Bauhaus-Universität Weimar

Experimental Psychology: A Manual of Laboratory Practice, Vol. II: Quantitative Experiments, part 2: Instructor's Manual
Titchener, Edward B.
The Metric Methods 
ences of vibration-rates.”1 That is to say, the sense-mean for tonal dif¬ 
ferences not exceeding the double octave is given with the arithmetical 
(not the geometrical) mean between the corresponding pitch-numbers. 
The result agrees admirably with the values of the j. n. d. for successive 
(4) In his Neue Grundlegung der Psychophysik, 1890, Münsterberg 
gives a brief account of extended experiments upon the estimation of 
tonal distances. He found that musical O's divide a given distance at 
the tone whose pitch-number is the geometrical mean between the ex¬ 
tremes, while unmusical 0’s divide at the arithmetical mean. The 
former, being unable to abstract from their musical knowledge, are of 
little value for the enquiry.3 
No further report upon these experiments has been published.4 In 
1 Ibid., 103. 
2 The publication of Lorenz’ experiments gave rise to an angry controversy 
between Wundt and Stumpf. The references are : Wundt, P. P., i., 1887, 428 ff. ; 
i., 1893, 455 ff-t 462 f. ; ii., 1902, 75 ff., 85 f. ; P. S., vi., 1891, 605; vii., 1892, 298, 
633 ; Stumpf, Tps., i., 1883, 250 f. ; if, 1890, 551, 557 f. ; Zts., i., 1890, 419; if, 1891, 
266, 426, 438. The author read the articles as they appeared ; read them through 
again early in 1893 ; and reread them at the end of 1901. In the first reading he 
was biassed in favour of Wundt; in the second, somewhat in favour of Stumpf. 
His judgment, however, has been the same in every case : that Stumpf’s criticism 
is too sweeping. Lorenz’ results are, of course, open to modification or correction 
by later work. That is the fate of all pioneer inquiries. But Stumpf’s interpreta¬ 
tion is surely one-sided. The article by G. Engel, Z., ii., 361 (written apparently 
in support of Stumpf), is interesting from the musical standpoint, but almost 
comically inadequate from the standpoint of psychophysics. Wundt, we may 
remark, is so thoroughly convinced of the accuracy of Lorenz’ results that he has 
made them the basis of a demonstration experiment : P. P., ii., 1902, 85 f. Stumpf, 
on the other hand, is so thorough a believer in the efficacy of his own criticism 
that he writes in 1901 : “die Theorie der arithmetischen Mitte scheint noch todter 
wie die der geometrischen ” (lieitr., 3, 93). Müller (M., 230, 241) finds unmistak¬ 
able evidence that Lorenz’ judgments were influenced by musical associations, and 
demands a careful analysis of the different factors concerned. 
In the P. S., vi., 634; vii., 300, Wundt says that experiments upon pure tones 
are in course in his laboratory; and in the P. P., i., 1893, 460; ii., 1902, 82, he 
figures the necessary arrangement of tuning-forks. The experiments were made, 
as the author remembers, by P. Krüger (P. S., vii., 1892, 56, 442), but so far as 
he is aware have never been published. 
3 II. Münsterberg, Beiträge zur experimentellen Psychologie, iii., 1890, 37, 39, 41 ; 
iv., 1S92, 149; cf. Stumpf, Tonps., ii., 551. Münsterberg interprets the results 
in terms, of his muscle-sense theory : “ in jedem Falle also basiert auch die Messung 
der Tondistanzen ausschiesslich auf den Aussagen des Muskelsinns ” (iii., 44). 
4 Münsterberg was induced by Stumpf’s criticism of Lorenz to undertake new 
experiments : Beitr., iv., 154 ; Zts., ii., 443.


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