Historical tuning in theory and practice, part 2: Just intonation
Journal Title: Notes Muzyczny - Year 2015, Vol 1, Issue 3
Abstract
The beginning of the article presents selected aspects linking the theories of the structure of scales and intonation with acoustics (e.g. the structure of sound, consonance of two sounds, frequency, comma). Then it describes the problem of defining the notion of just intonation on the basis of the entry by Mark Lindley (Just Intonation, in Oxford Music Online, 8.04.2013), among other examples; noteworthy is especially the description of the notion by David Doty (The Just Intonation Primer). In his article Pilch suggests two ways how to approach the presented problem: from the perspective of the theory of creating sound scales and from the perspective of performance practice – the way of intoning intervals. A separate subject is the rendering of just intonation on the basis of keyboard instruments in case when we need instruments with a division of an octave into more than 12 parts. The issue is not treated more fully in this article. Its further part is devoted to the practical construction of the basic natural scale on a traditional harpsichord. A two-manual instrument will be useful here due to the possibility of double tuning of some sounds. A natural scale is a result of tuning acoustically clean fifths and thirds. Characteristic features of this scale are the subject of analysis. Noteworthy is the chord built on the second step of the scale – the so-called „wolf” fifth between the sounds D–A, diminished by the syntonic comma. To be able to use the second step one must introduce the second D sound lower by the syntonic comma. Next the author describes the method of clean intonation in vocal ensembles. Performers not bound by an instrument with specific sound pitches (where temperament systems are usually used) are able to utter acoustically clean intervals. The problem in such kinds of performances is the so-called “intonation trap”. While singing clean intervals it is easy to lose the initial tuning pitch. The knowledge about the just intonation theory helps prevent this phenomenon thanks to the developed methodology. In order to achieve modulation to neighbouring keys one must suitably sharpen or flatten one of the common sounds by a syntonic comma respectively. Here noteworthy publications are Bettina Gratzki’s Die reine Intonation im Chorgesang and Doris Geller’s Praktische Intonationslehre. At the end the article mentions the usage of just intonation in pieces by the 19th century and contemporary composers. The concept of just intonation was traditionally based on the so-called 5-limit. In the 16th century the proportions based on lower prime numbers were used, recreating the ancient theories of sound scale structures. The Pythagorean system consisting of perfect fifths was a 3-limit tuning. Widening the system to 5-limit allowed to also include minor third in the system, the effects of which were the just intonation and meantone type systems. Thanks to modern options offered by electronic instruments and software the new scales based on the 7- and higher limit can be used in practice. Just intonation is not just a tool allowing to learn about the theory of scales structure and practise sophisticated intonation but it also makes various composition experiments possible. There are no limits which are characteristic of arbitrary closed tonal systems. Composers create their own unique world of sounds.<br/><br/>
Authors and Affiliations
Marek Pilch
Keywords
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