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Les gammes et le tempérament égal

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Two examples are given to show the way in which Euler provided a foundation for the grammar of musical scales; the genus diatonicum (common major and common minor scale) and the genus chromaticum (gipsies' scale and six-note scale of whole tones). By quotations from Haba and Bartok it is pointed out that the common equal temperament of 12 semitones is no longer adequate for autochtonic and modern music. From a mathematical formulation of the requirements one derives an equal temperament of 31 fifths of a tone per octave. This is Huygens' Solution.

Figures of Mr.F.-K.Ligtenberg are given showing the relative degree of ‘shortcoming’ of the best possible temperaments in the range from 10 to 60. Only Mercator's temperament of 53 is superior to Huygens' of 31. The remark that for a given error in cents the interval of a fourth will be rougher than the interval of a fifth, and the need to make the octave take its share of the imperfections embodied in the temperament lead to the choice of an elementary unit of 38.65 cents instead of 38.71 (= 1200/31) cents. A short description is given of the keyboard of an organ realising the temperament of 31 fifths of a tone.
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Document Type: Research Article

Publication date: January 1, 1951

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  • Acta Acustica united with Acustica, published together with the European Acoustics Association (EAA), is an international, peer-reviewed journal on acoustics. It publishes original articles on all subjects in the field of acoustics, such as general linear acoustics, nonlinear acoustics, macrosonics, flow acoustics, atmospheric sound, underwater sound, ultrasonics, physical acoustics, structural acoustics, noise control, active control, environmental noise, building acoustics, room acoustics, acoustic materials, acoustic signal processing, computational and numerical acoustics, hearing, audiology and psychoacoustics, speech, musical acoustics, electroacoustics, auditory quality of systems. It reports on original scientific research in acoustics and on engineering applications. The journal considers scientific papers, technical and applied papers, book reviews, short communications, doctoral thesis abstracts, etc. In irregular intervals also special issues and review articles are published.
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