Simon Stevin's equal division of the octave

References

• Huygens Christiaan Oeuvres Complètes… The Hague1888–1950 XX 32 32 22 vols (1940) 144. The editor of volume xx was J. Volgraff. From his correspondence with E. J. Dijksterhuis (preserved at the Museum Boerhaave, Leiden) it appears that the musical information contained in the copious notes and numerous ‘Avertissements’ was in the main provided by the latter.
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• Barbour , J.M. 1951 . Tuning and Temperament: A Historical Survey 7 – 7 . East Lansing, Michigan reprint New York, 1972
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• The one and only exception I am aware of is the brief passage on Stevin in Walker D.P. Studies in Musical Science in the Late Renaissance The Warburg Institute and Brill London and Leiden 1978 120 122
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• Dijksterhuis , E.J. and Forbes , R.J. 1963 . A History of Science and Technology Vol. II , 366 – 366 . Harmondsworth (The original Dutch version appeared in 1961.)
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• Fokker A.D. Introduction. Simon Stevin's Views on Music The Principal Works of Simon Stevin et al. Amsterdam 1955–68 V 418 418 in 5 vols (1968)
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• Pippard B. Pythagoras' Other Theorem Times Literary Supplement 1984 1469 1469 21 December This is a review of Quantifying Music, so the reviewer might perhaps have known better.
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• Barbour . 1951 . Tuning and Temperament: A Historical Survey , 7 – 7 . East Lansing^Michigan : Michigan . reprint New York, 1972
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• Dijksterhuis , E.J. 1970 . Simon Stevin: Science in the Netherlands around 1600 121 – 121 . The Hague This book is a highly condensed version of the Dutch original Simon Stevin (The Hague, 1943). Chapter 13 of this book was for a long time the best account of Stevin's musical theories available, and in fact I owe much to it. The more significant, then, that Dijksterhuis, too, missed the central point of Stevin's treatise, as I shall demonstrate further on in the present paper.
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• Fokker Introduction. Simon Stevin's Views on Music The Principal Works of Simon Stevin et al. Amsterdam 1955–68 5 418 418 in
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• The idea of reconstructing historical problem situations goes back, of course, to Popper K.R. Objective Knowledge: An Evolutionary Approach Oxford 1972 186 190 His most explicit discussions of the method is in his
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• For a more detailed historical exposition of the issues of tuning and temperament, see my Quantifying Music The Hague 1888–1950 XX 34 45 22 vols
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• For an account of the onset of the Baroque style in music, see the first two chapters of Bukofzer M.F. Music in the Baroque Era New York 1947
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• See, for example, the ‘Recercar con obligo del Basso’ from the ‘Messa delli Apostoli’ Fiori Musicali 1635 or bars 28 and 30 of the ‘Toccata per l'Elevazione’ from the same Mass.
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• There are three texts of Vande Spiegheling der Singconst. The manuscript is preserved in the Koninklijke Bibliotheek (Royal Library) in The Hague, where it is marked KA XLVII, pp. 624–705; it consists of two versions. Both were edited in 1884 by D. Bierens de Haan in Stevin S. Vande spiegheling der singconst’ et ‘Vande molens’: Deux traités inédits Amsterdam 1884 The early version, together with an English translation, was edited by A. D. Fokker in the work cited in footnote 5. Since Bierens de Haan's edition is both more accurate and far more complete, I refer to his edition rather than to Fokker's. For a more detailed treatment of the manuscript and its printing history, see Quantifying Music (footnote 1), note 46 to chapter 2.
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• There had been some experimenting before with ‘extravagant consonances’ (to use the title of some pieces by Giovanni de Macque); but Frescobaldi was the first really to explore the possibilities of the new style for the organ and the harpsichord. See also Apel W. The History of Keyboard Music to 1700 Indiana Bloomington 1972 457 457
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• For a more detailed exposition of the early history of the problem of consonance, see Quantifying Music The Hague 1888–1950 XX 1 7 22 vols
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• Johannes Kepler, Gesammelte Werke et al. Munich 1937– VI 104 105 1940
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• Stevin develops this argument in his book L'Arithmétique (reprinted in volume 2B of Stevin's The Principal Works of Simon Stevin et al. Amsterdam 1955–68 V 512 512 5 vols around in Vande Spiegheling der Singconst he refers to it on p. 69 (in Fokker's edition, on pp. 440–41).
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• The only link which Stevin establishes with the physical side of musical sound is his passing, and quite vague, use of the concept of ‘coarseness’ of a note as an unspecified measure for lowness of pitch: see Vande Spiegheling der Singconst 22 22
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• 1888–1950 . Quantifying Music Vol. XX , 58 – 60 . The Hague 22 vols
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• Barbour . 1951 . Tuning and Temperament: A Historical Survey , East Lansing : Michigany . evaluates these figures on pp. 76–77.
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• Stevin . Vande Spiegheling der Singconst , 61 – 61 .
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• Stevin . Vande Spiegheling der Singconst , 23 – 23 .
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• Adam , C. and Tannery , P. , eds. 1971–74 . Oeuvres de Descartes , second edition Vol. I , 142 – 142 . Paris and 295. In cents the difference between a pure octave and the interval that results from adding two mean tone augmented fourths is 41·1. I cannot possibly share Dijksterhuis' belief that Stevin must have been incapable of noticing this (Dijksterhuis, footnote 8, English version, p. 122).
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• Stevin . 1884 . Vande spiegheling der singconst’ et ‘Vande molens’: Deux traités inédits 30 – 31 . Amsterdam
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• Huygens . 1888–1950 . Oeuvres Complètes… Vol. XX , 73 – 73 . The Hague 22 vols
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• Verheyen's critique was bound together with Stevin's treatise in the manuscript volume mentioned above in Stevin S. Vande spiegheling der singconst’ et ‘Vande molens’: Deux traités inédits Amsterdam 1884 674 680 In Bierens de Haan's edition it is to be found on pp. 87–97.
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• Beeckman I. Journal tenu par Isaac Beeckman de 1604 à 1634 de Waard C. The Hague1939-53 II 292 292 4 vols The relevant places are III, 52, and IV, 157 (letter to Mersenne, 1 October, 1629).
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• Mersenne , M. 1636/7 . Harmonie Universelle Paris ‘Preface, & advertissement au lecteur’, preceding the ‘Livre premier des consonances’, second page.
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• Adam , C. and Tannery , P. , eds. 1971–74 . Oeuvres de Descartes , second edition Vol. I , 331 – 331 . Paris (cf. p. 295)
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• Huygens . 1888–1950 . Oeuvres Complètes… Vol. XX , 32 – 32 . The Hague 22 vols
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• Dupont , W. 1935 . Geschichte der musikalischen Temperatur 83 – 84 . Nördlingen
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