Actual basis of this suggestion. Why is the octave the most pleasing of all inter while those of other intervals always involve in one of the terms an proportion that coincident vibrations bear to those which "sound apart" [i.e. are dissonant]. The unison alone is perfect consonance, because therein only do all vibrations coincide1.' But the degree of consonance in the octave is greater than that in any other interval, because in this, whose total ratio is 1 : 2, the proportion between coincident vals? Beand non-coincident vibrations is I: I, i.e. greater than in cause its ratio is any other. On the proportionality thus maintained of conexpressible in integral sonant to non-consonant vibrations in the octave appears to terms, rest the 'equality' spoken of above; and on this equality, again, rests the 'approach to oneness' which causes the interval to be unnoticed and the sounds taken for one. Aristotle speaks with less subtlety of this matter. 'It is easier to perceive a thing (in its proper nature) when single improper than when blended with something else, e. g. wine when The octave unmixed than when diluted, or honey, or a colour, or the note highest in pitch (vnrn) when by itself than when in the octave 2.' 'Also the quarter tone escapes notice: one hears the melodic rise and fall of the voice as a continuum, but the interval between the extremes in the quarter tone passes unnoticed 3.' 'Why'-it is asked in the Problems*—' is the octave the most pleasing of all intervals? Perhaps because Fundamen- its ratios are expressible by integral terms, while those of the other intervals are not so. For since the string of highest pleasing pitch, the výrŋ, is (in its rate of vibration) double the string lowest in pitch, the vñáτη, for every two vibrations of the former the latter has one, and for every two of the latter But the rate of vibrations fraction. can be ex pressed as the ratio of one to an integral number (sc. two); the other intervals cannot. tal reason of the nature of συμφωνία. It is a óyos ἐναντίων, and Aoyos the former has four, and so on. involves τάξις, which is φύσει ἡδύ. of the výrη is once and a half that of the μéon. Thus the interval of one to one and a half in which the fifth consists is not ultimately expressible in integers; for while the less is one, the greater is so many and a half more. Hence 1 Cf. Chappell, History of Music, pp. 221-4; von Jan, op. cit. pp. 96, IOI nn.; Wundt, H. and A. Psych. p. 69 (E. Tr.). 2 Arist. de Sens. vii. 447a 17-20. 3 Arist. de Sens. vi. 446a 1-5. 4 xix. 35. 920a 27 seqq. 5 Only by this parenthesis can the sense be given. The výrŋ was but half as long as the vrárn. The passage, therefore, implies more accurate knowledge of the vibration of strings than Aristotle possessed. integers are not compared with integers, but there is a fraction over. The case is similar with the fourth: the interval 3:4 cannot be expressed as a ratio of one to any integral number; it appears 1:13. Or perhaps the octave is most perfect because it is made up of the fifth and the fourth, and is the measure of the melodic series 1' 'We are delighted with concordance of sounds because such concordance is a blending of contraries which bear a ratio to one another. But a ratio is a fixed arrangement— a thing which, as has been said, is naturally pleasing 2.' 'If we take two vessels equal and similar to one another, but the one empty, the other half full, and cause them to sound together, they form an octave with one another. Why is this? Because the sound coming from the half full vessel is double the other (in rate of vibration) 3.' The Problems, from which these extracts are taken, are later than Aristotle, and in some ways represent more highly developed theories of music and of harmonics than those of Plato or Aristotle. § 32. It would seem, and has been urged by many, e. g. Probable by Trendelenburg, Arist. de An. p. 107 (Belger), that portion of a portion of what Aristotle wrote on the subject of vocal the tract sound must have been somehow lost. In his work de Gen. treating of An. v. 7. 786b 23, we read: 'As to the final cause of sound. The voice in animals, and as to what voice and sound in treatise general are, an explanation has been offered already, partly cannot in our work on Sense-perception, and partly in that on 'AKOUσTV The Soul.' Again further down: 'With regard to voice, let this suffice for the information not definitely given already in the works on sense-perception and on the soul ".' 1 Prob. xix. 35. 920a 27-38. The Didot punctuation after μeλwdías (38) is here adopted; also Bekker's r' ékeîvo for teμeiv ö (a36). 3 xix. 38. 9218 2-4 συμφωνίᾳ δὲ χαίρομεν ὅτι κρασίς ἐστι λόγον ἐχόντων ἐναντίων πρὸς ἄλληλα ̇ ὁ μὲν οὖν λόγος τάξις, ὃ ἦν φύσει ἡδύ. 3 Probl. xix. 50. 922b 35-9. * Cf. 786 23 τίνος μὲν οὖν ἕνεκα φωνὴν ἔχει τὰ ζῷα καὶ τί ἐστι φωνὴ καὶ ὅλως ὁ ψόφος, τὰ μὲν ἐν τοῖς περὶ αἰσθήσεως, τὰ δ ̓ ἐν τοῖς περὶ ψυχῆς εἴρηται. 5 Cf. 7888 34 περὶ μὲν οὖν φωνῆς ὅσα μὴ πρότερον ἐν τοῖς περὶ αἰσθήσεως διώρισται καὶ ἐν τοῖς περὶ ψυχῆς, τοσαῦτ ̓ εἰρήσθω. loss of a de Sensu missing be that Περὶ In the de Sensu, however, while the physical properties of the objects of seeing, smelling, and tasting are examined and described, those of hearing and touching are entirely omitted. There, for the psychological import of the five senses, we are referred back to the work de Anima: while as to the physical character of the objects of all five, we are promised a discussion to follow; yet while three of these are discussed two are passed over. There is no formal or set treatment of them in that little tract1. The fragment Пeрì 'AкovσTv is un-Aristotelean. Its opening words agree with the views of sound-transmission ascribed by Alexander 2 to Strato, whom therefore Brandis (too hastily as Zeller thinks) regards as the author. According to the Пepì 'AKOVσTŵv (803b 34 seqq.), every sound is composed of particular vibrations (πλŋуaí) which we cannot distinguish as such, but perceive as one unbroken sound: high tones, whose movement is quicker, consist of more vibrations, and low tones of fewer. Several tones vibrating and ceasing at the same time are heard by us as one tone. The height or depth, harshness or softness, in fact every quality of a tone, depends (803b 26) on the quality of the motion originally created in the air by the body that gave out the tone. This motion propagates itself unchanged, inasmuch as each portion of the air sets the next portion of air in motion with the same movement as it has itself.' (Zeller, Arist. ii. pp. 465–6 nn., E. Tr.) 1 Cf. de Sens. iii. 4398 6–17 τί ποτε δεῖ λέγειν ὁτιοῦν αὐτῶν οἷον . . . ψόφον . . . ὁμοίως δὲ καὶ περὶ ἁφῆς. ... ἢ τί 2 Ad Arist. de Sens. (p. 126, Wendland). von Jan, pp. 55 seqq., 135, ascribes the περὶ ̓Ακουστῶν to Heraclides. THE ANCIENT GREEK PSYCHOLOGY OF SMELLING Alcmaeon. Alc- Function and organ through nostrils § 1. WE have little direct information respecting maeon's psychological theory of the sense of smell. that remains is the following, contained in two passages effected by which I extract, the one from Theophrastus, the other from air inhaled the late compilation of Aëtius. 'He taught that a person smells by means of the nostrils, and carried drawing the inhaled air upwards to the brain, in the respiratory process 1.' Not the nostrils alone, therefore, but these in connexion with the brain form the olfactory apparatus. 'He held that the authoritative principle-the intelligence -has its seat in the brain; that, therefore, animals smell by means of this organ which draws in the various odours 2 to itself in the process of respiration 3. Besides these two direct references to Alcmaeon, there is a probable allusion to him bearing on the same subject. Socrates in the Phaedo, reviewing the history of his own mental development, tells his friends that in his youth he had been interested in psychological questions, and that of these one which presented itself was whether it is the brain that furnishes us with the senses of hearing and seeing and smelling. The various theories referred to by Plato in this passage are sufficiently distinctive to show that in mentioning each he is thinking of some particular philosopher. The theory which referred sensation to the opera 1 Theophr. de Sens. § 25; Diels, Vors., p. 104 doppaiveσdai dè ῥισὶν ἅμα τῷ ἀναπνεῖν ἀνάγοντα τὸ πνεῦμα πρὸς τὸν ἐγκέφαλον. " In the following paragraphs the terms 'smell' and 'odour' are sometimes used indifferently for the object of the olfactory sense. So, too, 'taste' is sometimes used for 'savour.' 3 Aët. iv. 17. 1, Diels, Dox., p. 407, Vors., p. 104 év tô éykeþáλw elvai τὸ ἡγεμονικόν· τούτῳ οὖν ὀσφραίνεσθαι ἕλκοντι διὰ τῶν ἀναπνοῶν τὰς ὀσμάς. Plato, Phaedo 96 B, Diels, Vors., p. 105 TóτEρOV ὁ ἐγκέφαλός ἐστιν ὁ τὰς αἰσθήσεις παρέχων τοῦ ἀκούειν καὶ ὁρᾶν καὶ ὀσφραίνεσθαι. ... to brain. In the de Sensu, however, while the physical properties of the objects of seeing, smelling, and tasting are examined and described, those of hearing and touching are entirely omitted. There, for the psychological import of the five senses, we are referred back to the work de Anima: while as to the physical character of the objects of all five, we are promised a discussion to follow; yet while three of these are discussed two are passed over. There is no formal or set treatment of them in that little tract1. The fragment Пepì 'AкovσT@V is un-Aristotelean. Its opening words agree with the views of sound-transmission ascribed by Alexander 2 to Strato, whom therefore Brandis (too hastily as Zeller thinks) regards as the author. 'According to the Пepì 'AкovσTŵv (803b 34 seqq.), every sound is composed of particular vibrations (λnyaí) which we cannot distinguish as such, but perceive as one unbroken sound: high tones, whose movement is quicker, consist of more vibrations, and low tones of fewer. Several tones vibrating and ceasing at the same time are heard by us as one tone. The height or depth, harshness or softness, in fact every quality of a tone, depends (803b 26) on the quality of the motion originally created in the air by the body that gave out the tone. This motion propagates itself unchanged, inasmuch as each portion of the air sets the next portion of air in motion with the same movement as it has itself.' (Zeller, Arist. ii. pp. 465-6 nn., E. Tr.) . . ἢ τί 1 Cf. de Sens. iii. 4398 6–17 τί ποτε δεῖ λέγειν ὁτιοῦν αὐτῶν οἷον . . . ψόφον . . . ὁμοίως δὲ καὶ περὶ ἁφῆς. 2 Ad Arist. de Sens. (p. 126, Wendland). von Jan, pp. 55 seqq., I^* ascribes the περὶ ̓Ακουστῶν to Heraclides. |