Harmonics (Overtone Series)

General

– Harmonics Represent the Harmonic Overtone Series and the Fact that Every Key Correlates to another Key on the Piano (in Real Life via Air / Vibration / Waves)

– If the Overtones are Whole Multiples of the Fundamental then they are called “Even Harmonics” (as Horn or Cello)

– If the Overtones are Not Whole Multiples of the Fundamental then they are called “Odd Harmonics” (as the Clarinet)

– Overtones do Not include the Fundamental (where as the 1st Harmonic is a 440 for Example, the 1st Overtone is instead already 880)

– 32 Harmonics Range over 5 Octaves with all 12 Chromatic Pitches available as Harmonics

– Notice that “Harmonics” on Strings is another Thing and Describes Overtones that are Accentuated by Lightly Touching Harmonic Nodes on a Vibrating String (Due to Air / Vibration / Waves)

Harmonics Math

– We know that E6 is the 3rd Harmonic of a A5, i.e. it has a Frequency 3 Times the A (440+440+440 = E at 1320), then look at 3rd Harmonic of E which is B (1320 + 1320 + 1320 = B at 3960) etc.

– This Way you Include as many Harmonics (Notes) as you think is enough to Compose your Piece of Music, by adding (Additive) 440 + 440 + 440 + 440 etc. for any desired Number of Harmonic Overtones you Wish

Harmonics Examples

– When we Hit a Key, the First Harmonics are Very Clear Audible Intervals and Important 

– i.e. We Hear Fundamental, 5th, 4th, Octave and 3rd

a) We Hear the Octave (2:1) 

b) We Hear the 5th (3:2)

c) We Finally Hear the Difference between the 5th and the Next Octave is a 4th (4:3)

d) But we also Hear Up to the 5th Harmonic which is a Major 3rd (5:4)

e) Notice that some Notes Send Out More Harmonics than others

Harmonic Overtones On Note A440 = A4

A5 (2nd Harmonic 1st Overtone) 880, 2:1, Octave

E6 (3rd Non-Harmonic 2nd Overtone) 1320, 3:2, 5th, +1.95 Cents

A6 (4th Harmonic 3rd Overtone) 1760, Octave3

C#7 (5th Non-Harmonic 4th Overtone)  2200, 5:4, Major3rd, -13.68 Cents

E7 (6th Non-Harmonic 5th Overtone), 2640, 1.95, 

G7 (7th Non-Harmonic 6th Overtone) 3080, 7:6, 7th,  -31.17 Cents, the mysterious 7th Note that is “only” close to a F#7, see TTC Math

A7 (8th Harmonic 7th Overtone) 3520, Octave4

B7 (9th Non-Harmonic 8th Overtone) 3960, 9:8, Major2nd, +3.91 Cents

Chromatic Notes with Respective Harmonics 

– Based on A3 = 220

Harmonic 0   = Perfect Unison (A3 =  220)

Harmonic 1   = Perfect Octave   (A4 =  440)

Harmonic 2   = Perfect 5th (E4 =  660)

Harmonic 4   = Major 3rd (C#6 =  1100)

Harmonic 6   = Minor 7th (G6 =  1540)

Harmonic 8   = Major 2nd (B6 =  1980)

Harmonic 10 = Tritone (Eb7 =  2420)

Harmonic 12 = Minor 6th (F7 =  2860)

Harmonic 14 = Major 7th (G#7 =  3300)

Harmonic 16 = Minor 2nd (Bb7 =  3740)

Harmonic 18 = Minor 3rd (C8 =  4180)

Harmonic 20 = Perfect 4th (D8 =  4620)

Harmonic 26 = Major 6th (F#8 =  5940)