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Musical Scales and Tonality - University of Toronto Scarborough
Musical Scales and Tonality - University of Toronto Scarborough

... • Musical cultures make use of variation in pitch • Use tones of low to high frequency, and combine them in various ways • Pitch and frequency are continuous scales • Yet musical cultures use discrete pitches • Use of discrete pitches, as opposed to continuously varying pitches, a universal • Althou ...
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Intro to Music Theory - Hamden High School Music Program
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document - Far Western District

... • As we discussed in week 3, a goal of singing barbershop properly is to create and match/reinforce each other’s overtones. To that end, we practice “just intonation.” Fixed pitch instruments (e.g. pianos) are tuned to equal temperament, where the notes play exactly the same regardless of context. J ...
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... There is also another structure when we take into account the notes and pitches of every melody. It depends on the scale. A scale is a sequence of notes from which melodies and harmony can be derived. Scales are named according to the first note or degree. For example, in the C (do) major scale the ...
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Music Theory Essay. - Guitar Master Class

... note. Humans with good hearing can detect sound waves within a frequency range of about 20Hz up to about 20,000 Hz. In western music pitches of notes are named after the first seven letters of the alphabet (A B C D E F G). The notes we usually use are made relative to a reference frequency of 440Hz. ...
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... represented the same way. The idea is to build a "sawtooth" shaped wave. We usually use sawtooth waves when diagramming the standing waves produced by a musical instrument, for example, an oboe or a saxophone. This graph shows the fundamental (graphed in green), the smaller wave of its first harmoni ...
Tippett - Concerto for Double String Orchestra movement I (Harmony)
Tippett - Concerto for Double String Orchestra movement I (Harmony)

... harmony. The most important functions of the chords are subdominant, dominant, and tonic (S, D, T). They are usually represented by scale degrees II/IV, V, and I, but other degrees can be substituted for them as well. ...
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Just intonation



In music, just intonation (sometimes abbreviated as JI) or pure intonation is any musical tuning in which the frequencies of notes are related by ratios of small whole numbers. Any interval tuned in this way is called a pure or just interval. The two notes in any just interval are members of the same harmonic series. Frequency ratios involving large integers such as 1024:927 are not generally said to be justly tuned. ""Just intonation is the tuning system of the later ancient Greek modes as codified by Ptolemy; it was the aesthetic ideal of the Renaissance theorists; and it is the tuning practice of a great many musical cultures worldwide, both ancient and modern.""Just intonation can be contrasted and compared with equal temperament, which dominates Western instruments of fixed pitch (e.g., piano or organ) and default MIDI tuning on electronic keyboards. In equal temperament, all intervals are defined as multiples of the same basic interval, or more precisely, the intervals are ratios which are integer powers of the smallest step ratio, so two notes separated by the same number of steps always have exactly the same frequency ratio. However, except for doubling of frequencies (one or more octaves), no other intervals are exact ratios of small integers. Each just interval differs a different amount from its analogous, equally tempered interval.Justly tuned intervals can be written as either ratios, with a colon (for example, 3:2), or as fractions, with a solidus (3 ⁄ 2). For example, two tones, one at 300 Hertz (cycles per second), and the other at 200 hertz are both multiples of 100 Hz and as such members of the harmonic series built on 100 Hz. Thus 3/2, known as a perfect fifth, may be defined as the musical interval (the ratio) between the second and third harmonics of any fundamental pitch.
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