ScottOpus PRODUCTIONS
ScottOpus PRODUCTIONS
TOPIC:- Harmonic Series
(Overtone Series)**
by Kerry R. ScottIn music the Harmonic Series (Overtone Series)**is a series of frequencies or Pitches (see Topic "Pitch") produced "naturally" by a Resonating Column of Air (such as an Pipe Organ or Trumpet), a Vibrating String (such as in a Violin, 'Cello, Harp or Piano) or a Vibrating Membrane or a resonating solid item (such as a Timpani, Bell or Xylophone). Theoretically in a Harmonic Series there are an infinite number of notes emanating from a single and lowest note in the series called a Fundamental. Practically, however, for the human to perceive such a series they must exist within the confines of the human hearing of 20 Hz to 20,000 Hz (see Topic Pitch). Although naturally occuring in the instrumental types seen above there is in fact a mathamatical relationship between each of the notes within the Harmonic Series. The lowest note of any Harmonic Series as already indicated is called the "Fundamental". It is also called the "first harmonic"***. In order to find the frequency in Hertz (see Topic Pitch) of the next frequency in the series simply multiply the frequency of the Fundamental (first harmonic) by two (the harmonic number). Similarly to find the frequency of the third harmonic multiply the frequency of the Fundamental by three. This process can be repeated for as many times as applicable -- it should be remembered,however, that the series must exist within the range of the human hearing to be musically relevant.
For all this to be musically meaningful a transition must be made from "Frequencies" to "Pitches". Musicians measure Pitch generally with letter names -- A, B, C, etc.(See Topic Pitch). If the frequencies seen above are given letter names then between each frequency the "encompassed frequencies" are also given a name. In Music these "encompassed frequencies" are called "Intervals". It is beyond the scope of this topic to discuss the construction of musical intervals (see Topic Intervals) but the following table indicates the order of "Intervals" as they appear in the Harmonic Series.
-Harmonic #- -Freq.- -- Note. -- -- Interval -- -Harmonic #- - Freq - -- Note. --
Table assumes a Fundamental (Harmonic 1.) of C -- 64 Hz.
Harmonic 1. 64 Hz. -- C -- Octave Harmonic 2. 128 Hz. -- C -- Harmonic 2. 128 Hz. -- C -- Perfect Fifth Harmonic 3. 192 Hz. -- G -- Harmonic 3. 192 Hz. -- G -- Perfect Fourth Harmonic 4. 256 Hz. -- C -- Harmonic 4. 256 Hz. -- C -- Major Third Harmonic 5. 320 Hz. -- E -- Harmonic 5. 320 Hz. -- E -- Minor Third Harmonic 6. 384 Hz. -- G -- Harmonic 6. 384 Hz. -- G -- Minor Third Harmonic 7. 448 Hz. -- B(f)* -- Harmonic 7. 448 Hz. -- B(f)* -- Major Second Harmonic 8. 512 Hz. -- C -- Harmonic 8. 512 Hz. -- C -- Major Second Harmonic 9. 576 Hz. -- D -- Harmonic 9. 576 Hz. -- D -- Major Second Harmonic 10. 640 Hz. -- E -- Harmonic 10. 640 Hz. -- E -- Major Second Harmonic 11. 704 Hz. -- F#* -- Harmonic 11. 704 Hz. -- F#* -- Minor Second Harmonic 12. 768 Hz. -- G -- Harmonic 12. 768 Hz. -- G -- Major Second Harmonic 13. 832 Hz. -- A* -- Harmonic 13. 832 Hz. -- A* -- Major Second Harmonic 14. 896 Hz. -- B* -- Harmonic 14. 896 Hz. -- B* -- Minor Second Harmonic 15. 960 Hz. -- C -- Harmonic 15. 960 Hz. -- C -- Minor Second Harmonic 16. 1024 Hz. -- D(f)* --
Fig. 1. - The Harmonic Series * indicates the pitch is only approximate to that found on the modern piano.
** It should be note that the difference between the "Harmonic Series" and the "Overtone Series" is in name only. Everything discussed in this topic can also be directly applied to the "Overtone Series". Initially the name "Overtone Series" was thought to more aptly apply to the subject "music" and to differentiate it from the term "Harmonic Series" as applied to Mathematics and Physics/Accoustics. This is generally no longer the case and the term "Harmonic Series" is generally accepted.
*** With regard to the "Overtone Series" it should be noted that the First Overtone is not the "Fundamental" but rather equivilant to the "Second Harmonic". That is, the names in the "Overtone Series" are specified as follows:- Fundamental, First Overtone, Second Overtone, etc.
If the above table is represented in musical notation it looks as follows:-
It should be noted that after the seventh harmonic there is little similarity between certain notes of the Harmonic Series and the tuning of those same notes on the modern piano. The Harmonic Series was, however, the basis of a system of tuning attributed to Pythagoras (?580-?500 B.C.) and the basis of tuning of the so called "Just Tuning" systems prevalant in the Fifteenth, Sixteenth and part of the Seventheenth Centuries. They were replaced with the "Equal Temperament" (see Equal Temperament) system of tuning as demonstrated by J. S. Bach (1685 - 1750) in his Well-tempered Clavier.
It should be pointed out that the Harmonic Series impacts the music we hear in two ways. Firstly as discussed above it features in the tuning of the notes that make up the melodies we hear. In addition, however, it also features significantly in the kinds of tones we hear from musical instruments. In music this is called "timbre". The note an oboe produces for instance, is not only the pitch that we hear -- that is, the fundamental, 440 Hz, or an A for example -- it also sounds many of the harmonics within the harmonic series of that particular note. This is what gives the oboe its distinctive sound and what sets it aside from other intruments. The sound (timbre) the Clarinet produces for instance is said to only include the "odd harmonics" of the harmonic series and thus sounds the way it does. So why, when we hear the Clarinet play a particular note do we not hear all the odd harmonics all at once? The reason is that the harmonics that make up the sound are of such a soft (dynamic) level that all they do is enhance the timbre and are not recognizable as individual pitches.
Within the compositions of Kerry R. Scott there are numerious examples of many utilizations of the Harmonic series. In particular in his "pure electronic music" (that music written for electronic sounds and not that which is the synthesis of instrumental sounds) there are many instances where new timbres have been created and realized by manipulating the Harmonic Series. (see CD's Beyond the Virtual Creation.) In particular Mr. Scott is working on a system of dividing the octave into more than 12 notes as in the Equal Temperament system of tuning and is, therefore, designing a new system of notation to accommodate the new scale. For very detailed information on The Harmonic Series, Pitch and various tuning methods the paper titled "The Development of Musical Tuning Systems" by Peter A. Frazer can be recommended. Direct access can be obtained with the following link www.midicode.com
Electronic Music
Follow the following links for more information about the topic and navigate the:-
ScottOpus Productions Website
Further Information on The Tudor Rose School of Music
Further information on the Music CD -- Bubble and Squeak [atonal,tonal pitch systems]
Further information on the Music CD -- Beyond the Virtual Creation [atonal,tonal pitch systems]
Further information on the Music CD -- Brandy Butter, Brass and Bells [Modal, atonal and tonal pitch systems]
Further information on the Music CD -- The Old, The New, and an Eclectic Medley [Modal, atonal and tonal pitch systems]
Further information on the Music CD -- Smphony No. ! -- Soundscapes of a Forgotten Britian [modal, atonal and tonal pitch systems]
Further information on the stories and writings of Kerry R. Scott.