~ Theory of Music ~

The Modus

“In my music I use a specific type of tonality based on a hierarchical modus. I use the term ‘modus' to describe the constructed scale that I use. The word modus refers to the ‘mode’ of filling the octave with smaller intervals in order to create a usable scale.

A scale is a division of the octave into smaller intervals, that provides material for all of a musical work. Throughout history and different cultures, all kinds of division of the octave have been used.

Today, in Western cultures, and for centuries already, we are most accustomed to the major and minor scales of functional tonality — a division of the octave into seven notes with a set of rules that defines the relationship between and function of harmonic chords based on those notes, as used throughout the Baroque, Classical and Romantic period (roughly 1600-1900).

From the nineteenth century on, composers have applied other divisions of the octave to enrich their compositions, at first for passages only to invoke an exotic, magical, spiritual or ghostly atmosphere (think of Franz Liszt in his later years, Nicolai Rimsky-Korsakov, Claude Debussy, to name but a few).

At the very end of the century composers started to do without a scale at all (‘intuitive atonality’), consequently leading to the development of twelve-tone techniques at the begin of the twentieth century (Arnold Schoenberg and Josef Mattias Hauer) — although the scale in these cases is, of course, all twelve (equal tempered) tones of the octave, albeit without a tonal centre. In the twentieth century we see composers use all kinds of tone systems, often very or even strictly personal.

In 1979, I developed a division of the octave into eight tones. Octatonic scales have been used before and may even date back as far as the seventh century AD (‘zar ef kend’), but these scales consist of a division of the octave into repetitive patterns of intervals, either consecutive whole-half (major-minor second) steps:

or consecutive half-whole (minor-major second) steps:

Many beautiful compositions have proven that use of these scales can be very effective (Ruslan and Ludmilla by Mikhail Glinka, Kashchey the Immortal by Nicolai Rimsky-Korsakov, Petrushka and Sacre du Printemps by Igor Stravinsky, L’Isle joyeuse by Claude Debussy, to name but a few). However, I have always found the ‘traditional’ octatonic scales to be too restrictive in mood and expressiveness to be suitable for my music. This is inherent in the way these scales are constructed: a repetitive pattern of intervals, rather than built around a pivotal note, a tonal centre.

The octatonic scale I constructed and found highly useful and effective for the music I wish to write, is very much built around such a keynote. In fact, the scale consists of notes derived from the series of harmonics on that keynote and bases the hierarchy of notes in relation to the keynote on that very sequence. This hierarchy is only relevant for the harmonic (chordal) structure since the strength of intervals is determined by its approximation to a lower and stronger, or higher and weaker, position in the harmonic series. For pragmatic reasons I use the equivalents of the equal tempered twelve-tone scale.

With c as keynote this results in the scale:

As you will notice, the c” (in brackets) in this sample feels much more as an ‘end note’ of the scale, a logical consequence of the preceding notes, than the same c” did in the previous two samples. This scale allows me to write melodies and harmonies that feel ‘right’ and natural and permit any emotion and mood I wish to convey.

Although my modus is originally octatonic, I often add the minor third to allow for an even wider range of expressiveness. The addition of the minor third makes the modus repetitive within itself — the modus has then a limited number of possible transpositions, as in compliance with Olivier Messiaen's (1908-1992) definition [Technique de mon langage musical. Paris: Leduc, 1944]. In fact, with the addition of the minor third, the modus enharmonically equals Messiaen’s third ‘mode of limited transposition‘ — be it noted, though, that Messiaen constructs this mode in an entirely different way and for an entirely different purpose. All similarity with the music of Messiaen therefor ends right here.

This nonatonic scale is repetitive within itself: the end note of the first tetrachord is the start note of the second tetrachord, the end note of the second tetrachord is the start note of the third tetrachord and the end note of the third tetrachord is again the start note of the first tetrachord. Each tetrachord is equal (transposed by a major third). In this example c’ through e’ is the first tetrachord, e’ through a-flat’ is the second tetrachord and a-flat’ through c” is the third one. Since the scale repeats itself in structure in every major third distance, the scale can only be transposed thrice: up a minor second, up a major second and up a minor third. Yet, in spite of the repetitive pattern of intervals, the c” still feels as end note of the scale and therefor as a tonic.

As such, the modus intrinsically has three tonal centers, three possible tonics within one scale: the first note of each tetrachord. This offers an incredible array of harmonic opportunities, since every harmonic progression can lead to three different targets. It is therefor quite evident that this modal system offers a sheer infinite range of expressive possibilities.

Since the modus will repeat the set of notes with every transposition of a major third (or: instances, as I prefer to name them), the modus has but four transpositions within the constellation of twelve equal tempered tones that will result in a different set of notes. The four transpositions, of course, being every chromatic note within that major third (see the overview at the end of this article).

Because of the inherent hierarchy in notes (tonics are dominant, other tones are subservient), I refer to using this scale as employing a form of ‘tonality’, in the sense that there is a clear ‘tonic’, the central and most stable note of the scale (in terms of tension) and a mandatory hierarchy of notes, which has its consequences for harmonic structure and progression. This form of tonality, however, has nothing to do with the diatonic or functional tonality. In fact, use of the modus prohibits conventional diatonic harmonic progressions — the subdominant chord and the dominant seventh chord e.g. cannot be constructed within the modus. Nonetheless, the tonal centre is evident."