Musical genius has always intrigued me - I guess because I don't have it. How is it that one composer turns a few ordinary notes into pure creative gold, while another systematically turns a brilliant start into a dull conclusion? And why is my list of geniuses different from yours - and, in fact, different from my own list of a decade ago?

In an age of limitless data and visual domination, the mysteries of the more intangible senses - smell, taste, touch and sound - remain. Music, as a form of structured sound, still stands firmly at the frontier of human understanding. Richard Wagner recognised music as the "deepest" of the art forms because of its very intangibility. Words, stage design and choreography are all more tangible. But invisible, wordless music comes closest to something quintessentially human yet so elusive ... the soul?

One of the hardest questions I ever fielded as a music lecturer was: "What do you look at when you listen to music?" The cellist's legs? The conductor's wielding of the baton? The programme booklet? "You should try to transcend the visual" or "why not just close your eyes?" are not sufficient answers, for you have here basic human senses in conflict.

Recently I was at Kings Place, London's cool new concert venue near King's Cross Station. Peter Cropper (violin) and Martin Roscoe (piano) were playing the cycle of Brahms and Schubert violin sonatas.

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Cropper turned to Roscoe and raised an eyebrow. What was that bit of non-verbal communication about, I mused: "You're a bit loud"? "Let's move it on a touch"? "Hey, that was different!" Yes, that was it.

You can have played the same piece for 40 years and yet suddenly, this time, it's different. Sometimes it's so different that you wonder how you can have been so stupid for so long! Of course, now I see it - that was what the composer intended! Perhaps this new revelation is even expressed in a nuance of the musical notation: precisely where a bowing slur ended for the violin, or in the exact placement of a note on the page, or through the suggested fingering for the pianist. These are the visible or bodily signs of - indeed, the clues to - an aural intention.

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But let's not get too theoretical. In music, the piece never quite settles. A particularly neat landing after the helter-skelter of some fast scales, or an unusual balance of the notes between two instruments, makes you sit up and think. The notation of music hasn't changed since 1823, but our interpretation keeps on changing as we read and hear things differently. Like a novel, the musical work becomes a new act of interpretation every time we engage with it. We even suspend our knowledge of what we well know comes later on, in the desire to conceive the piece anew, in real time.

I guess that's why Herbert von Karajan recorded the entire set of Beethoven's symphonies four times - because, over time, new revelations led to new interpretations: same works, same conductor, often even the same orchestra, but different valuations and judgments.

Some of my greatest joys are these many "mini-eureka" musical revelations, where musical understanding is reforged and musical values reassigned. These revelatory moments leave, for instance, Prokofiev lower, but Rachmaninov higher, in my personal ranking of musical geniuses, compared with a decade ago. What I once took as trite, I now take as inspired - and the release of complete sets of Rachmaninov's own recordings helps one immeasurably along this track of revaluation. He is recent enough for us to be able to hear many of his own interpretations, and so we can go beyond the simple inheritance of his scores or verbal descriptions of how pieces were once played.

Last night, I was stumbling through an unfamiliar Brahms intermezzo and came upon the weirdest spelling. Musical spelling, I mean. I was playing one of the most common patterns in classical music, D-F -A, and yet Brahms had systematically spelled it as E -G -B. Now, you don't need to know what these different notations mean to get the point: Brahms had deliberately, for some reason, chosen a very different, more fussy, more obscure spelling of the notes he wanted the pianist to press. Why would he do that?

So, to the one and only "maxi-eureka" moment of my life. It's London, mid-1981. I'm a masters student at King's College London. One morning I woke up and said to my (then and now) partner: "I've just written my PhD!" I wasn't particularly prone to delusion, so he quickly reminded me: "Don't be stupid. You haven't written your masters thesis yet, and it's due in eight weeks!"

But that night the PhD had, in fact, been written. The conceptual breakthrough had taken place. (As with many breakthroughs, it just took another five years to write it out in full!) And as with most breakthroughs, it was so simple. I had dreamt that somehow, by "playing back" a composition's notations, I had re-entered the long-dead composer's mind. Exactly how?

In one manner of speaking, classical music has 12 notes. If you have a piano to hand, you'll notice there is a pattern to the keys. Start wherever you like and you'll find that there are seven white notes interspersed with five black notes before the pattern repeats itself. Yet when you look at musical notation you find that there are 21 (3 x 7) different ways in which you can "spell" those 12 notes. (Musicians know these as A, A, A ; B, B, B, etc., up to letter-name G.) In fact, in more complex music, like the Brahms mentioned above, it is 35 (yes, 5 x 7; A, A, A, A, A ; and so on.) Let's call this the 7-12-21-35 system.

Now, I'm hardly the first person to have noticed this. What was special about my dream was that it provided some really neat frameworks for analysing a composer's notations. In combination, these gave the main bases of notational theory: not just the theory of my PhD, but the wider precepts of the field of "notational musical analysis", as practised now by a couple of dozen scholars around the world.

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(At this stage, dear reader, you're probably thinking: "Well, what's the economic impact of that research?" Let me declare straight away that it's probably not nil, but rather, more probably, negative. Trees have been cut down and carbon footprints pressed through pursuit of such "useless" lines of thought. And a string of PhD students have been deflected from more economically productive lines of inquiry, although many have ultimately found good use for their skills in rather forensic types of work.)

One other thing emerged from my dream: compromise. Musical notation is a compromise between three things: first, theoretical purity - the most correct spelling of the musical thoughts; second, readability - what a player can quickly process; and third, instrumental features - how the strings, holes, keys and fingers are arranged. (Playing the piano, for instance, involves all ten fingers, while the violin effectively uses only four, all on the left hand.)

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So, while you can be like Brahms and write your fussy correct spellings, many composers will, past a certain point, ditch the purity and go for easier readability, especially if that accords with the arrangement of, say, the violin's strings.

Ask an experienced musician and they can tell you who the purposeful musical spellers are - that is, the ones who really seek to reflect the underlying bases of their musical thoughts in a work's notations. Use of a good cross-section of the total set of 35 spellings usually indicates a self-aware speller, although not necessarily a good one. And each composer, of course, draws a different line of compromise.

As with English spelling and grammar, there are regional and temporal variations. My favourite musical spellers are from Eastern Europe at the turn of the last century. Why? Well, because they had a particularly consistent form of musical education, yet were not as weighed down by tradition as the Germans, Austrians and some of the French.

Sergei Rachmaninov (1873-1943) is a most beautiful speller, with real depth of meaning in the way he uses the 35 spellings (and he uses all of them somewhere or other). Although relatively conservative in the style of music he was writing, his spellings are elegant yet relatively uncompromising in reflecting the many different layers of the music. In his notations for piano (although less so for other instruments), he reflects every nuance of his musical thinking, which was always highly pianistic. So, with a small book of rules, you can "play back" Rachmaninov's notations to gain an incredibly vivid impression of his underlying compositional intentions - much more convincingly than with most Austro-German composers of his time, such as Richard Strauss.

Aleksandr Scriabin (1871-1915), Rachmaninov's contemporary and fellow Russian, was much more radical. While Rachmaninov was still comfortably a 7-12-21-35 kind of man, Scriabin was a more daring thinker. Why not play with some of these variables, for instance by starting with 8 or 6 before the patterns replicate? (Musicians will recognise these as, for instance, octatonic or whole-tone bases.) What about 6-6-21-35? Or 8-4-21-35?

A real and tense drama is played out in Scriabin's scores as the theoretical purity of such radical music accommodates what is still readable to the player and matched to instruments designed for another musical age. Players will tell you that his music does not make easy reading, as he sacrifices purity as seldom as possible. His scores then are codes of real beauty and keys to deep levels of musical meaning.

The subject of my dream in 1981, however, was not a Russian, but a Hungarian, Bela Bart?k (1881-1945). I was trying to understand, and even play, his fiendish Sonata for Solo Violin, but was not making much progress with either pursuit. But I already knew Bart?k to be a dutiful and thoughtful speller. The experience of carefully notating and analysing thousands of folk songs had given him an almost scientific precision, the principles of which he even described in the prefaces to his folk-music volumes. That notation was the key to a world of brilliantly vibrant tonal mosaics. Even a work written for a solo violin - with a single line for much of the time - produced such wondrous and subtle "tonal thought". And as the years went by, I expanded the analysis to music for larger resources: chamber, choral, orchestral.

That night in 1981, my PhD was indeed written. The formalisation of the theory, the carrying out of case studies, the formulation of worthy conclusions remained to be carried out. But, as with most eureka moments, one knew one thing: the ultimate intellectual "problem" had been solved. The way forward could be taken, with confidence about its end point.

But was I right? Every seven years or so, I return to these theories and write a new paper. The general principles have withstood the test of time, but my interpretations and emphases continue to change. Like those broader musical valuations, a particular performance makes me rethink a piece, a conference paper suddenly presents a more enlightened analysis, and a new archival discovery solves one problem while often raising another.

That is what is so wonderful about humanistic research. Knowledge progresses; methodologies evolve; "solutions" become provisional, confirmed and then often become suspect. We keep ourselves humble before the evolving nature of artistic truth. As I became more involved in university administration, even that started to influence my views about how musical materials are organised, although I must admit that the influence the other way was probably stronger.

Musical eureka moments became a particular interest when I began to edit Oxford University Press' Studies in Musical Genesis, Structure, and Interpretation series, with its pragmatic, blow-by-blow focus on how great musical works came into existence. What is clear from the volumes in that series is that eureka moments come in many shapes and sizes, but that composers are very cagey about describing their moments of creative breakthrough. It's almost as if they fear that these magical moments will desert them if they try to analyse them or expose them to wider scrutiny.

There is, however, something of a common theme about sleep and creativity. Somehow, bedroom rituals jumble things up yet cause them then to settle into new, unexpected patterns. So my advice is to keep your BlackBerry under your pillow at night, and text yourself your own bright ideas. It's also useful for catching those early-morning calls from your vice-chancellor!

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