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# 10 How wide is an interval?

This course has so far employed exact numbers when discussing pitches and intervals, speaking for instance of 220 hertz or 240 cents. But this presents a misleading picture of how these phenomena exist in most actual musical practice.

First, there is a degree of tolerance around what is considered a note or an interval, even in relatively ‘strict’ traditions of music making. For example, Eric Prame’s 1997 study of pitch in 10 commercial recordings of a piece of Western classical music (Schubert’s Ave Maria) indicated that sung notes could be over 40 cents sharp or flat of the ideal – nearly a quarter tone. Evidently, professional singers and recording engineers didn’t find such inaccuracies worrisome enough to withhold them from public circulation. Thus, performances may stray significantly from an ideal without seeming to be out of tune (that is, too sharp or too flat), even to insider experts.

Second, instrument makers in some traditions deliberately manipulate octaves and/or unisons to be slightly and pleasingly out of tune. Builders of gamelan ensembles in central Java, the most populous island in Indonesia, deliberately stretch or compress octaves across the various instruments of an ensemble when tuning them (Vetter, 1989 [citing Hood, 1966]; Brinner 2001). Put another way, they deliberately tune octaves so that they are slightly larger or slightly smaller than the 2:1 relationship discussed earlier in this course. This approach helps produce the characteristic ‘shimmering’ sound of the ensemble. (If you are interested, you can hear the shimmer in this video, a compilation of gamelan music from the Royal Palace of Yogyakarta in central Java, for example from 08:00–13:20.)

A similar approach to tuning is evident in flute traditions from the Andes (the mountains along the western side of South America), where inexact tuning of instruments to one another helps the music project across outdoor spaces and creates a rich musical analogue for cultural concepts of ‘abundance and social harmony’ (Stobart, 2013, p. 27). Thomas Turino, writing of the flute music in an Aymara Indigenous community in southern Peru, describes a ‘dense unison’ in which some musicians play slightly sharp or slightly flat of one another (1989, p. 12). The result is musical notes that have ‘a “fuzzy” aura … in contrast to a “clear” or “sharp” sound’ (1989, p. 13).

Third, pitch systems do not always have fixed or stable components. The positions of notes and the intervals between them may vary. This is true even in some traditions where instrument-makers build the pitch system into the instruments. Central Java in Indonesia is a good example. The pitch systems sléndro and pélog are used in many different ensembles in that part of the country. However, instrument-makers interpret these pitch systems in a range of ways (Vetter, 1989, pp. 217–8), and as a result the size of the intervals between notes varies noticeably from ensemble to ensemble and from community to community (Brinner, 2001).

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OpenLearn - Introduction to music theory 2: pitch and notation
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