Concerto for Two Double Reeds in detail: IV — Rondo

This is the fourth in a series of post-performance analyses of my Concerto for Two Double Reeds. You can also read about I — TessellationsII — Meta-Canon and III — Loops. Click here to read the full score of movement IV — Rondo or listen to the live recording.

The fourth movement is an old-fashioned rondo with lots of tunes; however, the original idea was rhythmical rather than melodic, and these rhythmic concerns recur throughout the movement.

Perhaps the decisive moment for me in writing this movement was when I noticed a rhythmic parallel between a Latin poem and an Italian canzonetta.

Catullus 63 treats of a subject that wouldn’t be out of place in an Almodóvar film: a young man, Attis, a devotee of the cult of Cybele, enters a trance and emasculates himself:

Super alta vectus Attis celeri rate maria
Phrygium ut nemus citato cupide pede tetigit
adiitque opaca silvis redimita loca deae,
stimulatus ibi furenti rabie, vagus animis
devolvit ili acuto sibi pondera silice.

Aside from its rather provocative theme, what marks this poem out is its driving rhythm:


This rhythm is known as the Galliambic, and the first half (before the caesura — marked ‘||’) is also known as the Anacreontic. The Anacreontic rhythm can be considered as the result of anaclasis (inversion) of the middle two syllables of an Ionic dimeter:

⏑⏑––|⏑⏑–– becomes ⏑⏑–⏑|–⏑––

Now, if you go back and read my old teaser post for this concerto, you’ll see I discuss the patterns of bell ringing, which are based on swapping values in a series. The transformation from the Ionic dimeter to the Anacreontic follows the same technique (albeit in a fairly limited fashion).

The second source is the canzonetta Vi ricorda o boschi ombrosi  from Monteverdi’s L’Orfeo:

Musical example illustrating the Anacreontic rhythm in 'Vi ricorda o boschi ombrosi' from Monteverdi's L'Orfeo

Here is the same passage in modern notation:

The same excerpt in modern notation

The pervasive rhythm of this passage is again the Anacreontic:


I had been keen for a while to play with classical rhythms, and this observation prompted me to start playing with the technique of anaclasis.

The opening passage of this movement doesn’t apply this technique to the Ionic dimiter, but rather to an Anapaestic rhythm:


After anaclasis, this becomes the following rhythm:


Join the two rhythms, and you get this:


This is the rhythm of the opening phrase of the Final of my concerto:

Opening oboe theme, illustrating the anaclastic anapaestic rhythm

In addition to introducing an important rhythmic technique, this opening passage also sets out two other important aspects of the movement:

  1. The anaclastic rhythm cuts across the barline (the A♯ quavers tied from b.3 to b.4) giving a syncopated accent;
  2. The melodic material is derived from triads on C and F♯, which lie a tritone apart.

The entire first phrase shows how these three ideas are developed:

The entire first phrase. The two-bar syncopated rhythm is repeated slightly lower, and then finished with a falling anapaestic rhythm

This brief opening fanfare is played in the oboe and bassoon, and leads into the rondo theme at [A]:

The rondo theme: two phrases is straight/anaclastic anapaestic dimeter, then a phrase in straight/anaclastic ionic dimeter

The first eight bars of this theme are based around the Anapaestic dimeter rhythm already explained, but with a small variation in the second foot. The following four bars, in 3/4, oppose a straight Ionic dimeter with its Anacreontic variant. This material maintains the polytonal nature of the opening: the strings play a vamp rhythm alternative between C and F♯ chords every two beats — even after the change to 3/4 —, and the thematic material meanders between these two tonal centres:

The rondo theme with accompaniment

This material is interrupted with a harsh outburst in the strings, again varying the Anacreontic rhythm across an interval of a major 7th, which is then picked up by the oboe in the inversion of that interval: an minor 2nd, leading back into the rondo theme, which is rounded off with a descending variant of the broken chords that opened the movement.

Episode I at [E] takes the ideas of the rondo theme and explores them in a different context. The alternating chords are each moved by a semitone, from C and F♯ to C♯ and F. The vamp bass remains, but the upper strings now play counterpoint above it, rather than pizzicato, and the solo material is a duet between oboe and bassoon. The technique of anaclasis appears again, this time transforming a dactylic dimeter (which is not explicitly heard):

–⏑⏑|–⏑⏑ becomes –⏑–⏑⏑⏑

Concerto for Two Double Reeds IV: Rondo, first episode

This episode leads straight back into the rondo theme at [F], which is this time finished with arpeggi in the low strings, which recall the solo material at [E].

Episode II leaves behind anaclastic meters, and explores Aeolic rhythms instead.

The core rhythm of Aeolic meter is the choriamb:


This basic unit is extended by the addition of syllables before and after. The syllables before are anceps (either long or short), while those after tend to alter breve, longum. For instance, the rhythmic colon known as the Hipponactean looks like this:

⏓⏓ –⏑⏑– ⏑–×

In this episode, I decided to work freely with the principles of Aeolic rhythm, rather than adopting a preexisting verse form. Here is the resulting rhythm:

–– –⏑⏑– ⏑–⏑–
–– –⏑⏑– ⏑–⏑–
–– –⏑⏑– ⏑–
⏑⏑ –⏑⏑– ⏑––

In each of these lines the central Choriamb can be seen clearly.

The Episode II theme in the bassoon (and violin) at [G]

This is the first episode in which the bassoon is the only soloist, and the first to move away from tonality. Rather than diatonic scales, the melodic and harmonic material is drawn from a scale that Messiaen would have described as the 2nd Mode of Limited Transposition, and which is also known as the octatonic. This is made of alternating tones and semitones.

Octatonic scale on C

The bassoon explores this scale, while the upper strings play diminished triads — the chord that forms if you take alternate notes from this scale. As in the rondo theme, there is an ambiguity between 2/4 and 3/4 meter, but this time it is the string figurations that change:

The rhythm shows two 3/4 bars, one 2/4 bar; two 3/4 bars, one 2/4 bar; two 3/4 bars with a hemiola; two 2/4 bars; one 3/4 bar

The material of this episode is played three times:

  1. Bassoon solo with upper string triad accompaniment;
  2. Oboe solo, bassoon counterpoint in diminished arpeggi, upper string accompaniment with cello bassline;
  3. Oboe and bassoon have the melody, the upper string triads are spaced by octaves, the double bass joins the bassline.

The material then dissolves until only stratospheric violin and abyssal double bass are left. At this point a solo violinist picks up with the material first heard in the interruption to the initial rondo theme, which then leads into a statement of this theme in solo violin and pizzicato viola at [J]:

Rondo theme in solo violin and viola

With the soloist played at such a high pitch, and no harmonic accompaniment, this material sounds very different from its initial statement. The material is then picked up in both violin parts (tutti), with accompaniment from all the lower strings, but still no harmony, and we then then move into the next episode at [L].

The rhythm of Episode III is again Aeolian. A feature of Aeolian rhythms is that the central Choriamb can be expanded, either by full repetition or with Anapaests (which are equivalent to a Choriamb with the first syllable missing). This passage uses Choriambic expansion, moving between Glyconics:

–⏑ –⏑⏑– ⏑–

And their expanded equivalent, the Asclepiad:

–⏑ –⏑⏑– –⏑⏑– ⏑–

The combination Glyconic, Asclepiad, Glyconic, Asclepiad is known as the Fourth Asclepiad, and is used by Horace in his Ode 3.9:

–⏓ –⏑⏑– ⏑×
–⏓ –⏑⏑– –⏑⏑– ⏑×
–⏓ –⏑⏑– ⏑×
–⏓ –⏑⏑– –⏑⏑– ⏑×

Donec gratus eram tibi
nec quisquam potior bracchia candidae
ceruici iuuenis dabat,
Persarum uigui rege beatior.

The rhythm I use for this section is slightly different, being composed of two Glyconics followed by an Asclepiad:

–⏑ –⏑⏑– ⏑–
–⏑ –⏑⏑– ⏑–
–⏑ –⏑⏑– –⏑⏑– ⏑–

Also, unlike Horace’s practice, I chose to use a short value on the second value of each line, and to keep the final value long; this keeps each line absolutely symmetrical, which adds to the character of this episode.

Oboe theme of Episode III

The melodic material for this episode is based entirely on whole-tone scales, alternating each bar between the two possible transpositions of this scale. The solo material makes a lot of the major 3rd that emerges from this scale, while the accompaniment, spaced in major 3rds, traces consecutive notes.

Accompanying figuration in Violin I

This episode falls into four sections:

  1. Melody in the oboe, scales in violins;
  2. Melody in the bassoon, scales in viola and cello;
  3. Melody in violin II and viola, harmonics in cello and double bass, scales in oboe and bassoon;
  4. Scales in oboe, bassoon and upper strings, harmonics in cello and double bass, then inverting roles with the upper strings playing very high notes and the cello and bass playing scales.

After these discursions into non-diatonic territory, we return at [N] to the final statements of the rondo theme. This time it is stated in the bassoon,  and is fully harmonised.The interruption from the first statement reappears here, with the oboe’s lead-in slightly altered, and then the theme reappears in counterpoint at [P], first in the bassoon with bar-spaced oboe arpeggi, then at b.297 in the oboe with constant bassoon arpeggi. These arpeggi take over at b.305 in both soloists and upper string, leading into the final statement of the theme at [Q], in both oboe and bassoon, with the string pizzicati replaced with arpeggi:

Rondo theme plus C/F# arpeggi

At b. 321 the soloists abandon the rondo theme, picking up the movement’s opening material, and are joined by the entire orchestra playing this fanfare at b.329, before the movement closes with exact material that opened it, but across the whole ensemble:

Opening theme brought back tutti as the coda.

I have to confess to feeling slightly ambivalent about this movement. It is unquestionably a crowd-pleaser, and I have a feeling it’s good fun to play, but its very richness in tunes and compelling rhythms raise nagging feelings that it’s rather superficial and not serious music. Perhaps the analysis on this page is something of an apologia for it: an attempt to show that there are actually plenty of clever ideas behind its appealing tunefulness and vampish character. Or perhaps I should just relax and enjoy it!

(*Please read my note on copyright.)

Concerto for Two Double Reeds in detail: III — Loops

This is the third in a series of post-performance analyses of my Concerto for Two Double Reeds. You can also read about I — Tessellations and II — Meta-Canon.

The structure of this movement is fairly simple, building up a contrapuntal structure over a double-bass ostinato. Click here to have a look at the score or listen to the live recording*.

The ostinato itself is made of two 4-bar phrases, each repeated. Each phrase has 12 notes: each of the notes of the pentatonic scale, although the sequence is not used as a row. The rhythm alternates between 3-quaver and 2-quaver beats to give a distinctive rhythmic identity to the whole movement.

Bassline. Two 4-bar phrases repeated

Over this ostinato, the bassoon and orchestra conduct a dialogue which builds up a contrapuntal texture. High in my mind at the time of writing this were Kerry Andrew‘s wonderful performances of folk songs, delivered live with just a loop console for accompaniment. I love the textures she can create by laying down one part over another, and the way the piece slowly comes together, and wanted to explore this idea with an ensemble, acoustic piece. Another image that springs into my mind with this music is that of a 3D printer, which can create a solid artefact by laying down layer upon layer of 2-dimensional material.

The movement is divided into 16-bar sections. In each, the bassoon plays two 4-bar phrases, each of which is then repeated immediately in the strings. In the following section, the string part that has already been layed down is played again, and the new material is played by the next part up. This means that the cellos repeat their material 4 times, whereas the first violins only get one exposition.

This cumulative structure is repeated twice, with different material. In the first, the material of the ostinato is performed first, and played by the cellos (as well as continuing in the double bass); in the second part, this material is saved for the last entry, and appears in the first violins. As each section builds up, the dynamic increases; at the end of Section 1 we drop back to 16 bars of ostinato played pianissimo in the double bass; at the end of Section 2 we hear the ostinato played in octaves by all the performers, crescendo to fortississimo, and which point the movement stops dead.

The material is fairly straightforward. Some phrases are derived from the ostinato, and others play with chains of intervals. My intention was that there should be a range of different syncopations, so as to achieve a rhythmic counterpoint alongside the melodic counterpoint. I made no attempt to inject any harmonic meaning into the parts, but made sure there was a good range of tessitura so as to keep the identities of the parts fairly distinct.

Note: if you would like to listen to a recording of this performance, please get in touch and I can send you a link.

(*Please read my note on copyright.)

Concerto for Two Double Reeds in detail: II — Meta-Canon

I have already posted analyses of two aspects of this movement: the permuted chaconne in the lower strings, and the mathematical structure of the soloists’ meta-canon. In summary:

  • The lower strings play 13 permuted repetitions of a simple, 12-bar phrase
  • The oboe and bassoon play 12 phrases of different lengths, in different orders

In this post I will explain how the musical material of the solo parts is derived, and discuss a few other final details. You can also click here to read the full score of the movement and listen to the live recording*.

The melodic material is based on a 28-member interval row generated by rolling a die:

3 3 4 5 6 6 1
1 5 6 4 2 5 6
6 3 2 1 1 2 6
1 3 1 3 5 5 5

In writing the material for each section, I followed a simple set of rules:

  • The first pitch is always a D
  • Each new note is found by moving either up or down by the corresponding interval in the row
  • Any octave transposition is permitted
  • Hence in the oboe part, starting from d´, and with an interval of 3, the next note can be b, f´, b´, f´´, b´´or f´´´
  • Any note or succession of notes can be repeated, including sequences (eg u–v–w, u–v–w–x, u–v–w–x–y, u–v–w–x–y–z)
  • The pitch material for each section is derived separately, although certain techniques and motifs recur

The first two phrases of the oboe part illustrate these principles:

Eight-bar excerpt from the oboe part.

The first phrase uses the first 7 members of the interval row in sequence: 3 3 4 5 6 6 1. The second phrase repeats the notes of the first phrase, adding one more note, again generated using the interval row.

Another illustration can be found from a bassoon passage half-way through the movement:

Four-bar excerpt from the bassoon part

In this passaged again the material is generated from the beginning of the sequence, but the process is drawn out by the repetition of sequences of notes.

As the interval row is fairly large, it is only used in the 9, 10, 11 and 12 unit sections. In sections 1, 2, 3 and 4, only 7 members (one line) of the row are used for each section, and in 5, 6 and 7, 14 members (two lines) are used. Section 8 is silent.

The other patterns in the material are that in odd-numbered sections the oboe and bassoon parts are inversions of each other, while in the even-numbered sections they are rectus. Sections 1, 4, 6, 7, 9 and 12 are lyrical in nature, and sections 2, 3, 5, 8, 10 and 11 are more mechanistic (8 trivially so).

Here then is a brief analysis of each of the sections, following their order in the oboe part:

Section 12

The longest passage in the movement, the material in this section is lyrical, covering a wide tessitura. The passage falls loosely into two sections, the first  characterised by sustained notes which lead into arpeggio-like flourishes; the second by repeated notes leading into material which meanders around a small cell of pitches.

The material from this section recurs throughout the movement.

Section 9

This section is a reworking of the material in Section 12. It is rhythmically simpler and less discursive. Gestures from the solo material are picked up in the violins and form part of their ostinato (see below).

Section 6

This section picks up material from Sections 9 and 12 and develops it a little further.

Section 3

The first ‘mechanistic’ section in the oboe. This introduces the technique of gradually adding to a cell of pitches.

Section 2

This is the one point of true coincidence in the movement. At the beginning of the movement, Section 12 in the oboe is accompanied by Section 2 in the bassoon. At this point, this relationship is reversed.

The material is extremely simple: just a falling sequence notes. The number of beats between the notes decreases over the course of the 4 bar section.

Section 5

Section 5 is structurally fairly simple: a 2-bar phrase is repeated for two different sets of pitches. It’s then split in half, and each half is repeated independently. The opening motif is then repeated on its own.

Section 8

Section 8 is silent, primarily to give the soloists a chance to get their breath back!

Section 11

Section 11 is highly mechanistic. The excerpt of bassoon music above is taken from the beginning of this section, and illustrates the way the material is generated. Its nature is fairly relentless, and had to be reworked a couple of times to make sure the performers had enough space to breathe.

This is also one of the moments of minor coincidence in the movement, as the oboe starts this section 6 bars after the bassoon. This makes this passage one of the more obviously canonic parts of the movement (inverted of course, as 11 is an odd number), and the driving rhythms of the material make this the climax of the movement.

Section 10

Section 10 is fairly simple, and similar to Section 5: a phrase is repeated and then deconstructed.

Section 7

Section 7 provides another explicitly canonic passage in this movement, as the oboe starts this section 8 bars after the bassoon. The section is divided in two, and the second half is an exact inversion of the first. Because this division happens after bar 7, and because the oboe and bassoon parts are inversions of each other, this means that the second half of the section in the bassoon is in rectus canon with the first half of the section in the oboe, with a delay of one bar.

I am particularly fond of this section because of this canonic cleverness, so here are the bassoon and oboe parts on their own to clarify the structure:

Oboe and Bassoon parts demonstrating double canon

Section 4

Section 4 takes the movement’s opening motif as its sole source of material, and leads into…

Section 1

The final coincidence of the piece, oboe and bassoon play Section 1 simultaneously. The material again uses the opening motif, so in the oboe it follows directly from Section 4. As 1 is an odd number, the parts are inversions of each other, so they open away from middle d´.

Upper Strings

I have discussed the chaconne in the lower strings, which is made of 13 repetitions of a 12-bar phrase. The material in the upper strings is made of 12 repetitions of a 13-bar phrase, and uses entirely extended techniques: tapping the strings with the wood of their bows, playing the short lengths of string beyond the bridge, tapping the wooden body of the instrument, and playing notes with Bartók or snap pizzicato.

There are a few melodic elements in this material, principally echoes of the soloists’ material in Section 9, and I was keen on the idea of building a background soundworld, elements of which could then come into focus in the right context.

This movement is by far the most complex compositionally, and probably the most challenging to listen to, but I think that, despite all its complexities, it has a lyricism that works well within the structure of the whole work.

I also have a feeling that this movement would work well rewritten for oboe, bassoon and electronics. A project for another day!

Note: if you would like to listen to a recording of this performance, please get in touch and I can send you a link.

(*Please read my note on copyright.)

Concerto for Two Double Reeds in detail: I — Tessellations

This is the first in a series of post-performance analyses of my Concerto for Two Double Reeds. Click here to have a look at the score of movement I — Tessallations or listen to the live recording*.

The first movement of my Concerto for Two Double Reeds is for oboe solo and orchestra; it builds on two ideas:

The first idea is stolen from György Ligeti, and it is to divide the chromatic scale according to the keys on the piano: the white keys form a diatonic scale, and the black keys form a pentatonic one. In this case, the white notes are given to the oboe, and the black notes to the orchestra.

The orchestra play their notes with two textures: sustained chords, and descending pizzicati passed from instrument to instrument. The five notes of the pentatonic scale are divided between the five parts: Violin I, Violin II, Viola, Cello, Double Bass in a succession of narrowing, then broadening spacings:

The following chords:  [͵A♯ G♯ f♯ d♯´ c♯´´] –  [F♯ c♯ g♯ d♯´ a♯´] –  [c♯ f♯ a♯ d♯´ g♯´] –  [g♯ a♯ c♯´ d♯´ f♯´] –  [c♯ f♯ a♯ d♯´ g♯´] –  [D♯ c♯ g♯ d♯´ a♯´] –  [͵A♯ G♯ f♯ d♯´ c♯´´] –  [͵D♯ D♯ d♯ d♯´ d♯´´]

Throughout this sequence the second violins hold middle d´♯, which acts as a pivot for the other notes. Within the pentatonic scale, the first chord can be considered to be build on 5ths (A♯ – C♯ – D♯ – F♯ – G♯ is five successive degrees of the pentatonic scale), the second on 4rds, the third on 3rds, and the fourth on 2nds, so the spacing is entirely regular, albeit within an irregularly spaced scale.

The second idea is to base the oboe part, within the confines of the diatonic scale, around a repeating group of intervals. All the oboe material is based around a ladder, or tessellation, formed of rising perfect fifths and falling major seconds, a technique which acknowledges Messiaen’s modes of limited transposition, whilst doing pretty much the opposite!

Treble clef, in succession the notes e´ – b´ – a´ – e´´ – d´´ – a´´ – g´´ – d´´´ – c´´´

Pushed much further this pattern would encounter black notes, but then again, pushed much further it would exceed the oboe’s range!

The resulting movement is in two sections:

In Section 1, the strings hold each, successively narrower, spacing of the pentatonic pitch set while the oboe plays increasingly florid, improvisatory material. For each chord the oboe plays three phrases of increasing length, followed by the pizzicato string motif.

The final, close-spaced pizzicato motif of Section 1 becomes the first motif in Section 2, which is for strings alone. The abandon the sustained chords, and just play the pizz motifs in reverse order. Finally, reach a 4-octave span of D♯s, which they play three times, ending fff to end the movement.

In workshopping this movement, we discussed various ways to notate the oboe passages. I had originally been fairly specific about which notes should be triplets, and about dividing the material into bars, but felt that this detracted from the rhythmic freedom the performer should have in interpreting the material. Rhuti’s performance brought a lyricism to this movement that went beyond what I had envisioned, and even elicited comparisons — unexpected, but not unwelcome — to  Delius.

Note: if you would like to listen to a recording of this performance, please get in touch and I can send you a link.

(*Please read my note on copyright.)

Concerto for Two Double Reeds: performed!

On 6 July my concerto was performed. St Stephen Walbrook was filled with lunchtime concertgoers, and my many late nights of work, along with our intense rehearsals over the last day and a half, finally paid off.

I owe a great debt of thanks to our fantastic soloists, Rhuti Carr and Andrew Watson, to the Handel Collection and their leader Irina Pakkanen, and to Edward Adams, whose conducting and oversight brought the performance together, and who first suggested I write the piece.

I have already posted a little analysis of the second movement of this piece, and I plan to post more in the coming days, along with some score excerpts and perhaps some audio samples. In the mean time, I would like to jot down a few general reflections:

  • I was really fortunate to get feedback from Edward and Rhuti during the compositional process. I had early conversations with them about the shape of the piece, and we then ran two workshops while I was writing the work, which were invaluable in steering me towards writing more idiomatically for the oboe. (As an aside, it strikes me that this approach has certain similarities with Agile software development insofar as a dialogue is maintained between composer / programmer and performer / end user. A thought for another day.)
  • Another piece of luck was that Andrew was able to step in as bassoon soloist. The original plan had been to write an oboe concerto, but the second movement was calling out for another soloist, and once I had a substantial bassoon part in that movement, it seemed a little unjust to make the performer sit aside for the rest of the piece! The third movement, which is the bassoonist’s showcase, is in part a solution to this problem.
  • The other problem that the third movement attempts to solve is that the finale is completely stylistically incongruous. It started life as a little sketch which I played to Rhuti and Edward, and which they liked so much that the insisted I keep it in the piece. However, the transition from the atonal, rather austere second movement to the (poly)tonal, jaunty romp of a finale was really rather jarring, and needed something to act as a bridge. I hope that the syncopated, motoric rhythms and cumulative counterpoint of the third movement achieve this. The finale retains its original character, but I hope I’ve done something interesting with it, as well as showing I can write a good tune!
  • Even after the workshops, a few points did arise during the rehearsals, particularly to do with the string writing, and it was really useful to be able to talk through them with Irina and agree a few revisions to bring the performance closer to what I had had in mind.
  • Finally, I got the impression that the performers had fun playing the piece. Two moments particularly stick in my mind. First, about half way through the rehearsal of the third movement, the structure of the piece revealed itself to Irina, and I could see her face light up, and she turned to the orchestra and told them ‘Ok, I want to you stop counting bars and just listen to the bassoon, because whatever he plays, you repeat.’ The second moment that sticks with me is in the final movement, where I’ve given the double bass pizzicato slides from a very high note down as low as possible, and where I’m sure I caught the bassist exchanging grins with the viola section.
So, finally, a few more thank yous. First, to my husband Peer for putting up with me in the throes of composition and bad MIDI synthesis at ungodly hours. Second, to my colleagues at 7digital: I haven’t worked anywhere else where so many of my colleagues would come along to support me, particularly after only 6 weeks in the job. And finally to the woman who stormed out half way through the second movement hissing ‘I’ll come back when they start playing something with tunes’: no premiere is complete without the odd naysayer!

Oboe concerto teaser: II

This is part 2 of a series on my forthcoming oboe concerto. This is a commission for the Handel Collection, and will be performed on 5 July 2011, 13:0014:00 at St Stephen Walbrook (warning: site plays music), 39 Walbrook, London, EC4N 8BN. Please come along if you can!

I mentioned last time that the Sarabande is built on a meta-canon. Here’s how it works.

This movement is 156 bars long which is equal to 12 × 13 or 2 × (1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 + 10 + 11 + 12). This second formula is salient, because it’s based on a triangular number, and I’m rather fond of triangular numbers.

The oboe and bassoon parts are each divided into 12 sections, each of a different length 2n where n is a number from 1 to 12. The oboe’s sections are ordered n = 12, 9, 6, 3, 2, 5, 8, 11, 10, 7, 4, 1, and those of the bassoon n = 2, 4, 6, 8, 10, 12, 11, 9, 7, 5, 3, 1, so they both similar types of pattern.

As the sections are of different lengths, the beginnings of sections rarely coincide in the two parts, and only once on the same length of section: n = 1 in the final 2 bars. Other coincidences of note are that oboe 2 and bassoon 12 start together (mirroring the beginning of the movement, where oboe 12 starts with bassoon 2), bassoon 11 and oboe 11 overlap by 16 bars, and bassoon 7 and oboe 7 by 6 bars.

This structure then forms the basis of the meta-canon: the material for each value of n is the same in both voices, wherever they occur. This means that in sections 11 and 7 the voices really are in canon, and in section 1 they are in rhythmic unison. All of the other sections are not self-contiguous, so the voices perform a canon-at-a-distance. In addition to this basic canonic principle, odd-numbered sections are inverted between oboe and bassoon, while even-numbered sections are performed recte.

There’s not really much in the way of musical example I can post until I’ve explained the derivation of the material (and finished writing it all!), so in the mean time, here’s a colourful illustration of the structure of the canon:

Oboe concerto teaser: I

As I mentioned before, I am working on an oboe concerto. This is a commission for the Handel Collection, and will be performed on 5 July 2011, 13:0014:00 at St Stephen Walbrook (warning: site plays music), 39 Walbrook, London, EC4N 8BN. Please come along if you can!

I’m currently working on the central movement, which is a sort of meta-canonical sarabande. I thought it might be interesting to say a few words about it while it takes shape.

The movement is based around three key ideas:

I’m going to describe the chaconne here; the other elements will come in future posts.

Viola, Violoncello and Double bass staves

One of my favourite musical techniques is the process of gradual transformation found in bellringing. In this process, a row of pitches is repeated over and over, but with each repitition any two neighbouring pitches can ‘change‘, swapping places. In campanology, there is a great discipline to coordinating a group of ringers to perform a whole sequence, or peal, of changes without fault; on a smaller scale this is a great way to produce musical material that maintains unity while developing over time.

In my chaconne, two rows are transformed: the viola has a descending chromatic scale from a′, while the cello and double bass have a figure that opens chromatically like a funnel from A:

On the second repetition, I apply a simple transformation to each row: in the viola, places 1 & 2 swap places, as do 3 & 4, 5 & 6, 7 & 8, 9 & 10, and 11 & 12. In the bass, places 1 and 12 remain in place while 2 & 3, 4 & 5, 6 & 7, 8 & 9, and 10 & 11 all swap:

If I were then to apply the same transformation again, I would get back to where I started, so instead I apply the transformation originally used in the viola to the bass, and vice versa:

If I continued this long enough (24 changes), I would return to where I had started, having performed a plain hunt maximus (ie, the simplest possible pattern on 12 pitches); for this movement, I am more interested in moving from one row to another, rather than returning, so I finish the piece after 13 rows (12 changes), at which point both voices have reversed:

As you will see from the excerpt at the top, I have set these notes to an ostinato rhythm, whose purpose is to support the counterpoint above; each note in the row takes up a bar, so we have a total of 12 × 13 = 156 bars, which, anticipating my next post, happens to be 2 × (1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 + 10 + 11 + 12).