Introducing the C3663 Pentatonic Parallel Scales

Example 3663 Tonality composition in C. Details and playable link below.

Introduction: The C3663 Pentatonic Parallel Scales provide an alternative set of notes that can be used to compose melodies (note sequences), chords (sets of simultaneous notes), and cadences (sequences of chords) for compositions expressed within an overall tonal feel. The use of 5-note instead of 7-note scales can result in pleasing new compositions especially when adding techniques of using parallel scales together.

Basics: The C3663 Pentatonic Parallel Scales consist of two 5-note scales each starting on C. The minor scale starts on C and goes next to Eb (3 tone interval). The major scale starts on C and goes next to Gb (6 tone interval). Both scales continue with A, Bb, and B. They repeat beginning at octave C’. Here are the C3663 Pentatonic Parallel Scales:

ScaleScale Tones
C36 Pentatonic Minor C Eb A Bb B
C63 Pentatonic Major C Gb A Bb B

Theory: C36 and C63 are parallel minor and major pentatonic 5-note scales. Written in tone (pitch) notation they are C Eb A Bb B and C Gb A Bb B. Written in interval (pitch difference) notation they are C36111 and C63111. C36 is minor because its first characteristic interval is smaller (3). C63 is major because its first characteristic interval is larger (6). C is the root tone of both scales, Eb and Gb are the modes, A is neutral, and Bb and B are active. Bb is active because it immediately follows neutral A. B is active because it immediately precedes root C.

Comparison: C36111 and C63111 are analogous to the C minor and C major parallel minor and major diatonic 7-note scales. Written in interval notation those scales are C2122122 and C2212221. That they are minor and major can be seen by reexpressing them as 5-note scales C34122 and C43221. For those scales C is the root, Eb and E are the modes, G is neutral, and Ab and B are active.

Mirror Scales: C36111 and C63111 are mirror reflections of each other as can be seen by reexpressing them as C36111 <=> C11163. Continuing the comparison, C minor and C major are also mirror reflections (C34122 <=> C22143).

Negative Harmony: Mirror reflection is also called Negative Harmony. A note or chord selected from a minor scale can be reflected to a parallel note or chord in the parallel major scale.

Here are the C36111 and C63111 5-note scales shown using Negative Harmony where C reflects to A and back, Eb to Gb, and B to Bb:

C root
B active
Eb mode
Gb mode
Bb active
A neutral

Continuing the comparison, here are the C minor and C major 7-note scales shown using Negative Harmony where C reflects to G and back, Eb to E, and B to Ab. (D to F and Bb to A also reflect though they have no labeled function.)

C root
B activeD
BbEb mode
AE mode
Ab activeF
G neutral

Tonality/Borrowing: A note, note progression, chord, or chord progression can be written using a) only the minor scale, b) only the major scale, or c) both. Using chords from both scales together is called borrowing. A composition using both minor and major scales and their chords can be said to be written using their full tonality.

Tonality Benefits: Using minor and major scales together gives additional note (melody) and chord (cadence) options for writing songs while staying within an overall tonal feel. C36111 and C63111 have 5 notes each—together they have a total of 6. C minor and C major have 7 notes each—together they have 10. C36111 and C63111 have 3 trichords each—together they have a total of 10 (see table below).

Pentatonic Parallel Scale Motivation: The original motivation was to have a set of notes with which to compose tone sestets where, in each composition, six (6) musical expressions would be separated by five (5) musical spaces. This motivation has since been extended.

Chords: The use of trichords can be extended to include 2-tone intervals:

ScaleScale TonesChordsChord Tones
C36111C Eb A Bb BC36
A24
Bb23
C Eb A
A B Eb
Bb C Eb
C63111C Gb A Bb BC63
Gb42
Gb32
C Gb A
Gb Bb C
Gb A B
CombinedC Eb Gb A Bb BC33 (Cdim)
Eb33 (Ebdim)
Eb34 (Ebmin)
B43 (Bmaj)
C Eb Gb
Eb Gb A
Eb Gb Bb
B Eb Gb

Chord Functions: The use of trichord functions can be extended to include ambivalence:

Note TypeChord TypeEnergy
Root and/or ModeTonicRest
No Mode + No ActiveSubdominantFloat
No Mode + ActiveDominantUrge
Root and/or Mode + ActiveAmbivalentClash

Cadences: The use of cadences (chord sequences) can be extended to include ambivalence, statence, and driftance:

Chord SequenceCadence TypeMovement Energy
Ton-TonStatenceRest=>Rest
Sub-TonIndirect CadenceFloat=>Rest
Dom-TonDirect CadenceUrge=>Rest
Amb-TonHalf StatenceClash=>Rest
_-SubDriftanceAnything=>Float
_-DomHalf CadenceAnything=>Urge
_-AmbAmbivalenceAnything=>Clash

Additional Scales: Here are eight identified-to-date penatonic parallel scale mirror pairs and their tonalities:

TonalityScalesNumber of TonesNumber of Trichords
C2772C27111
C72111
C252111
5
5
6
2
2
4
C3663C36111
C63111
C333111
5
5
6
3
3
4
C2662C26112
C62211
C2421111
5
5
7
3
3
6
C2332C23331
C32133
C21212121
5
5
8
7
7
18
C3443C34113
C43311
C31311111
5
5
8
5
5
14
C4554C45111
C54111
C414111
5
5
6
3
3
0
C2442C24411
C42114
C22211211
5
5
8
4
4
14
C2552C25122
C52221
C23211111
5
5
8
5
5
14

Transposing: The C3663 Pentatonic Parallel Scale Tones and Chords can be moved up or down in pitch to start on / be associated with a different root tone.

Example Composition: Fresh Water 3663

Fine Print: This post summarizes work and studies by James G Neville / Sitearm Madonna over the last 20 months. Adaptations and extensions of traditional music theory topics and notation as expressed in this post and associated scores are mine. Comments, questions, corrections are welcome.

Recenter

Morning Aire

Morning Aire
Two people meet in morning walk
And greet the sun in stately waltz.
They tell their news with twirling steps
And part with friendly greetings.

Compassion

Morning Mantra

Shadowed

Dream