Please try this at home…

The book has many ideas devoted to getting you off the beaten track. This blog provides details of a musical portrait of the gardens at the Alhambra Palaces near Granada in southern Spain, which I visited a few years ago. The composition uses an unconventional source for its melodic and harmonic material, resulting in the need for a deterministic approach until familiarity with the idiom allows things to evolve more ‘naturally’.

I’ll begin my story at the beginning.

Greek philosophers and mathematicians knew of the close relationship between mathematical ratios and natural forms and we’re all aware of the formal similarity of music and architecture, especially with extended compositions.

For example, many organic forms in nature follow the ratios of the first summation series, 1 2 3 5 8 13….., also called the Fibonacci series. (The first summation series is one of many. Look them up.)

In music, these organic forms produce an organic effect. Try it out, they really do. (For the mathematically inclined reader, the Fibonacci series has symmetrical ratios.)

So where’s all this leading? Yes, it’s a fair cop. I’m involved in a fairly cerebral course of action, at least in the early stages of my musical portrait of the gardens.

Having chosen the first summation series, I wrote out a series of pitches so that 1 = semitone, 2 = tone and so on. Starting on C this gives C Db Eb Gb B G Ab F… I stopped at the eighth note since the more remote you are the more difficult it is for the ear to recognise associations:

You will find that the range of these scales soon becomes huge. The seventh note in the above series is already two octaves and a minor sixth above the ‘root’ C, and that’s nothing.

Next, I rearranged the octave placement of the notes so they all fell within the span of one octave to produce a compressed melodic form, which I also wrote in its retrograde, inverted and retrograde-inverted forms:

I also found out which triads, tetrads and pentads I had at my disposal, arranging them in intervals of both thirds and fourths (as described in the book).

In thirds:

In fourths:

I made a subjective choice of seven structures arranged predominantly in fourth intervals which I numbered 1-7 for simplicity. Some others were too dissonant, unless that’s what you want. Chords based on fourths are reminiscent of guitar chord shapes. Already I could feel the Spanish sunshine on my face once more.

Next, I just had fun sketching out as many effects, melodic fragments, harmonic progressions as I could. Those I don’t use will go in my scrapbook. An Alberti bass version of my harmonic progression was written and divided between the violas, cellos and basses. Any melody used above will need to be very static rhythmically otherwise it might become incomprehensible. An alternative solution is to increase the rhythmic activity of the melody to the point that melody/harmony associations are no longer recognized (similar to the use of arabesque forms in counterpoint).

Simultaneous use of the original range-compressed melody and its inverted form, played by the high woodwinds and strings, using rhythmic diminution, produce hurried melodic fragments scurrying across the sky:

I mustn’t forget the percussion section. My gardens will need the glockenspiel, marimba and xylophone (if someone will loan me a van) together with harmonics and pizzicato from the strings to suggest the midday heat. The pastoral effect of the double reeds will be a must and I’ve produced some mirror inversion chords which are highly evocative of the fountains and long reflective pools surrounded by Moorish architecture. Cue the liquid sound of flutes and clarinets.

I’ll probably use melodic ‘couplings’, where each principal note is accompanied by another note below or, sometimes, above. This is a useful way of varying texture and adding colour without introducing harmonic complications. Thirds and sixths will suit the flutes and fourths might go well with the spikier sound of the double reeds. Low strings will get fifths and octaves, I think. A more exotic effect will result from using locked intervals; all major thirds, all perfect fourths, etc. Narrower intervals such as a tone can be used in a colouristic piece such as this, but not too low down in the orchestral range. Stay in the treble clef with these fellows except for very special, mainly percussive, stab effects.

My biggest problem is maintaining some structure to the piece, but I’m wondering if I need worry too much on this occasion. I might just wander around the gardens in which ever direction I please, after all, I’m supposed to be on holiday. Perhaps I’ll just ensure there’s adequate contrast between adjacent sections in terms of tone colour, range and mobility (and we don’t want excessive mobility, it’s too hot).

I might have a loose story board so that I’ll begin at night, with the twinkling stars, and move on into the dawn. There’ll probably be a crescendo as we first walk out into the gardens and the suggestion of brilliant colours and flowers bursting into bloom. The low, resonant strings will seem to be rooted deep in the soil.

At first, I thought the brass section would be in the nearest bar during this number, but I’ve decided they’ll be useful to suggest the blazing midday heat. They’ll understand.

The compressed scale is reminiscent of Arabian music, which is handy. I’ll exploit this in the opening bars with low, unison cellos and basses on their own playing a broad melody with much emphasis on the ‘minorish’ Eb and Gb. I’ve written a centrifugal form with everything going for my climax which peaks with the entire eight notes of my scale rearranged to give a sonorous vertical distribution, although still using the root C as the bass. Quite coincidentally, this big chord has a bitonal flavour.

Although absolutists regard programme music with some disdain, listeners respond to music much more readily when they can relate to the title. A composer may be forced to accept this if he or she is to avoid working in a vacuum.

What appeared to be a technical exercise has stimulated a very different style of music. A degree of cerebralism is inevitable in cases where there is no traditional hierarchy. Added to this, it will be necessary to maintain stylistic consistency by not introducing notes foreign to the scheme, unless they arrive as a result of geometric inversions, mirrors, transpositions, couplings, parallels etc. But is there really much difference between what I have described above and thinking, say, ‘I’m in E minor, right? So my dominant is B7 and most of my F’s will be sharp….’?

I emailed Lorenzo Bohme in Granada enquiring if there’s a Spanish name I might use since the title will sound better in Spanish. He kindly emailed back saying: ‘Jardines de la Alhambra. There’s no other name as far as I know. The gardens were all built in modern times so there’s no Arab name either. It’s also the title of a famous piece by Granados or De Falla, I can’t remember which.’

So the search for a title continues.

(A search online brought up loads on this region. Don’t visit southern Spain without going to the gardens, I absolutely promise you won’t be disappointed. I travelled across the surrealistic central plateau of Spain, the Maseta, with an overnight stop in Madrid. I called one of my pieces La Meseta, only to discover that it also means ‘the landing at the top of the stairs’. Kuh!)

I’m finding out that the self-imposed discipline of the material described in the last blog is pretty tight, but I’ll persevere. I did in the end choose a loose ‘storyboard’ to hold everything together. It’s OK saying ‘this is just a trip around the gardens’ but the effect of too many seemingly random sounds in sequence was creating a very disjointed and untidy result. This isn’t background music.


The piece opens with the ‘stars’ over a sustained, low, open harmony chord eight bars long from the second violins, violas, cellos and basses. Strings can provide long sustained notes by rapidly reversing the direction of bowing which can be done without a perceptible break, especially since they don’t all reverse the bow at exactly the same time. The lack of vibrato indicated on the score increases the feeling of stillness and calm. The dynamic marking for the strings is pp.  We could ask the strings to bow away from the bridge (sul tasto) to soften the sound further, or to use mutes, or both.

Stars are represented by a glockenspiel and piano in the high register. The eight note scale is split so that the piano uses one set of four notes and the glock the other four.

The piano and glock notes are subjected to serial permutations as described in the book and their figures are literally placed one on top of the other, in the same register, relying on tone colour to achieve separation. The nature of the subject also permits this due to the seemingly random distribution of the stars in the night sky. Staggering the permutation forms avoids parallel motion between the two melodic lines, which would occasionally occur in a truly random pattern.

It was originally intended to use an open key signature for the piece but this isn’t working. The notes b and c both occur in the scale I’m using, implying the need for six flats (b = c flat). The problem is that the ‘root’ of my scale is c, which insists on cropping up. Most instrumental parts would be full of accidentals in an open key so, purely out of expediency, I’ve decided on a five flats signature and I’ll write the b = c flat as an accidental wherever it occurs.

(Musician joke: when Mozart wrote a piece in three flats was it because he’d already been evicted twice?)

Two clarinets in a ‘locked’ distribution of major thirds swoop in the background, joined a couple of bars later by a solo oboe. There is something about thirds that suggests the moon. At this point, half of the first violins gather up to a divisi trill using a rapid divisi* seven note tuplet, again in major thirds, followed by the remaining first violins an octave higher. The right player at each desk customarily plays the upper notes. All the remaining strings switch to a bowed tremolo (rapid reiteration of the note) and everyone now bows closer to the bridge, which will also enhance the gentle crescendo. The chimes strike 12 on middle C, a choice of note that appears suitably unmusical in relation to the surrounding chords. C is actually the ‘key’ note, but it really isn’t that simple, as I’m finding out.

* Although ‘divisi’ (or Div.) is used in jazz writing to warn players they’re about to fan out into voiced harmonies after a passage in unison or octaves, it originally instructed string players with two parts on one stave not to play double stops. Using opposite tails should also get that message across.

After a brief crescendo the cellos and basses begin a low, brooding melody with a Moorish flavour, soon joined by a simple countermelody from the unison violas. The stars continue without any regard for melodic or harmonic associations. In colouristic effects of this kind the ear tolerates these transgressions.

Violas soon take the lead, and the cellos and basses now play pizzicato couplings in major tenths (compound major thirds). Damped harp tenths double up on the pizz. The rhythm this bass part uses is 3 against 4 but I didn’t realize that at first. Still, it will probably be useful to know. Piccolo, flutes and clarinets scurry rapidly across the sky using the compressed version of the scale in original, retrograde and inverted forms in simultaneous pairs. The violins tutti (=all) take over the melody in rhythmic diminution and accented basses, cellos, bass trombone and tuba play the first three notes of the melody in augmentation underneath. The lower strings will use vigorous down bowings to match the trombone accents. The violins end on a high F trill, splitting into octaves to add strength and the stars stop twinkling. Below them the oboe, cor Anglais and two bassoons play a diatonically parallel figure in four part harmony, the unison French horns picking up on a restless alternation of B and C that occurs automatically in a harmonic passage that will follow. These (two) bars are repeated exactly.

The lead notes of this double reed figure are very characteristic and are worthy of a brief development/re-statement from entwined oboe/cor Anglais lines, solo. A solo bassoon plays a staccato bass pattern. This is followed by a lone clarinet accompanied only by a centrifugal harp gliss at the end of its solo. Coupled flutes/piccolo (major thirds again) in diminution over a solo cello complete this miniature set of variations.

The above double reeds chords are played again but without repeats this time, since we’ve heard it all before.

Now the strings in diatonically parallel four part chords begin a centrifugal crescendo picking up from the double reeds phrases and joined by almost everyone, brass included, to signal the rising of the sun. The bass instruments descend in contrary motion. They all end on a loud chord using all eight notes of the scale arranged in a sonorous vertical distribution. Following a thinned out portion of the piece, this loud ensemble is even more striking. Boy it’s hot here!

This is where we enter the gardens which stretch out before us. The landscape is represented by a continuity in four part harmony from the strings with bursts of colour (the flowers) from woodwinds, piano, xylophone etc.

Each chord of the harmonic continuity is numbered (how else can we name them?) and the notes of the master scale omitted in each chord are identified and listed under the same numbers to form a continuity of secondary four part chords for the purpose of creating the bursts of contrasting colour. These secondary chords are treated melodically by piano, as instrumental forms (see the book) by the xylophone and as rapid flurries and chordal trills from the woodwinds.

This treatment can only be carried on for a few bars and makes way for a melody constructed (for lack of a better word) from the notes of the secondary harmonies. The active rhythms used, with short note durations, avoid actual melody/harmony associations and the possibility of a conflict with the background. I’m thinking of giving the solo trumpet this part.

I complete the solo trumpet melody and it sounds very ‘tuneful’ despite the constraints, with desirable Arab inflections. I also decide to have two instruments play the melody in ‘relays’, one muted, the other open. They are panned in the mix, one of the rare occasions I use stereo effects in my music. This gives a feeling of space since the muted instrument will appear to be further away in the musical landscape, rather like an echo. It isn’t easy to perform in relays since each instrument in turn must pick up exactly from the preceding one, mimicking the interpretation, dynamics, etc. This really is an eye-opener to anyone convinced they are playing accurately.

In the next section of the piece, the string harmony reverts back to the ‘original’ note durations but this time the lower strings play a broken harmony form, pizzicato, and the violins play a simple melody in constant minims (half notes) with a fixed level of tension in relation to the harmony background. The treatment of the broken harmony (arpeggiated form) is noteworthy. As the melodic curve undulates up and down, each section of the strings takes over in turn, according to register. When played arco (or by wind instruments) this accumulating ‘bell’ effect is much more interesting than plain unison or octaves.

The background is in four parts and the melody supplies the 5th part of the diatonic sequence of five part harmony chords. An inactive rhythm had to be chosen over such an active background since it would otherwise be impossible to avoid undesirable parallels or false relations and still produce an appealing result. Melody/harmony relationships in the orthodox sense would also be obscured by my chosen treatment of the background. This short melody is played once and then coupled, once more in major 3rds, before being used in rhythmic diminution as a ‘run-up’ to another mini crescendo peaking with the woodwinds, which then falls away again in the approach to the next movement.

I’ve felt sufficiently happy with progress to date to begin entering the music into a sketch score in order to get a better overall grasp of things. It seemed a good time to press ahead with the second movement and flesh out the first movement later. What comes next will reflect back on all previous work, it generally does. I must certainly try to use more of the orchestra more of the time. Minimalism is fine at the right time and place but I’ve noticed that the music is disjointed and requires horizontal integration.

Perhaps we all try too hard to obtain the desired result first time. The ever self-critical Sibelius thought nothing of withdrawing and rewriting a score, even after it had been performed to an enthusiastic audience. While we’re on the subject of composers, Manuel de Falla, who lived in Granada and was lucky enough to have the Gardens of the Alhambra Palace as a back garden, was an intensely private person. It’s said that even the postman didn’t know where he lived.

The second movement of my composition came ‘out of the blue’ although what was originally intended to be the theme eventually turned into an extended introduction. The melody proper has an almost Mozartian elegance and is completely diatonic (to C major) apart from an inserted chromatic passing note in the accompaniment. After the exoticism of the first movement this diatonic purity is especially refreshing. The harmonic basis turned out to be the familiar I > VIm7 > IIm7 > V7 although you would never guess this because of the simple movement of the unessential notes.

The marking of the second movement is ‘andante’ (=walking) and the music seems to suggest the urbane European visitors walking around the gardens. They were mainly German and English on the day of my visit but an uneasy peace prevailed despite the fact that England had just beaten Germany 5:1 in a football match.

I’m already thinking ahead to the third (probably final) movement which, since I chose to have a programmatic theme to the composition, will have to suggest the approach of dusk, the departure of visitors and the return of night time. Or we might have hoards of Moors caught in a time warp as they were finally kicked out of Europe, in which case I’ll write a scherzo.

The second movement of my composition is sketched out and the promised improvements to the continuity of the orchestration have been made, with a few more to come later. Just as we avoid spending hours meticulously drawing eyelashes before the whole figure is sketched, so we pull back from many detailed commitments until the composition as a whole has more or less taken shape.

The second movement is similar to the three part song form (the more developed AABA form that is used by so many standard tunes, rather than ABA). The first A sentence mainly features second violins, violas and cellos in the middle register, whereas the repeat, A2, involves all the strings, the violins playing up an octave, with added woodwind figures. This simple variation is most effective and propels the music along nicely. Occasional semitone intervals between the lower octave doubling of the melody and its adjacent harmony parts add spice and poignancy.

The minor mode variation that constitutes the B sentence comprises a minor key version of the A sentence melody (beginning on the root instead of the third, causing a modal as well as a tonal shift) moving in tenths (cellos and basses, arco) beneath an inverted dominant pedal provided by the second violins. This B sentence has now become two, the second part being in the form of a harmonic continuity featuring melodic movement in the voices played by all the strings. They stay in the middle register again, for contrast with the second sentence. The double reeds and the clarinets double up on the parts for added colour and to give a thickening of texture, combined with a natural rise in dynamics (caused by the adding of instruments, more than by a change in dynamics as such). The harmonic basis is a simple diatonic (to C minor) cycle of 5ths progression, except that the customary dominant 7th is used instead of the modal minor 7th (to use jazz terminology). Passing notes, suspensions and anticipations are used resulting in four part counterpoint which, having a strongly defined harmonic basis (which counterpoint need not necessarily have), is nicely focused to give a smooth cadence back to C major, but not before the chimes ring out 6pm on the note g, the same pitch as the inverted pedal used by the second violins a few bars earlier. (This is blatantly programmatic but it really works.) The use of the dominant pedal was a classical standard during the course of a movement, whereas the tonic pedal was often used at the beginning and/or end. The scheme is often found in jazz arrangements of the past and present. (See the free score of ‘Cool City’ in the book.)

The A3 sentence of the second movement, 12 bars in length, comprises fragmentation forms of the introduction and main theme which are literally joined together in sequence (again, it works naturally and smoothly). A coda follows which, at 23 bars in length, is almost twice as long as the preceding sentence. I have a mental picture of people reluctantly leaving the gardens and someone has to be the very last to leave. A repeated phrase, again reminiscent of the first few notes of the theme, goes major/minor/major/minor after which the horns and celeste, followed by middle register strings, respectively play an inversion and retrograde inversion of the most characteristic chords of the theme, resulting in a change of tonality each time. This, too, threatens to be far too cerebral** as described on paper, but the result is the musical equivalent of glancing back over the shoulder, as people do when they’re sad to leave. A change of time signature to 3/4 now occurs and an increasing fragmentation (disintegration) is played by muted trumpets, literally collapsing in mid air.

**(This is an example of how devices such as inversions and retrograde forms, together with, for example, polytonality, are much more successful when they are integrated into the music as a result of relevance. Bitonality can say ‘meanwhile, back at the ranch…’, or announce the impending arrival of the villain in a film or opera. Once more, there are jazz applications for you to try. The music can refer back to a characteristic phrase played by the featured soloist or announce an impending modulation a few bars before it actually happens. Don’t forget that bitonality and polytonality can be simultaneous and/or sequential.)

The base (not bass) harmony eventually moves up a semitone from C to Db, raising the harmonic tension of the unchanging melodic fragments above. We could call these melodic fragments ‘ostinato’ (=obstinate) forms. Most ostinato forms are found in the bass, but they can go anywhere we put them and can be melodic, harmonic, rhythmic, or a combination of all three. Db is the nominal key signature of the first movement, but it really isn’t that simple because of the unconventional scale used.

Compound time signatures such as 3/4 are interesting. It’s impossible to avoid associations with physical experiences around us, which evolve from one era to another. In engineering, threes, sixes, nines and twelves of anything are smoother since, when we divide the circle into equal segments, there are no points in direct opposition. (This is why six cylinder cars, especially straight sixes, are inherently smoother than fours and eights.) Of course 6/8 is a compound duple and 12/8 a compound quadruple, which means they’re hybrid time signatures with two and four beats to the bar respectively.

The truly ‘rotary’ feel of the 3/4 time signature as used in the closing bars of the second movement is reminiscent of the spinning wheel of an overturned carriage, which continues to spin until the angular momentum dies.

The final movement is still very vague and I still don’t have a title. I also hear someone at the back of the hall shouting ‘pep it up a bit, will ya!’. Why should I care? The truth is, I do care, so a scherzo or fantasia may do the trick, in which case my composition would be in four movements.

My indecisiveness regarding whether to use a 6 or 5 flat key signature caught me out, causing one or two accidentals to be omitted from the interim short score from which the final full score will be produced on computer. I had used an open signature in all the rough sketches, naming all notes manually, so it was easy to sort the mess out.

One area where I was in danger of not practising what I preach involved the question of formal considerations. Conventional wisdom is sometimes difficult to un-think and I felt obliged to follow in the footsteps of the Greats and write a 3rd movement to pep things up a little before returning to a recapitulation of the original. I was concerned that the piece required a livelier interlude but it’s important to bear in mind that a single item in a program is part of the entire live performance (or sequence of tracks on a record, tape or CD) and the individual pieces will be arranged to provide contrast and variety. Selecting a program order is the final part of the compositional process. Possibly the very last part of the process is the two-way response generated by the audience/orchestra interaction which actually shapes the music at each performance.

I’ve decided that, since the piece is unashamedly programmatic and the European visitors to the gardens have drifted away, we merely need the return of the night. But this time it will be different. The effect of starlight created by the glock and piano will begin sporadically, in the way that stars gradually appear in the evening sky, brightest ones first.

Although the effect will appear to be sporadic it will be achieved by a systematic serial scheme of reducing rest values between melodic fragments, gradually returning to the constant note values used in the intro as the sky darkens sufficiently for the faintest stars to be visible. This will take place above the sustained strings as in the intro, dying away to a barely audible pianissimo, perhaps accompanied by the restless clicking of claves. The percussionist using the claves could be off stage somewhere, an old trick used with horn and trumpet soloists sometimes.

Brief snatches of the piece will be heard, corresponding to the memory traces we all carry with us, and the original low brooding melody in the strings will appear once more as a violin solo, edited down in length.

Returning to the formal aspect of my piece, the book stresses the need to consider unorthodox formal structures, for example starting loud and gradually dying away to nothing. This is how my composition will end. Audiences don’t always know when to start clapping since they’re used to a formal end such as a sustained chord. It would help if the conductor turned and bowed immediately as a good clue. In the case of my piece it may be a case of turning and ducking, who knows?

So there you have it. I began with a desire to experiment with the Fibonacci note series because it creates an organic feeling. I wondered if this was too cerebral. I hesitated over the formal structure and key signature. I made mistakes. Now I’ve got to find an orchestra to play it. I can do this easily enough but will it join the large number of musical wallflowers gathering dust on shelves? Some of these are taken out for a first airing on the radio, often years after their creation, and turn out to be very good indeed.

I’ve begun the computer score which is tiled in two horizontal A4 sized pages one above the other in the music program page set-up. With a short run such as this, it isn’t viable to use a print shop so the two halves will be tacked together with a low tack glue stick, neatly copied onto A3 vertical sheets printed both sides, and bound (one way or another). I’ve decided to disregard the US letter size which isn’t a problem except that parts that are slightly taller than the rest of a band’s book are more likely to become dog-eared. I always use 100gsm paper for band parts and scores.

I’ll use three staves in the score for the percussion: one for the piano, the other two being shared by glock, cymbals, timps, xylophone, vibes and chimes. Double staves won’t be necessary. To make the piece a practical proposition only two percussion players are required, unless we include the piano as a percussion instrument (which it is). All percussion instruments will appear on each of the two parts which not only cues everyone in but also allows the performers to choose the instruments they are happiest with (or own).

I’ve given the harp a double stave at the bottom of the score, a location which is especially appropriate in my composition since the harp spends a lot of time doubling the pizz cellos and basses. It also uses non-arpeggiated chords, indicated by the usual square bracket, punctuating woodwind accents.

I stayed away from Manuel de Falla’s musical portrait of the gardens since I feared influence. A day or so after I finished my piece, his turned up on the radio and the comparison with mine turned out to be interesting. They couldn’t be more different. Like many composers, Manuel used the folk music of his native country in his work. Unfortunately, the use of Spanish imagery by popular composers and film writers causes poor Manuel’s piece to sound like a series of clichés of a kind they serve up to the tourists. It wasn’t conceived this way and he’s just another victim of the cruel way the passing of time distorts values. At the end of the day, Manuel’s piece has been played on the radio. I’ve a feeling I’ll have to wait a long time to hear mine.

Here is a link to the file on YouTube:

Mixed using native Logic Pro instruments
(with the exception of the solo trumpets and solo violin)


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