288 REPORTS ON THE STATE OF SCIENCE, ETC. 



group the observer was asked what percentage of an original (i.e. reference) 

 loudness was ' left in ' a comparison loudness. In the second, the observer 

 was required to select from a range of seven or eight variables a value which 

 appeared nearest to a given fraction (^, ^, i) or a given multiple (2, 3, 5) of 

 the standard. The stimuli used consisted of warble tones, single frequency 

 tones, and room noise recordings, all reproduced on special records. The 

 frequencies covered were 250 to 2,500 cycles, and the intensity levels varied 

 from 34 to 84 db. Plotting multiple increase of original loudness or re- 

 ciprocal of remaining fraction of original loudness (v) against energy change 

 in db, it was found that an equation of the form 



y = a + be'" 



gave the best fit to the data. The best results were obtained with the 

 second of the methods noted. In all, 175 subjects were tested. Each 

 individual's judgments were consistent over a wide range, though they 

 might differ from those of other observers. The authors proposed a noise 

 measurement scale on the basis of their results — a straight line relation 

 between multiple loudness units on a logarithmic scale and db above 

 threshold. 



Geiger and Firestone (18) worked on rather similar lines to those of the 

 researches just described. In this experiment the observer himself set the 

 variable loudness to a value bearing the required relation to the standard. 

 The fractions required were J, |, ^o- t^o ! the multiples were 2, 4, 10, 100. 

 Tones of 60 and 1,000 cycles, and a complex noise of over forty components 

 were studied at three intensity levels : 30, 35, and 80 db. Results similar 

 in some respects to those of Kingsbury (28), and showing a good degree 

 of self-consistency were obtained ; on the other hand, they seemed to 

 be at variance with those of more recent experimenters. The general 

 conclusion was that loudness judgments are made on the basis of actual 

 sensation. 



Riesz (47) advanced the hypothesis that two tones of different frequencies 

 would sound equally loud when their intensities were such that the ratios 

 of the number of distinguishable steps above the absolute threshold to the 

 number of such steps above the threshold for a reference tone of the same 

 frequency were the same for both tones. This was put to the test using as 

 reference one of Munson's equal loudness contours, and a good corre- 

 spondence between observed and theoretical values was obtained, except 

 at the two highest intensities, at which the influence of the threshold of 

 feeling was probably operative. 



The most authoritative work to date on the measurement of loudness is 

 that of Fletcher and Munson (14), whose results have been adopted by the 

 American Standards Association (4). The intensity levels at which pure 

 tones of frequencies from 62 to 16,000 cycles sound equally loud was 

 determined by comparison with a 1,000-cycle reference tone. Both ears 

 of eleven observers were tested, at all intensities. The results are sum- 

 marised in two sets of curves. The first set shows equal loudness contours 

 relating frequency to sensation level (i.e. db above the threshold for that 

 frequency). The second shows a similar set of contours, but with intensity 

 levels (i.e. db above a uniform reference level) as ordinates. The greater 

 part of the authors' paper is devoted to the calculation of the loudness level 

 of a steady complex tone ; the empirical formula derived is of rather a 

 complicated character. 



A new loudness scale designed for free-space listening, was devised by 

 Churcher, King and Davies (9). To begin with, a scale based on a number 

 of just perceptible increments above the absolute threshold of an 800-cycle 



