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Download Free PDF. Construction and interpretation of equal-tempered scales using frequency ratios, maximally even sets, and P-cycles. Richard Krantz. 2000. See Full PDF. Download PDF.
1 sty 1986 · PDF | On Jan 1, 1986, J. T. Kent published Ternary continued fractions and the evenly-tempered musical scale | Find, read and cite all the research you need on ResearchGate
13 sie 2020 · A scale system that tries to correct for the problem of being able to play in any key is called a temperament. The chosen starting note of a scale is called the tonic and a musical fifth consists of the tonic and the fifth note of the scale.
1 cze 2021 · Several steps were undertaken to create an optimum of frequency relationships, an important one being the well-tempered scale used in the baroque period. Today the “equal temperament” is mostly used, a mathematically created scale with logarithmically equal intervals between half tones.
Equal temperaments of non-octave intervals. The equal-tempered version of the Bohlen–Pierce scale consists of the ratio 3:1 (1902 cents) conventionally a perfect fifth plus an octave (that is, a perfect twelfth), called in this theory a tritave (play ⓘ), and split into 13 equal parts.
What’s a Scale? ‣ A scale is a pattern of notes, usually within an octave ‣ In Western music we use the diatonic scale. ‣ This scale contains seven distinct pitch classes and is part of a general class of scales known as heptatonic ‣ Doubling the frequency of a tone in this scale requires going up by 8 notes: hence the term “octave”
Scales constructed from pure harmonic ratios often contain enharmonic note pairs that do not sound in tune when played together. We examine the mathematics behind equal tempered scales that avoid this problem by insisting that the harmonic ratios between any pair of successive notes be identical. The mathematical
