18: Modulor pt.3

Because the deduced scale begins on a whole tone, the semitone between (C) does not appear; we have to wait for the interval of a minor 13th (in the second chord) to provide that pitch.

So, some kind of knotting (like Bartok’s kernel) was required to make a viable construction, and to incorporate the octatonic scale, which clearly belongs in the overall scheme of things.

The keyboard diagram shows a solution. I have 2 Fibonacci spans which in both A and B reach beyond instrumental possibilities at this given level. I’ve chosen this level, which can fit in with chord 1. I can also make good use of an initial 1 of the series 1 2 3 5 8 13 and 21, and in both, mirror versions. This gives me a kernel lock between the series in its opposite (opposing) directions.

When Modulor chords 1 and 2 are combined, the differing scales on B bring in the problematic/interesting A.

Now by some extraordinary good fortune, the octatonic scales, locked in a minor third of semitones, all the way up and down this construction, actually do fit together in the Modulor structure. The top real note is the highest A on the keyboard for today’s examples. Almost the only one! I need the higher D and then the B flat – off scale.

The deduced first scale, the Modulor mirror and the octatonic overlaps, even in both directions (out from the central B/ D minor third) slot into place.

You can see that the patterns repeat themselves on B G and E flat rising, and on D F sharp B flat falling. Over the range of the first pair of overlapping Modulor/ octatonic scales, from B through the G to the F sharp the whole chromatic is revealed.

You can see how the initial 2 chords fit into the two octatonic, Modulor Scales.

And how the deduced scale from Chord 1 fits into the Modular scale for chord 1.

One little observation: the 3 kernel semitone groups also contain whole tone pairings, giving six related whole tones; the semitone groups combine to give the whole chromatic. It might be more obvious and helpful if I give you the more appropriate semitone groupings than those presented on the sheet. That would be: B flat, A, A flat G, G flat F E, E flat and D C sharp C natural B. Of course, that supplies all twelve semitones.

Of course, it might be possible construct a composition using every conceivable level for Modulor. For today, it is enough for me to employ just 2, based on the 2 initial chords. The entire chromatic is covered. So it is entirely possible to create linear, chromatic material, which can then run in between the two M (to infinity) scales. And thereby come closer to writing in serial mode.

To effect Corbusier’s idea of a second series embedded in the first I can either insert the 2nd octatonic mode inside the first, OR, draw in the different levels of M 1, inside each other (from either below or above, depending on the musical context: to effect a more complete chromatic, or to draw in the extremities which are beyond instrumental viability).

If we look at the Modulor page more carefully we can see that from the central B in M1, reading up the ladder (“scala” does mean ladder or stairway), we have 3 groups of 8 notes which equal 24 notes. If I pair 2 of these, including the semitone kernels we cover the whole chromatic. However, if I exclude the kernel element (using only the interval of the minor third), it takes all three scales to provide the whole chromatic – useful for me when I might be in serial mode.

If we have time, I can show how the 13 note sequence of pitches are rotated to produce new combinations which DO themselves create diatonic, modal and whole-tone segments, as well as the full chromatic. However a full and thorough explanation is reserved for Lecture 2.