16: Modulor pt.1 - M - Lectures

MODULOR + Internal Rotation, consequent vertical chords and revealed scales

(Explain the refrain and how it fits into my diagram – see Modulor Frame, Chord 1 centring on B; the use of glissandi – the 2 M scales combined create the entire chromatic; the ‘hidden’ Arabic scale (octatonic); the leaping, deduced rhythmic patterns and the sustained passage at B).

After the first limb of the refrain (sounded on horns who lead the work through its various transformations throughout), section A follows and is introductory, releasing all the types of material explored in this 28 minute composition. Section B settles on M scale 1 and centres on B, where melodic contours are coloured by pitches drawn from both the depths and heights of this scale.

Play the CD, circa the first 3 minutes. The CD has 2 tracks. Track 2 is at c. 14 minutes, more or less at the work’s centre. The high harmonics heard in the opening passages are focussed on and bowed cymbals are used to suggest higher sounds beyond the instrumental realm. Page 44 in the full score. It is circa 1 minute’s duration.

The written text appears hard going. It is much easier to follow when the MODULOR page is viewed and I play through the various points raised, at the piano.

Now, the chords that supplied the basic material for Fox and hence, the orchestral trilogy are placed at the top of this page. The outer pitches (A flat / G sharp) supply the missing pitch in a chromatic run. Chord 2 is simply the inversion of chord 1. The result is a D in both chords, placed at a different, octave level. The outer A flats have a centring minor third G A B flat. I then present this as a series. You can see that hidden in, and between the 2 chords is a scale D E F sharp G A B flat C D. It is mirror symmetrical and may well be one of the 72 scales/ragas of Indian music.

I set out the first chord from bottom to top and then cycle the intervals of the chord so that every pitch is made to relate at every level. It is also possible to read through the intervals off the initial B (tone, minor third, fourth, tri-tone, minor sixth) and place them on all the levels. Since the tri-tone above D is an A flat, it brings in to play a foreign note at that level and helps to create the octatonic scale (which itself is Fibonacci, based on 8 notes with combinations of 1,2,3,5,8 semitones). The use of the octatonic scale is common to Liszt, Rimsky, Debussy, Ravel, Bartok and Stravinsky.

The A flat is anomaly interesting and caused me to puzzle. Bartok’s “kernel” came to the rescue. His 4th Quartet, and all that came after, has been my constant guide. But it took some time to fathom. I’ll simply say kernel for now.

The list of deduced vertical chords travel through the diagram A – O, where A B C D E paired duplets are placed, always beginning on the initial B (I’m trying to set up a complete vertical structure). So: the group/letters B - F reads as a whole tone beginning on the initial B, which = C sharp, then the next interval is a minor third, but placed above the C sharp, which = E. Next is another minor third which gives us G, next is a fourth which gives us C (above the G), and a further fourth, which give us F. This is the second deduced chord.

This is the procedure throughout.