Abstract
This sentence sums up a good deal of the fundamentals of Isaac Beeckman’s (1588–1637) mechanical philosophy: all qualities of things are reduced to the motions of atoms of various shapes and sizes in the void. Beeckman was quite aware of the close link with the ancient atomic theory of Democritus and Epicurus, with which he was acquainted primarily through its poetical expression in Lucretius’ De rerum natura (‘On the nature of things’.) To Beeckman the atomic theory was not the end product of a chain of scholastic reasoning on the structure of matter, but rather a fertile starting point for the explanation of the most varied aspects of nature. (It has even been hypothesized that he was the man who suggested the idea to Gassendi, the first scientist to make the atomic theory palatable for a Christian public.)2
As all things consist of atoms of diverse forms at diverse distances from each other, that is, [distant] by intermediate empty spaces, without doubt all essential difference comes from them.1
The Corpuscular Theory of Sound
From H. Floris Cohen, Quantifying Music. The Science of Music at the First Stage of the Scientific Revolution, 1580–1650 (Dordrecht/Boston/Lancaster: D. Reidel, 1984), pp. 120–147.
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References
Isaac Beeckman, Journal tenu par Isaac Beeckman de 1604 à 1634 (=JIB), ed. Cornelis De Waard, 4 vols. (Den Haag: M. Nijhoff, 1939–1953), 1:201: “C¨´m omnes res constent atomic diversae formae diversisque à se invicem distantijs, hoc est spacijs inanibus intermedijs, procul dubio omnis differentia essentialis ab illis sumitur.”
Bernard Rochot, Les travaux de Gassendi sur Épicure et sur l’atomisme: 1619–1658 (Paris: J. Vrin, 1944), 34 ff.
Cornelis De Waard, “Isaac Beeckman 1588–1637,” in Eduard J. Dijksterhuis and De Waard, Twee Nederlandsche figuren uit de zestiende en zeventiende eeuw (Den Haag: M. Nijhof, 1941) discusses various corpuscular theories of Beeckman’s (pages 302–306, 320323, 327) without trying to make them consistent; probably they were not. In JIB 1:329 Beeckman seems to state a finite divisibility of the sound globules, but in JIB 3:56, this seems to be denied again. Also the globules do not move in the void, but rather fly through the air. Moreover, under certain circumstances the globules could be broken: see the explanation of the overtones in Cohen, Quantitying Music, p. 127, and of overblowing, ibidem, p. 148. So the ambiguity remains.
For the first time in JIB 1:92: “Sonus est idem numero aer qui fuit in ore loquentis.” The translation of `numero’ (for which the dictionary gives both `quantitatively’ and `exactly’) has given rise to some misunderstandings. Both Andr Pirro, Descartes et la musique (Paris: Fischbacher, 1907; reprint ed., Genve: Minkoff, 1977), pp. 4–5, and De Waard, JIB 4:177, footnote 3, translate it by ‘quantitatively;’ De Waard thus hopes to render the theory slightly more plausible. But to this it may be objected that (1) this translation is not compatible with Beeckman’s theory, according to which the air globules that reach the ear simply are the same ones that were cut off by the vibrating string, the glottis, etc.; (2) even if this were not so, it is not clear how, if they would be something different, the quantity could possibly be the same; (3) Descartes, who knew Beeckman’s theory from actual conversations with him, interpreted it as an identity rather than a numerical equality (if only to reject it contemptuously: letter to Mersenne from January 1630; JIB 4:177;) (4) when Beeckman states the principle in Dutch, he says, at one place, criticizing Bacon’s incorporai idea of sound: “Daerom en volcht hier niet uyt, dat (gelyck ick vooren dickwils geseydt hebbe) het geluydt niet en soude syn deselve locht, die in de mont was” (JIB 3:56), which means: “Therefore from this it does not follow that (as I have often said before) sound would not be the same air that was in the mouth.” Similarly JIB 2:302.
The experiment is described in JIB 1:210; in JIB 3:247–248 the conclusion is drawn explicitly. Cp. JIB 4:159.
JIB 2:37–38: “oe kompt, dat het water geroert wert, dewyle de wint op elck deelken des waters even styf schyndt to dringhen? Ick antwoordde, dat de wint, gelyck oock de locht, kan gedenseert ende gerarifieert werden, dat is, aise opt water valt ende daertegen stoot, so wort se door den drangh van volghenden wint ineen gedronghen. Dese densatie end rarefactie gaet al bevende toe, gelyck een snare, die davert, waerdoor het gebeurt, dat de wint op het een deelken des waters altemet meerder drangh maeckt dan op het ander; ende so haest alser een kleyn voorken in het water gemaeckt is, so wort het terstondt grooter, want de wint, die op een effen lichaem lanckx het lichaem henen schuyfde, die wort nu in dat groefken gehouden ende maeckt den drangh grooter.¡de bare verheft sich so langhe totdat de swaerte van het water der bare swaerder is dan het door de kracht des wints omhooghe kan gehouden worden; maer de bare sackt neder als de wint, niet meer konnende het water verhooghen, sich relaxeert ende, gelyck vooren geseydt is, gerarifieert wort, al bevende. Daervan kompt het, hoe stercker de wint is, hoe hoogher ende grooter baren, tensy dat het water seer ondiep is¡ ”
JIB 1:92: “Dico igitur, c¨´m corpus durum percutitur aerque intercipitur, aut aer, quovis modo quo sonus fit, movetur, primum aerem quem percussio immediat¨¨ movet, non protrudere aerem proximum eodemque modo movere atque ipse motus erat, atque hunc iterum sibi proximum impellere dum successione aures impingantur, ut in aquâ fieri diximus, sed ilium ipsum aerem, qui tangitur immediat¨¨ et afficitur a re durâ, violenter discuti, disjici et partit¨¨ se undique diffundere, ita ut ipse aer impulsus aures nostras feriat, co modo quo flamma candelae se spargit per totam aulam et vocatur lux.” Beeckman never gave up this view: JIB 4:161, 185. Cp. JIB 2:71–72, where he rejects superposition in the case of interpenetrating ripples from two stones thrown into the water simultaneously.
Derivation of the proof: JIB 1:54–55; communication to Mersenne: JIB 4:146; publication by Mersenne: Harmonie Universelle (Paris: S. Cramoisy, 1636–1637: reprint ed., 3 vols., Paris: CNRS, 1965), 1:157–158 (“Livre troisiesme des mouvemens du son des chordes,” proposition 1.)
Clifford A. Truesdell, “The Rational Mechanics of Flexible or Elastic Bodies 16381788, in Leonhardi Euleri Opera Omnia, series 2, vol. 11, section 2 (Zurich: F¨¹ssli, 1960), pp. 25–26; here also a comment on the validity of the proof.
JIB 4:158 and 182. After Mersenne’s demonstration (cp. Harmonie Universelle 3:4546 (“Livre premier des instrumens,” proposition 19.) Beeckman also suggested an improved method of pitch standardization, namely, to use a bronze wire of given length, weight, and tension instead of a pipe or string: JIB 3:132.
Admittedly there is a fourth property, the phase of the wave, but this does not influence the sensation of sound; see Juan G. Roederer, Introduction to the Physics and Psychophysics of Music (New York: Springer, 19752), p. 38.
JIB 1:249; see Cohen, Quantifying Music, p. 30 (for Kepler), and p. 101 (for Mersenne).
JIB 4:187, 214–215: “Chorda tremore sua aerem dispergens, eum in aequales fer¨¨ globulos frangit; attamen c¨´m omnes partes chordae aequ¨¨ frequenter, sed non aequ¨¨ celeriter tremant, et aliae aeris particulae alijs fortasse fragiliores sint, nec chordae crassities ubique sit exact¨¨ aequalis, fit ut eorum globulorum quidam in duas, tres, quatuor etc. partes frangantur. Quae in duas frangantur, octavam auribus repraesentant, quia eodem tempore duplici puncturâ afficiuntur¡”
For a discussion of Beeckman’s ideas on this subject, see Cohen, Quantifying Music, p. 139.
JIB 1:249: “At etiam ex tarditate hac incitatio languescit, ita ut non semper aequali violentiâ aures feriat, unde fit ne tantum discrimen sit qu¨¤m ant¨¨ inter ictum ipsum et silentium, id est quietem; atque ictûs non sunt tam diuturni, extremitatibusque eorum derasis neque ad auditum pervenientibus; unde fiunt silentia majora. C¨´m igitur parva est differentia inter sonum ipsum et silentium, auris non distinguit sonum ¨¤ quiete, eo modo quo oculus longinqua, perforata et discreta habet pro continuis, propter parvum discrimen quod apparet inter imagines foraminis remque ipsam ipsaque foramina: parum enim lucis e longinquis rebus oculos ingreditur. Sic sonus videtur continuus perpetuumque murmur.”
JIB 1:250: “C¨´m haec ita se habeant voxque perpetu¨¤ languescat magisque continua fiat¡ ”
JIB 1:250: “Sic igitur etiam sonus continuus facillim¨¨ omnium bisecatur, quia, ut in visibili, una tant¨´m est medietas, undique aequaliter affecta.”
JIB 1:251: “Diapason per se placet maxim¨¨, quia medietas silentij chordae acutioris exact¨¨ coincidit cum medietate vocis gravions, ita ut auditus graviorem secet in duo aequalia per medietatem silentij, quae bisectio dicta est facillima ide¨¤que gratissima.”
JIB 1:250: “patet octavam graviorem, quae paucioribus ictibus explicatur, repraesentari et subaudiri.”
JIB 1:324: “Superior ver¨¤ chorda non potest repraesentare inferiorem, neque inferior superiorem, quia id, quod superius est, auris perpetu• pro superiore ducit atque id, quod est inferius, auribus nunquam alteri superi¨´s potest videri. Inferior igitur chorda languescendo dividitur; superioris ver¨¤ ictûs multiplicantur, id est in inferiore chordâ duo ictûs habentur pro uno; in superiore unusquisque ictus mediatur atque habetur pro duobus ictibus.”
JIB 1:324: “Hint patet quartam 4.3. degenerare in undecimam 8.3., pejorem decimâ majore 5.2., ide¨¤que in contrapuncto rari¨´s adhibetur.”
Daniel P. Walker, Studies in Musical Science in the Late Renaissance (London: The Warbug Institute, and Leiden: E.J. Brill, 1978), pp. 136–138.
Starting with Hermann Helmholtz, Die Lehre von den Tonempfindungen als physiologische Grundlage fur die Theorie der Musik (Braunschweig: Vieweg, 18774), in particular chapters 7, 11 and 12; cf. A. Wood, The Physics of Music (London: Chapman Hall, 19757), pp. 165–170 (ed. revised by J. M. Bowsher).
Cp. JIB 1:338, where Beeckman talks of a “harmony conceived by the soul,” which is caused by the fact that “any given note supplies the sensation [sensum] of the octave below, and many people naturally dividing this octave harmonically” thus make heard the fourth below the written note, whether or not they actually sing it, or “impress it on the soul¡ by a tacit effort of the mind [tacito mentis nisu].” A reference to more recent theories of consonance that are based on non-existing notes in Geza R¨¦v¨¦sz, Einf¨¹hrung in die Musikpsychologie (Bern: Francke, 1946), pp. 95–98.
JIB 1:58: “Cur consonantia harmonica, quam vocant, praestat arithmeticae? id est: cur jucundior fit harmonia, si quis quintam canat contra bassum et quartam contra superium, qu¨¤m si quis quartam caneret contra bassum et quintam contra superium? Respondeo: Quia quarta est imperfectior quintâ, qubque quarta est inferior, eel magis auribus nostris est perceptibilis. Tard¨¦ enim voces inferiores moventur, proptereaque soni intermedij diuti¨´s moventur antequam soni coincidant et unisonus fiat; superior verb vox, quia sonos suos velociter mittit, statim unisona fit cum illâ quae ips¨¤ quartâ inferior est. Ergo discordia quartae, aut poti¨´s diversitas sonoris ejus ab unisono, vix est perceptibilis; quintae verb perfectior concordantia auribus nostris gratior est citi¨´sque natura sua cum basso unisona fit, quia ejus proportio est ut 3 ad 2.”
This scale is not stated explicitly. However, it follows immediately from the combination of the pertinent statements in JIB 4:158, and JIB 3:164–165, made in 1629 and 1630, respectively. (JIB 1:191 gives a slightly different order, but it is made in passing; it is dated 1618, and may safely be assumed to be just a mistake.)
Johannes Kepler, Harmon ice Mundi, ed. Max Caspar, in Kepler, Gesammelte Werke, 20 vols. (Munich: C.H. Beck, 1938–1988), 6:106: “tune sonus unius [chordae], id est species immateriata corporis chordae, constitutae in vibratione, delapsa ¨¤ sua chorda, ferit chordam alteram¡ ”
JIB 3:67: “Nunquam enim ego sonum vocaverim speciem immateriatam. Qui enim immateriatum movere possit materiatum?”
Mersenne apparently raised this objection in a 1630 letter to Beeckman: JIB 4:180; but Beeckman had been aware of it from the beginning: JIB 1:165–166 (1618).
JIB 4:206–207: “dico nervum tactum pastim, particulas aeris disijciendo, ¨¤ se nervum intactum repellere, partim aerem sibi proximum movere, suo corpore, qui motus movet sequentes usque ad nervum intactum; at quando nervus tactus recurrit, solo motu (quem vulgo, sed mal¨¨, fugam vacui vocant), moveri.” This passage from a letter to Mersenne renders in a more succinct way Beeckman’s diary notes from c. 1617, see JIB 1:165–166. See for Beeckman’s ideas on the `fuga vacui’ Cornelis De Waard, L’exp¨¦rience barom¨¦trique. Ses ant¨¦c¨¦dents et ses explication (Thouars: Deux-S¨¨vres, 1936), chapters 6 and 13.
JIB 1:249: “Exactam vim, qui volet, graphicâ delineatione per circinum et regulam, accurati¨´s examinet.” This is the final line of the first diary note in which sound-silence patterns are applied to comparing the strength of resonance at different intervals. The note was written in December 1618, occasioned by Descartes’ observation that resonance occurs at the fifth, but not at the fourth (Beeckman learnt the method of graphic representation also from Descartes, whom he had just met for the first time.) I have not been able to find a completely consistent interpretation of Beeckman’s attempted proof that, in contrast to the fourth, the fifth, and also the major third (!), do give rise to resonance.
JIB 4:206: “Ver¨´m in 1.5/ [i.e., 1:5], cam superior chorda quinquies movetur eo tempore quo gravior semel movetur, ictus primus medius et ultimus cum graviori chordâ conveniunt; secundus verb et quartus illi occurrunt, nec tantum secundus et quartus videntur superare primum et quintum quantum tertius solus secundum et quartum; toto igitur ictu convenientia est fortior.”
JIB 1:313: “Sic corium tympani baculo pulsum, edit sonitum quia aer intrinsecus in se pellitur, cogitur, movetque latera retrogrado motu, ad ipsumque corium statim resilit.”
This omission is rather strange, since the inner ear is mentioned in at least two modern anatomical descriptions of the sense of hearing that were known to Beeckman. Hieronymus Fabricius ab Aquapendente, De visione, voce, auditu (Venice: Francesco Bolzetta, 1600), Book 2, repeatedly mentions the cochlea and the labyrinth, for instance on pages 1 and 8. Giulio Cesare Casserio (I. C. Casserius), De vocis auditusque organis historia anatomica (Ferrara: Vittorio Baldini, 1601), describes the structure of the inner ear in quite some detail, but Beeckman, who had the book at his disposal for only a few days (JIB 3:42), must have overlooked this passage. See for a detailed history of the anatomy and physiology of the sense of hearing Adam Politzer, Geschichte der Ohrenheilkunde, 2 vols. (Stuttgart: Enke, 1907), 1.
Galen’s conception of spirits is discussed in Karl E. Rotschuh, Geschichte der Physiologie (Berlin: Springer, 1953), pp. 14–17, and Rudolph E. Siegel, Galen on Sense Perception (Basel/New York: S. Karger, 1970). See for the properties of the spirits mentioned in the text JIB 1:121, 124, 126, 136, 157–158, and 2:28, 123.
JIB 1:124: “C¨´m cutis nostra scinditur, vel acu pungitur, dolemus quia tota structura corporis nostri patitur. Nam spiritûs animales fusi sunt per totum f¨¹xoriicoouov, fissâ igitur aliquâ parte, finditur etiam apiritus, at fisso spirito, retrahitur ad se, non aliter atque aer expansus et dilatatus sese contrahit.” JIB 1:125: “Patitur igitur cum omnibus membris etiam cerebrum, sensus communes¡ quôque ille est crassior minusque sectus se contahit, eb sensus est obtusior.”
JIB 1:177: “Impraesentiarum, quod ad quantitatem attinet, mihi solae voces supra modum subtiles videntur injucundae, solâque subtilitate pungere spiritum cerebri, non aliter qu¨¤m acicula cutem pungit; crassiores voces sold quantitate non laedere, ut neque lux Iaedit nisi summâ suâ claritate, nimis celeriter et acut¨¨ oculos feriens.”
JIB 1:177: “sic ex diversis instrumentis, ex quibus vox excutitur, oritur qualitas quaedam aliquando delectabilis, aliquando minus, quia aer in partes secatur quae poris cerebri, vel membrarum, vel collectionis spirituum, non respondent.”
JIB 1:161: “erit tarnen centenus motus trepidus chordae sensilis.”
JIB 1:161: “Hine sequitur notas majoris morae exactiores chordas requirere difficili¨´sque perpetuis integris notis melodiam cani, harmoniamque suavem et delectabilem fieri, quia, ut dixi, tempore vitium latens innotescat.”
JIB 3:51: “so klopt hy de pypen so, dat de geluyden teghen een gaen, gelyck of se seyden wou, wou, wou, het een wou van het ander in tyt soveel verschillende als den eenen pois in arteriâ manûs van den anderen doet, ende dan ist wel. Maer so hy die dan noch wat ongelycker maeckt, so kommen die wouwen wel 5 of 6 mael dichter opeen; ende so hy die noch erger maeckt, so gaet het gelyck oft het ratelde.”
JIB 3:51: “so gaet se alle 30 mael of so eens to veel over, twelck nu de behaeghelickheyt van de quinte begindt wech to nemen. Maer noch erger synde, so ratelt het ende is heel quaet, dewyle het nu niet meer en gaet gelyck 2 tegen 3, maer gelyck 17 tegen 18 of 20 tegen 21 of 10 tegen 11 etc., twelck al dissonantien syn, want instede dat d’een snare 3 mael behoort to gaen teghen de ander tweemael, so en passen de slagen maer in elf of 12 reysenns op n, of so.”
Another inevitable defect results from the fact that Beeckman does not discuss beating at the unison, but at the fifth, in which case not the fundamentals, but rather the respective second and third partials cause the beating.
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Cohen, H.F. (2000). Isaac Beeckman. In: Gozza, P. (eds) Number to Sound. The Western Ontario Series in Philosophy of Science, vol 64. Springer, Dordrecht. https://doi.org/10.1007/978-94-015-9578-0_11
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