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November 19, 2019 — SitearmIntroducing the C2772 Pentatonic Parallel Scales
November 13, 2019 — Sitearm
Introduction: The C2772 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 C2772 Pentatonic Parallel Scales consist of two 5-note scales each starting on C. The minor scale starts on C and goes next to D (2 tone interval). The major scale starts on C and goes next to G (7 tone interval). Both scales continue with A, Bb, and B. They repeat beginning at octave C’. Here are the C2772 Pentatonic Parallel Scales:
| Scale | Scale Tones |
| C27 Pentatonic Minor | C D A Bb B |
| C72 Pentatonic Major | C G A Bb B |
Theory: C27 and C72 are parallel minor and major pentatonic 5-note scales. Written in tone (pitch) notation they are C D A Bb B and C G A Bb B. Written in interval (pitch difference) notation they are C27111 and C72111. C27 is minor because its first characteristic interval is smaller (2). C72 is major because its first characteristic interval is larger (7). C is the root tone of both scales, D and G are the modes, A is neutral, and Bb and B are active.
Comparison: C27111 and C72111 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: C27111 and C72111 are mirror reflections of each other as can be seen by reexpressing them as C27111 <=> C11172. 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 C27111 and C72111 5-note scales shown using Negative Harmony where C reflects to A and back, D to G, and B to Bb:
| C root | – | ||||
| B active | D mode | ||||
| – | |||||
| ⇑ | ⇑ | ⇑ | – | ||
| ⇓ | ⇓ | ⇓ | – | ||
| – | |||||
| Bb active | G mode | ||||
| 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 active | D | ||||
| Bb | Eb mode | ||||
| A | E mode | ||||
| Ab active | F | ||||
| 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. C27111 and C72111 have 5 notes each—together they have a total of 6. C minor and C major have 7 notes each—together they have 10. C27111 and C72111 have 2 trichords each—together they have a total of 8 (see table below).
Pentatonic Parallel Scale Motivation: The original motiviation 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:
| Scale | Scale Tones | Chords | Chord Tones |
| C27111 | C D A Bb B | C27 (=A32/C) A23 | C D A A B D |
| C72111 | C G A Bb B | C72 (=G23/C) G32 | C G A G Bb C |
| Combined | C D G A Bb B | C25 D52 G34 (Gminor) G43 (Gmajor) | C D G D G A G Bb D G B D |
Chord Functions: The use of trichord functions can be extended to include ambivalence:
| Note Type | Chord Type | Energy |
| Root and/or Mode | Tonic | Rest |
| No Mode + No Active | Subdominant | Float |
| No Mode + Active | Dominant | Urge |
| Root and/or Mode + Active | Ambivalent | Clash |
Cadences: The use of cadences (chord sequences) can be extended to include ambivalence, statence, and driftance:
| Chord Sequence | Cadence Type | Movement Energy |
| Ton-Ton | Statence | Rest=>Rest |
| Sub-Ton | Indirect Cadence | Float=>Rest |
| Dom-Ton | Direct Cadence | Urge=>Rest |
| Amb-Ton | Half Statence | Clash=>Rest |
| _-Sub | Driftance | Anything=>Float |
| _-Dom | Half Cadence | Anything=>Urge |
| _-Amb | Ambivalence | Anything=>Clash |
Additional Scales: Here are eight identified-to-date penatonic parallel scale mirror pairs and their tonalities:
| Tonality | Scales | Number of Tones | Number of Trichords |
| C2772 | C27111 C72111 C252111 | 5 5 6 | 2 2 4 |
| C3663 | C36111 C63111 C333111 | 5 5 6 | 3 3 4 |
| C2662 | C26112 C62211 C2421111 | 5 5 7 | 3 3 6 |
| C2332 | C23331 C32133 C21212121 | 5 5 8 | 7 7 18 |
| C3443 | C34113 C43311 C31311111 | 5 5 8 | 5 5 14 |
| C4554 | C45111 C54111 C414111 | 5 5 6 | 3 3 0 |
| C2442 | C24411 C42114 C22211211 | 5 5 8 | 4 4 14 |
| C2552 | C25122 C52221 C23211111 | 5 5 8 | 5 5 14 |
Example Composition: 2772 Trial Song Work Area – Lyric Two FINAL
Fine Print: This post summarizes work and studies by James G Neville / Sitearm Madonna over the last 18 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.
