Teoria El Tono Virtual

Application of virtual pitch theory in music analysis
Llorenç Balsach
Abstract In the course of this article a model of harmonic analysis is worked out based on certain properties of the auditory system, which I think will shed new light on the study of cadences and local harmonic resolutions. This model consists basically of extracting the two main fundamentals (roots) which are to be found in93.3% of chords of less than 6 notes. To do this I apply the basic concepts of virtual pitch but taking into account only those harmonics which are in a prime position in the first seven, which in our thesis include the rest of the harmonics as far as the human auditory is concerned. With this model we found new information about the "internal" harmonic tension which is created by every singlenote and the tendencies of chords towards resolutions. I compare and discuss other models which apply the theory of virtual pitch in harmonic analysis. Introduction E. Terhardt's concept of "virtual pitch" is used in psycho-acoustics as a method of extracting pitch(es) from (harmonic) complex tone signals (see Terhardt, Stoll & Seewann (1982b, 1982c), Meddis & Hewitt (1991), van Immerseel & Martens(1992), Leman (1995)). The concept could be briefly described as the pitch which the auditory system perceives from a sound or group of sounds. There have been some attempts to bring the acoustic concept of virtual pitch into musical theory. Terhardt himself (1982a) applied his theory to extract the root(s) of a chord. R. Parncutt (1988) saw that the results obtained from Terhardt's model did notfit in sufficiently with conventional musical theory; he worked out a revised version of the model, producing significantly different results from Terhardt's original. Although theorists are in agreement about the concept of virtual pitch when applied to chords, its practical application to musical theory has been the subject of some discussion. As I have mentioned, the models proposed by Terhardt(1982a) and Parncutt (1988) differ considerably, especially in the results obtained from minor and diminished chords. They also differ considerably from Hindemith's notion of root (1937) and Riemann's classification of all chords into just three functional categories, (tonic, dominant and subdominant). When Terhardt, Stoll & Seeward's model (1982b, 1982c) for extracting virtual pitch(es) fromcomplex tonal signals, was applied to chords played on the piano, the results from minor chords were not what would have been expected from Terhardt's model (1982a); results even differed depending on the inversion of the chord1, something which reinforces Hindemith's theories but goes against the very essence of the concepts of root and virtual pitch. Finally, it will come as no surprise that allresults obtained from all the above theories and experiments differ from the dogmatic definition of a root as the lowest of a series of notes ordered in thirds. This article will discuss the models mentioned above and analyse the differences between the results obtained from each model. I will also propose a new model for functional

analysis of chords, based on the concept of virtual pitch andthe "internal" tension which harmonics create in every single note. Unlike earlier systems, the ease of application of this model allows it to be applied directly to the score without the need for a computer. It is important to note that the model serves not only to extract the roots from chords or arpeggios, but also provides us with new information concerning the tension existing between chordsand cadences. It also allows us to track the tonal centres of harmonically complex scores. Virtual Pitch The concept of virtual pitch applied to chords has its origins in the historic concepts of "basse fondamentale" (Rameau)2, the "terzo suono" (Tartini)3 and Riemann's harmonicfunctional theory, concepts which in the course of history have unjustly come to lose their meaning as the basis of...