Although Changed, I Arise the Same (The Spirituality of Spirals) by Calum Builder

Although Changed, I Arise the Same (The Spirituality of Spirals) is a personal artistic exploration into the artist’s shifting context & practice derived from the utilisation of spiral formations in the creative process. Originally conceived as an intervallic system based on spiral formations, this project evolved to encompass an investigation into the metaphorical and conceptual implications of spirals. This is a different form of a system — one not built on intervals but on swirling water & howling winds. It is a story about shifting from the concrete & practical to the abstract & conceptual. It explores how, where & why I utilise spiral formations. Yet, more pertinently, it discusses how working with spirals redefined my own artistic context. A spiral became a symbol that transcended inspiration. It became a form of spirituality.

Although Changed, I Arise the Same

Polymorphic Shapes and Spiralic Patterns (PSSP) is an intervalic and harmonic system designed to be utilised as a compositional and improvisational device in specific regards to the development of pitch material. What are the characteristics specific to a spiral? A spiral is a cycle that augments or diminishes upon each revolution- moving clockwise or anticlockwise with a rate of expansion/contraction that increases or decreases.

This system originated from an extensive investigation into Nicolas Slonimsky’s ‘Thesaurus of Scales and Melodic Patterns’ ten years prior. At its core ‘Thesaurus of Scales and Melodic Patterns’ is about cyclic intervals.  The fundamental is ‘how many times is an interval repeated before it reaches the same starting note?’.  Below is an elaboration on PSSP, beginning at a similar place as Slonimsky’s work.


Within our equal-tempered system, every interval has a natural cycle.
I have listed them all in ascending pitches:

The octave is the fundamental — a 1 note cycle (eg. C1 - C2).
The semitone is a 12 note cycle, going through all 12 notes.
The Whole tone is a 6 note cycle, moving through the whole tone scale(eg. C1 D1 E1 F#1 G#1 A#1 C2)
The Minor 3rd is a 4 note cycle, a diminished chord (C1 Eb1 Gb1 Bbb1 C2)
The Major 3rd is a 3 note cycle, an augmented triad (C1 E1 G#1 C2)
The Tritone is a 2 note cycle (C1 F#1 C2)

 
From here on we move past the 1-octave cycle and move into the division of multiple octaves into equal parts

Minor 6th divides 2 octaves into 3 parts (C1 Ab1 E2 C3)
Major 6th divides 3 octaves into 4 parts (C1 A1 Gb2 Eb3 C4)
Perfect 4th Divides 5 octaves into 12 parts it is the first interval again to have a 12 note cycle C1 F1 Bb1 Eb2 Ab2 Db3 Gb3 B3 E4 A4 D5 G5 C6)
Minor 7th divides 5 octaves into 6 parts (C1 Bb1 Ab2 Gb3 E4 D5 C6)
Perfect 5th divides 7 octaves into 12 parts (C1 G1 D2 A2 E3 B3 F#4 C#5 G#5 D#6 A#6 F7 C8)
Major 7th divides 11 octaves into 12 parts (C1 B1 Bb2 A3 Ab4 G5 Gb6 F7 E8 Eb9 D10 Db11 C12)

 (The Spirituality of Spirals)

In order: 
Semitone - Whole tone - Minor 3rd - Major Third - Tritone- Minor 6th - Major 6th - Perfect 4th - Minor 7th - Perfect 5th - Major 7th

We can also group the intervals as such as:

Semitone, Perfect 4th, Perfect 5th, Major 7th (equal division into 12 parts)

Whole tone and Minor 7th (equal division into 6 parts)

Minor 3rd and Major 6th (equal division into 4 parts)

Major 3rd and Minor 6th (equal division into 3 parts)

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Tritone (equal division into 2 parts)
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Octave (1 part)
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With this reordering of the intervals, and grouping them together I began making shapes out of the cycles, and patterns (for example scales). Breaking them into three categories:

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Equal Symmetrical Shapes
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Unequal Symmetrical Shapes
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Unequal Asymmetrical Shapes
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1). Equal Symmetrical Shapes

Triangle Cycle Major Third or Minor 6th. Splitting an octave into three equal parts

C1  E1 Ab1 C2 (Major 3rd) or C1 A1 Gb2 C3 (Minor 6th)

2). Unequal Symmetrical Shapes

Made up of a cyclic/symmetrical intervallic structure utilising more than one interval.  
Eg. A Symmetrical Octagon.  In this case, the Octagon represents the Diminished Octatonic scale

C - D - Eb - F - F# - G# - A - B - C which uses a cycle of Whole Tone Semitone cyclic pattern. Another Shape is a Septagon representing a C melodic Minor b9 heptatonic scale (using a ST-WT-WT-WT-WT-WT-ST Cycle)

3).  Unequal Asymmetrical Shapes

For example a Minor Pentatonic Scale C - Eb - F - G - Bb - C

(an unbalanced makeup of intervals Min3rd - WT - WT - Min3rd - WT)

I combined the shapes into different octaves (right).

The four main ways I utilised PSSP in my compositions and improvisations were:

1). Reordering of Intervals

As listed above, reordering intervals according to their full cycle m2/M2/m3/M3/Tritone/m6/M6/P4/m7/P5/M7. Utilising pitch sets to create compositions and improvisation that intervallically expand and contract (specifically in three to four part harmonies).

2). Multi-Octave Uneven Scales
Scales that are based on three types of shapes: equal-symmetrical, unequal-symmetrical and equal-asymmetrical shapes. Scales that span more than one octave, or only use smaller portions than an octave (2/3rds of an octave).

3). Scales Based off Dividing Octaves into Different Parts (sometimes symmetrical, sometimes equal, sometimes equal and symmetrical)
I utilised this aspect for tonal material when I developed my piece Messe. Dividing three octaves into seven - where I arrived at this intervallic set C- Ab - A - F - F# - Eb- E (m6-m2-m6-m2-M6-m2). Throughout the Messe the tones are presented in several ways. Firstly as a scale: C-Eb-E-F-F#-Ab-A and secondly in Major 7 groupings (E-Eb is the first set): E F# A C Eb F Ab (B is the next in line).

4). Spirallic Sequences from Pre-existing Systems
Taken from a pre-existing pattern [eg. Fibonacci sequence (1,1,2,3,5,8,13,21,34,55,89...)] (see figure on the right) 1= Semitone, 5= Perfect 4th. All numbers were organised into a 12 note cycle- (13 = octave + semitone). The Fibonacci sequence creates a perennial 24 note intervallic set: C Db D E G C G# A F# A E B E E A D C Eb E G# Db Bb C B C.

(below)

Part I: Practical Part II: Metaphorical Part III: Conceptual Th e Reconstructed Organ Appendix (PSSP)

Appendix

Home About Me Introduction Considerations Time Spiral Projects Final Concert

There are ulterior motives for this system too —it has the added benefit of allowing me to compose in the moment, providing an opportunity to draw on particular harmonic and tonal material without hesitation. If the system presented a C major chord (eg. voiced C G E) I would not protest and legitimise the C major chord — even though I would be in doubt whether to write something like that on my own accord. However, if I vehemently dislike the quality of the C major chord then I, of course, reserved the right to change it (whether that be through voicings, tonality or just removing it entirely). I take Messiaen’s Banquet Celeste (1928) as precedence. Besides Messiaen, there were many others I took inspiration from in developing this system: Barry Guy, Ingrid Laubock, Anthony Braxton, Henry Threadgill, Steve Coleman, George Garzone, John Cage, Karlheinz Stockhausen.

Polymorphic Shapes & Spiralic Patterns

¹ In Banquet Celeste, Messiaen ‘breaks’ his system in the 2nd bar.

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