b5 bb7;

2 4 #5 7.

Chords rooted on 1, b3, b5, and 6 are inversions of one fully diminished seventh chord. Chords rooted on 2, 4, #5, and 7 are inversions of the other.

The scale also contains four dominant seventh chords whose roots form the second diminished seventh chord: 2, 4, #5, and 7. Correctly spelling these chords often requires enharmonic reinterpretation.

C Diminished Whole-Half contains C D Eb F Gb Ab A B. Its two diminished seventh chords are:

Cdim7—C Eb Gb Bbb, enharmonically C Eb Gb A;

Ddim7—D F Ab Cb, enharmonically D F Ab B.

The first collection also functions as the rootless upper structure of D7b9, F7b9, Ab7b9, and B7b9.

Diminished Whole-Half is used primarily over fully diminished seventh chords, written dim7 or °7. C Diminished Whole-Half, for example, is used over Cdim7. Degrees 1 b3 b5 bb7 exactly match the chord tones, while 2, 4, #5, and 7 fill the spaces between them through the alternating whole-step and half-step pattern.

In functional harmony, the scale is used over leading-tone diminished seventh chords, vii°7, secondary leading-tone chords, passing diminished chords, and common-tone diminished chords. The selection and resolution of individual notes must follow the chord’s specific function and destination.

A single fully diminished seventh chord can be reinterpreted enharmonically in four ways. Each chord tone can act as a leading tone to a root located a semitone above it. The notes of Cdim7—C Eb Gb A—can therefore lead toward centers on Db, E, G, or Bb.

Because of the symmetry, one scale fits every inversion of the same dim7. C, Eb, Gb, and A Diminished Whole-Half contain the same pitch collection; only the perceived root and the functions of the degrees change.

The scale should not be confused with Diminished Half-Whole. Whole-Half begins with a whole step and is used primarily over dim7; Half-Whole begins with a half step and is used primarily over a dominant 7b9 chord.

Diminished Whole-Half is also used as an independent octatonic collection in symmetrical and nonfunctional harmony, although the intended center must then be reinforced through repetition, bass, register, or musical form.

Diminished Whole-Half and Diminished Half-Whole are two rotations of the same octatonic collection. Beginning C Whole-Half on its second degree, D, produces D Half-Whole with the same notes:

C Whole-Half — C D Eb F Gb Ab A B;

D Half-Whole — D Eb F Gb Ab A B C.

In twelve-tone equal temperament, there are only three distinct octatonic collections. Transposing the scale by a minor 3rd returns the same pitch collection. C, Eb, Gb, and A Whole-Half are therefore different centers of one collection.

The fully diminished seventh chord 1 b3 b5 bb7 divides the octave into four equal minor 3rds. Diminished Whole-Half inserts a second diminished seventh chord, 2 4 #5 7, between its chord tones.

Ordinary Locrian has the formula 1 b2 b3 4 b5 b6 b7 and contains a half-diminished m7b5 chord rather than a fully diminished dim7. Locrian and its variants are therefore not direct substitutes for Diminished Whole-Half over °7.

Harmonic Minor contains a fully diminished vii°7 chord on its seventh degree, but it is a nonsymmetrical seven-note scale. Diminished Whole-Half expands the dim7 chord tones with four additional notes to produce a symmetrical eight-note collection.

Over dim7, begin with the chord tones 1 b3 b5 bb7. The last tone is written as 6 in the scale formula, but when constructing the arpeggio it is useful to hear and spell it as a diminished 7th. Over Cdim7, for example, the primary arpeggio is C Eb Gb Bbb, enharmonically C Eb Gb A.

The second diminished seventh chord, 2 4 #5 7, provides a set of passing and neighboring tones. Each note lies a whole step above one tone of the primary dim7 and a semitone below the next:

1–2–b3;

b3–4–b5;

b5–#5–6;

6–7–1.

The complete scale can be organized as an alternation between two arpeggios:

primary dim7 — 1 b3 b5 6;

neighboring dim7 — 2 4 #5 7.

Moving between them exposes the complete octatonic structure without reducing the line to a mechanical scale run.

Because of the symmetry, patterns, arpeggios, and melodic sequences can be transposed upward or downward by a minor 3rd without leaving the pitch collection. This movement weakens the sense of one root, however, so return regularly to the tones of the specific dim7 chord and account for its resolution.

In functional use, follow the destination chord above all else. A fully diminished seventh chord can resolve toward four different centers, so the direction of any scale tone depends on the harmonic context.

Over a leading-tone dim7, emphasize the semitone motion of the leading tone into the next chord’s root. Over a common-tone diminished chord, retain the common tone and resolve the remaining voices by step. Over a passing dim7, connect the surrounding chord tones through the shortest chromatic motions.

Do not continue playing Whole-Half mechanically after the dim7 resolves. When the harmony moves to a major, minor, or dominant chord, change the target tones and follow the actual pitch content of the new harmony.

Diminished Whole-Half is a symmetrical eight-note scale alternating whole steps and half steps: 1 2 b3 4 b5 #5 6 7. Its foundation is the fully diminished seventh chord 1 b3 b5 bb7, with bb7 written enharmonically as 6 in the scale formula. The remaining degrees, 2 4 #5 7, form a second diminished seventh chord. The scale repeats when transposed by a minor 3rd and is used primarily over dim7 and °7, while its Half-Whole rotation is used over dominant 7b9 chords.