VIII. RANGE OF INDIVIDUAL DIFFERENCES
In a previous chapter it has been pointed out that quantitative psychology is still struggling toward the invention of scales which shall measure mental traits in terms of units, every one of which shall be equal to every other, as every inch is equal to every other inch. Until this is achieved, we cannot use “times as” comparisons in speaking of the relation of one individual to another, in respect to a function. We can now say that one person is three times as heavy as another person, because we can measure them in pounds, each one of which is equal to every other. But we cannot yet say that one person is three times as intelligent as another, because we have not captured the unit which would enable us to do so.
In some of the traits which go to make up musical talent, it is possible to use the “times as” comparison, because we have physical units whereby the differences may be gauged. Pitch, for instance, may be measured thus. It depends physically upon the frequency of vibrations, proceeding from a sounding stimulus, and is measurable in terms of the constant number of double vibrations per second. Seashore has found variations in power of discrimination from one-fourth of a double vibration to fifty double vibrations per second. This means that there exist individuals who are at least two hundred times as sensitive as others to pitch, in terms of the physical unit.
Other elements in musical sensitivity cannot be so readily measured in stimulus units, so that the “times as” comparison cannot be made. The great diversity of sensitivity to pitch may, perhaps, be regarded as a token of the range of individual differences in musical sensitivity, especially since pitch is a fundamental capacity. It is probably no exaggeration to say that, in an ordinary class in the elementary school, children are being taught together, some of whom are at least a hundred times as musical as others. If children of the same age differed as much from each other in height as they do in sense of pitch, it would be impossible to teach them in unassorted groups, for some would be two hundred times as tall as others. The diversity in mental traits, so much greater than in physical traits, leaves us complacent, for the eye cannot behold the incongruities, as it can in physical matters. The eye cannot see the waste of time, effort, and joy which follows from the attempt to train, equally and together, children of such widely differing capacities for learning.