frequency ratio

music

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June 26, 2026

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In music, the relationship between tones is described by consonance and dissonance. Consonance creates a sense of stability, while dissonance creates tension. These perceptions have evolved over time, with intervals like the third once considered dissonant but now generally accepted as consonant.

The Pythagoreans discovered that musical harmony is linked to simple whole-number ratios of frequency. For example, an octave has a frequency ratio of 1:2, while more complex ratios, like 8:15 for a major seventh, are perceived as more dissonant. This connection between simple ratios and consonant sounds, and complex ratios and dissonant sounds, forms a fundamental aspect of musical theory.123

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sound
Dynamic range of the ear
…musical intervals is associated with frequency ratios rather than absolute frequency differences in hertz. As a result of this empirical observation that all octaves sound the same to the ear, each frequency interval equivalent to an octave on the horizontal axis of the Fletcher-Munson scale is equal in length.
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…musical intervals is associated with frequency ratios rather than absolute frequency differences in hertz. As a result of this empirical observation that all octaves sound the same to the ear, each frequency interval equivalent to an octave on the horizontal axis of the Fletcher-Munson scale is equal in length.
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tuning and temperament
… of tuning are those of frequency ratio and of consonance and dissonance. A given musical pitch is determined by the frequency of vibration of the sound wave that produces it, as a′ = 440 cycles per second. An interval, or distance between two pitches, can thus be mathematically described as…
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… of tuning are those of frequency ratio and of consonance and dissonance. A given musical pitch is determined by the frequency of vibration of the sound wave that produces it, as a′ = 440 cycles per second. An interval, or distance between two pitches, can thus be mathematically described as…
Read More

keyboard instrument
Reed pipes
The frequency of the pulsations of air that enter the shallot is determined by the effective length of the reed and, in turn, determines the pitch of the note. Thence, the pulsations pass out into the tube, or resonator, which further stabilizes the pitch and decides…
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The frequency of the pulsations of air that enter the shallot is determined by the effective length of the reed and, in turn, determines the pitch of the note. Thence, the pulsations pass out into the tube, or resonator, which further stabilizes the pitch and decides…
Read More

musical sound
Tone
…motion that are expressible as frequency ratios of 1:2, 3:4, etc. This means that the reed (or string or air column as well) is vibrating in halves and thirds and fourths as well as a whole. Another way of expressing this is that half the body is vibrating at a…
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…motion that are expressible as frequency ratios of 1:2, 3:4, etc. This means that the reed (or string or air column as well) is vibrating in halves and thirds and fourths as well as a whole. Another way of expressing this is that half the body is vibrating at a…
Read More