Max F. Meyer

Listeners Can Be Seduced to Perceive the Paradoxical Ratio 51:87 as Either One or Another Truly Melodical Interval

The ratio 51:87 (1,706), musically paradoxical, is found to be interpreted as 4:7 when surrounded by the terms 63, 76, and 101; and interpreted as 3:5 when surrounded by the terms 34 and 68.

Helmholtz's Aversion to Tempered Tuning Experimentally Shown to be a Neurological Problem

Experiments show that the brain of people of ordinary musical endowment, when unsophisticated, enables them to esthetically appreciate melodies that are even more mistuned than the equally tempered scale.

Temporal Irregularity of Excitations: How Much Is Accepted by the Brain for Reporting Pitch?

For many years the only obstacle standing in the way of crediting the theory of the hydraulic‐cochlea model [M. F. Meyer, Am. J. Psychol. 72, 293–296 (1959)] as a hypothetical “theory of hearing” has been the notion that the brain reports a pitch to consciousness only when it receives excitations from the auditory sense organ in strictest temporal regularity. The test of this notion has now been accomplished by experimenting with a siren—and the obstacle has been removed.

The Salient Features of the Functioning of the Cochlea, with Demonstration of a Transparent Hydraulic Model

In constructing a model for demonstration of the function of the cochlea two assumptions are what we ought to keep clearly out of our mind: (1) that the living cochlea might contain dead building material of such physical properties as vulcanized rubber or tensile metal, (2) that the cochlea might contain contractile tissue, muscle tissue, that is, building material, which, in itself or in the supports in which it is inserted, could, from time to time at least, actively produce any stresses.A mechanical theory must recognize four salient features: (1) that any sound pervades the cochlea no matter whether the window flexibility is considered in theorizing or put down as negligible in theorizing or is actually (pathologically) impaired—just as any sound pervades any building with all its rooms and partititions, and that such a primitive function is almost certain to have at least a weak and otherwise limited stimulating effect; (2) that the main and more adequate (but not exclusive) stimulating effect in ma...

Neurological Theory of Beat Tones

Tartini pitches and beat tones behave differently and must have different physiological origins. Tartini pitches are heard only if the primary tones remain below 2000 cycles per second, preferably for clear observance below 1000. The cochlea is essential for hearing them. Beat tones are not so limited. Their observation is easiest (least confusing) when the primaries are chosen in the region from 3000 to 5000 cycles per second. But lower tones may be used (although there may then be an overlapping of Tartini pitches and beat tones). The cochlea need not exist for the existence of beat tones.

Observation of the Tartini Pitch Produced by sin 11x+sin 15x and sin 11x+2 sin 15x

The result of experiments with sinusoidal airwaves is that the ratio 11:15 makes the Tartini pitch 7 clearly audible, while neither a summation tone pitch nor a difference tone pitch nor any kind of aural harmonic is audible.

Observation of the Tartini Pitch Produced by “sin 9x+sin 13x”

The combination of the physical tones of the frequency ratio 9:13 makes the secondary pitch 5 clearly audible; but neither the difference tone pitch nor the summation tone pitch, nor any so‐called aural harmonic is audible. The theoretical discussion is based on the hydraulic (nonvibratory) mathematics of cochlear mechanics.

Tartini Versus Helmholtz Judged by Modern Sensory Observation

Concerning the frequency location and the origin of the Tartini pitches the dogmatic assertions found in the textbooks of psychophysiological acoustics are the unhappy evolution of the hopeful guess ventured by Helmholtz that these secondary pitches and the physical combination tones produced by an air pressure tank could be regarded as analogous. In fact, they are incompatible.

Observation of a Further Tartini Pitch Resulting from a Physical Sinusoid Added to a Tartini Pitch

The sinusoidal air waves 9+6+2, shaking the skull, produce not only the commonly expected Tartini pitch 3 but also the rather surprising pitch 1, but none other. However, these occur only within a total range that barely encompasses the human voice. For this restriction a plausible evolutionary hypothesis suggested. The mathematical theory for the pitches 3 and 1 is furnished on the basis of a strictly hydraulic, i.e., nonvibratory, function of the cochlear phragma.

Demonstration of a Hydraulic Model of the Cochlea having a Soft Partition Lengthwise

I introduce fundamental facts requiring explanation: First: Giuseppe Tartini in 1704 discovered that, when two musical tones were presented to it, the sense organ not only gave him the musical interval but added one or more bass tones, which he named terbi suoni. In 1954, Max F. Meyer extended this discovery over nonmusical intervals and also showed that the terzi suoni failed to deserve the Helmholtzian term “difference” tones. Example: For the interval 19:13, the terzi suoni are the frequencies 7 and 3, by no means 6. Second: About 1830, Rudolf Koenig made known the remarkable fact that in all mistuned consonances the beats of the higher and those of the lower pitch were never heard at random times: they always strictly alternated. Third: To this, Carl Stumpy in 1895 added the discovery that the beats of 1:2 and 3:2 (because odd:even) mistuned by “d” came at the rate of “2d,” i.e., were doubled.—The demonstrated model prescribes the fruitless place theory and offers a mechanism by which all those facts ...