User:Aura/Aura's Ideas of Consonance: Difference between revisions

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Connectivity is a property that only exists between a given Tonic and its various harmonics and subharmonics- something most clearly indicated when a pure power of 2 is in either the numerator or the denominator of the fraction expressing the frequency ratio- and appears to be one of the factors controlling both the degree of timberal fusion between pitches as well as the appearance of a virtual fundamental the same pitch class as the Tonic, with both of these properties lending themselves well to expressions of tonality. While it can be generally said that the larger the numbers involved, the smaller the degree of connectivity, I should point out that even harmonic entropy minima where the fraction expressing the frequency ratio lacks a pure power of 2 would count as "disconnected". This would explain why a Minor triad built on the Tonic from the bass upwards doesn't have the same degree of timberal fusion, and why a virtual fundamental of the same pitch class as the Tonic fails appear in the bass whatsoever, and why the utonal equivalent of a virtual fundamental that *does* appear for a 5-limit minor triad as a result of all three notes sharing a single harmonic- a property that is characteristic of all utonal chords- also doesn't belong to the Tonic's pitch class.

Inferring from what I know so far, degrees of connectivity may perhaps be quantified by taking consecutive sections of [[Harmonic_Entropy#a.3D.E2.88.9E:_Harmonic_Min-Entropy|the the minimum Rényi entropy curve]] corresponding to single octaves of the harmonic series, and overlaying them on top of another and ~~averaging~~ the values of the different sections together. If this type of transformation is performed repeatedly, overlaying more consecutive octave sections, I hypothesize that harmonic entropy minima with high connectivity should become more clearly emphasized as the different sections of the harmonic entropy curve repeatedly hit octave-equivalent harmonics, while other, less well-connected intervals will either be canceled out, or simply won't be emphasized as quickly. That said, I don't know what other effects of this will be.

Inferring from what I know so far, degrees of connectivity may perhaps be quantified by taking consecutive sections of [[Harmonic_Entropy#a.3D.E2.88.9E:_Harmonic_Min-Entropy|the the minimum Rényi entropy curve]] corresponding to single octaves of the harmonic series, and overlaying them on top of another and adding the values of the different sections together. If this type of transformation is performed repeatedly, overlaying more consecutive octave sections, I hypothesize that harmonic entropy minima with high connectivity should become more clearly emphasized as the different sections of the harmonic entropy curve repeatedly hit octave-equivalent harmonics, while other, less well-connected intervals will either be canceled out, or simply won't be emphasized as quickly. That said, I don't know what other effects of this will be.

== Connectivity Ranks ==

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 Connectivity is a property that only exists between a given Tonic and its various harmonics and subharmonics- something most clearly indicated when a pure power of 2 is in either the numerator or the denominator of the fraction expressing the frequency ratio- and appears to be one of the factors controlling both the degree of timberal fusion between pitches as well as the appearance of a virtual fundamental the same pitch class as the Tonic, with  both of these properties lending themselves well to expressions of tonality.  While it can be generally said that the larger the numbers involved, the smaller the degree of connectivity, I should point out that even harmonic entropy minima where the fraction expressing the frequency ratio lacks a pure power of 2 would count as "disconnected".  This would explain why a Minor triad built on the Tonic from the bass upwards doesn't have the same degree of timberal fusion, and why a virtual fundamental of the same pitch class as the Tonic fails appear in the bass whatsoever, and why the utonal equivalent of a virtual fundamental that *does* appear for a 5-limit minor triad as a result of all three notes sharing a single harmonic- a property that is characteristic of all utonal chords- also doesn't belong to the Tonic's pitch class.
-Inferring from what I know so far, degrees of connectivity may perhaps be quantified by taking consecutive sections of [[Harmonic_Entropy#a.3D.E2.88.9E:_Harmonic_Min-Entropy|the the minimum Rényi entropy curve]] corresponding to single octaves of the harmonic series, and overlaying them on top of another and averaging the values of the different sections together.  If this type of transformation is performed repeatedly, overlaying more consecutive octave sections, I hypothesize that harmonic entropy minima with high connectivity should become more clearly emphasized as the different sections of the harmonic entropy curve repeatedly hit octave-equivalent harmonics, while other, less well-connected intervals will either be canceled out, or simply won't be emphasized as quickly.  That said, I don't know what other effects of this will be.
+Inferring from what I know so far, degrees of connectivity may perhaps be quantified by taking consecutive sections of [[Harmonic_Entropy#a.3D.E2.88.9E:_Harmonic_Min-Entropy|the the minimum Rényi entropy curve]] corresponding to single octaves of the harmonic series, and overlaying them on top of another and adding the values of the different sections together.  If this type of transformation is performed repeatedly, overlaying more consecutive octave sections, I hypothesize that harmonic entropy minima with high connectivity should become more clearly emphasized as the different sections of the harmonic entropy curve repeatedly hit octave-equivalent harmonics, while other, less well-connected intervals will either be canceled out, or simply won't be emphasized as quickly.  That said, I don't know what other effects of this will be.
 == Connectivity Ranks ==