String quartet in the woodshed

In the March 4 Blog I said that ‘next time’ I’d resume the discussion of the quartet, using number 24 in the list of thirty-six 7 unit scales presented on page 122 of the book. The work was virtually complete, it’s just that I had a vague feeling of unease which, from experience, usually means trouble. Since I’m not on a time limit I could afford the luxury of giving it a rest, which I did.  

In fact, I’ll continue now. Once more I’m turning an experiment into a performable piece as I go.

The required refinements were made with the result that I have a piece of music approximately 8 minutes* long with a 24 bar introduction, two expositions of the first theme, a modulation, 14 bar bridge, 13 bar fughetta (short fugue), 17 bar fantasia, followed by an 8 bar march and finally a modulation back to the original key where the first theme is repeated. The piece concludes with a coda. That really means ‘coda’. So often the term is used to save paper.

Remember that theme does not always mean tune; it does in this case since melody, rather than rhythm, harmony, instrumental resource etc., is the principal thematic characteristic. The fughetta, fantasia and march jointly comprise the second movement. 

*If you have digital editing software you will obviously have control over timing. On the other hand, in the traditional score and band parts environment, once you have made the tempo markings (quarter note = 100 or whatever) you can count all the units in terms of which they are expressed (it might have been half note = 100), divide the resulting total temporal value by the number of units and arrive at a duration for the whole work. Round up or down to allow for fermata (pauses), rallentandos and accellerandos and remember not to skip over any time signature changes, which may or may not be l’istesso. L’istesso indicates that the ‘count’ of, say, a 4/4 tempo is followed through in the following 3/4 time signature, or whatever. L’ostesso (a term that is hardly ever used) indicates that the note value takes over the same tempo, i.e. crotchet = minim, or dotted quarter note (6/8, 9/9…..) = quarter note in 4/4 etc.

If you record your music on CD, the computer CD software will indicate the duration of the piece (as performed) in the pop-up window where you select tracks. I think everybody knows that. A composer is often asked to state the duration of a work. All we can do is offer a close estimate. A range of tempos is evident in different recorded works by the best conductors. Added to this, interpretation will affect tempo and vice versa. If someone tells you a piece was played at the wrong tempo, it’s sometimes a sign they don’t know what they’re talking about.

The introduction uses a series of motifs characteristic of the piece. This wasn’t consciously planned but after years of experience these things somehow arise naturally. The first two expositions of the theme that follows were described in the last issue. The second exposition, which ultimately featured the  solo viola (not cello as first proposed), ends with a ‘falling leaf’ pattern of diminished triads from the two violins and viola over a dominant pedal. The dominant (5th degree) of this particular scale on root C is Gb. Although the decision was made to maintain strict adherence to the tonality in order to maintain a stylistic consistency, the foreign notes arising in this succession of two different diminished chords are OK. In any case, strict parallelism can always be used in any key or mode (see below). Diminished chords can’t stand up straight. Place one on a table and it will fall over. A string of them will often occur in the passing notes situation in jazz voicings, especially in a minor key.

A brief motif followed by rotational (permed) derivatives announces the new tonality in the inverted form of the scale (see the last Blog). The short fugue that followed gave me a little trouble. In view of my claim that the book builds the analytical skills that lead to a mastery of musical materials and methods, I was dismayed by my own struggle here. Physician heal thyself. So I stopped and asked ‘why’? The answer came quickly. In a scale of fairly even intervallic structure, it is easier to control melodic lines. In the case of the current scale, an augmented second interval was constraining the way the parts could move. In the traditional harmonic minor mode we switch to the melodic minor derivative to avoid the augmented interval with alterations to the 6th and 7th degrees but we can’t do that here. That’s a limitation imposed by the choice of these unorthodox scales, where notes foreign to the scale will be perceived to be wrong.

To recap, we can use chromatics, which are tonally neutral, modulations to the same master structure on a different root or to another master structure (on the same root or another), inversions and retrograde forms. Our harmonies may also move in exact parallel motion (often equivalent to multiple unessential notes). Apart from these exceptions, we use diatonic forms. It is only by building such a firm foundation that we are able to condition the listener and make free use of certain harmonies and effects later in the piece otherwise THEY would sound wrong. Conditioning has a powerful influence on our response to works of art. The bonus of our self-imposed discipline is that we unleash an infinite amount of musical resources with sounds and textures you wouldn’t dream of. There is, as always, a trade-off.

The first voice of the fugue, traditionally called the subject, is a retrograde version of the principal theme but with durations halved, providing the animated style that is ideally suited. It just so happens that it has other desirable features such as syncopated patterns tied over the bar. Contrapuntal writing is enhanced by a lack of simultaneous vertical stresses which help it to avoid homophonic (vertical) tendencies (fugues and canons are special cases of the wider concept of counterpoint).

The sequential order of entries of the three parts in the fugue is violin, viola, cello, probably the most obvious top-to-bottom sequence. The second voice enters on the first beat of the second bar and the third voice enters half way through the same bar. This kind of variety introduces rhythmic subtlety and can be even more adventurous. The intervals between the entry of the parts is a perfect 5th (or perfect 4th if the part appears above = inverted). They can enter at the octave or any other interval. Most people know that a fugue (and canon) that changes key at each new entry is called a real one and those that don’t are called tonal. Obviously, a fugue where voices are answered in the octave will remain in the same key anyway (unless you tell it not to).

Often the intervals will be compound (octave + 5th etc.) to preserve separation of the parts but the lower voices can cross over where there is a distinct melodic advantage (i.e. there’s an inevitability that can’t be ignored).

I wanted to introduce the third voice on the last beat of the second bar to really throw a rhythmical spanner in the works but it led to an undesirable parallel that would have required an alteration in the subject. This I did not allow because the melody is a retrograde version of the principal theme and any fundamental deviation other than embellishment would seem unnatural. A fugue needs to be built like a Mercedes Benz.

I like throwing myself into situations to find out what happens. Some art theorists talk of using chance effects. David Bowie used to cut words out of magazines and shuffle them around on the table to see what he could find as a stimulant to ideas which he then developed. Artists can use found elements. Some of the graphics for an old Rolling Stones tour were done this way.

A rhythmic pattern in the second half of the fourth bar existing in the top voice is seized upon by the other voices which has the effect of introducing a new principal theme, something we often find in fugues. In all my years of writing I’d never arrived at a new theme in this way before. Because the other two voices were finishing off the scheme of things within the same bar, this new entry required more emphasis to single it out. Lacking the diversity of instruments in the full orchestra, the solution was to play the first part of the fugue pizzicato, changing to arco (bowed) for the remainder of the fugue as the new subject enters. The other violin takes over here. The entries now are all at the half bar, which gives the counterpoint a little gain in momentum, again at intervals of a 5th.

The retrograde form has now exhausted itself and reappears in the ninth bar, this time provided by the cello part, followed by the violin and, lastly, the viola. The entries, bottom-top-middle, now revert to the original time delays and are once more at the interval of a 5th.

The short fantasia that follows is decidedly less grand than those found in classical works and comprises three recurrencies of the 5 bars of harmony that the composition is based upon, each time with a different set of instrumental forms (these are examined in the book). A virtuoso violin part enters in the high register in the last set of five bars.

The harmonic structure of the original theme of the first movement is three sets of 5 + 1 (the reappearance of the tonic chord) = 16 bar sentences.

The march that follows reiterates four bars occurring in the intro, with doubled note durations and melodic figuration, transposed into the new key. The falling leaf pattern mentioned above reappears but in an ascending line, again in the present tonality, leading into the final section of the piece, involving a repetition of the original theme in the original key. The tempo is slow and grand. The amount of melodic figuration is now increased, using both notes of the scale and neutral chromatic steps.

Unessential notes of all kinds are covered in the book.

The way we add movement where, at first glance, it appears to be impossible, is to look at the harmonic sequence as a series of vertical cross sections. If there is already movement in a voice and we add similar movement in another voice (or voices) the various parts will have to form acceptable parallels (generally 3rds and 6ths and their compounds) unless we are in the raunchier jazz environment or they will be in contrary motion. Single notes in a voice may be split into two or more notes of smaller values using passing notes, auxiliary notes etc. The wider the interval between successive chordal notes, the more unessential notes we can fit in, if we so desire. Some of the ‘rules’ of voicing are in force here and we also have to be cautious about congestion in the writing where similar pitches in the octave or double octave start to get tangled up.

Where a group of voices in counterpoint are functioning as a recognizable ‘family’ we can’t add a series of sustained bass notes to get us out of voice-leading trouble. The lowest voice in the counterpoint will be perceived to be the bass.

We can also use anticipations and retardations. At one point, a note of harmony is brought forward in time by two whole beats and tied over the bar line.

It’s here that the various bowing styles and accents are used to effect. They’re different in each part, accentuating the individual movement and emphasis present at each point. Subtle nuances can be extracted that are not possible with other instruments (except the human voice).

The Coda ends the piece using distinctive fragments occurring throughout the composition. The ending features a series of triadic inversions ascending to heaven over a cello ostinato that uses the worrysome figure mentioned last time. Rimsky-Korsakov used a similar device to superb effect in **Sheherazade. He’ll be hearing from our lawyers. The upper three notes of the major 7th chord with an augmented 5th found on the 7th degree of our scale were chosen here because of the remote sound of the resulting triad. The viola goes pretty far out in its range, peaking on the Db on the second leger line above the treble clef. We have to change clefs in this piece occasionally both in the cello and viola parts. I’ve been told off for saying that cellists don’t use tenor clef very much these days. Seems that they do, occasionally.

**Most students know that the score of Sheherazade is compulsory viewing since virtually every orchestral device is used at some point.


The nature of the second key deserves further clarification. If we invert the selected triads of the original scale we get the chords F sharp diminished, E minor, B, C, and D sharp augmented. How can this be when our derivative scale is also on a C root? It is because the roots in upside down music are at the top! It’s so obvious we all miss it. We agreed last time that we wouldn’t go that route and, in any case, my second movement eventually settles into a modal derivative of the current scale producing a minor(ish) mode with E root. I noticed that, when I mentally heard a dominant inverted pedal, it turned out to be a B natural, so I went along with it and that’s how it happened. We even have a B7th as our dominant chord, exactly as grandma would have wished.

Remember that the scale under discussion has D sharp and F sharp as the signature. Whereas it was expedient to write the opening key in 5 flats and write the Bbb’s as accidentals, this time we will write in an open key and manually insert all the D sharps and F sharps.

In the last Blog we asked ourselves if we are justified in approaching music in a cerebral manner. JS Bach didn’t worry about this one little bit and he lived at a time when everyone assumed that music was a manifestation of divine messages. I hope it is. That way I won’t get the blame.

An incident happened many years ago that was partially responsible for my approach to writing. Normally, if I return to a composition after an interval, I can soon pick up the pieces. This is helped by making clear and tidy sketches and verbal notes. It’s amazing what you’ll forget.

On one occasion, I’d toiled over a section of writing and came away convinced that the ideal had been achieved. After a longer than usual delay, I returned to the same passage, toiled over it again and produced an entirely different result, again believing in its inevitability. Eventually I compared the two. The point is that, although immediacy of expression is desirable in improvised solos, (we live through the feelings of the player at his moment of discovery) our writing must avoid situations where our decisions are governed merely by what we ate for breakfast. Do we go ‘doop doopy doop’ or ‘der doopy doop doop’? Many writers haven’t a clue why they made their choice and the result can be an inconsistent mess. Our composition will be played virtually the same way every time and must therefore have a more monumental stature, like the buildings we see every day.


We’ve previously discussed the fact that band/orchestral leaders and audiences relate more easily to music where a descriptive, or programmatic concept exists. This composition is chillingly remote and melancholic. I fear we may all be approaching an apocalypse so I’ve called the piece Aftermath. It evokes images of a survivor of a nuclear holocaust picking his way through what is left of his memories, his emotions blowing from hot to cold and back again.

That should wreck the atmosphere at any party.

Woodshedding: checking the score

The work commenced seven blogs ago, where I began an experiment with the Fibonacci series as a source of chords, scales and rhythms, was put aside for a while. It’s often a good idea to do this (not always possible in commercial situations) when the process of writing begins to lose the joy of ‘discovery’ (and I don’t want to delve further into the implications of that statement here).

But there’s an extra reason.

In experimental work of this kind the familiar hierarchy of chord families and their interrelationships is lacking, a situation that brings with it the danger of producing solutions that are more constructed than created (and I don’t want to delve into that here, either).

Overall, I was pleased with what I heard in the playback from the notation program, assisted by the use of a better sound font. My claim in the book that knowledge of the control of musical resources will produce results that would not be produced by ‘blind’ intuition alone has been strongly reinforced and the effect of some passages in the composition is stunningly different.

The deletion of two x four bar bridge passages has resulted from my self-imposed lay-off. They were embarrassingly twee, heard with my fresh ears and, in any case, the piece flows better without them.

Annoyingly, checking the extracted band parts revealed omissions and errors in the score, which had already been checked through. With more complex scores, especially for full orchestra (as this one), it makes sense to leave the final print out of the score until last, checking parts against the pencil-corrections and making further corrections on the way. Second generation amendments can be marked in a different colour.

There were cases where sections of the orchestra did not have beginning or ending dynamics. There were also cases where the instruction for the strings to play without vibrato, or pizz., had not been cancelled and one situation where the horns, which had been muted, were not asked to play open. Nothing life threatening, but we’re aiming at a high standard of presentation. My methodically ticked-off quality control check-list is proving itself!

Although separate parts are provided for each player, the clarinets, flutes, horns, trombones, bassoons and trumpets have one stave per section to save vertical space and arrive at a generous print size. Opposite tails were only used where the rhythm of each part is different. Hand-editing will be needed in the extracted parts. I don’t like combined voices in band parts.

The first violins are split (divisi) into double 3rds at one point, requiring the two sets, with their differing rests, to be combined on one stave using the ‘voices’ provided in the program. These are independent ‘layers’ that can be selected for individual treatment. The two lots of 3rds are divided between left and right desks, in the conventional manner. An added complication is that the septuplet run-ups to the sustained note, in thirds, overlap and then end on a trill. The second (answering) septuplet occurs under the trill, in thirds, already being played by the first part. I was unable to control the sound of the trill with sufficient detail in my program, so the effect had to be written in full notation, which stretched my skill, and the program, to the limit. The integrity of the layers isn’t up to the job, either. At one point, I had to input the notes an octave lower and then individually nudge them up with the direction arrows.

I wrote some conductor notes, including a mention that the open key signature in the piano part is intentional;  anything that might be useful to someone who has never seen or heard the composition before. This forms the first right hand page of the score rather like the title page of a book and turns over to the first page of music. Page 1 of the music is on the left and 2 on the right and so on.

Two columns of type side by side were chosen as the typographic layout. The two column format gives shorter line lengths. Long lines are harder to read since there’s a tendency for the eye to miss a line as it scans back to the left.

Ugly ‘rivers’ of white space can occur with justified text in very narrow columns (or ‘measures’), running down vertically through the even grey of the text. Judicious hyphenation and kerning/tracking will solve the problem in most cases. The narrower the measure the more likely the problem is to arise but some typefaces, such as Times Roman, are designed especially for the narrow columns prevalent in newspapers. If you use the left aligned (ranged left) format the problem doesn’t arise.

My printer can’t handle large paper sizes but assembling the score can use one of two methods. Either print on A4 (or American letter, which  is shorter and fatter) and then enlarge on a photocopier or print out in a horizontal (landscape) format and tack the top and bottom halves together before copying same-size. Enlarging will not cause quality issues with the final image where 600 dpi resolution (or better) is used.


Some orchestral parts extend to 3 and 4 pages, so the parts had to be edited to ensure that a rest, or compressed group of rests, allowed time for players to turn the page. In some cases this left a half page or more of blank space.  With some instruments, the part begins on the cover and turns over to a double page centre spread and in others the V.S.* is at the end of the right hand page, with a continuation on to the back. The string parts are double pages front and back.

Sometimes this rearrangement of the flow of bars just can’t be done so a third page has to be taped to the double page. This is often the case in rhythm section parts in jazz arrangements where there are no bars rest or their duration is too short to allow time to turn over. I don’t like taping published parts together if I can help it but this has to be judged alongside my desire to produce good, generous sized, legible parts. Years ago I attended a Stan Kenton concert in my home town and clearly remember the bassist cleverly man-handling a part that must have been ten feet long.

*V.S., literally translated, means ‘turn over suddenly’ but the marking is often used as a convenient abbreviation.

Woodshedding II

The previous blog dealt with using number 24 in the list of thirty-six 7 unit scales, presented on page 122 of the book, as the basis of a composition. Once more, an attempt has been made to turn a technical exercise into a reasonably performable piece.

We wrote out the chords of the ‘key’, made our selective choice, wrote a progression with melodic figuration of chordal notes and composed a melody.

Because of the intonational range and dexterity of the piece and the lack of rests, I’m more and more inclined to write for the relatively tireless string quartet, something I definitely had not planned for.

Playing around with figures, instrumental forms etc., has provided the material for what has turned out to be a lengthy introduction. That wasn’t originally planned for either. When the melody proper enters, it’s all the more effective. This is a good example of advice given in the book being put to practical use. We learn to stand back, only committing ourselves at the correct moment. With experience, you’ll know.

The continuity (last blog) featuring melodic figuration of harmony is the first exposition, followed by a solo cello with accompanying violins playing undulating arpeggiated patterns in thirds. The unusual tonality gives the thirds an intriguing quality. They are in 16th notes to avoid unfortunate parallels and other correlation problems with the cello melody. With sufficient difference in rhythmic activity, anything will go with anything. This comment is not made to suggest the use of cheap tricks, but to establish a principle. Realizing this will help to overcome what I call two dimensional thinking and the disjointed, gappy orchestration that results. You can’t duplicate some orchestral techniques at the keyboard (overlapping instrumental sections etc.).

It would be possible to ‘engineer’ the violin figures to work using 8th notes, or some other rhythm, without conflicting with the cello melody but this would cause the backing to begin to acquire the attributes of a featured element. The regular anonymity of the chosen method is better, especially this early in the composition.

The link between the two expositions of the melody is interesting. The three lower voices drop down to the dominant chord (which is not a ‘dominant 7th’, remember, in our chosen scale). Simply taking all voices down in parallel turned out to be crude and obvious, with ugly parallels, so the bass drops down scalewise and the other two notes of the triads reciprocate: 3rds connect with 5ths and vice versa, the bass being allocated root = constant to arrive stepwise on a sustained chord in root position. This creates a different sequential pattern in each of the upper two voices that I like, one of which has already cropped up again in my later sketches. The ‘device’ ends on a low minor triad in open harmony (I had to choose the correct starting point to end up where I wanted to be) and the top voice enters using the upper chordal functions of the 13th master structure as a descending arpeggio. The two strata produce a Gb minor natural 7th with an F minor 7th on top (if both chords share the ‘f’ in the middle). These two chords are next played sequentially in the middle register using a triplet form. The sense of musical ‘belonging’ this creates surprised even me, and I wrote it. The bass then drops again, echoing the ‘Fm7’ arpeggio form above, to lead into the second exposition from the solo cello.

I’ve also noticed something else rather cute. Every chord contains either Ab or Bbb (=A) so I wrote a repetitive, worrysome device using only these two notes that carries on relentlessly through the harmonies, each note becoming chordal or non-chordal in the appropriate place. This is done by ensuring that the rhythm gives a greater (total horizontal) duration value and emphasis to the chordal note than to the non-chordal one. There aren’t enough instruments in a quartet to use both this device and the melody against the 3 part harmonies but it can be used with the instrumental forms derived from the harmonies (the thirds mentioned above, arpeggiated bass line etc. etc.). 

I couldn’t resist trying out a retrograde version of the melody, but in the tonality of the inverted form of the scale, which features a key signature of D sharp and F sharp, starting on a C root. This will give the computer another headache. Is life never simple? The contrast in tonality (modulation) is very satisfying and a 3 voice fugue is taking shape as a second movement. I say ‘movement’ for lack of a better term because the music will probably move seamlessly from one place to another. There are variations, of a simple nature, and imitations are also creeping in, but not of the prolonged, cerebral kind.

The retrograde melody works very well, which isn’t always the case, without fine tuning of the rhythms. Conventional thinking uses a predominance of conjunct patterns where the longer note values come first (dotted groups etc.). The converse involves a predominance of disjunct rhythms. Nothing wrong with that, really. It seems strange for the same reason that a colour negative seems strange after prolonged exposure to positive images throughout our lives.

I’m also happy with some simple variations and patterns in the new ‘key’ that sound freshly different and will be used as link material. (Although I’ve placed the word ‘key’ in inverted commas, my scale has just as much right to be called a key as any other.)

A reminder here that to find the inverted form of a scale we write out its ascending form numerically with regard to its intervallic structure, 1=semitone 2=tone etc. Our chosen scale has the following structure: 1221213. We then write the series backwards and use it in ascending order. Strictly speaking, we should start at the top and work down from left to right since upside down music is, well, upside down. The roots are at the top! My advice is not to think anymore along those lines because of our up-down/north-south orientation and the overwhelming influence of gravity (something else we haven’t a clue about yet). The harmonic series, which has its fundamental tone at the bottom, also affects the acceptability, or otherwise, of the position of the various chordal functions in orchestration.

I made an exact (‘real’) inversion direct from the original progression. A rhythmically compressed (very short note values) version of the resulting three part harmonies produces three horizontal motifs (each of the voice lines) that I’ve played around with using ‘rotation’ forms. This involves repeating the motif, beginning on each successive note in the series until you exhaust the process. The motifs are eventually combined vertically in an acceptable distribution, quite different to the original harmonies (I won’t enlarge on this since every case will be unique – learn by doing) and come to rest on what we would call a diminished chord, which happens to be common to both the keys we’re using. Now that will be useful.

Often, an inverted chord progression will require us to rearrange the voices to achieve an acoustically satisfactory solution. It’s still the same progression, essentially.

While we’re on the subject, does anyone know of a music notation program that allows customised key signatures? I only have hands-on experience of two programs. It does everything else I need and I’ve never been inclined to switch tools because of my own shortcomings.

The signature can be inserted as a text object or graphic but I always have to paste this onto the master copy. The accidentals then all have to be inserted or cancelled out manually, a method which takes time and is prone to errors. The first part of the current composition can be written in 5b’s and the Bbb’s put in manually (on a C root). But what about this new key, with D sharp and F sharp? I’m not trying to turn base metal into gold, I’m just writing music.

Having said all this, on second thoughts, since we’re all conditioned to reading orthodox signatures, perhaps it’s simpler for all concerned to stick with them and write in the accidentals.

Once more, questions will be asked about the topics under discussion. Should we approach music in this way? What about ‘creativity’? Are these methods too cold-blooded and mechanical (especially for jazz)? Etc. etc.

I have definitely (that means absolutely definitely) found that the techniques we have been discussing always (=always) lead, directly or indirectly, to results that are freshly different and represent an excellent method of jetting yourself out of the tyranny of well-worn clichés. It really is like going on vacation. You don’t have to accept any result as inevitable although you may have to avoid the temptation to reject music just because it sounds a little eccentric. There will always be a reluctance to accept the ‘new’ because it threatens familiar habits and anything that does that disturbs our sense of security. On the other hand, if you look at the guys who are doing OK (nowadays that primarily means making money) you will find that they understand the need to write in a style that is easily assimilated and trendy. They understand the consequences of leaving the public behind.

The choice is yours.


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. Once more, computers don’t provide the facility of unusual key signatures. It will 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, 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 merely 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, temptingly placed a mere semitone away. 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 (all tending to be referred to as ‘passing notes’ by jazzmen). Because of the tied notes there are 2, 3 or 4 ‘attacks’ in each bar. The two attack patterns will most likely involve chordal notes (including extensions of each chord, 9ths, 11ths and 13ths) whereas the bars with 4 attacks will be more likely to feature unessential notes. With a little patience I’m able to devise a melody that flows, without awkward leaps. In keeping with the spirit of the book it has to be pointed out that a writer may require awkward leaps at some point. You do? Well go for it and make it work.

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. Once the basic transformations have been carried out, voices retain their original path through the harmonies when the chords are expanded but we can’t always guarantee things will work automatically. For example, a string of second inversions in a conventional setting produces 4th intervals between the middle voice and the bass although the first inversions work fine. I’ll also have to ensure I don’t take notes too low, acoustically. Page 40 in the book explains this. For example, the lower limit for the 7th is the Bb on the second line of the bass clef. (Incidentally, I didn’t use the number identification here because of the lack of standardization).

Having said that, textured results can be achieved with notes of short duration when this ‘rule’ is broken, especially when using instruments that naturally possess a good low register.  

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…