Many of you know that you can play harmonics by placing a finger of your playing
hand so that it lightly rests against a string and by using your picking hand
you can pluck the string and get a higher pitched tone.
What you are actually doing is masking or hiding/preventing the fundamental
tone or frequency of the open string from sounding. Depending on the position
of your masking finger on the string, you can further mask various overtones
on that same string.
Let's choose the A string. The fundamental frequency of that tonal A is 440
cycles per second. "Concert A". If you find the exact middle of that string
and pluck the string while laying your playing hand finger lightly on that point,
you will mask the 440 cps, or Hertz, from sounding. Since that string sound
is not a pure sinusoidal wave or sine wave, it contains many multiple frequency
components in that envelope. The most prominent and dominant comprise the overtone
These frequencies have a mathematic relationship called superparticular.
440 - A -
Open 880 - A - Octave - 1st harmonic - halfway on the A string, dividing the
string in half.
1320 - E - Fifth - 2nd harmonic - 1/3 the way up the A string (from either
direction!) dividing the string in thirds as in over the 7th fret
1760 - A - Octave - 3rd harmonic - 1/4 the way up the A string (from either
direction!) as in over the 5th fret
2200 - C# - Major 3rd - 4th harmonic - 1/5 the way up the A string, 2/5 the
way up as in over the 4th fret
The superparticular ratios of freqencies are as such:
Octave (2*440=880 to 440) - the most consonant internal
Fifth (3 * 440=1320 to 2* 440=880) - the perfect fifth
Fourth (4 * 440=1760 to 3 * 440=1320) - the perfect fourth
Major Third (4 * 440=1760 to 5 * 440=2200)
Minor Third (5 * 440=2200 to 6 * 440=2640)
These intervallic relationships define consonance and physical harmony.