Harmonic Major scale & harmony
The Harmonic Major scale is a simple alteration of the major scale. The sixth degree is lowered and this creates an augmented second between the sixth and seventh degrees. In contrast to the Harmonic Minor scale it is a major type scale with a major third between the first and third degrees. Written out as an alteration of the major scale using numbers (1 2 3 4 5 6 7) the steps are 1, 2, 3, 4, 5, b6, 7. Viewed as two four-note tetrachords and compared to modes in the major/minor system, the lower tetrachord is major (Ionian) and the upper tetrachord is harmonic minor.
Starting from the note C the scale is:
C D E F G Ab B
The harmony in triads is
C Maj D dim E min F min G maj Ab aug B dim
As sevenths
C Maj7 D min7b5 (D dim7) E min7 F min/maj7 (F dim7) G7 AbMaj7#5 (Ab dim 7) B dim 7
I particularly like the fully extended seven note arpeggios which can be created using this scale.
C E G B D F Ab
D F Ab C E G B
E G B D F Ab C
F Ab C E G B D
G B D F Ab C E
Ab C E G B D F
B D F Ab C E G
Neapolitan Scales & Harmony
The intriguingly named Neapolitan Minor and Major scales are unusual seven note scales. They can be seen as the harmonic and melodic minor scales with a lowered second (supertonic).
NEAPOLITAN MINOR
The Neapolitan Minor works really well for improvisation and has a Middle Eastern sound with an augmented second between the sixth and seventh degrees. This scale can be viewed as an altered harmonic minor scale with the second degree lowered by a semitone or a Phrygian mode with the seventh degree raised by a semitone to form a leading tone and it is sometimes written as a Phrygian #7 scale. It can also be seen as a Double Harmonic scale with the third degree lowered by a semitone. Viewed as two four-note tetrachords and compared to modes in the major/minor system, the lower tetrachord is Phrygian/Locrian and the upper tetrachord is harmonic minor. Written out as an alteration of a major scale ( 1 2 3 4 5 6 7) the steps are 1, b2, b3, 4, 5, b6, 7.
Starting from the note C , the notes are:
C Db Eb F G Ab B C
As with all scales and modes, I often play this scale from E and use the bottom string of the guitar as a pedal tone. Playing the scale from E, the notes are:
E F G A B C D#
As a scale starting from E, it is interesting to play it as an alteration of E Phrygian and treat is as a tonal extension of the C major system with subsidiary modes.
Triads (leading tone chord has a major second interval instead of a third between the root and the third note in the scale series due to the presence of two adjacent semitones)
E min F Maj G aug A min B Maj b5 C Maj D# 2(9) b5 (third contracted to major second)
Seventh chords * the last chord is in effect a diminished seventh with the third lowered to form a second or ninth.
E min/maj7 F Maj7 GMaj7#5 A min7 B7b5 C Maj7 D#6/9 b5
It is also interesting to play starting from A as an alteration of the A harmonic minor scale and look at how this changes the structure of harmonic minor chords.
A Bb C D E F G#
Triads (leading tone chord has a major second instead of a third between the root and the next note)
A min Bb Maj C aug D min E Maj b5 F Maj G# 2(9) b5 (third contracted to major second)
Seventh chords * the last chord is in effect a diminished seventh with the third lowered to form a second or ninth.
A min/maj7 Bb Maj7 C Maj7#5 D min7 E7b5 F Maj7 G#6/9 b5
NEAPOLITAN MAJOR
The Neapolitan Major also works well for improvisation with its unusual series of tones and semitones. This scale is the Neapolitan Minor with a raised sixth, and is actually a minor scale, due to the presence of a minor third step between the first and third degrees. The scale has a series of five consecutive whole tones (major seconds) imparting a whole tone character and the scale has the same series of intervals in its retrograde version. This scale can be viewed as an altered melodic minor scale with the second degree lowered by a semitone. Viewed as two four-note tetrachords and compared to modes in the major/minor system, the lower tetrachord is Phrygian/Locrian and the upper tetrachord is major and melodic minor. Written out as an alteration of a major scale ( 1 2 3 4 5 6 7) the steps are 1, b2, b3, 4, 5, 6, 7.
Starting from the note C , the notes are:
C Db Eb F G A B C
I play this scale from E and use the bottom string of the guitar as a pedal tone. Playing the scale from E, the notes are:
E F G A B C# D#
Triads (leading tone chord has a major second instead of a third between the root and the next note)
E min F aug G aug A Maj B Maj b5 C# dim D# 2 b5 (third contracted to major second)
It is also interesting to play starting from A as an alteration of the A melodic minor scale and look at how this changes the structure of melodic minor chords.
A Bb C D E F# G#
Triads (leading tone chord has a major second instead of a third between the root and the next note)
A min Bb aug C aug D Maj E Maj b5 F# dim G# 2 b5 (third contracted to major second)
Diminished scales & harmony
Diminished scales have eight notes. They consist of a symmetrical series of alternating tones and semitones. This scale may have originated in Persian music. Passages of music implying a scale of this type occur in classical music in the 18th century. The scale was set down in the late 19th century and later termed the octatonic scale. In standard theory the diminished scale starting with a tone followed by a semitone is the fundamental version. Starting from the note C, the scale is written out with four flats with the seventh degree treated as a double flat. This is sometimes referred to as the whole half scale and abbreviated as WH.
C D Eb F Gb Ab Bbb Cb C
This can be simplified:
C D Eb F Gb Ab A B C
The flats be written down enharmonically as sharps:
C D D# F F# G# A B C
Starting from the note C there is also one other diminished scale. This starts with a semitone, and is sometimes called the half whole scale and abbreviated as HW. It is also referred to as the auxiliary diminished scale:
C Db Eb E Gb G A Bb C
There are three diminished scales, and each one can be treated as a self contained system which has separate linear and harmonic applications from the others. The third scale does not contain the note C and can be written ascending from a Db:
Db D E F G Ab Bb B Db
Any one of the twelve chromatic tones can be used to build two different diminished scales, either the one starting with a tone (whole note) or a semitone (half note). In other words there are potentially 24 scales, if diminished scales are treated as having a starting point. As diminished scale patterns repeat symmetrically in minor thirds, there are in effect only three discrete scales. Diminished scales are not approached theoretically as having a tonic.
On the guitar, I particularly like using diminished scales with one note as a starting point, or central note. The obvious one is open E at the bottom of the instrument. This is not a tonic, but instead can be treated as a pedal tone and as a root for a series of chords. This is a more advanced and interesting way of looking at these synthetic scales consisting of alternating tones and semitones with a symmetrical form.
Initially I’ve chosen the scale starting with a semitone or half step HW. It’s inspiring to focus on this scale and listen to the notes and their resonance and colour. Playing ascending and descending scales from all the other E notes on the guitar and treating this as a central note makes it much easier to build sophisticated frameworks. This scale can function as a powerful chromatic language which is often superimposed over a dominant chord such as E7, E7#9, E7b9 and E7#11, E13, E13b9 and a number of other combinations of chord tone extensions. These can then be resolved to a tonic minor such as A minor. This is why it is sometimes called the dominant diminished scale.
This is the ascending scale starting with a semitone, written with sharps with enharmonic equivalents (which are important) running from E. It contains the same notes as the third scale above , the HW ascending from Db.
E F G G#(Ab) A#(Bb) B C#(Db) D E
These notes can be written out as chord tones for an E dominant type chord with alterations.
E (root) F (b9) G (#9) G# (third) A#/Bb (sharp eleventh/ flat fifth) B (fifth) C#(sixth/thirteenth) D (seventh)
In contrast, here is the other diminished scale ascending from E, which starts with a tone followed by a semitone. This scale is normally the version which is used running from the root of a diminished chord. It contains the same notes as the second scale above , the HW ascending from C.
E F#(Gb) G A A#(Bb) C C#(Db) D#(Eb) E
Autumn Leaves
Autumn Leaves is outlined as a basic chord progression in E minor, which works well on the guitar, G minor, the most widely used key in jazz and A minor which is great as a reference key. Bars 27-28 are written with the fundamental harmony, just the tonic minor chord. These two bars are altered in most jazz fake book versions. Autumn Leaves has a 32 bar AABC form.
E minor
Am7 | D7 | GM7 | CM7 | F#m7b5 | B7 | Em7 | Em7
Am7 | D7 | GM7 | CM7 | F#m7b5 | B7 | Em7 | Em7
F#m7b5 | B7 | Em7 | Em7 | Am7 | D7 | GM7 | CM7
F#m7b5 | B7 | Em7 | Em7 | CM7 | B7 | Em7 | Em7
G minor
Cm7 F7 BbM7 EbM7 Am7b5 D7 Gm7 Gm7
Cm7 F7 BbM7 EbM7 Am7b5 D7 Gm7 Gm7
Am7b5 D7 Gm7 Gm7 Cm7 F7 BbM7 EbM7
Am7b5 D7 Gm7 Gm7 EbM7 D7 Gm7 Gm7
A minor
Dm7 G7 CM7 FM7 Bm7b5 E7 Am7 Am7
Dm7 G7 CM7 FM7 Bm7b5 E7 Am7 Am7
Bm7b5 E7 Am7 Am7 Dm7 G7 CM7 FM7
Bm7b5 E7 Am7 Am7 FM7 E7 Am7 Am7
This version in G minor , with bars 27-28 altered is the Real Book type version based on the Miles Davis approach to Autumn Leaves
Cm7 F7 BbM7 EbM7 Am7b5 D7 Gm7 Gm7
Cm7 F7 BbM7 EbM7 Am7b5 D7 Gm7 Gm7
Am7b5 D7 Gm7 Gm7 Cm7 F7 BbM7 EbM7
Am7b5 D7 Gm7C7 Fm7Bb7 Eb7(#9) D7 Gm7 Gm7
Return from Gaul
Approaching a cold and mist wreathed English channel from a hot and sunny France, I was reminded of the writings of the 6th century historian Procopius concerning the island of Britain-
“They imagine that the souls of the dead are transported to that island. On the coast of the continent there dwell under Frankish sovereignty, but hitherto exempt from all taxation, fishers and farmers, whose duty it is to ferry the souls over. This duty they take in turn. Those to whom it falls on any night, go to bed at dusk; at midnight they hear a knocking at their door, and muffled voices calling. Immediately they rise, go to the shore, and there see empty boats, not their own but strange ones, they go on board and seize the oars. When the boat is under way, they perceive that she is laden choke-full, with her gunwhales hardly a finger’s breadth above water. Yet they see no one, and in an hour’s time they touch land, which one of their own craft would take a day and a night to do. Arrived at Brittia, the boat speedily unloads, and becomes so light that she only dips her keel in the wave. Neither on the voyage nor at landing do they see any one, but they hear a voice loudly asking each one his name and country. Women that have crossed give their husbands’ names.”