User:FloraC/Hard problems of harmony and psychoacoustically supported optimization: Difference between revisions
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The same cannot be assumed for tuning optimization, since that is a vastly different scenario. In a just major triad, the 15th harmonic exists in three ways: as the harmonic of the root, of the 3rd harmonic, and of the 5th harmonic. The figure below is the frequency spectrum of the triad played in the semisine waveform, which has been proposed as the standard ear-training waveform in ''Proposed Standard Ear-Training Waveform''. | The same cannot be assumed for tuning optimization, since that is a vastly different scenario. In a just major triad, the 15th harmonic exists in three ways: as the harmonic of the root, of the 3rd harmonic, and of the 5th harmonic. The figure below is the frequency spectrum of the triad played in the semisine waveform, which has been proposed as the standard ear-training waveform in ''Proposed Standard Ear-Training Waveform''. | ||
[[File:Frequency spectrum of just major triad in semisine wave.png|Figure 1: Frequency spectrum of just major triad in semisine wave]] | [[File:Frequency spectrum of just major triad in semisine wave.png|thumb|Figure 1: Frequency spectrum of just major triad in semisine wave]] | ||
If we play such a triad in a tempered tuning profile, the quality of the chord is determined by how the three components said above line up. In a tuning profile characterized by the mistuning map | If we play such a triad in a tempered tuning profile, the quality of the chord is determined by how the three components said above line up. In a tuning profile characterized by the mistuning map | ||