File:Dyadic harmonic entropy graph (optimized for low resolution).png

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English: Shows harmonic entropy for dyads, horizontal axis shows the size of the interval in cents.Low points on the graph are more consonant. So for instance the dip at 2:3 shows that the interval 2:3 (pure fifth) is the most consonant dyad after the octave in this model, as expected.

This models one of the components of dissonance as a measure of the uncertainty of the virtual pitch ("missing fundamental") evoked by a set of two or more pitches. This measures how easy or difficult it is to fit the pitches into a single harmonic series. For example most listeners rank a 4:5:6:7 chord as far more consonant than 1/7:1/6:1/5:1/4. Both have exactly the same set of intervals between the notes but the first one is easy to fit into a single harmonic series. The other components of dissonance not modeled by this theory include critical band roughness as well as tonal context (e.g. an augmented second is more dissonant than a minor third although the interval, 300 cents, is the same for both).

For details of how harmonic entropy is calculated see Harmonic Entropy from Bill Sethares' book Tuning Timbre Spectrum Scale and described in more detail here and here
Date
Source File given to me by author
Author Paul Erlich
Other versions High resolution version: File:Dyadic harmonic entropy graph.png
File:Harmonic entropy Farey sequence.png

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5 February 2014

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current05:07, 2 June 2014Thumbnail for version as of 05:07, 2 June 201412,000 × 5,918 (115 KB)JeffyPI'm here to make the world a little bit smaller ☺
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