The Measurement of Timbre
Authors: Lewis Don , Larsen M. J. 
Published: September 2005

Research designed to measure timbre as a function of harmonic structure, frequency level, and intensity level is in progress. This paper, the first of a series of projected reports, includes a description of apparatus, a brief discussion of problems of measurement, and a summary of some of the data already secured.
The apparatus consists mainly of an electrostatic generator, described in part elsewhere. This instrument produces complex tones constituted of desired combinations of any or all of sixteen consecutive harmonics, the frequencies, intensities, and phase relationships of which are subject to control. Each harmonic is reasonably free from stray components. A calibrated Western Electric 555 receiver is used with the generator. The current flowing through the receiver (current being proportional to the r.m.s. value of pressure developed in the ear canal) is measured with a vacuum tube voltmeter. As many as five different test tones, each to be paired a required number of times with a suitable standard tone, may be set up in advance for random presentation to a listener. When adjustment is complete, a test series may be run more or less automatically. To avoid undesirable transients which arise when tones are interrupted suddenly, the circuit is arranged to start and stop the tones gradually. Considered as a whole, the apparatus meets experimental requirements fairly adequately.
Several problems arise in connection with attempts to measure timbre. One of the most perplexing of these is the choice of meaningful criteria (preferably a single criterion) in terms of which two timbres can be differentiated. Other important problems have to do with choosing suitable standard tones, with finding methods of obviating possible changes in pitch and loudness when harmonic structure is altered, and with deciding whether individual harmonics should be adjusted in terms of intensity level, sensation level, or loudness level. It is admitted that rather arbitrary decisions were sometimes made.
Most of the investigations to date have dealt with the measurement of what are called masked absolute thresholds and masked differential thresholds. When a single harmonic is raised in intensity level until it is barely perceptible in the presence of other harmonics, its intensity level at that point is called its masked absolute threshold. The amount that a single harmonic, already at or above its masked absolute threshold, must be raised in intensity level in the presence of other harmonics to give rise to a just perceptible change is called its masked differential threshold. Masked absolute and masked differential threshold values are held to be measures of the sensitivity of the ear to timbre differences. Data at hand show that discrimination varies with both frequency level and intensity level, in addition to its variation with harmonic structure. Particularly close is the relationship between masked differential thresholds and harmonic structure. It is likely that masked absolute thresholds vary with phase, but evidence on this point is too fragmentary to warrant a definite conclusion.