The Harmonic Series

     The harmonic series is probably the most fundamental aspect upon which music can be understood. As we will see, it is the basis for an effective chord voicing, to understand chord tones and tensions, scale construction and also rhythm.

    Briefly, the harmonic series, also referred to as the overtone series, occurs whenever you play a pitch in your instrument. When you play a C, what you are hearing is a collection of overtones associated to this pitch and this is applicable to any sound you hear coming from an instrument or otherwise. It’s a natural physical phenomenon; the sounds within one sound. Using an analogy, just as the colors of a rainbow combine to make white light, the related notes in a harmonic series combine to make what we hear as a single pitch.

     But these harmonics also contribute to how we perceive the timbre or tone color of a sound. It is affected by the construction material of the instrument that produced that sound, and in turn that affects the relative strength of each overtone. This balance of overtones, or partials, is what gives the sound we hear its tone quality.

     When you play a C, the first sixteen overtones associated to this particular pitch are:

– Mind you that these pitches do not correspond exactly to our equal temperament tuning system that adjusted the relative pitches distance for convenience (*see footnote).

     Timbre is directly related to the harmonic series and now we see a collection of tones that properly arranged can be used as basis for scales (like the C major pentatonic scale) and for chords inspired or derived from the series – like the C major chord with the notes C E and G. Another musical element that we can derive from the overtone series is rhythm. To do so, first we need to address what pitch really is.

     Sound is frequency, and a frequency is basically the number of occurrences of a repeating event per unit of time. Simply put, rhythm and pitch are exactly the same thing, only at very different speeds. To reproduce this, you simply have to insert a bar with thirty-second note triplets (for example), and crank up the tempo in your DAW. You will start to distinguish a pitch that can be changed depending on how fast the tempo is (or frequency):

      To take this example further, if you put a given note duration against another note that has half of the duration , like a whole note against a half note, you will clearly start hearing an octave. This happens because we are reproducing the relationship of the overtones series that tells us that in order to hear the same sound an octave higher, you will have to double the frequency of its rhythmic pattern:

     And if you want to hear a perfect fifth above that sound, you will just have to superimpose a triplet note over the previous subdivisions – this is basically a 3:2 polyrhythm:

     Finally, if you want to make a major chord, with all the notes in the same octave, you just have to divide the beat in 4, 5 and 6 parts and then play these simultaneously: 

     You can definitely use the overtone as reference to make your polyrhythms and the pitches for building chords and scales.

     All considered, the Harmonic Series is a natural occurrence from which we can naturally derive the main elements of music – Timbre, Pitch and Rhythm; and many of the basic principles and harmonic developments of music originate from this acoustic make up of a single tone. Throughout the posts, I will continue to present to some of the implications of the harmonic series for scales, chords and rhythm construction.

THE UNDERTONE SERIES

     The undertone series is an inversion of the overtone series, meaning that if we have an ascending perfect fifth then the inverted interval becomes a descending perfect fifth from the same root note. Here is the comparison between both series:

– Being a polar opposite of the overtone series, from which we can derive the major chord, it is possible to retrieve the origins of the minor chord – in this case the Fm chord with the notes F A♭ and C.

     The undertone series may be argued as being a purely theoretical stretch because undertones do not seem to occur at the same time as the overtones when a sound is produced. Anyway, discussing this matter is beyond the scope of this post as our main interest lies in its implications to the process of music making. Intervallic inversion is a useful tool that will be recurrent while exploring different chords and scales possibilities.

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* In musical tuning, a temperament is a tuning system that slightly compromises the pure intervals of just intonation to meet other requirements. Tonal purity is thus sacrificed for freedom of modulation. Pure intervals are important in music because they correspond to the vibrational patterns found in physical objects which correlate to human perception.