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  • Cited by 7
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    This chapter has been cited by the following publications. This list is generated based on data provided by CrossRef.

    Smethurst, Reilly 2018. Alternatives to Semitones and Quartertones: Music-Theoretical Suggestions. The Mathematical Intelligencer, Vol. 40, Issue. 3, p. 37.

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    Dixon, Simon Mauch, Matthias and Tidhar, Dan 2012. Estimation of harpsichord inharmonicity and temperament from musical recordings. The Journal of the Acoustical Society of America, Vol. 131, Issue. 1, p. 878.

    Tidhar, Dan Mauch, Matthias and Dixon, Simon 2010. High precision frequency estimation for harpsichord tuning classification. p. 61.

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  • Print publication year: 2002
  • Online publication date: March 2008

7 - Tuning and temperament

from PART II - SPECULATIVE TRADITIONS
Summary
In the medieval and Renaissance periods, theories of tuning were usually formulated in terms of relative string lengths on a monochord, to be calculated by arithmetic methods. Tuning and temperament theory was especially developed by eighteenth-century German authors. The time-honored monochord remained in use as the basic tool of tuning and temperament theory. Glarean's description of Pythagorean tuning will serve to explain both the use of the monochord at that time and the Pythagorean system. Despite its high theoretical prestige in the sixteenth century, just intonation was already known to be inappropriate as a tuning system for keyboards. Gioseffo Zarlino did work out a meantone temperament in his Dimostrationi armoniche. The calculation of tempered intervals was first performed towards the end of the sixteenth century by the Dutch mathematician and engineer Simon Stevin for the calculation of equal temperament. In the calculation of temperaments, logarithms serve especially well in the geometrical division of intervals, where they replace root extraction by division.
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The Cambridge History of Western Music Theory
  • Online ISBN: 9781139053471
  • Book DOI: https://doi.org/10.1017/CHOL9780521623711
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