If I have one regret, it is that I was never taught to play a musical instrument when I was younger. OK, I strummed my way around a guitar in my youth, but I never had any formal music lessons and I never learned the arcane skills of music-making. The small rural grammar school I attended in the 1960s offered piano and organ lessons, but they were private and extracurricular and, since no one ever actually asked me if I would like to do them, I didn't.

So, you might say, who cares? Does it really matter, given that I've come to enjoy music in its many different forms? (Well, OK...there are exceptions - I still can't cope with opera under any circumstances once the singing starts, and German romantic lieder leave me cold.) Some might say it was even an advantage - my now ludicrously eclectic musical tastes (or, as the musically sniffier might say, complete lack of taste) would have been strangled at birth by any kind of formal training. That may be so, but let me make a plea for music being far more important than that - in fact, let me try to persuade you that it ought to have a central place in the school curriculum.

I'll probably upset quite a few educationalists by doing this, but let me begin by pointing out that chanting the multiplication tables as a class was probably the fastest and best way of learning them, or anything else, if it comes to that. How often do we complain that the young can no longer do mental arithmetic? How could they? Since the abolition of rote learning and tables, there has been no real opportunity to acquire the rapid-fire automated responses that lie at the heart of this inestimable everyday skill. I'll also hazard a guess that it helps train the memory more generally as well, thereby making it easier to learn other things.

The real point is that chanting is one of the oldest forms of music-making. It has much in common with those ubiquitous nursery rhymes we so enthusiastically teach our children. It seems that the simple rhythmic melodies that characterise these forms of singing make them particularly easy to remember. It's not for nothing that stroke patients who have lost the power of speech are encouraged to sing the nursery rhymes they learned as children. The words and tunes are so deeply entrenched in memory that they are among the few things patients can still easily articulate in a way that can be used to scaffold the relearning of the motor skills required for speech.

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Even if we ignore all this practical stuff, music has a great deal to offer in the classroom. There is history in the development of Western music from pre-medieval times to the present, social history in the role that religion (in particular, organised religion) played in promoting music through the ages, and economics and politics in the way powerful families bought and sold musicians to enhance their status, as well as in the way the great Tudor composers such as Thomas Tallis and William Byrd managed to ride the waves of religious fanaticism to produce music of stunning beauty and exhilarating uplift for Catholic and Protestant services alike.

And there is all the wealth of cultural comparison that arises out of the rich veins of world music. It is music that anyone can appreciate and enjoy, without need of language or a Rough Guide, any more than you need to understand Latin to appreciate the deep angst of Allegri's Miserere when you hear the treble's haunting embellishments hung around that achingly high C. Or the emotional wrenchings in the sometimes extraordinary chromaticisms of Gesualdo's Sacrae Cantiones motets heard in the semi-dark of a medieval chapel.

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And speaking of Gesualdo, there's nothing like a good murder mystery and a bit of scandal to spark the interest of youth, and the social history behind much early music is packed full of exciting stuff. Gesualdo famously did for his wife and her lover, having caught them in flagrante, in a manner that was considered spectacularly gory even for the 1590s. It's all there in the court records, even though he got away scot-free because he was the local toff (more social and a bit of legal history here - not to mention some psychology, as he was obviously a very tortured bloke).

Incidentally, and only slightly tangentially, this reminds me that during the 13th century, a tradition developed for motets redolent with double meanings. A nice religious text such as an Alleluia, often in Latin, was set to a well-known ecclesiastical tune (usually plainchant) in the tenor line (known as the cantus firmus), and an often decidedly raunchy secular text (a knight recounts how he tried to seduce some poor shepherdess), usually in the vernacular, was set as the corresponding triplum line in the upper voice that embellished on the tenor's cantus firmus.

There's a particularly cheeky one that has always bemused me entitled Hiprocatae, pseudopontifices (hypocritical pseudo-prelates). In it, the bigwigs of the Church are praised as upstanding citizens in the tenor line (sung to the then-popular Ascension plainchant Et gaudibus) and damned as greedy, self-interested gluttons in the triplum. "The deeds of prelates shine forth like stars in the heavens. They are the basis of the holy edifice, the fount of virtues...clouds dripping honey...etc, etc," sings the tenor, while above him we hear: "The hypocrites, false prelates, hardened killers of the church, clink their glasses in their boozy orgies." Or, as one particularly resonant line has it: "In crapulis edulis calices germinant" (loosely: they sow the seeds of profit with tears). Sounds like an anthem for bankers to me. Who says history isn't fun?

But before you're tempted to think that music is good only for the humanities, don't forget that music itself is a physical process that exploits a physiological one. So understanding how instruments work teaches us about physics, and understanding how we hear music gives us physiology, while understanding why we respond to it so appreciatively teaches us about both psychology and evolution (how, why and when did our species come to acquire this capacity?), not to mention comparative biology (are we the only species that can produce and appreciate music?).

There's even maths buried in there. Mathematicians are often said to be particularly drawn to Vivaldi's musical precision and clarity. But if musical mathematics really grabs you, you could do worse than try Pachelbel's Canon in D major. Composed towards the end of the 17th century (some have suggested for Bach's wedding in 1694), it is a masterclass in the mathematics of canonic composition. Its exquisitely simple rocking eight-note base line is progressively developed in the melody lines into elegant variations with controlled mathematical precision. It's a form of composition that depends not just on musical skill, but a deep appreciation of the arithmetic of permutations.

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And before you get sniffy about all this musty old music from musty old times, let me remind you that Pachelbel's Canon is still hot stuff. Its mesmerically simple base line, or the chord progression based on it, has provided the basis for more than 80 pop songs since the 1960s. Iconic examples include the Bee Gees's Spicks and Specks, Ralph McTell's Streets of London (check out especially Mary Hopkin's cover version), Brian Eno's Fullness of Wind, and the Oasis hit Don't Look Back in Anger, as well as the Village People (they of YMCA fame) hit Go West (very clear in the Pet Shop Boys' cover version). Not to mention the unashamed borrowing in Monty Python's Decomposing Composers. Such is modern music's debt to the past.

All this mention of early music prompts a personal confession. In the late 1960s, I spent three years as an undergraduate at Magdalen College, Oxford, but I never once heard the college choir sing. In my musical ignorance, I simply did not appreciate what was on offer from a world-class choir, then at the height of one of its many halcyon phases under the tutelage of the sainted Bernard Rose. For reasons that continue to baffle me (except that going to chapel probably wasn't exactly cool in the 1960s), I just never made the connection between a chapel choir and good music - and no one told me otherwise. Having found myself back at the college four decades later, it's been pure pleasure to extirpate all that remorse by making time to hear the choir sing at least once a week. Five-and-a-half centuries (sorry, more history) of tradition and dedication has culminated in a choir capable of moving effortlessly from medieval plainchant in faultless Latin to Bach cantatas in German and contemporary pieces, and all within the same half-hour.

Of course, none of this music-making comes for free. It is the product of an enormous amount of hard work, commitment and hours of dedicated practice - by some very young boys in the case of the college choir. Which should remind us that, besides all the academic advantages, the performance of music has important practical benefits. It teaches discipline, integration, coordination and synchrony. You just don't get good music by slapping away at a bass in a social vacuum. It's about timing and how you coordinate your actions with everyone else. These are skills that are fundamental, not just in everyday social life, but in the pursuit of any kind of scholarship. I often wonder whether choirboys do disproportionately well in their exams - there must be some statistics somewhere.

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But there is also a social side of music that is important. Chanting in unison in class is probably still the best way of engendering a sense of community. Would we have a more cohesive sense of community, more commitment to the common project, if we had more singing and music in school? One need only think of work songs such as sea shanties (more social and world history, by the way) and the way they seem able to ramp up the work effort in collaborative tasks.

Actually, if you want to hear work songs at their most exuberant, you can't do better than the women's waulking songs (orain luaidh in the Gaelic) of the Outer Hebrides. Their powerful rhythmic drive (traditionally created by thumping raw tweed cloth on the table to stretch and soften it) combined with their sense of fun (though often the words are just nonsense phrases, they can sometimes be extremely raunchy) creates an extraordinary uplift. The key is rhythm and synchronicity again - and doing it socially. Alas, they are all in Gaelic, but then there's the added benefit of being able to learn a new language in the process.

Music, when you think about it, is genuinely weird stuff. It has a capacity to move us - literally so on the dance floor - like nothing else. And sometimes that can be at its most basic level. There is something deeply compelling about highly synchronised dancing that seems to play a very strong role in social bonding. The sociologist ?mile Durkheim referred to this phenomenon as effervescence, but I'm not sure that really captures quite what's involved. It's certainly an emotional uplift, but the real power of it comes from the way it creates a sense of belonging, of being part of a community.

There's something in the synchrony of simple dance that creates this effect. Aficionados of salsa as much as Scottish country dancing know well the buzz that comes from successfully completing a perfectly timed and coordinated sequence of moves with a partner, as two bodies literally become one. Timing, rhythm and synchrony are everything. It's not for nothing that the military continue to use marching drills several centuries after their original purpose (coordinating firing lines with muzzle-loading rifles) ceased to be of any relevance.

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So, my bottom line is that we should do away with the entire school curriculum and have one long music lesson instead (not forgetting the salsa class in the middle). That way, we would cover pretty much everything in the national curriculum, all within an overarching themed structure - and have a great deal more fun doing it. I sometimes wonder whether we haven't missed the point of education.