As with the flexibility of performance pitch, the intervals between notes in Western art music have not always been standardised. Various tuning systems are known as temperaments. Outside the HIP movement, and a rise in use of microtonal tunings and temperaments in new composition over the past several decades,[1] equal temperament has dominated Western art music since the beginning of the 20th century.[2]

Temperaments on baroque violin:

As stated at the beginning of this section, most baroque violinists are accustomed to playing in a variety of different historical temperaments. For any new temperament, a period of adjustment may be necessary to become acquainted with the slight variations in intervals, but this should be easily achieved in time.

The following is a description of the just intonation temperament used in Natasha Anderson’s The Target Has Disappeared (2018, p. 3).

Figure 22.1 – excerpt from legend of The Target Has Disappeared by Natasha Anderson (2018, p. 3)

Suggested notation:

Where exact intervals are required between each scale degree, it may be necessary to provide a scale with exact frequencies in Hertz as part of the legend at the beginning of the piece, as in Figure 22.1 above.

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[1] See, for instance, the just intonation explored by composers such as Alvin Lucier (b. 1931), and Harry Partch (1901-1974). See also composers Catherine Lamb at http://sacredrealism.org/catlamb/, and Marc Sabat at http://www.marcsabat.com.

[2] For a detailed study of temperaments, see Ross Duffin’s book How Equal Temperament Ruined Harmony and Why You Should Care (Duffin, 2007).