Music and the Quadrivium

Music and the Quadrivium

Music is delivered to us via our sense of hearing, which when young hears a wider range than when we are older. Our mind processes the complex mathematical formulas of sound waves, and that processing, can affect our mood, thoughts, feelings, and memories. Music is found in all cultures, at all human times – humming, hitting things together, singing, instruments. We have found a way, through music, to sounds and words much more integral to our lives than mere language.

There are so many aspects of music that it is impossible to scratch even the surface here. In a recent conversation, I asked a Brother, proficient in music theory, playing music, and song, what he felt the most important aspect of music was. Without hesitation he said, “The perfect fifth.” I asked him to explain.

M_Octave_Fourth_FifthThe human mind likes consonance, or harmony in its music. We find our minds like notes to be evenly spaced, and those that are not are “out of tune.” The perfect fifth is considered the most consonant of musical intervals. However, the musical scale cannot, mathematically, work with all perfect fifths, up octaves and down. There must be adjustment, otherwise it sounds “off.” This equal  interval spacing, what we’re familiar with today, is called equal temperament. There are several tuning methods, and several types of equal temperaments. These differences come from how the octave is divided mathematically.

This brings us to The Well-Tempered Clavier. The Well-Tempered Clavier is a collection of two series of Preludes and Fugues in all major and minor keys, composed for solo keyboard by Johann Sebastian Bach. It is sometimes assumed that by “well-tempered” Bach intended equal temperament, the standard modern keyboard tuning which became popular after Bach’s death, but modern scholars suggest instead a form of well temperament. There is debate whether Bach meant a range of similar temperaments, perhaps even altered slightly in practice from piece to piece, or a single specific “well-tempered” solution for all purposes. There are 24 pairs of preludes and fugues, in each book (48 total) each representing the entire set of musical keys.

Johann Sebastian Bach

Johann Sebastian Bach (1685 – 1750), German musician and composer playing the organ, circa 1725. From a print in the British Museum. (Photo by Rischgitz/Getty Images)

This set of music is significant for a few reasons. The first is that it is really Bach’s catalogue of the styles and techniques of Bach’s day. It inspired many composers and it can be seen, in some ways, as a type of “color card” for music – not unlike the paint chip cards you find in a hardware store. The music exploits tuning methods, temperaments, and construction that Bach would have used on any keyboard instrument.


Interesting book on humankind and music here: The Singing Neanderthals: the Origins of Music, Language, Mind and Body by Steven Mithen. London: Weidenfeld & Nicholson, 2005. ISBN 0-297-64317-7 374 pp.