For example, assuming octave equivalence, the intervals between the tones of the major pentatonic scale are nearly the same as the intervals between the first nine harmonics of a harmonic series. More recently, Bernstein suggested that scale structure is determined by the appeal of the lower harmonics that occur in naturally generated harmonic series. Helmholtz first proposed that the relative consonance of musical dyads derives from harmonic relationships of the two tones.
Classical compositions unusual scales series#
The comparison of musical intervals to a harmonic series is not new. Here we examine the possibility that the thread tying together the scales that have been preferred in music worldwide is their overall similarity to the spectral characteristics of a harmonic series. In short, none of these approaches explains the widespread human preference for a small number of particular scales comprising five to seven tones, or provides a biological rationale for this predilection. Other analyses have predicted scales with as many as 31 intervals, which are rarely used to make music. Moreover, no basis was provided for the underlying assumptions. This method can account for the structure of the equal-tempered 12-tone chromatic scale but cannot account for any of the five to seven-tone scales commonly used to make music. A third approach has used error minimization algorithms to predict scale structures under the assumption of competing preferences for small integer ratios and equal intervals between successive scale tones. Again, this concept has not been applied to the prediction of preferred scale structures. A different approach to understanding scales has depended on the concept of a generative grammar in linguistics, asking whether musical patterns might define a “musical grammar”. This method has not, however, been used to predict any specific scale structures. One approach has used consonance curves to show that the consonant harmonic scale tones are defined by small integer ratios. Not surprisingly, a number of investigators have grappled with the general issue of scale structure. Scale tones are represented on keyboards for didactic purposes only in this and subsequent figures and should not be interpreted as being tuned in equal temperament (see Methods). Although the scales shown begin and end on specific notes of the keyboard, each could begin on any note and retain its identity as long as all intervals between notes remained the same. There are three unique forms of the minor heptatonic scale: the natural, harmonic and melodic (the melodic minor scale shown is designated as ascending since this scale is identical to the natural minor scale when descending). Seven of the nine heptatonic scales shown are also modes that entail the same notes in different arrangements (the exceptions are the harmonic and melodic minor scales). The five pentatonic scales are modes of the same set of notes, the only difference being the starting note or tonic. Pentatonic and heptatonic scales (included tones are indicated by red dots). The analysis also highlights the spectral similarity among the scales used by different cultures.įigure 1. These findings suggest that humans prefer tone combinations that reflect the spectral characteristics of conspecific vocalizations. Here we show that the component intervals of the most widely used scales throughout history and across cultures are those with the greatest overall spectral similarity to a harmonic series.
Why humans employ only a few of the enormous number of possible tone combinations to create music is not known. Nonetheless, compositions in Western classical, folk and popular music as well as in many other musical traditions are based on a relatively small number of scales that typically comprise only five to seven tones –. Since humans can distinguish about 240 different pitches over an octave in the mid-range of hearing, in principle a very large number of tone combinations could have been used for this purpose. Scales are collections of tones that divide octaves into specific intervals used to create music.
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