The Seventh Harmonic

By: R.C.L.

As a touch of cosmic irony, the "key" to PrimaSounds is what is "out of key" for all other music.

music-note.gifPrimaSounds form a pentatonic scale with unique frequencies, chords, intervals, summation and difference tones. This differentiates its musical scale from all others, including other five tone scales.

The PrimaSounds scale is based on the acoustic phenomenon of the deviation of the natural seventh harmonic from all other tones. The seventh harmonic sounds out of tune with other notes. For that reason the seventh harmonic is excluded and avoided as much as possible in other musical scales. As a touch of cosmic irony, the "key" to PrimaSounds is what is "out of key" for all other music.

It's as if our ears had a built in programming allowing us to hear - if we listen very carefully that is - that the seventh was fundamentally different from other harmonics. It sounds "sour" whereas other basic fractions, intervals, sound "sweet." In more precise musical terminology, the seventh sounds "dissonant," whereas the others sound "consonant." Most musicians with good theoretical training, or a very good ear, have long known about the phenomena of the seventh harmonic. A few physicists studying acoustics also know about the anomaly. But it was just considered one of those many quirks of nature with no special meaning. Arnold Keyserling appears to be the first in modern times to realize the significance of this acoustic phenomenon.

harmonics.gifBut what do musicians and scientists mean by seventh harmonic? Harmonics pertain to reciprocal vibrations. Every time one tone, one vibration, is sounded, a series of discrete secondary sound vibrations are also created. This is an automatic phenomenon of nature, as natural and inevitable as gravity. Vibrations never exist by themselves. They always create secondary vibrations. These secondary vibrations are the harmonics.

In music the secondary, reciprocal vibrations are called the undertones and the overtones. The undertones are lower in pitch with longer waves, and the overtones are higher in pitch with shorter waves. For instance, a string when vibrating at the pitch or frequency we call "low C" (sixteen times per second) will necessarily form the following secondary overtones to low C.

1   2   3   4   5   6   7   8   9   10  
   c   c   g   c   e   g   x   c   d   e  

The overall string is vibrating at low C and this is the principal tone we hear. But if we listen carefully we can also hear the secondary tones, the higher C tones, the G tones, D and E. These secondary reciprocal tones are produced automatically. One of these secondary tones, the seventh shown with an x above, sounds dissonant with the rest. But all of the others sound consonant with each other - pleasing to the ear - and so they are given a place in music, and are part of our musical scale. The secondary tones are known as the "harmonics" of the fundamental vibration.

The harmonics or overtones whose frequencies are exactly double or one-half are called the octaves. They extend the scale, but preserve identity - the octave notes sound the same, but are higher or lower in pitch. This, by the way, is one of the best examples in nature of the scientific principle of "fractal scaling" showing how self similarity is preserved over different scales of magnitude.

overtonewaves.gifThe next discrete series of overtones are the thirds, called "fifths" in music, then the fifths, called "major thirds" in music. The overtones are the places on the string where the nodes and sub-waves, or harmonics, naturally form. The sounding of any one tone will naturally create these particular fractal tones as overtones and undertones. The fractal tones follow the fractions of the rational numbers. For example, when the tone C is played all of the overtones are also created, and the string includes fractal waves such as a wave one-third as long as that of C. This one-third size wave produces the note called G, forming the musical interval of the perfect fifth. (It's called a fifth because it forms the fifth note of the C scale, even though it's a third of the string length.) Other fractal waves include one which is one-fifth as long as that of C. This produces the note E, forming the musical interval of a major third. (Again, although it's the fift harmonic, it's called the third, because it is the third note of the major scale.) This animated graphic should help non-musicians get a better feel for this phenomena by showing the movements on a string:

Like the overtones, the undertones appear in sound waves automatically whenever one vibration is initiated. The undertone harmonics sound lower in pitch than the fundamental tone, they move at lower frequency, and produce a longer wave. Thus, unlike the shorter overtones, the undertones can only be found on certain musical instruments, like bells, which can reverberate at a pitch lower than the fundamental.


      c       c       f       c       a       f       x       c       b       a      
      1       2       3      4      5      6       7       8      9      10    

As mentioned, the frequency and harmonics of the natural acoustic seventh are dissonant when compared to virtually all known tuning systems of the world. Although the acoustic seventh is avoided as an unacceptably sour note, the interval is still always present as a natural acoustic phenomenon. The seventh harmonic can be heard as an overtone or undertone in some instruments, particularly those rich in timbre (which means harmonics) such as a violin.

When the acoustic seventh is taken as the basic interval for the creation of a musical scale, new tones and intervals (distances between the notes) result. The 7 to 4 ratio of the natural seventh harmonic creates a new musical scale, a five tone, pentatonic scale. The PrimaSounds scale uses twelve hertz is used as the fundamental tone (12 hertz is the mean value of alpha brain waves which are considered to be brain waves of between 10 to 14 hertz). Some temperament of the scale is then made to create a functioning musical scale. Temperament is a slight adjustment to tone frequencies which is made to preserve octave identity over scales, and is used in most musical scales, not just PrimaSounds.

When the scale was first invented by Professor Keyserling, he used the normal octave temperament employed in diatonic scales involving the square root of two. Experimentation over the years showed me that this was not the optimal temperament. I have developed a more effective temperament system based on the natural harmonics of the seventh itself. This temperament is unique, and for now remains confidential. To go deeper into an inderstanding of Music Theory and mathmatics see Chapter 2 of Chance and Choice.

Last Modified on June 30, 2010 9:10 AM | Edit

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