Bach v Handel v Scarlatti v Telemann (and so on)

My most advanced student and I sat down the other day to decide exactly which works would go into his diploma program (exam in November/December) and which would get the flick. My student had been working on the Bach C minor Partita, but as much as we both loved the Capriccio we were struggling with the notion of turning the other required movements into part of his performance program. It all just seemed so turgid, with a displeasing noise to signal ratio.

Could we get away with dispensing with this major work from his program? How would the balance of the recital be affected by taking this out of the equation? We pulled out the syllabus and thought about replacing this selection with a Prelude and Fugue. And we had no trouble identifying some Preludes on the list that would show off this student’s strengths and sensitivities to best advantage. It’s just that when we came to think about him learning a Fugue it just didn’t seem right. For him.

Now, I usually find that fugues are a bit of an IQ test – it doesn’t really matter what the personality of a student, a very clever student will find joy and beauty in a fugue. But this student is as smart as they come, and fugues simply aren’t his thing. I can see that quite clearly, even though we’ve only been working together for a couple of years. His insistence that he doesn’t like fugues is also not immaterial to this judgment.

So back to the drawing board.

A lone Handel Suite (No. 8 in F minor) sat on the list, pretty much the only alternative if we were to include a Baroque presence in the program. I pulled out the Henle collection and to our mutual delight we found that the spirit of this suite exactly suited the student. The suite still has a fugue in it, and has pretty much the same kinds of forms and movements that we’d been working on with the Bach, but the mood, the tone, the energy of the music was of a completely different nature, and we happily agreed that this was the new direction needed.

I’ve been practicing the suite since that lesson (I had only a passing familiarity with the various movements) and discovering that while there are plenty of tricky passages and technical challenges the music feels ‘easier’ – not so much easier to learn as easier to relate to. I’m kind of a Bachophile (or Bach maniac, if you will), so this discovery is challenging my sense of musical identity in a fairly substantial way.

Meantime, I’ve (finally) been reading Charles Rosen’s Piano Notes, a book that was published in 2002 and that I first came across in a massive chain bookshop in a London shopping mall in 2006 when I should have been collecting some groceries. Having gone out of my way to buy the book in unlikely circumstances (and delaying dinner for a group of 4 to boot) one might think I’d have read it without delay. Of course, it’s just this week I’ve plunged into this profound and refreshing book about playing the piano.

Right there in the first chapter Charles Rosen talks about the ‘gymnastics’ of Scarlatti. ‘Gymnastics’. Never a truer word spoken, about Scarlatti at least – his music is the absolute embodiment of the gymnastic spirit. Many a gesture in a Scarlatti sonata feels as if one is performing a complicated tumble with the ambition of landing again on the balance beam once the skillful leap is complete. I’ve always loved playing Scarlatti. His music resonates with the larrikin in me.

But if given a choice I would generally choose Telemann over Scarlatti. So very many of his keyboard works feel natural to me, like meeting someone whose sense of humour, taste in movies or political orientation exactly matches your own. Telemann moves the way I like to move, physically (the gestures required to perform the music) and harmonically/rhythmically and structurally. Scarlatti feels more like quirky friend.

Meantime, Rameau mostly seems like a complete alien*.

Bach brings tears to my eyes while Handel induces my lips to smile. I feel happy delight with both Telemann and Scarlatti, one because he does what I would do, the other because he does what I would not.

Can it all be explained by a Myers Briggs assessment? By the times in which we live? By the teachers we’ve had along the way? By our star signs?

All theories welcome…

*Disclaimer: I have not played a fair percentage of Rameau’s keyboard music, so I would be very excited to be dissuaded from this current position. Please share your Rameau favourites with me!

POST-SCRIPT: Yes, I know. I start talking about Charles Rosen’s fabulous book and then just leave it at that. I will certainly be talking about Piano Notes some more in the weeks to come.

Music and Mathematics Part 1

The past year or so seems to have hosted a steady trickle of articles, blog posts and public debates about the connection (or, more usually, the lack thereof) between music and maths.

Discussions involving mathematics bring on a sense of alienation/torpor to many in the general public, but I’m one of those who find mathematical thinking exciting, exacting, exhilarating. And as music is (really quite literally) on my mind all the time, I am deeply interested in the assertions of others regarding the links (or lack thereof) between these two (musical and mathematical) aspects of organisational thought and expression.

It turns out that many of those who spend time disputing the existence of links between music and mathematics go on to reveal that they were never that good at maths. In fact, they confess that they’ve failed key mathematical assessments throughout their schooling. What they don’t acknowledge is that they have a vested interest in denying connections between mathematical and musical thinking, and no one seems to think it worth mentioning that someone who is no good at maths probably won’t have a very nuanced idea as to what mathematics actually is [and therefore is probably not best equipped to detail how unconnected music and maths might be].

Along these lines, if you think that mathematics is just a fancy word for “counting” the argument will go something like this: maths and music are linked because in music you do counting (of beats and intervals). That’s it. As soon as we notice that music is more than counting (either beats or intervals) it’s no great stretch to be convinced the hoopla about maths and music having all that much in common must be based on a trite understanding of what music is.

The problem is that the trite understanding isn’t of music so much as it is of mathematics. Mathematical thinking does involve quantity (which concept does involve, amongst many other things, “counting”), but it also necessarily involves spatial thinking/awareness as well as pattern recognition, two substantial non-counting aspects of how to think in and about the world.

But even within the confines of “quantity” we find ourselves in a world of relationship: “this is bigger than that” might not sound particularly profound, but a lot about our experience of music can be described within this single concept of quantity. No matter which way we hear it, louder, longer, faster, further, more (and their corresponding softer, shorter, slower, closer, less) describe nearly everything that can happen in music.

Stephen Hough makes a quite convincing case that it is the ambiguities of music that make it wildly different to mathematics, that mathematics is about stasis and containment while music is about flow and escape. But this argument only convincing as long as you buy into its proposed divide before you debate the possible connections; if you see pattern as being the apparatus through which emotion/heart is experienced (and expressed) in music, then a head/heart divide doesn’t make much sense, for example. And where Stephen Hough’s sees the experience of rhythmic ‘irregularity’ as taking music away from any connection or analogy with mathematics, I suspect a mathematician might immediately think of prime numbers, and other ‘irregular’ or singular mathematical entities.  And the notion of ‘unexpected’ reflects pattern-spotting competencies and experientially or culturally based perceptual expectations rather than anything intrinsically structural. Saying that music is nothing like maths because it includes unexpected developments is like saying a list of numbers is not mathematical simply because you can’t figure out (or predict) the next number in the sequence.

Say we were to ask ourselves what links between music and mathematics we could find, rather than the ways in which we could refute possible links, I think we would quickly establish that playing a musical instrument involves an exceptional degree of mathematical thinking. From spatial thinking (up, down, high, low, near, far, close, beside, under, above, and all manner of prepositional variations of ways we map and describe spatial relationships) through to fractional thinking (subdividing) through to symbolic representation of relationship, shape and direction and garden-variety counting: even when a musician is completely focussed on an emotional journey or an artistic truth, the expression of that journey and truth can take place without the aid of mathematical thinking.

So how do a significant number of musicians manage to persuade themselves that their music has no relationship to mathematics (if we accept that the two are deeply linked)? My first instinct and considered judgment is to blame it on poor mathematics education in primary and early secondary schools; if you don’t understand what maths is then you are unlikely to credit it as being much use or relevance to the things that define your identity.

I’ve been fascinated to learn this week that the mathematical knowledge that a preschooler brings to their first year of primary schooling is by far the strongest “predictor of a host of social-emotional skills” (see Early Childhood Mathematics Education Research: learning trajectories for young children, p.6).

I mean, wow.

I’ve not explored the research or analysis of that finding (what is it about early acquisition of mathematical skills and concepts that facilitates enhanced social and emotional skills?, is this a causal or a casual link?, etc.), but the idea that mathematical skillfulness has emotional and social benefits surely challenges every cliché that exists in the western educational model about maths and the limits of its purpose in education.

So far I am deeply persuaded that music and mathematics have complex connections, overlaps, correspondences and links, and the fact that we debate the existence of those links is mostly a sign of how little western culture understands what mathematics is.

To be continued….

Key Signature ≠ Key

It’s the 21st Century. We’ve had modulations and chromaticisms, bitonalities and even atonlities, and you’d think that in 2011 we’d have a modicum of sophistication regarding the tonal centres and key relationships we discover in the music we play.

But no, an insistence that the key signature tells us the tonal centre of a piece of music has gone from being an example of anachronism to being a deplorable trend in most major Australian cities (!).

To be fair, we do call those congregations of accidentals at the beginning of each line of music a key signature; that is, this term implies that the accidentals signify a key rather than simply the notes required to be played a tone or semitone higher than the straight note name pitch. But in a post-atonal, neo-modal world it defies experience to assume that an absence of key signature signifies the C Major/A minor duopoly.

Imagine my horror/bemusement/outrage/despair some 10 years ago on seeing a well-respected examination board describe a piece they’d included in their syllabus as being ‘in C’ simply because there were no flats or sharps in the key signature (and precious few in the music itself). If the writer of their teaching notes had played the music through they could surely, surely have been in no doubt that the piece began and ended on a G, and that G was ‘home’ in the way that only  tonic can be.

As egregious as this error was I’ve been noticing a far worse trend in the past twelve months: examiners who mark students wrong when they correctly identify the key of a signature-less piece of music as being other than C Major/A minor.

A teacher in Melbourne told me of a student presenting a Christopher Norton piece that is clearly in F Major (the left hand part consists of a descending F Major scale pattern, for goodness sake, played twice, and then that’s the end of the piece) whose report came back announcing that the student had failed to identify the piece as being in C Major. A teacher in Brisbane told me of a student presenting my piece, Safari, whose report came back saying that the student had incorrectly named the key as E flat minor [you'll notice there are only 5 flats in the key signature?!].

I’ve also had conversations with examiners who think a piece with one flat cannot be in the Dorian mode, even though the first and last bass notes are G (and G is clearly the home note); examiners who think that music with uniformly altered notes are still in the unaltered major or minor tonality; and examiners who fail to notice that pieces are in the Mixolydian mode.

This is a massive problem for assessment boards, for teachers, and for students who take their studies seriously. Examiners should not be the last to the party in music education, and it’s just embarrassing to think that teachers are having to explain to young students that they shouldn’t waste their emotional energy on the ignorant comments in the General Knowledge section of their piano exam reports.

Composers are going to keep writing music that doesn’t comform to the theory exam expectations; teachers understand this, and put considerable effort into understanding for themselves (and into teaching their students to understand) the way the composer is working.

The difference for the examination boards is that, for their integrity as assessment providers to be maintained, every single one of their examiners has to be up-to-the-moment in their comprehension of contemporary tonal languages. That’s just not the case at the moment.

It’s honestly not all that hard in most contemporary pieces:

  • which note feels like it’s the note the piece started on?
  • which note feels like it’s the note the piece ought to end on?
  • are the answers to these questions the same note? If yes, this is absolutely, without doubt, your tonal centre.
  • Now you know the tonal centre, is the piece in a mode? If yes, figure out which one.
  • If the piece is not in a mode, then just leave your answer at “the tonal centre is X” – that is sufficient for 2011 music assessments.
I’d love to hear more horror stories, but I’d much prefer to hear of examiners who are leading the way in getting it right.
And piano teachers: be confident in your sense of ‘home’ in a piece, and remember to train students to explain why they are convinced the tonal centre is the one they say. Maybe we can educate recalcitrant examiners by stealth.

Talking About Music….

You know the line “talking about music is like dancing about architecture“? It’s true: talking about music is a little like dancing about architecture (or singing about economics, if you prefer that version of the line), but I make this claim as someone who loves to sing about economics and who constantly dances about architecture.

Talking about music is one of my favourite things to do. I’m both fascinated by the way music works and astonished at its power to unite and divide, to motivate and to soothe. I think about music nearly all the time; admittedly, this is my ‘job’ as a composer, music educator, music publisher and marketer, but I’m certain that my musical jobs are the result of my thinking about music nearly all the time, rather than the other way around.

Mostly, I like to think and talk about the way music makes us feel.

This makes me a tad unusual in academic and art music circles, where a commonly held view is that “talking about how music makes you feel isn’t really talking about music at all” (Andrew Ford, Meet the Music mid-concert talk, Concert Hall, Sydney Opera House, October 21, 2010).

My view is the complete reverse: unless we are talking about how music makes us feel (in the sense of describing our feelings and in the sense of exploring how music elicits these emotional responses) we aren’t really talking about music at all.

All the chatter we can engage in regarding compositional devices and timbral effects really only makes sense when we apply that analysis to how these devices and effects change our physical and emotional worlds, whether we are performers or listeners, or both.

All this is by way of prefacing some recent talking about music that I’ve been engaging in.

Yvonne Frindle, the publications editor of the Sydney Symphony Orchestra, contacted me a couple of months ago about trying my hand at writing a program note for Matthew Hindson’s yet-to-be-premiered double piano concerto. Of course I jumped at the chance, and was soon collecting the score and some scraps of interviews and quotes in order to create the note.

I’m looking at scores all the time in my role as a composer and as an print music editor, but working through a full orchestral score is something I’ve not done for many a year, I realised wryly as I began to read through page after page. This is a BIG work by contemporary standards, where commissions are usually so modest that a new orchestral piece might only last for 12 minutes or so. At 25 minutes, roughly, this is a very substantial work. On top of this, having two pianists soloing against the orchestra creates new levels of compositional intrigue!

The first thing to strike me about the work was the emotional kaleidoscope Matthew Hindson has applied to his subject matter (the concerto is a commission to celebrate the marriage of the two pianist-soloists!) – the music really does explore what ‘marriage’ is about from a number of angles, rather than just paying lip service to the circumstances of the commission.

Now, I find this ‘first thing to strike me’ very interesting: it wasn’t any of Hindson’s compositional effects or devices that caught my attention, but rather the way the music was (is!) going to make the audience feel from one moment in the composition to the next.

After getting a sense of the emotional content of the work I went back and started looking at exactly what the audience would be hearing from a technical point of view: the melody in this instrument or that, the arpeggiated figures in this or that register, which particular interplays between ensemble and soloists. It was at this point that I noticed the very many ways in which Hindson has created bell-effects throughout the work.

I then went through the work again, this time with an ear for formal properties and an eye for traditional ways of explaining/analysing the construction of the work.

And then it was time to start writing: you can read the program note that ensued here.

One of the aspects of the composition that was most important in generating an emotional response from the audience was the use of the Lydian mode. In the program note you can see the breakout box we made explaining what the Lydian mode is, how it differs from the major scale, and so forth. Yvonne then asked me to create an audio feature for the SSO website, as a further means of explaining how the use of this mode works to create this emotional response.

Now while my singing about economics is rare, and my dancing about architecture rarely witnessed, my talking about music is now very much on the public record. And rather than being an irrelevant and tangental self-indulgence, talking about music is as much a part of musical culture as tuning a guitar before a jam-session or choosing just the right mix for a personalised playlist. Talking about music is about sharing our enthusiasms and our insights, and just as conversation makes people feel included and valued, so talking about music demonstrates the value music brings to our lives.

Talking about this particular new orchestral work has been a delight, and even more delightful is hearing back from people who’ve listened to the audio feature and have then gone and booked tickets to one of the concerts. Conversation creates community: long may we dance about architecture.

Major Harmonic Revisited

The last scale-of-the-day I blogged about (back on February 20) was the Major-Harmonic scale, and when I wrote my post about this particular pattern I found myself with little good to say about it (much to my own surprise). I complained about the clichéd cadence that this pattern allowed, and surmised that it may well have been the first scale to which I was impelled to give a thumbs down.

This negative assessment was no doubt impacted on quite considerably by the fact that that weekend I was supposed to get my first 8 hour sleep since 2006 (pregnancy, newborn, toddler who doesn’t sleep through) and thanks to noisy hotel neighbours it just didn’t happen.

But I think maybe more germane to my disdainful summary was that I was only thinking about this pattern in its C incarnation. This is an important point, because I know full well that the physical sensation of any pattern changes from one semitone to the next, and these physical changes impact on one’s imaginative interaction with that pattern.

On the weekend, in the throes of giving a presentation about P Plate Piano, I realised that one of the pieces I’ve composed for that series, “Hickory Dickory” uses this major-harmonic pattern (no other scale pattern fits), and “Hickory Dickory” is far from the hackneyed composition my assessment of the scale would suggest.  But then, it’s not on C.  It’s on F sharp.

Here’s the difference.

When we think of the Major-Harmonic scale on C it’s just the usual sequence of white notes interrupted just once, and by A flat. Once you have that particular geographical scene firmly pictured (along with the chord possibilities that immediately spring to mind) now move to the next image: the same pattern on F sharp.

The group of three black notes, followed by the start of the B minor scale (B C sharp D) and the raised 7th, E sharp, so that the pattern is black-black-black-white-black-white-white-black, with the gap between the two consecutive white notes being an augmented 2nd. And an augmented 2nd created by two white notes is always going to register somewhere in your pianistic mind as being just another way of spelling a minor 3rd (even though you definitely experience the interval in the scale pattern as a 2nd with an augmented quality).

“Hickory Dickory” mobiles these black note/white note patterns thus: the left hand only ever plays the three black note group, and the right hand only ever plays the three white notes of this major harmonic pattern (B, D and E sharp).  But of course, this is educational piano music for students in their first year or so of tuition, so the white notes are notated B D F, and in the context of this piece (with no 5th degree of the scale present) it definitely creates the impression of a diminished chord.

Here’s the first line of this piece:

Most of the piece is spent exploring this one run (across the full length of the piano keyboard), and beginner students find the piece both easy to learn and engaging to practice and perform.

The lesson for me here (besides being warned off reducing every pattern to an on C version) is that when working with new patterns don’t be constrained by the diatonic idea of using triads that skip every second note!  The major-harmonic pattern produces this wonderful, shimmering contrast between major melody and diminished chord, and if I hadn’t been fiddling about on the black notes I would have missed it altogether.

Scale of the Day: Major-Harmonic

This week let’s look at what I regard as being a kind of reverse of the mystery scale from the previous scale-of-the-day post.   Just as in our ‘mystery scale’ this is a major scale with a change made to only one note, but whereas last time we raised the 5th, this time we are lowering the 6th: same pitch, different degree, and very different end result.

Here it is on C:

It’s called Major-Harmonic in a fairly obvious way, the tail of the harmonic has been attached to the head and torso of the major pattern, and here’s our hybrid.

Being, to our diatonic ears, a hybrid, one might unthinkingly assume that this scale is a curiosity, rather than descriptive of real life music-making.

But take a listen to the chords this pattern makes:

The most significant change from the major scale triads is the chord IV is now chord iv – yep, it’s minor. [And along with that we have a diminished ii and an augmented VI.] This minor chord ivand diminished chord ii are what we need to make one of the most used cadences of the 20th century:

I’ve heard this referred to as the Hollywood cadence, and that label really sums it up!

The chord progression

or even more commonly

is a staple of the popular song – just hearing these chords moving from one to the other (especially with a soft electronic piano sound) evokes a torrent of lyric clichés just aching to attach themselves to this progression.

And once you have these clichés in your head, it’s hard to think what else this scale is good for.

Am I being too harsh? Dismissing the pattern as being of limited and prescribed value? Dissing the emotional content as pre-fabricated and predictable?

Well, one disclaimer: the scale is rarely strong enough to sustain an entire composition – one section of a song or piece might utilise this pattern for a while, but relief is needed, and it nearly always comes in the form of both a modulation to a new tonal centre and a new scale pattern.

Does this observation reflect how things need to be, or simply that composers have found this a convenient quick-fix for whatever emotional short-comings their compositions may have had? Are there pieces out there that do something with this scale beyond exploiting the tug of that minor chord iv?

I’d love to think this scale is the basis of something more profound than generic unrequited love songs!

Scale of the Day #2: The Simpsons Scale

Rather than alter the original post (which would make the comments below somewhat hard to follow) I will leave it as is, but point out that “The Simpsons Scale” certainly does have a name within the jazz tradition, the Lydian-Dominant (just as last week’s scale has a name within the tradition of South Indian classical music, “Mayamalavagowla”), so in reality when I call this scale “The Simpsons Scale” I am boldly naming what hundreds of thousands in the world of jazz have named before. (And note that this scale has a name in the South Indian tradition  [Mouli's comments below]).

Now this scale isn’t actually called “The Simpsons Scale”, but since it isn’t actually called anything [in western theory] I have decided to boldly name what no one has named before.

In reality the Simpsons scale is the melodic ascending pattern starting on the 4th degree, but it happens to be the pitch pattern used for the tonic harmonies in the theme music to The Simpsons, so I decree that the scale henceforth be known as…..

Here’s the pattern, in F (because the pattern of white/black notes is identical to that of G Major):And here in C (so it is easy to see at a glance which notes have been altered, and by how much, from a ‘neutral’ major pattern):

And here is how the theme from the Simpsons goes (in seriously truncated form, so that all the notes of the pattern as evident):

This sounds like the Lydian mode, to a casual listener, because the raised 4th is the predominant note in the melodic sequence, while the Mixolydian marker, the flattened 7th, only makes an appearance as the theme wraps up at the every end .  But a careful listener will notice that this is the only kind of 7th note that occurs in the harmony also.

Yes, this pattern has the Lydian and the Mixolydian marker notes, so it’s a kind of Hyperlydian, succeeding in doing both the fundamentally major modes at once.  It’s a sensationally modern take on major, sounding quirky but smart, and full of a very contemporary energy.

I used this “Simpsons Scale” as the basis for my trumpet composition, Go-Goanna, published by Faber Music in their Fingerprints series, and now an ABRSM exam piece (Grade 4). But while Danny Elfman creates the feeling that we are flickering between C Major and D Major, in Go-Goanna the melody is shaped so that it feels like an alternation between C Major and G minor (in transposition), with the G minor leading note (F sharp) as part of the equation.  It’s interesting to me that this same scale produces two equally successful harmonic partnerships from its triads.

It takes a while to become accustomed to playing this scale, obviously to the ear, which is expecting neither the raised 4th or flattened 7th, but more especially to the fingers, who simply refuse to believe that a major-sounding pattern has its two semitones positioned so close to one another.  This is why I included the scale pattern in F – one’s fingers can be tricked into playing this correctly quite swiftly if one focuses on playing that G Major pattern that we know so well, but hearing this brand new pattern! As it turns out, starting on G is a similar proposition: play the white/black note pattern of F Major and you’ll get it first try.  Starting on F sharp can be quite rewarding also, as one can concentrate on playing the C (really B sharp) and the E around the two black note group.

Have a play, and then have your say.  How do you like it, and what does it make you feel?  And is this name, The Simpsons Scale, really the right one??!