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.

Here is a link to the file on YouTube (played by the full string section):

The above audio file omits the introduction. This is the preferred format for commercial use.


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