We turn to a consideration of the laws of tonal fusion. (1) If we grant Stumpf's postu late, it is clear that we may speak of degrees of fusion, according as the tendency to fusion, in herent in tonal material, is more or less complete ly realized. The musical interval of the octave may readily be confused, even by practiced ob servers, with a simple tone; the octave, then, represents the highest degree of fusion. On the other hand, the intervals of the major and minor second and major and minor seventh are rarely taken to be unitary, even by unpracticed and unmusical hearers; these intervals, then, repre sent the lowest degree of fusion. Between the two extremes stand, in order from better to worse fusion, the intervals of the fifth, of the fourth, of the major and minor thirds and sixths, and of the subminor or natural seventh and the tri tone. We have, in other words, a scale of six: fusion degrees within the octave of the musical scale. The facts are summed up in the primary fusion law that "the degree of fusion is a func tion of the vibration ratio of the component tones" (Stumpf). In general, the consonances are the best fusions, the dissonances are the worst, and the imperfect consonances occupy an intermediate position.
Certain other laws of fusion may be formu lated as follows: (2) The dependence of intra octave fusion upon the vibration ratio of the component tones persists over all regions of the musical scale. Above and below the limits of this scale the discrimination of degrees of fusion becomes difficult or impossible. (3) The degree of fusion is independent of the intensity, abso lute and relative, of the component tones. A weak chord fuses as does a loud chord; and a loud tone, accompanied by weak tones, gives the same fusion degree as would be produced if the same tones were all sounded at equal intensities. (4) Stumpf asserts that the fusion degrees of intervals wider than the octave are identical with those of the corresponding intra-octave intervals. Thus, the "ninths have the same fusion as the seconds, the tenths as the thirds, the double oc tave and triple octave as the octave." This law is not generally accepted. We must, of course, not be misled by the fact that discrimination of the tones of the tenth, as compared with those of the third, is facilitated by the greater distance separating them upon the tonal scale. This has nothing to do with degree of fusion; our analy sis may be made easier or more difficult by the concurrence of extrinsic conditions, while the degree of fusion remains absolutely the same. The question is: When analysis of the third- and of the tenth has been performed, and the ob server is able by effort of attention to single out the component tones in both complexes, do the third tones 'go together' (blend) as well as or better than the tenth tones? Is the sense re lationship, which we term fusion degree, the same or different in the two cases? The answer seems to be that the tenth, though a better fusion than, e.g. the tritone (a member of the intro
octave group lying next below the group of thirds and sixths), is still a worse fusion than the third, to which it corresponds. (5) Except in certain specific cases, falling under the laws already formulated, clang-tint does not influence degree of fusion. (6) Spatial separation of the tones, though it facilitates analysis, does not affect de gree of fusion. (7) If two tones are simultane ously ideated (reproduced, as, sounding together, in memory or imagination), the resultant idea always evinces the degree of fusion that the same tones would show in perception. (8) The pitch of a fusion is never that of a tone lying midway between the pitches of the component tones, but rather the pitch of some one of these components. "In a continuously sounding compound clang," as heard by a musical observer, "the whole ap pears to possess the pitch of its deepest tone, even if this be not the loudest" (Stumpf). Un musical observers are apt to estimate the pitch of a simple clang as somewhat lower than that of a compound clang based upon the same funda mental tone.
Other instances of fusion are to be found in the complexes of organic sensation that form the body of the feelings (q.v.) ; in the qualitative taste-smell mixtures (the taste of coffee or lem onade) ; in the perceptions (weight, resistance) mediated both by external skin and by the sense organs of muscle, tendon, and joint; perhaps in all the impressions that we call colors (mixtures of color proper and of brightness) ; and, accord ing to Kuelpe, in such affective formations as emotion, impulse, and feeling. It is, however, doubtful whether the connections of sensation and affection can be brought under the same conceptual heading as the fusion. connections of sensations.
Consult: Stumpf, Tonpsychologie, vol. ii. (Leipzig, 1890) ; Wundt, Grundriss der Psycholo gie (Leipzig, 1897; Eng. trans., London, 1898) ; id., Grundzilge der physiologischen Psychologie (4th ed., Leipzig, 1893) ; Kuelpe, Outlines of Psychology, translated by Pillsbury and Titch ener (London, 1895) : Titchener, Experimental Psychology (New York, 1901).