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Exercise:
Small differences between ervals can be expressed in em cents. A cent is defined as the hundreth part of an equally tempered semitone i.e. as a ratio of ^/. For humans a single cent is too small to be perceived. abcliste abc Calculate the frequency of a note centsO cents higher than faO. abc A just major third slightly differs from an equally tempered major third four halftones. Express the difference in cents. abcliste

Solution:
abcliste abc f' fbF fatimes ^cents/ resultfbP abc The ratio between the just and the equally tempered major third is given by r sscIet:sscIjust frac^// This ratio can be expressed as a number N of cent ervals: r leftsscIcentright^N Solving for N leads to N fraclnrlnsscIcent centsF fraclnleft^///rightln ^/ cents approx resultcentsP abcliste
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Exercise:
Small differences between ervals can be expressed in em cents. A cent is defined as the hundreth part of an equally tempered semitone i.e. as a ratio of ^/. For humans a single cent is too small to be perceived. abcliste abc Calculate the frequency of a note centsO cents higher than faO. abc A just major third slightly differs from an equally tempered major third four halftones. Express the difference in cents. abcliste

Solution:
abcliste abc f' fbF fatimes ^cents/ resultfbP abc The ratio between the just and the equally tempered major third is given by r sscIet:sscIjust frac^// This ratio can be expressed as a number N of cent ervals: r leftsscIcentright^N Solving for N leads to N fraclnrlnsscIcent centsF fraclnleft^///rightln ^/ cents approx resultcentsP abcliste
Contained in these collections:
  1. 3 | 19
  2. 3 | 16

Attributes & Decorations
Branches
Acoustics
Tags
cent, equal temperament, interval, just scale
Content image
Difficulty
(2, default)
Points
0 (default)
Language
ENG (English)
Type
Calculative / Quantity
Creator by
Decoration
File
Link