Blues & the Abstract Truth

The 6th century BC mathematician Pythagoras is known best for his theorem relating the length of sides and hypotenuse of a right triangle. But to my mind his greatest invention was the blues scale. Pythagoras and his followers built a religion full of rituals, and believed in immortality and transmigration of souls at the heart of which was a universe based on numbers. Every aspect of life was expressible in number. Marriage for example was the number 5 as the union of a man =3 and a woman =2. Musical harmony was similarly expressible in number – the length of string determined the note produced, and that note was then related exactly to other notes by fixed ratios of string length. The heavens were ruled by a pentatonic harmony, with each of the five known planets of Pythagoras’ day occupying a sphere whose radius allowed it to vibrate harmonically with the others – what came to be known as ‘the music of the spheres.’ Indeed, these pentatonic harmonies of planetary motion have their modern scientific restatement in Bode’s Law.

Pythagorean tuning is based on geometric note relationships; the pentatonic scale was devised with the use of only the octave, fifth and fourth (i.e., a fifth down). It produces three intervals with ratio 9/8 and two larger intervals. Think of this as a minor blues scale (sans 5b) on the piano – in C this would be C, Eb, F, G, Bb (this is also called the "rock" scale). Think of building a scale only with 5ths and octaves, from C you go up a 5th for the G, down a 5th for the F, down another 5th for the Bb, and down another 5th for the Eb. These are ‘just’ intonations (there are no beats or dissonances in the notes in the scale) so that scale is, from a human hearing standpoint, an ideal scale. Unfortunately, this neat Pythagorean number system breaks down for intervals other than the octave, fourth and fifth (Pythagorian thirds just don't cut it) which was the reason that other tunings were invented. Modern equal temperament, for example, keeps the fourths and fifths within 5 cents of the Pythagorean tuning, and spreads the dissonance across all the notes of a diatonic or chromatic scale.

The intervals of the pentatonic scale are integral to the psychology of music and to human hearing; it somehow resonates with us at a very fundamental level. I think this and the importance of stringed instruments in most musical cultures must be the reason that the pentatonic shows up in folk music around the world. It is the musical counterpart to Noam Chomsky's “deep structures” universal grammar underlying all languages and corresponding to an innate capacity of the human brain.

In the Middle Ages, the church outlawed pentatonic melodies along with major-minor (Ionian, Aeolian modes) and substituted the church modal systems for religious music. The mediaeval church wanted people to pull away from the sensual and secular; to get people to stop dancing and tapping feet. The pentatonic came back into use in the Renaissance with the waning of church influence.

The modern jazz blues scale grew out of impromptu pentatonic harmonies in the folk music of the rural South. At the turn of the 20th century, W.C. (“Father of the Blues”) Handy composed a campaign song for E.H. Crump, the candidate for mayor of Memphis Tennessee, using harmonies that he first heard from a banjo player while waiting at a train station in Mississippi. The song, "Mr. Crump," was later retitled "Memphis Blues" and became very popular, to be followed by St. Louis Blues, and so forth. Handy's "blues scale" added the flat 5th (in C this is C, Eb, F, Gb, G, Bb) which I would guess arose out of folk banjo music with the flat 5 a 'bent' note sliding into the dominant. On the piano for which Handy’s music was published, with its tempered, enharmonic tunings, the blues scale became something else; a scale that could fit with a diverse array of harmonies. Given some of the barroom pianos that I've had the experience of playing on, I could see how pentatonic versatility would be a real asset.

The blues scale along with convincing voice leading in the bass line are two of the most powerful inventions in music, contributing as much to excitement, forward motion and ‘groove’ in music as does the underlying rhythm. It’s ironic that we can trace the emotional force of the blues scale back directly to the mathematical proclivities of Pythagoras.