A semitone like E-F also emerges, and the ratio 256/243 suggests dissonance. For example, the octave 2:1, fifth 3:2, and fourth 4:3 are presumed to be universally consonant musical intervals because most persons in any culture or period of history have considered them to be pleasing tone combinations and have built musical compositions around them.įor example, in the buildup of a pentatonic scale by a circle of fifths, a natural whole tone of ratio 9/8 emerges, satisfying the condition for consonance. The ratio determines the musical interval. The simplest approach to quantifying consonance is to say that two tones are consonant if their frequencies are related by a small integer ratio. Two tones are said to be consonant if their combination is pleasing to the ear, and dissonant if displeasing. Intervals represented by exact integer ratios are said to be Just intervals, and the temperament which keeps all intervals at exact whole number ratios is Just temperament. The intervals which are generally the most consonant to the human ear are intervals represented by small integer ratios. From 100 Hz to 200 Hz is an octave, as is the interval from 2000 Hz to 4000 Hz. For example, an octave is a music interval defined by the ratio 2:1 regardless of the starting frequency. The term musical interval refers to a step up or down in pitch which is specified by the ratio of the frequencies involved. A typical strategy for using these univerally consonant intervals is the circle of fifths. The octave, fifth, and fourth are the intervals which have been considered to be consonant throughout history by essentially all cultures, so they form a logical base for the building up of musical scales. The intervals which are perceived to be most consonant are composed of small integer ratios of frequency.The ear is sensitive to ratios of frequencies (pitches) rather than to differences in establishing musical intervals.Musical Scales and Intervals Musical Scalesīackground Material for Tuning and Temperament The building up of a musical scale is based on twoĪssumptions about the human hearing process:

Octave music definition