|Overtone Series||Overtone Series|
Overtone Harmonics See MUTATIONS for more complete list. C: First Octave 1 = c Second Octave 2 = c' 3 = g' Third Octave 4 = c'' 5 = e'' 6 = g'' 7 = bb (it's actually about half way between a and bb) Fourth Octave 8 = c''' 9 = d''' 10 = e''' 11 = f#''' (halfway between f and f#) 12 = g''' 13 = a''' 14 = bb''' (sort of) 15 = b''' 16 = c 17 = c#/db 18 = d 19 = eb (a bit flatter) 20 = e 21 = ??? 22 = f# (sort of) 23 = f# (a bit sharper) 24 = g
Rod Fixed at Both Ends "A rod fixed at both ends and caused to vibrate transversely divides itself in the same manner as a string vibrating transversely.
"But the succession of its overtones is not the same as those of a string, for while the series of tones emitted by the string is expressed by the natural numbers, 1, 2, 3, 4, 5, etc., the series of tones emitted by the rod is expressed by the squares of the odd numbers, 3, 5, 7, 9, etc." [from "Sound" by John Tyndall]
Rod Fixed at One End "A rod fixed at one end can also vibrate as a whole, or can divide itself into vibrating segments separated from each other by nodes.
"In this case the rate of vibration of the fundamental tone is to that of the first overtone as 4:25, or as the square of 2 to the square of 5. From the first division onwards the rates of vibration are proportional to the squares of the odd numbers, 3, 5, 7, 9, etc.
Differentiation Figure 8.5 - Summation Tones Harmonic Harmonic Series Interval Law of Harmonic Pitch Law of Harmonic Vibrations Master Tone master tones Mid-tone octave tones Overtone Overtone Position Overtone Series Overtones Developed Musically Resultant Tone Scale Sympathetic Vibration Sympathy Undertone Vibrating Rod Harmonics 1.23 - Power of Harmonics through Summation Tones 9.8 - Spontaneous Creation of Harmonic Series 9.9 - Sympathy or Harmony Between Harmonics or Overtones