[Smt-talk] The Triad and Nature

Ninov, Dimitar N dn16 at txstate.edu
Mon Jul 21 10:02:53 PDT 2014

Dear Colleagues,

One may not be able to hear naturally the harmonic tone series but since the existence of so many beautiful instruments (including the guitar and the contrabass) one constantly enjoys hearing real, sonorous overtones. It is like setting up fire in natural conditions. Fire is not directly given us on a daily basis, but  it is a natural phenomenon, and we are capable of recreating it at desire, because of our human discoveries of the laws of nature.

I like Rameau's theory of obtaining the major triad from the harmonic series (4:5:6) and also the minor triad (10:12:15) because it uses relationships which are latent in the natural tone series, thus making the justification of triads as natural as it can be.  For one thing, one must be aware that  the presence of the harmonic tone series is a big step towards the development of harmony as contemporary discipline but is not the only one, and it does not have to be torn apart to justify every single event or relationship that musicians use in tonal music today. For instance, the D-T relationship may be associated with the relationship between the third harmonic and the fundamental, but the S-T relationship would seem odd if we want to immediately justify it with the interaction among the first six partials. However, with the knowledge that the tonic in a tonality is not an exact replica of the fundamental in a partial tone series (because it can be approached from both directions - from above, and from below) it is not difficult to create a mirror image of the D-T connection  and thus enjoy a "plagal"  relationship with the tonal center. Perhaps we do not need a whole dual system of overtones and undertones as Riemann suggested, but only the notion that the tonal center functions like a star in a stellar system, attracting  all the surrounding elements at a different extent.

As for pitch set analysis, my opinion is that  it is totally detached from any musical event and for that reason it cannot be a serious analytical tool. It is like a weapon developed in a laboratory which has never underwent "real battle" tests and has fallen into the category of "museum curiosities". You may write books about it, built your career on teaching it, but in all those activities music and analysis will go immediately in their separate ways.  You have to be musical and to understand the principles of harmony to apply Schenkerian analysis, but for a pitch set analysis all you have to only know is the notes and intervals. The music is irrelevant - its melodic curves and its harmonic support, its creative hints and originality of the composer have nothing to do with the procedure of obtaining pre-set visual formulas  In this sense you could analyze anything with pitch set tools (from early music to contemporary atonal music), and your analysis will always yield the same results - "scientific" destruction of the original passage, resulting in the inability to tell who the composer is and what the style or epoch is. On the other hand, a musical analysis never destroys the characteristic features of an epoch or personal style. It only helps us to enhance our sensitivity to the interaction of various  musical elements.

Thank you,


Dr. Dimitar Ninov, Lecturer
School of Music
Texas State University
601 University Drive
San Marcos, Texas 78666

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