count it off

In 1623 Galileo declared that "Mathematics is the language of the universe," and he might have added, echoing the words of Pythagoras who preceded him by 2,000 years, that mathematics is also the music of the spheres. For music, with all of its emotions and passion, is based on the same kind of mathematical, clockwork-like relationships that govern the movements of the celestial bodies.

A musical note is a vibration, producing a measurable and predictable number of waves per second, and it's always the same number whether that note is plucked on a string or blown through a horn. If you shorten the string by half or reduce the empty space in the horn's chamber by the same amount, you'll produce the same note exactly one octave higher. Double the string's length and you get the same note an octave lower. The relationships among the notes get more complex from there, for example, if you shorten the string by one-third, you'll produce the fifth note in the eight-note scale determined by the original note. But no matter how complicated they are, the relationships between and among notes, including harmonies, are all by the numbers.

Some music is arhythmical, and marrying rhythms with tones combines two independent sets of mathematical relationships into an interdependent whole. Rhythm, after all, is just the musical counting of time, and the pulse which gives rise to the dance. Rhythms can be as simple as counting to two, or disarmingly complex even though natural-sounding. Have some fun here, seeing if you can discern the time signature of the Afghan National Dance.

Speaking of dance calls up another separate but related universe of mathematical relationships, one which translates numbers into muscular movements and numerically-expressed postures.

To paraphrase Gottfried Leibniz, melody, rhythm, and dance are "pleasures the human mind experiences from counting without being aware that it is counting."

This topic was derived from a random blog topic generator.

Photos: top left -- Wild Bill Davison (left) and Tony Parenti at Jimmy Ryan's Club, New York, 1946. Bottom right -- rembetika singer and dancer Marika Papagika, New York, early 1920's.

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