Woodshedding the Big Band

Here’s another blow-by-blow account of the creation of a piece using a jazz composition I wrote about 8 years ago entitled Flameout. This is a term used in aviation circles to signify that a jet engine has stopped working, which is very worrying if the aircraft is airborne at the time.

Overview: the piece changes from medium slow to double tempo and back and is based on three keys, actually the Dorian mode (a favourite in jazz circles since the ’60’s) on three different roots. These three keys are also used in simultaneity at certain points in the arrangement, in both harmonic and contrapuntal writing. The result doesn’t sound contrived. The roots are: C, E and Ab (=G sharp), i.e. a major third apart. A further major third above would take us back to C so this symmetrical arrangement of tonalities is useful for the polytonal portions of the work. I generally use equal intervals between the tonalities in polytonal writing but this isn’t compulsory, especially if the chosen scheme relates to other characteristics present in the particular piece. (There are three major thirds and four minor thirds within an octave before the reappearance of the root.)

Much use is made of chords built from 4th intervals which, lacking the traditional diatonic hierarchy, require systematic chord transformations (voice leading) as described in the book. An open key signature is used because of the number of accidentals that would occur if a key signature had been ascribed. This is mentioned in the conductor’s notes in the score.

Three bars of clipped, rhythmic, unison motifs splitting to 4th interval chords on the accents lead into a sustained open position 4th interval chord from the trombones. Above them, muted trumpets swirl in a pattern of rhythmically rotated forms, each of the three trumpets used being in a different key and using a different mute. The 5 saxes cut through it all with a unison (not octaves) semiquaver run based on the three keys in rapid succession.

Next, the drums play a wicked vamp which is formed from the serial development of rhythm described in the book. This really has to be played by a hooligan to work. Both hands and both feet are required here and good taste has to go through the window. I can’t remember who said that ‘Good taste is the enemy of great art’ but he or she had a point.

(Apparently, a number of people involved in the arts have made this comment.)

Four trombones pick up the rhythm in 4th interval open chords, rotating the three tonic chords of the chosen keys in a circular permutation. In traditional terminology, the functions used are root, 4th, 5th and 9th. Tenors and baritone play a unison theme (the range is wrong for the altos) in crotchet triplets which is easy to play except for the breath control. Non-circular breathers have to stagger their breathing and snatch a breath as well as they can to preserve the effect of an unbroken line. The theme is based on the three keys used, again rotated as a circular perm. The trombones and saxes are out of synch in terms of their vertical correspondences so that the melody at any one point is not written in terms of the underlying chords from the trombones. Again, this does not sound contrived because by now the listener has had time to assimilate the process leading up to the content.

The most likely application for this ‘displacement in time’ is in the lead-in, or anacrusis, if you prefer, where the tonality anticipates that of the ensuing passage, rather than the underlying harmony. This is an example of how music can develop in maturity when the mastery of musical resources is exploited to full effect.

The triplets are needed to avoid undesirable correspondences with the unusually active background. The marked difference in rhythm also assists with orchestral separation since the melody and background are in the same register; saxes and trombones are not all that different in tone colour.

At the repeat of this passage the trumpets enter (actually, the saxes do not repeat the previous section but continue with the development of the permed harmonies and serial development of rhythm). The trumpets are written as the trombones but in close position clusters instead of open position. Their rhythm and harmonies are displaced in relation to the trombones, creating a futuristic, interlocking, bitonal ‘oompah’ style which is really hairy.

A full ensemble version of the vamp rounds off the passage, using the full range of the big band in 4th intervals.

The jazz solos begin here and the instructions to the players are simply ‘Dorian mode in C’ but transposed to D and A for the trumpet and alto soloists respectively. Initially, just soloists and the rhythm section are used. A background figure of walking minims by three trumpets in unison and three trombones in unison enters at this point. The interval between the two sections is a perfect 4th. This grows to double 4ths (the same two parts in octaves) played by four saxes and four trombones doubling up on the parts. The trumpets add to the growth with unison phrases growing to octaves. Their rhythm is diminished to half note values as the piece evolves.

(One point: the bass needs to be a five string or a four string bass with the bottom string tuned down to Eb. Notes can’t be taken an octave up without wrecking the acoustics of the low register chords.)

The slow portion of the arrangement ends with each of the three sections in a different key (the three keys used). The trumpets trill on their cluster chord, the trombones walk in open position minims and four saxes, also in clusters, cut through the middle of the ensemble using the characteristic ‘kernel’ of the rhythm. There is much use of four part chords which also happens to free the trumpet, alto and trombone soloists to stand in front of the band for much of the time. Ten brass are required in this arrangement.

The composition changes to double time here and the trombone soloist enters over a series of wraith-like five part harmony passages from the saxes shifting rapidly in arpeggiated figures. When the piece was first test flown I advised the saxes to have a quick glance over this part of the arrangement but the young players sight read it to perfection leaving me feeling slightly foolish. One of them deftly prevented her music stand from going over with one foot at the same time.

Interlocking trumpet and trombone stabs urge the thing along, again providing a high-tech oompah.

A brief three part counterpoint continues the freedom of the ad libs. The instrumental split is trumpets/altos, trombones/tenors and trombones/baritone. The rhythm is a serial form given extra plasticity by the quaver rests which receive different stresses as they move in relation to the bar lines and accents. Occasionally, a rest is replaced by a tied note group. From the point of view of developing rhythms, rests and notes are the same thing. The rhythm is identical in each part, with staggered entrances from the top down at the half bar. I usually write the top part and then cue in the rhythm in the other part between the staves before attending to the pitches. A mixture of agreeable parallels and contrary motion between all parts cleans things up and each voice stands alone as an acceptable melody.

In counterpoint, I prefer using unison trumpets, unison trombones and unison saxes to benefit from the similarity of articulations and inflections of the families of instruments. The orchestration chosen here leads into the voiced ensemble that follows more naturally.

A brief ensemble leads into a four bar ‘bell’ effect which doesn’t go from the bottom up, as is more common. Instruments enter in pairs in a seemingly random up and down order before the trumpets ascend in a more traditional bell pattern leading into a powerful ensemble, in 4th intervals once more.

The composition returns to tempo 1 here with the drums playing the original vamp. A repeat of the theme occurs except that, instead of building, instruments now drop out in the second eight bars. The three part counterpoint reappears but this time treated bitonally, each voice using one of the three keys of the piece.

After another passage of organised noise from overlapping voiced sections in the three different keys the trombones and saxes lay down an open position Cm7 chord written (from the bottom up) C, G, Bb, Eb and G. The five trumpets then enter together as a section on Bb, D, F, A and ‘top’ C concert. The Cm7 and Bbmaj.9th chords jointly form a Cm13 chord but the effect is quite different. I would call it a 15th chord. It’s true that the top note is a reappearance of the root but two notes an octave apart (in this case the chord spans four octaves) are not the same note. An octave is in such a simple ratio, 2:1, that we give the constituent parts the same letter name. The reappearance of the root also chops the music into the scale structures we’re all familiar with.

The treatment of this last chord gives a very common harmony an element of surprise and the trumpets seem to be much higher than they really are, possibly because of the elevation in the status of the top ‘root’.

At the blow-through, I was prompted to notice how much more convincing a performance is when the bells of the trumpet and trombone sections point out horizontally in a straight line from left to right. It isn’t merely a visual consideration. Balance can be badly affected by mumbling down into the desk, especially on cramped bandstands. A number of bands perform with the trumpet section standing throughout the performance.


Manfred Von Snitzelgruber

One of the first problems I ran into when I first began to self-publish music was with regard to my own personalization. I began to realize that, if I wrote a lot of easy listening music, because it sells more copies, people would judge me accordingly. They will think ‘He only writes simple, tuneful stuff’. Top level bands like to show their prowess and, however much we dislike the use of technique for its own sake, it’s often this factor which makes them stand out from the crowd. Obviously, if you’re writing for a top band there’s very little they can’t play and some dissonant effects have to be played perfectly to work at all.

Some writers use a pen name for the more profitable aspects of their work and use another, even their real name, to build their reputation. So why do I stick to ‘John Morton’, a name that conjures up images of a Presbyterian minister? I don’t know. You’ve got me there.

(You might try Googling your own name. My name brought up over 52,000,000 web pages. The search even found me, which boosted my self-esteem a lot. It turns out that, whenever there was trouble throughout history, John Morton was never far away.)

Another idea is to use a different publishing brand name for the commercial work or to divide the catalogue into separate headings such as Easy Pieces, Light Entertainment, Concert Items, Serious Works etc. Publishers also use different pricing levels and people still expect something really good to cost more, even in these tough times. This tends to offset the low volume sales of specialized works.

And then there’s jazz…

It’s worth considering that a big proportion of the commercially available arrangements finding favour with jazz orchestras are stylistically confined to a narrow band of happy go lucky, bitter sweet, cool, funky, groovy, doowapdewapwap….(you know), swinging type stuff that sounds as if it was all written by the same computer.

I’m opposed to any directives which imply that if we don’t do this or that then the music we produce won’t be ‘jazz’. The extraordinary contribution that jazz has made to the world of music is due to various characteristics that are different by degree not essence. All of these characteristics are also found in straight music to some degree, even block scoring and improvisation. Without cultural isolation (which is disappearing fast in the modern world) there would be far fewer pigeonholes available to us for filing away our music nice ‘n’ tidy.

More on notation…

I skimmed the surface of this subject in a previous Blog but I thought I’d add some more comments on and around the subject.

Having set the scene, my next point refers to the difficulty of being truly objective about music notation. This is where it goes off on a tangent for a while, but please stay with me.

In my early teens I used to watch the fingers of the clock, my face about a couple of inches away. I used to hear worried voices in the background. I noticed that the minute hand would be approaching the hour and then, immediately, be receding from the hour. ‘Is it ever actually AT the hour?’ I wondered.

There’s always something ready to spoil the fun in life and I later discovered that quantum physics had been into this in a big way in the 20’s. I was pleased to find that they, too, were puzzled by the same problems that worried me in the 50’s: Is time (and matter) ultimately divisible into discrete portions that can no longer be subdivided? Does time consist of individual phases, each of which is stationery?

I know about Planck time etc. but this Blog is primarily about music.

To the musician, all this is crucial. Without the waveform (field) view of the universe, our ideas about the spiritual plane in general and our cherished notions about creativity and intuition will be put to the test. It’s very worrying that, as knowledge increases, those aspects of our experience attributed to the supernatural recede. How can a guy believe in his own genius with all this going on? Added to this, as musicians, we’re joined at the hip with subjective time since music is a temporal medium. Time within human experience represents our attempts to organize cause and effect in ways that can be measured and specified when we communicate with one another.

The problem of systemizing music notation lies in the difficulty of identifying the units with which to construct rhythmic patterns. For everyday practical purposes, we agree on the lowest common denominator used to construct rhythms and make various monomial and polynomial subgroups out of this raw material. Theoretically, these building blocks will be equal subdivisions of the total duration of the piece, discounting rallentandos, accellerandos, fermata (pauses) and tenares (where we dwell on a note momentarily). Time is conceived in terms of a continuum, or ‘pulse’, based on temporal units which are in turn subjective subdivisions of Earth years, days, hours and minutes (so-called ‘clock time’).

As stated in an earlier Blog, most music requires the notation groups to add up to the total duration group of each bar as specified by the time signature, with the exception of ‘alien’ tuplets (triplets, duplets etc).  We can also have five, seven… note tuplets in 3/4 time, etc. The problem is that a quaver (eighth note), for example, may be half of something or a third of something…. it has no precise duration value and any value ascribed to it will be lengthened or shortened by the tempo used during an actual performance.

Modern composers have used pure notation independently of a regular metre, using bar lines to subdivide the piece as and when they see fit.

Superficially, popular music has evolved from a two beat feel, to a smooth four, to eight in a bar rock and roll, to sixteen in a bar (and more) funk rhythms. These funk rhythms need to be produced with almost mathematical precision. There’s simply too much going on for there to be very much room for interpretational debate, and they’re a bitch to sight read until you get into them. Miles Davis was deeply involved in all this later in his musical career.

If anyone does have trouble with certain 16/16 rhythms, conceive the music at double tempo and double the note durations, i.e. evolve back a generation, and then translate the feel of the thing into 16/16 (or even 32/32).

Interestingly, asymmetric time signatures such as 11/8 etc. demand so much conscious effort amongst musicians in western cultures that interpretational disagreements occur less often in my experience. Guys are just glad to end the piece together. There has been a reasonable amount of jazz and popular music written in duple, triple and quadruple compound forms (6/8, 9/8 and 12/8) and the so called ‘jazz waltz’, typically felt at one in a bar. There is also less risk of disagreement when playing in these compound signatures but expect to be pulled over by the MD if you’re playing the quarter note/eighth note triplet group and you make the eighth too short. It sounds like a dotted group if you do that. This triplet form ratio is 2/3 : 1/3 and the dotted group is 3/4 : 1/4.

In jazz music notation, we may wish to exploit the subtle differences between, for example, dotted eighth groups and triplet and quasi-triplet forms. Both of these duration issues are affected by other non time-related factors such as stresses, accents and articulation forms.

All this may appear to be a lot of fuss about nothing. The problem is that, in a large ensemble, players can’t play with perfect precision which has the effect of lengthening all notes (further compounded by echo and other acoustic peculiarities). The remedy is to exaggerate all differences. This is especially true of staccato articulations at volume, which have to be played ridiculously short in the player’s perception, and yet sound correct to the audience. At the opposite end of the scale, where smooth playing is required, the more instruments papering over the cracks, the better the result. The string section is a good example, especially where bowing reverses direction during sustained notes that are too long for a single stroke.   

Even if we eventually fall in line with the ‘wave form’ view of physics we can still digitally synthesize music to the point that you can’t ‘see the join’. Yamaha produced a digital piano has that’s so authentic even concert pianists failed a blindfold test. And if experts can’t tell then, effectively, there IS no difference. If it can be analyzed, it can also be synthesized, available technology permitting. Similarly, digital music programs are offering ‘humanization’ of various kinds, including rubato, with growing authenticity. We’re some way from perfection yet, though. Mathematicians use a unit of deviation and a formula exists for this purpose.

One way or another, it’s all done by quantifying rhythms, tone qualities, volume scales, tempo, velocity etc. into determinable (quantum) packets which, if carried through with sufficient subtlety, give the illusion of continuity and of belonging to a realm that’s beyond our understanding.

Life’s always a matter of looking at the balance sheet of trade-offs. To a young composer, the ability to offer an authentic orchestral demo from the computer without the trauma and expense of assembling a full orchestra is very attractive. Conventional instruments evolved in the first place because they were the only means of producing musical sounds at the time they were built. Having said that, they still build houses with thatched roofs and Aston Martin in Britain still make cars with stitched leather dashboards. I can’t understand it, personally.

More on scale inversions…

The subject of changing the physical orientation of music so that it’s seen from a different viewpoint is covered in some detail in the book. These changes allow the derivation of fresh material which truly ‘belongs’ and which serves to stimulate fresh avenues to explore. The methods involve inverted, retrograde and inverted retrograde variations. The inverted forms can be tonal or real.

I had an email from a reader asking about inversions of the Dorian mode, a jazz favourite. It might have been a trick question. To simplify scale comparisons we always write down the intervallic structure (semitone = 1). The Dorian mode appears as follows when expressed in this way: 2122212. If we turn this upside down (or write it backwards) we get the same pattern 2122212. Theorists have long found it useful to classify seven note scales plus the octave in terms of two tetrachords. The Dorian mode has two identical tetrachords, 212 and 212, joined by a whole tone 2. To state the obvious, four notes in sequence (hence the word ‘tetra’) will have three intervals between them. This symmetry of construction may account for the free-wheeling, horizontal style of modal improvisers when playing in the Dorian tonality (it’s a key just like any other scale).

Contrast this situation with the major scale which has the structure 2212221. Turned upside down it becomes 1222122, something totally different. Inverting a major scale produces the Phrygian mode. C major, for example, will acquire a four flats signature. The problem with this mode, at least as far as conventional wisdom goes, is that the dominant triad is a diminished chord and the dominant seventh is a leading tone seventh, (m7b5).

I wrote a piece predominantly in the Phrygian mode and avoided the problem (intuitively at first) by changing to its relative major at each cadence (Eb > Ab in the above case). This is roughly analogous to using the so-called Tierce de Picardie, or Picardy Third in ecclesiastical music, where the tonic major triad was used at the cadence in a minor key. It was considered just a little too daring to end on a sustained minor chord. You could be thrown in the slammer, or worse, for using the flattened 5th (tritone) in those days.

You can decide to use an unorthodox scale and its family of harmonies in its pure form, and to hell with the consequences, but remember not to leave the listener too far behind where situations such as those existing in the Phrygian mode (above) occur. If you’re asked to write the background music for a documentary about creatures existing miles down on the ocean floor then that’s a different matter.

Referring back to the major scale, it’s significant that the more successful a form (any form) is, the more plasticity it is found to possess. A greater capacity for metamorphosis produces an increased chance of survival*. Some artists believe that form and function can’t be separated from aesthetics. I’ll think about that some more, if I get the chance.

*Obviously, we’re discussing the fitness for purpose of formalized, ‘European’ (for lack of a better word) music. There are parts of the world that, to this day, have never developed their music formally.




Countermelodies in the woodshed

An email asked for help on the subject of writing countermelodies. This subject is part of the wider field of counterpoint and is covered extensively in the book. My reply is reprinted here for the benefit of anyone else having trouble.

A countermelody may be subservient to the principal theme or it may be of equal importance. It will also tend to avoid a similarity of vertical stresses and accents. This helps prevent the combination of the two (or more) melodies from developing a homophonic (vertically conceived, harmonic) structure. On this same subject, too many chord changes in close succession will create a homophonic rather than polyphonic style. To quote an obvious example, if we placed a chord change on every note of the melody, there’d be little space for counterpoint at all.

The number of changes is governed partly by the tempo of the music. Fast tempos are usually characterized by harmonic inactivity (see old standard songs such as Limehouse Blues, Lover etc.).  

The rhythm and phrasing of the ‘original’ can be used to create effective countermelodies. Switching bars around in their vertical correspondence (diagonally, for lack of a better word) can achieve results that are inherently homogeneous because everything has a common origin. Similarly, rhythms within a bar (or within a phrase) can be divided into cells, which can also be moved around to form effective contrasts in adjacent voices.

Tip: write in the rhythm of the proposed countermelody below the staff where the part will go. Just indicate the ‘pure’ rhythm, the actual intonations will follow. Check for excessive similarity in vertical cross-sections, keeping the tyranny of the bar lines under control with tied-over (or accented over) phrasing to enhance the horizontal, linear style.  

Everything we do will probably be altered and refined, especially when the harmonies exert their influence.

Or we can try making the rhythm of the countermelody the same as the original but entering a bar or half bar later. We might have to tweak all the parts to make this work.

Another technique is to use activity where there is a sustained note in the melody voice and vice versa. The countermelody can split into voiced section writing (to use jazzspeak) for this purpose (under sustained or slow moving notes in the melody). The example of The fully versatile ensemble in the book is a fair example.

The countermelody can use the same rhythm as the principal but with doubled or halved note values (augmentation and diminution). Doubled values can be amazingly effective in producing lead voices in background harmonies that truly ‘belong’ to the style of the piece, especially where the harmonies allow duplication of the intonations of the melody. But, in any case, the resulting melody/harmony correlations may produce higher extensions and altered chords, with surprising results.

A simple countermelody of equal note durations may already be present (or potentially present) in the existing harmonies. It will usually move downwards but it may be important to the form and structure of your arrangement to have an ascending, rather than descending line. This can always be created, if you know how. The movement may not always be in semitones, although semitones predominate in the most effective cases when moving downwards. The basic movement can be decorated with rhythmic fills or grace notes.

Fugue writers often use retrograde (backwards), inverted or retrograde/inverted (upside down and backwards) versions of the principal for the counterpoint. They justify this by pointing out that the music hasn’t changed, just the ‘point of view’.

Pop and Jazz writers may rebel against what they perceive to be excessive cerebralism but it really can be a good way to start. Thinking about it, the selection of rhythmic patterns is the main problem since intonations are governed by the harmonies, plus available unessential notes and chromatics, and by the need to avoid undesirable parallels or other voice leading problems. Attend to these essentials and there is often very little else left to do.

Another tip: where there is a marked contrast of rhythm, accent and mobility between two (or more) lines, voice leading problems hardly ever occur because the ear can’t recognize individual vertical correspondences. (Look up Arabesque forms in counterpoint.)

The countermelody and the melody (or lead voice of the section playing it) should avoid getting tangled up with each other. Very brief encounters are OK and a countermelody can cross over the melody voice where a distinct advantage occurs, especially when there’s a marked difference in tone colour. The countermelody can also be in octaves. The lower octave is heard as an amplification of the top part, not as a note of harmony, so that clashes with harmony voices are not a problem except for long notes at slow tempos (especially in the low register). We often need the robustness of octaves to fight loud ensembles.

A mixture of parallel, oblique and contrary motion is good, too.

It’s generally better to avoid beginning the theme and countermelody simultaneously. Use a lead-in (anacrusis in straight-speak) or a delayed entrance.

The rhythm of the countermelody will often feature rhythmic retardation both within the bar and tied over the bar lines. Where the melody is intended to dominate, a countermelody that ‘lags behind’ rhythmically will help achieve this aim.

Cheap trick?

There’s another useful, quasi contrapuntal technique which can be most effective and useful without modification. It’s not suited to the ‘mainstream’ development of music but may be used in bridge passages and codas, for example. A feeling of immobility is created, like treading water.

(1) Take one (or two…) bars of a passage in three or four part harmony. (2) Write out all the voices, beginning from the top down, continuously on one staff. (3) Repeat the process in the second staff, this time beginning with the second voice of the original harmony, and carry on until all bars are used up (the top voice now comes last because these are circular permutations). (4) Continue the process from the third voice (etc….) of the original harmony until the sequence is exhausted. Because the original harmony worked, this new scheme, which has converted simultaneity into continuity, will also work. Call and answer figures are created automatically, being handed about from one voice to another.

There are reservations. Higher extensions may be forced below their acceptable acoustic limits. Where the melodic lines are rhythmically active, the ‘offending’ notes will be too short in duration to cause problems, and can create intriguing textures, but we can rearrange the octave placement of parts as required.

We will not usually employ this technique for too long because of its lack of formal content but if we do (the book never bosses you around), we simply continue with the permutations. Or we can change key or mode, or key and mode, using any of the 36 seven note scales.

Where bluesy, interwoven sections combine to produce a jazzwise version of three part counterpoint, the methods discussed above may produce results that are too rigid (uncool in jazzspeak). With practice and ingenuity, we can produce movement where initially it seemed impossible. Parts demonstrating a marked difference of rhythm, accent and stress can coexist even when brief semitone ‘kisses’ occur. Each voice develops its own ‘logic’ and stands up in its own right. There will be a mixture of notes on the beat and notes tied over. The unique (to jazz and blues) tendency for a major/minor conflict to occur between the melody and harmonies will also be present.

Personally, and I know this might upset a few people, I prefer section by section writing in jazz counterpoint: trumpets with trumpets, trombones with trombones, saxes with saxes, because the instruments share a common form of articulation and similar methods of producing legato phrasing etc. It’s easier for instruments of like-kind to capture the subtle nuances of interpretation. This kind of ‘vocalization’ has been an integral part of North American music since it all started.  



Polymetres and polyrhythms

In a recent blog I referred to symmetry in rhythm. The meaning was clear enough within the context but I decided to think a little more about the notation of rhythm, a subject most of us take for granted due to the conditioning we receive from an early age.

Talking about music is always tricky, and sometimes irrelevant. As Duke Ellington once remarked: ‘Too much talk stinks up the place’.  But if we’re here to exchange information and advice via a blog, which is essentially verbal in nature, then we can’t really avoid it. The point is this: different classifications often overlap one another.

The following extract from the book is a good place to start:

The most significant difference between the work of the graphic artist and the musician is that music is a temporal art form. Musical ideas are linked to the elusive notion of time. Our perception of time relates to the coordination of the sequence of events in our lives in a way that can be ordered and measured. If we promise to be at a certain place at an agreed time we are able to ensure, by reference to the metrics involved, that we arrive when expected.

That which we perceive to be the flow of time is, in everyday experience, a system of classifying the process of cause and effect. This is certainly true of the planning and arrangement of the temporal configuration of musical materials.

No one understands exactly what time is but, as musicians, we can only accept the idea as ‘given’. The Earth’s orbit is responsible for the years and seasons, its axial rotation the days and nights, which are further subdivided into hours, minutes and seconds. Further subdivisions are necessitated by specialist requirements of one kind or another where fractions of a second might become significant.

Why is time such an important concept to a composer? Here’s another book extract:

When an artist has been concentrating on an area of fine detail in his picture he can take a few steps back to obtain an overall view of the work. The more he moves away, the more he perceives it to be a single, unified whole. A composer faces a different set of problems. His composition may occupy a considerable period of time and he needs to develop specialized skills to achieve the same end. The controlled arrangement of the components of music to produce a balanced and unified whole as they extend through time is what we refer to as form.

Form and rhythm

Form and rhythm are inseparable. A composer can achieve a consistency of style, not only regarding the rhythms within the bars, but also the arrangement of bars, phrases, sentences, harmonic changes and thematic groups. It is exactly the same process but over a longer period. Rhythm is the unifying factor.

The beat is the underlying pulse, or scheme of regularity, representing our notion of time as it affects our daily routine. There is no doubt in my mind that the patterns we superimpose on to this continuum, constituting the rich variety of rhythms in the various styles of music, are the result of interference patterns that are a common feature of physical systems.

Time signatures

When the need to commit music to paper arose, enabling composers to share their music with people who hadn’t heard it before, musicians needed to represent the temporal features of music in a way that would be widely understood. They developed an ordered approach that has links with the structure of verbal language in poetry. The numerator in the time signatures they invented usually expresses the number of beats to the bar and the denominator shows the temporal value of each beat. Popular music written in 4/4 was often conceived as being in 8/8, since the quaver was generally the smallest unitary building block from which the rhythms were constructed. Cut common, though written with four beats to the bar, is conducted in two due to the difficulty of conducting in four at faster tempos.

The 6/8 and 12/8 series are hybrids – compound time signatures but with two and four beats in the bar. 6/8 is a compound duple, 9/8 a compound triple and 12/8 a compound quadruple.

9/8 is a true compound. Introducing duples into this metre leaves a remainder (1), but 2+2+2+3 (or its permutations) could still be used, just as 12/8 could use 3+3+2+2+2 and its permutations, or 4+3+2+3. There are other possibilities but if you want your music to ‘swing’ best give them a miss!

It will occasionally be necessary to make a judgement regarding which time signature to select. Common and cut common time signatures overlap at slower tempos so that either can sometimes apply. The compound quadruple (12/8) signature should only be used where triplets predominate in both the melody and underlying rhythms. We can write 12/8 feeling above the part or use a dual time signature, 4/4 (12/8). The more general use of multiple signatures can also obviate the need to write a profusion of time signatures throughout a composition featuring regular changes of metre.

My computer notation program can’t cope with this but the bracketed signature could be typed in as a text object. This would still necessitate turning off the automatic spacing option (if possible), where the computer’s understanding of the set metre is contradicted.

Similarly, a waltz may have an underlying 9/8 feeling although we may write in 3/4, with the triplet being implied in the performer’s interpretation.

Music in compound time signatures often groups itself into numbers of bars that are also divisible by three. As a result of habit and conditioning, there’s a tendency to add bars to produce duple or quadruple phrase construction. The symmetry of our own bodies may cause us to assimilate duple and quadruple forms more naturally. We should also consider using phrases and sentences that are divisible by three, where applicable.

At faster tempos, a waltz in 3/4 may be counted or conducted in one, i.e. one beat to the bar. The jazz waltz is often conceived and performed in this way.

2/2, 3/2 and other metres encountered in straight music are used to avoid the incongruous effect of eighth notes at slow tempos. Dividing the beat into quarter notes instead of having a quarter note divided into eighths is more in keeping with the longer duration of the notes.

2/2 is read the same as cut common and differs with regard to the characteristic degree of activity of the rhythms.

Other time signatures, such as 5/8, 7/8, 11/8 etc., have geographic associations and occurred in primitive societies.

Continuity and simultaneity

There are two methods composers can use to combine different musical forms: in continuity and in simultaneity. Differing rhythms and time signatures in continuity are fairly common but using them in simultaneity is more difficult to handle. Interestingly, the simultaneous use of different keys is easier for the listener to assimilate than the use of simultaneous time signatures. Various reasons have been offered to explain this. My own favourite is the importance of momentum and inertia in our daily experiences, which is disturbed by irregularity.

Polymetre in this blog refers to the simultaneous use of different time signatures. Here again, there are two methods. We can maintain the vertical alignment of bar lines, or not. If we combine, for example, 4/4 and 5/4 signatures, whilst keeping bar lines in alignment, we can no longer express the rhythms in the two signatures by means of a common, symmetric* system of units, for the obvious reason that a fifth of the temporal (clock time) duration of a bar cannot be equal to a quarter. This is why musicians have to work so hard to play such music and the less the two (or more) time signatures have in common, the stranger it gets.

*To revert back to the incentive for this blog, the word symmetric will hereby refer to a regularity of structure. Some writers on this subject use the word to refer to other characteristics, e.g. reversibility, etc. 

On the other hand, we can allow the longer metre to overlap the bar line delineated by the shorter signature(s). (We can use more than two simultaneous metres.) There was nothing new about this when modern composers began to experiment in these areas. Mozart’s Dissonance Quartet had already featured 5/4 figures over a 3/4 metre, although they really resulted from an interesting treatment of delayed resolutions, rather than from a conscious attempt to use polymetres.

It’s a matter of choice whether the shorter or the longer metre forms the basis of the piece.

The effectiveness of this latter technique can be enhanced by using harmonic, orchestral and other characteristics to delineate the subdivisions, otherwise they can become buried. Anyone who paid attention at school will realize that the different metres will ‘come out even’ when the divisors reach a common product, or denominator. In the case of 4/4 and 5/4, 20 (= 20 quarter notes) will end each cycle. That means 4 bars in 5/4 and 5 bars in 4/4.

Some composers, Charles Ives, for example, used complex simultaneous combinations of metre. The main difficulty, apart from the mental gymnastics involved, is in laying out the score. Each line of orchestration will not end conveniently at the edge of the page and blank areas will be left here and there because the conventional score layout doesn’t use a ‘piano roll’ method of notating music on paper. Similarly, the vertical alignment of bar lines can only be approximated because of the lack of symmetry. In a funny kind of way, music evolved to the point that it required written forms of expression but now finds itself hemmed in by them.


The definitions we use are often chosen out of expediency, so it’s worth pointing out that the terms polymetric and polyrhythmic are also, occasionally, interchangeable. (The book has a number of references to overlapping definitions such as that existing between accented passing notes/suspensions/auxiliary notes etc.)

The main distinguishing factor that defines polyrhythms is the use of symmetric (see above) structures where rhythms can be expressed by the use of common units. If different, coexisting rhythms can be written on graph paper, using orthogonal lines without cheating, they’re symmetric polyrhythms.

Obviously, 2/4 against 4/4, or 3/4 against 6/4 (for example) will possess the above characteristics, leading to another instance of an overlap of identification (as is 2/4 against 3/4, which would come out even after 2 bars). Often, these forms will result from the distribution of accents and stresses, not from an awareness of metre. A decision must then be made regarding whether or not to use more than one metre. Which makes more sense? Which will seem more natural, consistent or easy to read?

A slight complication occurs in the case of 3 against 2, and vice versa (the hemiola). These effects are sometimes called ‘cross metre’ or ‘cross beat’. In the case of a quarter note triplet in 6/8 and 2 quarter note triplets in 12/8 (the double hemiola) the rhythms employed possess a regularity of structure (in these examples, the eighth note). The unitary ‘building blocks’ are rearranged to form both rhythms without leaving a remainder. This is why these rhythms are called hybrids.

2, 3, 4 and 6 are all factors of twelve, and 2 and 3 are factors of 6.

Quarter note triplets against a 4/4 metre cannot be explained in this way without reference to the 12/8 rhythm, which is alien to the metre. The clock time duration of the bar is divided by 12 units in 12/8 but by only 8 in 4/4. The resulting polymetre effect might be another instance of overlapping terminology but, in any case, the original stimulant for the introduction of ‘threes’ was the desire to insert compound ‘fluidity’ into the more rigorous duple metres. Theoretical justification comes later.

Tuplets, where a group of notes foreign to the underlying metre occur, are regarded as embellishments, rather than as rhythmic entities in their own right. The forms are: duplets, triplets, quadruplets, quintuplets, sextuplets, septuplets, octuplets, nonuplets etc. (Look them up. Your notation program will have a sub-menu.)

Primitive cultures created complex and highly arresting polyrhythms that were produced intuitively and yet are difficult for even well trained musicians to assimilate. Obviously, cultural traditions and day-to-day conditioning are an important factor. Complex polyrhythms extending over more than one bar are found in various parts of the world.

The best way to appreciate these forms is to look them up on the www. Actions speak louder than words, something else the Duke would have agreed with.