QUANTITATIVE ESTIMATES OF SENSORY EVENTS 287 



following paragraphs the work is discussed in chronological order, but a 

 classification may be attempted as follows : 



(a) The observer matches for loudness sounds of different frequencies 

 or frequency spectra, and the results are compared with those of 

 physical measurement methods. 



(b) The observer selects from a given range a sound which he believes 

 to bear a given numerical relation to a standard sound. 



(c) The observer estimates in numerical terms the ' loudness-value ' of 

 a given sound, as compared with a standard sound to which the value 

 unity is assigned. 



The pioneer work, apart from that of Wien (59), was that of Sabine (48), 

 who performed an experiment in which organ notes of different frequencies 

 at octave intervals were balanced for loudness. The results, described as 

 ' surprisingly concordant,' can be expressed in the form of a ' loudness 

 contour,' which, except for a sharp drop at the two upper frequencies, is 

 not unlike those of Fletcher and Munson (14, see below). 



Fletcher and Steinberg (15, 52), investigating the estimation of overall 

 loudness of a complex sound, showed that a total loudness could be obtained 

 by summing a fractional power of the weighted energy of each frequency 

 region. Calculated and observed values were found to be in good agree- 

 ment, and a rather complicated empirical equation determined. This 

 formula has not found universal acceptance. 



Kingsbury (28) made a direct comparison of the loudness of eleven pure 

 tones within a frequency range of 60 to 4,000 cycles, with a 700-cycle tone 

 as reference. A series of curves relating sensation-level and loudness has 

 been much quoted by subsequent investigators. 



Richardson and Ross (45) were the first to use what have sometimes been 

 called ' intuited ' loudness units. A tone of pleasant loudness was chosen 

 as standard, and assigned the value i-oo. This (S) was presented along 

 with variables (V) in the form SVSV, and the observer wrote down his 

 estimates of the numerical value of the variable. Of the eleven observers, 

 all were able to perform the task with some measure of success, although 

 many found it difficult, or complained that they were only guessing. 

 DiflFerent forms of relation were obtained for diflferent subjects, but in no 

 case was it found that the estimates conformed to the formula S = k log R. 



Marvin (34) applied the loudness-balance method to the measurement 

 of ' noises ' of various kinds, these being matched against a 1,000-cycle 

 reference tone. It is not quite clear whether Marvin was testing aural 

 balancing or the meter which he used, but good agreement between the 

 two was obtained. 



Laird, Taylor and Wille (30) were the first to study ' fractional ' and 

 ' multiple ' loudness. An audiometer buzz was presented along with 

 another of lower intensity, and the observer was asked to say whether the 

 latter was half the previous loudness, or whether it had to be raised or 

 lowered to give half the loudness of the original. The same procedure 

 was carried out for reductions of one-fourth and three-fourths. The 

 estimates of half loudness were checked by ' doubling,' i.e. asking for a 

 loudness judged to be twice that of a standard. Curves drawn on the basis 

 of the results show a fair degree of consistency, and the authors drew up 

 a ' tentative law ' to express the results. No marked individual differences 

 were revealed. 



Ham and Parkinson (21) carried out experiments similar to those both 

 of Richardson and Ross, and of Laird, Taylor and Wille. In the first 



