|Overtone Series||Overtone Series|
(See MUTATIONS for more complete list.)
1 = c
2 = c'
3 = g'
4 = c''
5 = e''
6 = g''
7 = bb (it's actually about half way between a and bb)
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.
"With rods of different lengths the rate of vibration is inversely proportional to the square of the length of the rod." [from "Sound", John Tyndall]
1.20 - Evolution and Devolution of Frequency
1.23 - Power of Harmonics through Summation Tones
12.18 - Multiple Octave Progression
12.19 - Fibonacci Relationships
12.21 - Fibonacci Whole Numbers v Irrational Decimal near Equivalents
12.38 - Orbital revolution
14.15 - Movement Caused by Spirit
15.15 - Progressive Dissociation
15.15.05 - Progressive Association
3.04 - Power Accumulation via Fibonacci-like Patterns
8.17 - Law of Harmonic Vibrations
8.22 - Law of Harmonic Pitch
9.8 - Spontaneous Creation of Harmonic Series
9.9 - Sympathy or Harmony Between Harmonics or Overtones
Additive and Subtractive Synthesis
Overtones Developed Musically
Figure 8.5 - Summation Tones
Genesis of the Scale
Law of Harmonic Pitch
Law of Harmonic Vibrations
progression of adjacencies
progression of keys
Ramsay - PLATE II - The Genesis
Vibrating Rod Harmonics