=Harmony and Discord.=--When several tones sound together we may get peculiar feelings of pleasure or displeasure designated as consonance and dissonance respectively. A note sounds most consonant with its octave. When with the octave the 'third' and the 'fifth' of the note are sounded, for instance _c--e--g--c´_, we get the 'full chord' or maximum of consonance. The ratios of vibration here are as 4:5:6:8, so that one might think simple ratios were the ground of harmony. But the interval _c--d_ is discordant, with the comparatively simple ratio 8:9. Helmholtz explains discord by the overtones making 'beats' together. This gives a subtle grating which is unpleasant. Where the overtones make no 'beats', or beats too rapid for their effect to be perceptible, there is consonance, according to Helmholtz, which is thus a negative rather than a positive thing. Wundt explains consonance by the presence of strong identical overtones in the notes which harmonize. No one of these explanations of musical harmony can be called quite satisfactory; and the subject is too intricate to be treated farther in this place. =Discriminative Sensibility of the Ear.=--Weber's law holds fairly well for the intensity of sounds. If ivory or metal balls are dropped on an ebony or iron plate, they make a sound which is the louder as they are heavier or dropped from a greater height. Experimenting in this way (after others) Merkel found that the just perceptible increment of loudness required an increase of 3/10 of the original stimulus everywhere between the intensities marked 20 and 5000 of his arbitrary scale. Below this the fractional increment of stimulus must be larger; above it, no measurements were made. Discrimination of differences of _pitch_ varies in different parts of the scale. In the neighborhood of 1000 vibrations per second, one fifth of a vibration more or less can make the sound sharp or flat for a good ear. It takes a much greater _relative_ alteration to sound sharp or flat elsewhere on the scale. The chromatic scale itself has been used as an illustration of Weber's law. The notes seem to differ equally from each other, yet their vibration-numbers form a series of which each is a certain multiple of the last. This, however, has nothing to do with intensities or just perceptible differences; so the peculiar parallelism between the sensation series and the outer-stimulus series forms here a case all by itself, rather than an instance under Weber's more general law. CHAPTER V. TOUCH, THE TEMPERATURE SENSE, THE MUSCULAR SENSE, AND PAIN.