What is harmony? In music school we get taught something to do with beats and ratios and the harmonics of vibrating strings, but when we stop to actually ask people, that elegant old model very quickly falls apart. In the two and a half millennia since Pythagoras we've tended to all agree on the unison, octave and the perfect fifth as somehow consonant, but what of the tritone? Or the minor second and major seventh? Why one more than another, why do our harmonic tastes vary culturally and regionally, and temporally, and yet despite this apparent relativism of harmonic aesthetics, why do we universally all find it so very easy to put these twelve possible intervals into a preferred order, and why is it so easy to spot intervals falling outside the basic twelve tone series, even with no actual musical training, even by those who profess to be tone-deaf?

What is this goddess Harmony?

... and where does she come from? Says Dale Purves, our universal human Muse of Harmony is closer than we think: she rises naturally from the very sounds we need to tell a boat from a boot:

The frequency ratios at which sound energy is concentrated in speech sounds accord with the fundamental frequency ratios that define the chromatic scale intervals (Figure 6). Moreover, the difference in the amount of sound energy concentrated at each frequency ratio predicts the consonance ordering of chromatic scale tone combinations
[ Purves Lab / Research / Explanation / Sound and Music / Hearing Pitch and Music ]

the harmonic error

Now here's where it gets interesting: our current 12-tone scale is largely an artifact of our science, commerce and convenience, borne of a necessity to manufacture a standard set of instruments capable of playing together in any of standard keys surrounding our SI metric A-440. This was adopted apres Beethoven to replace the mathematically founded Well-Tempered intonation pioneered by the likes of J.S.Bach, itself a 'correction' of the Just (as in Justice) scale wrenched from the Greeks.

Ok, it was a bit more complicated than that, but here's the thing: our intonation models were not based on people, they were all based on mathematics, on abstracts. These models were devised to distribute the error (sic) from the old Pythagorean model of vibrating strings in an effort to compromise on a pragmatic least-bad harmonic system for ensemble (ie court and church) playing. These systems also make a tacit assumption of the correctness of the original Pythagorean model, and of the righteousness of the mathematical method.

"It doesn't matter how beautiful your theory is, it doesn't matter how smart you are. If it doesn't agree with experiment, it's wrong" -- Richard Feynman

In music, our empirical observation is the spread of the spark. I've been re-listening to the old Alan Lomax appallacian tapes lately, and the old field recordings from the Kentucky hills and the southern blues men back before Beale Street got 'remodelled'. A lot of this is music before Sears and Roebuck injected the 'correct' intonation fretted guitar and mandolin into a folk music that had existed outside of the conservatory mainstream; black performers were the first to take to the guitar -- they'd long before recognized how to rip the sound you want from anything you could get -- standard tunings slowly dispersed out across an ancient music that was soon to be discarded, abandoned as sure a 'betrayal' of your base 'ignorance' and your poor heathen roots as the dirty overalls and rough hands. Because it was 'wrong'.

Grandpa Jones was once asked if he could read music. "Not enough to hurt my playin'!"

Seems to me the musicians, the better musicians, the master musicians who can ignite a room with their playing, they all learn ways to bend these conservatory rules. Classical players and composers use propitious glissando and vibrato to tickle the boundary frequencies at the right spots - John Cage writes in 'Silence' on how even the most conscientious performance of Bach or Mozart cannot play to score, and most competent performers never pretend to because they want the music to come alive. Jazz and blues musicians use bends and slides trying to reach the right spots; I think it was Duke who became enlightened upon seeing a busker play guitar with a knife-blade for a slide. Mingus said Ornette "couldn't play a C scale in tune" but confessed that Ornette played right -- Ornette and Don Cherry were said to spend their days at Lenox playing long tones at each other, searching, searching for a 'better' sound; Ornette later called that Harmolodics, a new musical aesthetic he's yet to articulate in words, but one that nonetheless clearly informs his work and that of everyone to ever pass through his band.

Sun Ra would tell his band, "There are a million notes between C and D." -- rehearsals would often spend hours on a phrase, over and over, searching for that Unknown as Ra called it. Sun Ra may have had a palette of those million tones, but it was clear he didn't arbitrarily use just any of them. Ra said he was 'correcting' the harmonies of the old Henderson standards. Ra called his aesthetic Tone Science, and I think it was also Mingus or maybe Monk who said of Sun Ra that he "Played wrong right."

Played wrong --- there's an ugly side to that labelling, and if you look at the chart here, you'll see something: Dale's intervals do not match exactly to the Just Intonation ratios! Some fall just slightly short of the 'correct' pitch, and, curiously, those that do are, just so happens, among the intervals these musicians like to torque into place! Coincidence? Or are the particularly sensitive (and those innocent of the 'training') musicians inescapably drawn to correct their harmonies?

the music of Is

Could it be, is it possible, is it even thinkable that the past 2500 years of the Theory of Music neglected to consider the reality of the creature who makes and hears the music, blindly striving only toward some artificial mathematical map handed down through the ages, founded on nothing more than a dogma chained to a bad assumption?

And could we be closing in on a new Theory of Music that will not just exonerate 'primitive' musics as de facto empirically correct? Imagine, a School of Music 180-degrees turned around toward modeling the music of Is instead of idolizing at a music of Never Was!