What does the square root of 2 sound like?
Mar 19, 2018 08:59AM
When I am a speaker for high school math classes, I begin by asking “If anyone knows what the square root of 2 sounds like?” Dead silence. Having already requested a tuned piano in our presence, I ask a volunteer to simultaneously hit any F# key and the C key immediately to the left. The ratio of those keys’ frequencies (F#/divided by C) is exactly the square root of 2 This square root is an irrational number where sequences of the digits do not repeat. The sound is discordant in our brain.
The ratio of frequencies in a C Chord is a rational number where sequences of its digits repeat and result in a pleasant sound.
Our brain performs instant mathematics when listening to musical chords. Irrational ratioed chords are discordant (as in Jazz , in Blues and in much of today’s popular music).
The ancient Greek music scale had only 8 notes vs. our 12
note scale. An ancient Greek could not
play a C chord. He or she did not
perform too many chords!
My background includes being a pianist and having a career
in mathematics, an actuary involved in climate change and health care.
Math Footnote: Our modern 12 note scale has each key’s frequency increasing by the 12th root of 2. Middle C on an 88 note piano has a frequency of 261.6….Hertz or cycles per second. The F# key above has a frequency of 370.0… Hertz. The ratio of 370.0…/261.6… is 1.41421…., the square root of 2.
The frequencies ratioed
middle G E & C keys (G
divided by E divided by C or (392.0../329.6../261.6..) is
.0045458989… a rational number since sequences of digital numbers do repeat.