Speaking of tuning, before there was Cosmos and Carl Sagan, there was BBC’s Ascent of Man. (Make that “humankind” now, of course.) And there’s something charming about its breathless reminder of the mystical magic of Pythagorean tuning, and its mythical discovery in folklore. Fact check – as the film sort of suggests, we don’t really know how this discovery took place since our knowledge is fragmentary. It may not have involved any individual named Pythagoras, or indeed taken place on Samos. But the power associated with the harmony of mathematics, sound, and perception does have historical basis – in the Classical era, in the resurrection of those ideals (in the Middle Ages and Renaissance), and in modern times.


BBC Ascent of Man – 04 – Music of the Spheres von infinitradiant

Actually, interestingly, it may be the notion of “Western,” if anything, that’s breaking apart. The disclaimer the BBC attached to what is or isn’t pleasing in tuning may artificially separate western European civilization from everything else. In reality, tuning systems were historically diverse up until the belated standardization on 440Hz A and 12-tone-equal temperament in modern times – and even those aren’t universal across America and Europe in classical concert music, let alone when you take into account everything else. To look at it the other way, the audiences watching this BBC documentary in the UK were already used to harmonies in popular music that contain far more complex sonorities than whole tone ratios would suggest.

Likewise, I’ve never read any convincing argument that any particular tuning is definitively pleasing to the ears. Our ears are, however, sensitive to tuning, and can learn to appreciate alternative tunings just as they can learn to hear different rhythmic or metrical structures.

But what is more consistent is the sense of wonder about Pythagorean findings and the early human understanding of the world. And why not? The Pythagorean Theorem and the discovery of tuning is pretty darned cool, fellow humans.

  • PaulDavisTheFirst

    Bronowski was a treasure. He entranced me as a 10 year old, both on “The Ascent of Man” and elsewhere. Sad when he died (I was 11). Can you imagine being a curious 10 year and hearing this person linking gravity, the horizon and music?

  • CayceP

    Finally someone taking about Pythagorean tuning system! What I find most interesting about comparing Pythagorean versus Equal Temperament is the breakdown of the ratios. Pythagorean uses the octave (2:1), the fifth (3:2), and the fourth (4:3), thereby having mathematically perfect ratios (or simple) at the cost of the “leftover” Pythagorean comma (between 75:74 and 74:73). This leftover amount (often described as a wolf tone) plagued many systems of tuning over the centuries as they tried to redistribute it.
    Enter Equal Temperament (centuries later) and a system that finally spreads tones across the entire octave. This freed the fixed tuning keyboard instruments to play any music in any key with any other instruments.
    But – in the Equal tuning the only mathematically perfect ratio is the octave (2:1) while everything else (especially the fifths) are slightly off.
    But what does this all mean?! Is there is a breakdown between theory and practice, and does it even matter that our modern system of tuning is based on imperfect fractions?
    I have actually always found that, in isolation, the intervals on a piano sound “off” to my ears (except for the octave) – could my brain be picking up on this?
    I ask you – Peter, and CDM readers – how would I go about trying to write music using Pythagorean tuning? I think Synthmaster lets you upload tunings – how would I go about trying to make music using perfect ratio intervals?
    If anyone is interested you should check out “The Manual of Harmonics” by Nichomachus the Pythagorean.

  • TheDalaiSputnik

    Thought it was going to be James Burke, saw it is Bronowski. Not disappointed. I remember seeing the series eons ago, I think PBS picked it up in the States. Absolutely brilliant. All the chapters are available at DailyMotion.

  • Roikat

    Pythagoras may have learned what he is noted for in both geometry and music theory during the years he was a court philosopher in Persia. Ancient music theory seems to have been pioneered in China and traveled west on the silk road. There was no “eastern” vs. “western” culture before the Mongols exterminated the cultures of Central Asia, creating a cultural gap in the region.