Skip to main content

What does the square root of 2 sound like?

Mar 19, 2018 08:59AM ● Published by Editor

By Doug Sanders, Grand Marais Community Member

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.

Student Voices
Boreal Ship Spotter - larger view here

Weather Alerts Provided by Willy Weather