Abstract
When we listen to two musical sounds chosen at random, their successive or simultaneous impact on our hearing will in general not be pleasant: nearly all musical intervals are dissonances. However, when passing through this continuum of dissonances, we hit from time to time upon a combination of musical sounds which is not rough and unpleasant, but strikes us as sweet, restful, and pure; these intervals are the so-called consonances. Owing to this pleasant effect on our senses, consonances have become the next-to-universal building-blocks of music. In all Western music up to and partly including the 20th century, and in nearly all non-Western music as well, the selection of the notes to be used in the various tone scales has been guided primarily by the consonances, either melodically (one constituent tone of the interval heard after the other) or harmonically (both heard at the same time). Why is this so? Where do these exceptional intervals called ‘consonances’ come from?
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Notes
See for a recent overview of the Pythagorean contribution to the problem of consonance Van der Waerden (1979), Ch. 16.
The connection between outer and inner harmony appears to be so self-evident in Greek thinking that this aspect of the problem of consonance is virtually never explicitly discussed. An example of this feeling of self-evidence is given in Plotinus, Enneads II, 9, 16. (I am grateful to Rein Ferwerda for providing me with both the information and the reference to Plotinus). See for an overview of ancient theories of consonance Stumpf (1901).
This cannot be the place to discuss the origins of the rise of polyphony and of the triad, which together informed Western music in a unique way, setting it apart from all other musical systems, primitive and otherwise. Beside the current music history textbooks like Grout’s and Reese’s, a fascinating essay by the sociologist Max Weber (1921) may be mentioned especially. See also Gut (1969).
Zarlino (15733), 28–34; cp. Zarlino (1571), 75; 92.
Salinas (1577), 67/8.
Cp. S. Themerson, Professor Mmaa’s lecture (London, 1953), 77–80; in particular Prof. Soul’s apt remark that, as this way of explaining things is both final and metaphysical, it does not call for further inquiry.
This oft-quoted phrase is not literally to be found in the Ed. Naz. It seems to be contaminated by Galileo’s famous statement in the Saggiatore (Ed. Naz. 6, 232): “La filosofía è scritta in questo grandissimo libro che continuamente ci sta aperto innanzi a li occhi (io dico ľuniverso), [...]. Egli è scritto in lingua matematica . . . “, and by Viviani’s biography of Galileo in which it is said of him (Ed. Naz. 19, 625), “che la liberta delia campagna fosse il libro della natura [...]; dicendo che i caratteri con che era scritto erano le proposizioni, figure e conclusioni geometriche, per il cui solo mezzo potevasi penetrare alcuno delli infiniti misterii dell’istessa natura”. Cp. also Ed. Naz. 18,295.
GW 6, 104/5: “Geometria enim [...], Deo coaeterna, inque Mente divina relucens, exempla Deo suppeditavit [.. .] exornandi Mundi, ut is fieret Optimus et Pulcherimus, denique Creatoris similimus”. Similar sentiments are expressed in Kepler’s work at many places, e.g. GW 1, 24; GW 13, 113; GW 14, 27; and GW 6, 279; “ . . . quod magis delector Geometria in Physicis rebus expressâ, quam abstractà illâ .. . “.
Dijksterhuis (1955) and (1961), passim; esp. the final line of the book (p. 501) that sums up the whole argument. Kuhn (1977), Ch. 3: ‘Mathematical Versus Experimental Traditions in the Development of Physical Science’, esp. 52–55.
It is well known that Newton himself did not find this new harmony quite so harmonious as later generations would: he never gave up the attempt to find a corpuscular substratum for the forces he worked with. Westfall’s thesis is to be found in his (19772), Introduction and Chs. 7/8.
GW 6, 94: “ . .. causae tarnen intervallorum latuerunt homines; adeò ut ante Pytha-goram ne quaererentur quidem; et quaesitas per duo millia annorum, primus ego, nisi fallor, exactissimè proferam”.
Ed. Naz. 8, 143: “... impero che stetti lungo tempo perplesso intorno a queste forme delle consonanze, non mi parendo che la ragione che comunemente se n’adduce da gli autori che sin qui hanno scritto dottamente della musica, fusse concludente a bastanza”. 146: “... potremo per awentura assegnar assai congrua ragione ondeawenga che di essi suoni, differenti di tuono, alcune coppie siano con gran diletto ricevute dal nostro sensorio, altre con minore, ed altre ci feriscano con grandissima molestia . . . “. The English is taken from the 1730 translation by Thomas Weston (see Note III, 24), 145,150/1.
JIB 4, 142: “Ipsissimus est D. des Chartes [...]. Ipsus, inquam, is est, cui ante decern annos ea quae de causis dulcedinis consonantiarum scripseram, communicavi
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 1984 Springer Science+Business Media Dordrecht
About this chapter
Cite this chapter
Cohen, H.F. (1984). Defining the Problem Situation. In: Quantifying Music. The University of Western Ontario Series in Philosophy of Science, vol 23. Springer, Dordrecht. https://doi.org/10.1007/978-94-015-7686-4_1
Download citation
DOI: https://doi.org/10.1007/978-94-015-7686-4_1
Publisher Name: Springer, Dordrecht
Print ISBN: 978-90-481-8388-3
Online ISBN: 978-94-015-7686-4
eBook Packages: Springer Book Archive