E7#9 guitar chord — root mapping, fingerings, arpeggios, triads, pentatonic, scales

The half-whole diminished scale is an eight-note symmetric scale used over dominant 7th chords. It contains b9, #9, the major 3rd, #11, perfect 5th, natural 13th and minor 7th, making it especially suitable for 7b9 and 13b9. Its fingering repeats every minor 3rd, and only three distinct pitch collections exist. In jazz it is commonly used over tense dominants before resolution.

Diminished Half-Whole is a symmetrical eight-note scale that alternates half steps and whole steps: H–W–H–W–H–W–H–W. The major 3rd 3 and minor 7th b7 preserve the dominant seventh foundation, while b2, #2, and #4 supply the b9, #9, and #11 tensions. Unlike Altered, the scale contains a perfect 5th 5 and natural 13, but no natural 9 or b13. Because of its symmetry, the same pitch collection repeats when the root is moved by a minor 3rd. Its defining profile is a dominant seventh chord, 1 3 5 b7, surrounded by b9, #9, #11, and 13.

1 — chord root: the center against which the dominant foundation and altered tensions are heard.

b2—minor 2nd / flat 9th: functions as the b9, lies a semitone above the root, and creates strong tension.

#2 — augmented 2nd / sharp 9th: functions as the #9 and lies a semitone below the major 3rd 3. It is enharmonically equivalent to b3, but is normally labeled #9 over a dominant seventh chord.

3 — major 3rd: establishes the dominant quality and forms the chord’s essential tritone with b7.

#4 — augmented 4th / sharp 11th: functions as the #11; in chord notation it may also be labeled b5.

5 — perfect 5th: a stable dominant seventh chord tone. Its presence distinguishes Diminished Half-Whole from Altered.

6 — major 6th / 13th: functions as the natural 13 and is one of the scale’s principal defining degrees.

b7—minor 7th: an essential dominant seventh chord tone that forms a tritone with the major 3rd 3. In a functional resolution, it normally moves downward.

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

1–#2–#4;

b2–3–5;

#2–#4–6;

3–5–b7;

#4–6–1;

5–b7–b2;

6–1–#2;

b7–b2–3.

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

1 #2 #4 6;

b2 3 5 b7.

The second is particularly important over a dominant chord: b2 3 5 b7 forms a diminished seventh chord rooted on the b9 and simultaneously represents a rootless 7b9 chord. Over C7b9, for example, it is Db–E–G–Bb.

The scale also contains four dominant seventh chords whose roots form a fully diminished seventh chord: 1, #2, #4, and 6. A single C Diminished Half-Whole collection contains C7, Eb7, F#7, and A7. All four chords use the same eight pitches, but the function of each pitch changes relative to the selected root.

C Diminished Half-Whole contains C Db Eb E F# G A Bb. Its two principal diminished seventh chords are Cdim7 (C Eb F# A) and Dbdim7 (Db E G Bb).

Diminished Half-Whole is used primarily over dominant seventh chords with a b9 or #9 when the harmony retains a perfect 5th and supports a natural 13. Typical chord symbols include 7b9, 7#9, 13b9, 13#9, 7b9#11, and 13#9#11. A particular voicing does not have to contain every scale tone simultaneously.

Its most common setting is a functional dominant in V7–I or V7–i motion. G Diminished Half-Whole, for example, may be used over G7b9 resolving to Cmaj7 or Cm when the melody and accompaniment support the natural 13, E.

The scale is also used over secondary dominants. A7b9 preceding Dm or Dmaj, for example, may be approached with A Diminished Half-Whole when the harmony supports its natural 13 and does not require a b13.

Because of its symmetry, one pitch collection fits four dominant seventh chords separated by minor 3rds. Dominant arpeggios and melodic figures can therefore be moved up or down by a minor 3rd without leaving the scale.

Diminished Half-Whole contains no natural 9 or b13. When the chord or melody requires a b13 or #5, Altered or Phrygian Dominant may be more accurate. When a natural 9 is required without altered 9ths, Mixolydian, Lydian Dominant, or another scale matching the specific chord is normally preferred.

Diminished Half-Whole is one of the two orientations of the symmetrical diminished, or octatonic, scale. Beginning the same pitch collection on degree b2 produces Diminished Whole-Half, which alternates whole steps and half steps and is used primarily over fully diminished seventh chords. C Diminished Half-Whole and Db Diminished Whole-Half, for example, contain the same notes.

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, F#, and A Diminished Half-Whole are therefore different centers within one collection.

In Olivier Messiaen’s system, the octatonic scale is the second mode of limited transposition. It has two possible rotations—Half-Whole and Whole-Half—and three distinct transpositions.

Altered has the formula 1 b2 #2 3 b5 #5 b7. Its first five functions match Diminished Half-Whole: 1 b9 #9 3 b5/#11. Altered then uses #5 or b13, whereas Diminished Half-Whole contains a perfect 5 and natural 13.

Whole Tone has the formula 1 2 3 #4 #5 b7. It shares 1, 3, #4, and b7, but contains a natural 9 and #5 and lacks the b9, #9, perfect 5, and natural 13.

Mixolydian has the formula 1 2 3 4 5 6 b7. It preserves the same dominant foundation, 1 3 5 b7, but uses natural 9, 11, and 13 instead of the altered b9, #9, and #11.

Over a dominant seventh chord, begin with 1 3 5 b7. The major 3rd and minor 7th form the guide-tone tritone and preserve the chord’s function within the symmetrical patterns and altered tensions.

Then add b9, #9, #11, and 13. Characteristic motions include 1–b9, #9–3, 3–#11–5, and 5–13–b7, together with their reversals. The semitone motions 1–b9 and #9–3 reveal the Half-Whole structure particularly clearly.

The complete scale can be organized as two fully diminished seventh chords separated by a semitone:

1 #9 #11 13;

b9 3 5 b7.

The second arpeggio is a rootless 7b9 chord. Over C7b9, for example, a Dbdim7 arpeggio supplies Db E G Bb, or b9 3 5 b7. A Cdim7 arpeggio supplies C Eb F# A, or 1 #9 #11 13.

The scale also contains four dominant seventh chords separated by minor 3rds. Over C7, the following arpeggios may be used:

C7—1 3 5 b7;

Eb7—#9 5 b7 b9;

F#7—#11 b7 b9 3;

A7—13 b9 3 5.

These arpeggios use the same pitch collection but group the chord tones and tensions in different ways.

Symmetrical figures may be transposed upward or downward by a minor 3rd. Because this symmetry weakens the sense of one root, return regularly to 1, 3, 5, and b7, place them on strong beats, and connect phrases to the resolution of the following chord.

In G7b9–Cmaj7, B, the dominant’s major 3rd, normally rises to C, while F, its minor 7th, falls to E. Ab (b9) may resolve to G, Bb (#9) to A or B, C# (#11) to C or D, and E (13) may remain as a common tone with Cmaj7.

Do not sustain a natural 9 or b13 when a pure Diminished Half-Whole sound is intended, since neither degree belongs to the scale. Once the dominant moves to the tonic or another chord type, change the scale and target tones with the harmony.

Diminished Half-Whole is a symmetrical eight-note dominant scale alternating half steps and whole steps: 1 b9 #9 3 #11 5 13 b7. Degrees 1 3 5 b7 form an ordinary dominant seventh chord, while b9, #9, and #11 add altered tensions without removing the natural 13. The scale consists of two fully diminished seventh chords, repeats when transposed by a minor 3rd, and is used primarily over 7b9, 7#9, and 13b9 chords with a perfect 5th and natural 13.