A recent blog dealt with using a scale of notes related to the Fibonacci series as the basis of a composition, instead of the familiar major and minor scales and their modal variants. It was done in the form of a blow-by-blow account of the actual process of writing the composition, although a reasonable attempt was made to turn the ‘exercise’ into a performable piece of music.
This time I’ll follow a similar path but use number 24 in the list of thirty-six 7 unit scales presented on page 122 of the book. Again, I’ll restrict myself to strict adherence to the scale although I may decide to use inversions and retrograde forms in addition to temporary modulations (to the same scale on a different root or to another scale) and chromatic embellishment:
Because listeners don’t carry with them years of exposure to these unorthodox tonalities, I’ll needs to be careful to ensure I don’t confuse the listener (and myself). In particular, melodic figuration of harmony will use notes present in the original scale (diatonic). Chromatic figuration, featuring semitonal motion, is tonally neutral and may be used as decoration using notes of short duration. This will most likely occur in the form of development, once the sound and style of the piece has been assimilated by the listener.
On a ‘C’ root my chosen scale, in its original, non-expanded form, from the bottom up, is: C, Db, Eb, F, Gb, Ab, Bbb, plus the upper octave C. I used Bbb instead of A natural since all notes must carry a different letter name if I’m to preserve the appearance of thirds of one kind or another when I expand the scale to form harmonies (in other words they’ll all appear either on lines or spaces). I will also avoid having to change the A to Ab and back again many times over. Some computer notation programs are able to cope with unorthodox key signatures but I decided it would be expedient to use a Db major signature for the above scale and put in all the Bbb’s manually. For my sketches I can use Db and write ‘all B’s are double flats’ verbally at the top of the page. As long as we know what we’re doing that will be fine.
The first job is to explore the harmonies available to me, which I always look forward to. To do this I write the scale in its expanded form to produce a master structure tonic 13th chord (above), although quite different to the 13th chord furnished by the major scale. My choice of master structure gives me 4 minor thirds and two major thirds (but not in that order). We usually refer to 4ths as being perfect or augmented since a diminished 4th is tonally identical to a major third. Chromatic spelling is a different matter and had I used ‘A’ natural instead of Bbb I would have ended up with a diminished 4th between the A and Db. In the system of harmony we’re using, all harmonic intervals of chords in root position must be 3rds of one kind or another. (Harmony of 4ths is produced by the appropriate expansion of the original scale as discussed in the book).
The book also mentions that it’s convenient to classify all 7 unit master structures in their expanded form in terms of a 7th chord of some kind with a triad above. This is analogous to describing scales in terms of tetrachords, a practice which helps us to make comparisons between scales. I’ve lived an eventful and fulfilling life and I haven’t missed tetrachords one little bit. In this case, the master structure is in the form of a diminished 7th chord with a major triad above. There’s another reason for choosing this method of classification. When mixing different master structures within one composition (I strongly advise a maximum of three), the music will benefit if we use structures where the lower half remains unchanged while the triads differ, or vice versa. If we lived on a planet where everyone used scale number 24 of the book, who knows what might happen.
Next, I catalogue the chords existing on each degree of the original scale; all the triads, then all the 7th chords, 9th chords etc. Using jazz/pop music terminology the following 7th chords (for example) occur: diminished 7th, major 7th, minor 7th flat 5th, minor 7th, minor chord with natural 7th, dominant 7th, augmented natural 7th. These are numbered 1 to 7 for reference purposes:
We’re about to enter another ‘dimension’. Because the traditional hierarchy of harmonies and their interrelationships doesn’t exist, I have to find another way. The most obvious step is to make a selection of chords I like the sound of, using chords that are not too similar in flavour. I chose chords 1,2,4,5,7 but used in the order 1,2,5,4,7 to decrease the obviousness of choice and hopefully increase plasticity. We’re at a stage now where anything might go!
Using unorthodox scales, chords will occur that are too dissonant for many people but, in the spirit of the book, we’re not here to judge, merely to advise. It will also be pertinent to remind ourselves that the chords in common use in popular music, denoted by chord symbols, represent a small part of musical resource as a whole.
The next consideration is the frequency each chord occurs and its temporal duration. These factors govern the predominance of a chord or chords, which will also affect the style of the music.
Our tonic chord is a diminished 7th and our dominant is a minor natural 7th. A conventional dominant 7th occurs on the 6th degree of the original scale, so things might get tricky.
Music doesn’t have to be in the form of melody and accompanying harmonies (chord sequence) but my next move will nevertheless be to write a harmonic sequence and melodize it. Again, traditional methods won’t help me very much. The book describes how the interchange of functions applicable to any sequence of unitary combinations (such as a sequence of chords) may be used to provide the systematic ordering of harmonic transformations (voice leading) in situations where a hierarchy is absent or difficult to recognize.
I’ve made the decision to write the piece of music resulting from this discussion for a string quartet. This means that, as a starting point, I shall initially write a continuity of triads for three of the voices and write a melody to it for the remaining voice. It isn’t certain if the result will ever appear as it stands in the final piece. I’m also considering ‘presenting’ the scale and its chords to the listener at the beginning of the piece. I may do this by playing the scale followed by the harmonic sequence in notes of equal duration. This will establish the tonality in the ears of the listeners and make it easier for them to assimilate the music. Serial composers used to do this, too, by setting out the tone row.
Once this is done the melody will receive my attention. Yet again, I’m in the wilderness, so I write a melodic rhythm using the techniques for the serial development of rhythmic patterns presented in the book. Melodies will benefit, above these rather saturated harmonies, if they’re relatively inactive. My initial attempt is too active so I simply doubled the note values. This seemed an easy way out but I had to admit I was happy and decided not to write another rhythm just for the sake of it. The original is put on one side for almost certain use at some point in the development of the music.
Now I have to consider the intonations of the melody. In order to maintain some kind of order, the next note up from each triad (a 7th of one kind or another) is placed above each chord on the first beat of the bar to be used as melodic axes. This may appear to be unduly restrictive but the melodic rhythm ensures variety by providing notes on the beat and notes tied over, both retarded and anticipated, together with notes of different durations. The 7ths themselves vary, too, with major, minor and diminished 7th intervals all being present. (Remember that the diminished 7th, correctly ‘spelled’, is the same, intonationally, as the major 6th.)
These 7th intervals may not necessarily follow traditional routes. We know that the minor 7th interval present in the dominant (g – f in C major) contracts at the cadence because the 7th (f in C major) resolves to the adjacent note in the tonic triad, e.
All chromatically altered 7ths generally continue in the direction of their alteration (diminished intervals contract and augmented intervals expand). I may choose to override this and establish an inner logic by repetition and consistency that the musically aware listener will begin to recognise and respond to. The ‘dominant’ 7th type of chord on the 6th degree of our chosen scale might well behave traditionally if it precedes the major chord on the 2nd degree (Ab7>Dbmaj.7) and conditioning may drag me in this direction. The composer must be the judge. In my melody, 7ths occasionally rise or they perform delayed resolutions, ascending before finally descending. Pure, diatonic melody/harmony situations in the major key require fairly rigid adherence to classical principles but our chosen scale is a different matter.
The nature of the melody will result from the possibilities for melodization resulting from bringing together the melodic rhythm, the 7th functions at the beginning of each bar and the availability of diatonic ‘unessential’ notes. Because of the tied notes there are 2, 3 or 4 ‘attacks’ in each bar. With a little patience I’m able to devise a melody that flows, without awkward leaps, retaining the 7th as the melodic axis and using extensions of each chord, 9ths, 11ths and 13ths, and diatonic unessential notes. In keeping with the spirit of the book it has to be pointed out that a composer may require awkward leaps at some point.
After a while, the scale we’re working with becomes familiar territory and intuitive snatches of melody have been cropping up, as I go about my daily business, which are entirely consistent with the tonality.
Now that I’m happy with the melody/harmony continuity I set about inserting melodic figuration into the harmonies by using anticipations, retardations and passing notes. Open harmony, as opposed to close position, gives more space for this:
The music is already beginning to possess intriguing textures of a kind that would not have resulted from intuitive methods, where the accumulated influences of a lifetime (half remembered themes, major/minor conditioning etc.) would govern our ideas. There’s even a possibility that we can inherit these influences. Babies progress from vocal utterances to language at a pace that implies forces other than mere imitation are present. At the very least there is powerful evidence that the unborn child receives influences from the audible sounds around it.
Some of the motifs within the melodic figuration of harmony are cropping up in other voices, both identical and similar, in different octaves, giving a call and answer effect. Things are beginning to take shape and it’s at this point that composition becomes more joy and less toil. I might write out quartet parts of progress to date and get it played to inject extra enthusiasm. We all tend to think that it’s our duty to write a piece of music and present it ‘job done’ to the band. Duke Ellington’s music was great not only because he was a genius but also because he wrote on the road, in, around and for the band. Many straight pieces we admire were also re-thought and altered, I’ve absolutely no doubt. It isn’t cheating.
That’s probably enough to chew on for now. Next time I’ll delve further into the current topic, if I make good progress, that is. Right now I haven’t a clue which way to go next, that’s the truth of the matter. The next few bars are sketched out, which I’m pleased with, and there will probably be a series of harmonies leading back to the tonic and a re-statement of the tune, differently treated. As is usual with my work, I avoid a lengthy, deliberate series of variations. Been there, done that. I will probably meander my way through, casting backward glances as I go to ensure cohesion, rather than pre-plan, at least for a while.
Watch this space…