Restarting Pitch Space

Originally developed by Carson Cooman in 2005, Restarting Pitch Space is a modal harmony system that uses fragments of a scale to generate an extended “pitch space” for use in a composition.

The pitch material is completely and exclusively defined by a chosen number of initial notes of a mode/scale transposed again and again. The ending note of one fragment becomes the starting note for the fragment’s next transposition. Thus the notes available in any given register are determined and prescribed. The importance (difference) of this system from other modal methods is that the register of the pitch is important. One thus has different inflections in different octaves—e.g., a G natural in one octave and a G# in another.

In a sense, what is created is a kind of “super mode” across many octaves. Unlike a typical mode (or other pitch generating methods, such as traditional 12 tone technique), the mode goes across more than just 12 notes, because of the variants in register. (The mode is thus not octave equivalent.)

This PDF shows an example of a Restarting Pitch Space. It begins on a low C with the first five notes of the Lydian mode and then is written out for four octaves. As one can see, the 5th note (G) is both the end of the five note fragment of the Lydian mode, and then begins the start of a second five note fragment. The process continues across the entire four octaves.

The total pitch material for the piece/section is then defined by those pitches in the registers in which they appear.

There are obviously a great number of Restarting Pitch Spaces possible: both by using different modes (the traditional modes and invented/synthetic modes) and by using different fragment lengths. Mixed modes and stratification are also possible, especially in works that employ a large registral space.

A key principle and result is that a given pitch in a given register is never inflected differently (e.g., that particular G# in that given register will always be G#, never G natural or G-flat).

The intended result for a composition using RPS is a combination of audible consistency mixed with freedom, within a modally-derived language. Audible consistency, because the modal fragments/scales result in specifically heard patterns occurring in the different registers in different transpositions. Freedom, because the resulting harmonic and contrapuntal language produces many combinations that are non-traditional.

(Special thanks to Tom Johnson, Carlotta Ferrari, and the late Arnold Rosner for their comments on RPS in development.)

An Italian site devoted to RPS can be viewed here.

Example works composed employing RPS methods

Carlotta Ferrari
Ricercata sopra le trasposizioni lidie (2016; organ)
Toccata e fuga sulle trasposizioni frigie (2016; organ)
Toccata phantastica super transpositionem ionicam (2016; organ)
Preludio, cavatina e saltarello (2016; organ)
Florilegium modalis (2016; organ)
Tre passacaglie RPS (2017; organ)
Introduzione e passacaglia RPS (2016; organ)
Monodie per organo (2016; organ)
Triptych of Peace (2016; organ)
Trittico sulle trasposizioni misolidie (2016; organ)
Ricercare in epidiapente (2016; organ)
O ignis Spiritus paracliti (Fantasia per organo) (2016; organ)
Il sacro cuore di Gesù rivelato (2016; organ)
Three Trumpet Tunes (2016; organ)
Lady Frankenstein (2016; organ)
Trittico della Trinità (2016; organ)
David (Ricercare per organo) (2016; organ)
Tre preludi e fughe RPS (2016; organ)
Ceremonial Suite (2016; organ)
Corali RPS (2016; organ)
Historia Gullielmæ (2016; organ)
Ricercari pro diebus hebdomadis (2016; organ)
Paolo della Croce (2016; organ)
Pastorali RPS (2016; organ)
Benedictus (Rapsodia per organo dopo il terremoto di Norcia) (2016; organ)
Drone Triptych (2016; organ)
Rapsodie a colori (2016; organ)
Maria Restituta (2016; organ)

Profondissimi affetti (2016; viola da gamba)
Quatour RPS (2016; saxophone quartet)

Camille (2017; organ and string quartet)

Veni sancte Spiritus (2016; SATB chorus)
Innario RPS con preludi all’organo (2016; SATB chorus and organ)
Karitas habundat (2016; 2-part voices)

Fantasia di collaborazione (2016; organ) — written in collaboration with Carson Cooman as an “exquisite corpse”

and many other Ferrari compositions from 2016 onwards


Carson Cooman
Ricercare in epidiatessaron
(2016; organ)
Aria RPS (2023; organ)
Pastorale RPS (2023; organ)
Postlude RPS (2023; organ)