In an earlier column, I discussed how Pythagoras’ harmonic fractions (1/8, 1/4, 1/3, etc.) are related to the development of the musical scales used to create harmony today.

The device he experimented with was an ancient instrument called the monochord. It consisted of a single string with a movable bridge stretched over a sound box, upon which one could mark the positions of mathematical intervals.

It was through that process of musical exploration that he identified the primary relationship between fractions and the harmonic overtone series found in nature.

The seven-note scales derived from those fractions are called modes. They are referred to as diatonic scales because they consist of whole and half-step intervals.

Early depictions of the seven-stringed kithara, an ancient Greek predecessor of the guitar, indicate Greek modes were played against a drone which provided a context for the intervallic relationships of the various scales to a tonal center or tonic.

Changing the pitch of the drone would change the mode being played, and consequently the melodic possibilities of the scale.

Plato is credited with naming these modes after the Greek city states, so musicians use the esoteric names of Ionian, Dorian, Phrygian, Lydian, Myxolydian, Aeolian and Locrian to describe them.

A great deal of Plato’s philosophical musings are dedicated to nature of the modes, and his beliefs that behaviors, attitudes, abilities, and even social welfare were tied to their qualities.

He recommends, for example, that soldiers listen to the Dorian or Phrygian modes to gain strength, and warned weak minds would result from prolonged exposure to the Myxolydian.

Most would argue today that tempo, inflection, rhythmic meter, context, expectation and harmonic progression have more to do with the mood of a song than the mode, but it seems happier songs are played more often in major keys, and sadder songs are played in minor ones.

Perhaps there are innate emotional qualities to the scales themselves.

Considering that an unlimited number of pitches exist in nature, it is amazing to find such a seemingly endless array of musical styles and expression based on just a few seven note scales. Most of us understand the emotional appeal of a particular song, but it is more difficult to put a finger on just what creates the mood of the piece.