![]() ![]() ![]() Following a much longer Pythagorean tradition (but extending it in new ways), Rameau and other eighteenth- and nineteenth-century theorists also held triads to correspond to ratios of whole numbers, such as 4:5:6 for the major triad. ![]() The lowest note in the stack is identified as the root, implying that this pitch has the function of a psychological reference when the chord appears in a musical passage. The 3rds can be major (M3) or minor (m3), so the resultant 5th can be perfect (P5), diminished or augmented. The following sections present further examples.įollowing a long tradition in music theory established by Rameau ( 1750 cited in Christensen, 1993) and suggested by earlier music-theoretical treatises since Lippius ( 1612), a triad is constructed by stacking two intervals of a 3rd to create a 5th. But that does not necessarily reflect their consonance: the suspended-4th chord occurs five times in this scale (on C, D, E, G and A), but it is less consonant than the major and minor triads.Ĭontradictions and inconsistencies of this kind are typical of the history of theoretical attempts to explain the harmonic vocabulary of Western tonal music. They also are common in that they occur more than once in the structure of a single diatonic scale: within the C-major scale, one can build major triads on C, F and G and minor triads on D, E and A. They are common in that they occur commonly or frequently in music (we will use the word prevalent). The major and minor triads are also called common chords. The suspended-4th chord, although evidently common, is not treated as a triad in its own right, but as an alteration of a major or minor triad in the European classical tradition it invariably progresses to (resolves onto) a major or minor triad. What these four sonorities have in common is a root, third and fifth when notated in root position, all notes appear on either lines or spaces. Other trichords 1 (chords of three pitch classes) are not considered ‘triads’. Randel, 1986) expound or imply that Western tonality in the ‘common-practice period’ (roughly 1650–1900) is based on four chords: the major, minor, diminished and augmented triads. Standard music theory texts, music dictionaries and encyclopaedias (e.g. To get some insight into how the consonance and dissonance (C/D) of vertical sonorities was perceived historically, we will compare results of our database analyses with predictions of simple psychological models. We will then describe a new approach to vertical consonance that is based on a simple statistical analysis of a database of polyphonic music from seven centuries of Western music history. We will begin by surveying and evaluating relevant ideas from the history of music theory and the history of science. We aim to reconstruct something about the way music was perceived at the time it was written and composed, but we also acknowledge the bias of our modern perspective. We will assume that the prevalence of pitch-time patterns in musical scores reflects the degree to which composers and listeners of the time liked them for the purpose of this study, we will make no distinction between liking and consonance, nor will we consider voice-leading (the ease with which a sonority can be approached or quitted). Our aim is first to clarify some basic questions about the harmonic vocabulary of mainstream Western tonal music, including the rank order of prevalence or consonance of trichords as it changed from one historical period to the next, and then to explain those rank orders by means of quantitative models based on psychological or perceptual theory.
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