Musical ScalesBackground Material for Tuning and Temperament assumptions about the human hearing process:
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Index Temperament and musical scales | ||
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Musical IntervalsThe term musical interval refers to a step up or down in pitch which is specified by the ratio of the frequencies involved. For example, an octave is a music interval defined by the ratio 2:1 regardless of the starting frequency. From 100 Hz to 200 Hz is an octave, as is the interval from 2000 Hz to 4000 Hz. The intervals which are generally the most consonant to the human ear are intervals represented by small integer ratios. 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.
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Consonance and DissonanceTwo tones are said to be consonant if their combination is pleasing to the ear, and dissonant if displeasing. The simplest approach to quantifying consonance is to say that two tones are consonant if their frequencies are related by a small integer ratio. The ratio determines the musical interval. 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.
When you define "consonance" as "pleasing to the ear", then of course you have to ask "whose ear?". You can get into such intense debate about what is "pleasing" that some have come to define music as "sounds organized by human beings" to accede the endless variety. The use of consonance here is limited to giving a suggestion of a simple rule that yields musical intervals that are pleasing to most people, i.e., "consonant". |
Index Temperament and musical scales | ||
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Circle of Fifths
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Index Temperament and musical scales Reference Rossing Science of Sound, 2nd ed. | |||
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