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

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== Application ==

In light of Connectivity Hypothesis and its implications, I propose we classify consonances according to not only their harmonic entropy, but also their connectivity. For example, the 3/2 Perfect 5th is both a harmonic entropy minima and has high connectivity with the Tonic, resulting in the 3/2 Perfect 5th being classified as a "Perfect Consonance". As another example, although the conventional 5/3 Major Sixth may be both close to the Tonic on the harmonic lattice as well as a local harmonic entropy minimum, but because it's combination of disconnectedness with the Tonic and close connection with the Serviant seeming proving to be a liability for those who seek to establish a decent sense of tonality, this consonance is thus best classified as an "Imperfect Consonance". However, dissonance, on account of its crucial function as a propulsive force for harmonic motion, is not to be dismissed- rather, it too should be split into two classes based on how they relate to the Tonic in terms of both Harmonic Entropy and Connectivity. For example the pitch related to the Tonic by an interval of 11/8- an interval which I call a "Paramajor 4th"- displays a high degree of Harmonic entropy relative to the Tonic- although less so that the pitches immediately surrounding it- on the flipside, it demonstrates a high degree of connectivity to the Tonic, lending to this interval being classified as an "Imperfect Dissonance". On the flipside, the 17/12 Tritone not only exhibits high degree of Harmonic Entropy, but is also disconnected from the Tonic, leading to its classification as a "Perfect Dissonance".

In light of the Connectivity Hypothesis and its implications, I propose we classify consonances according to not only their harmonic entropy, but also their connectivity. For example, the 3/2 Perfect 5th is both a harmonic entropy minima and has high connectivity with the Tonic, resulting in the 3/2 Perfect 5th being classified as a "Perfect Consonance". As another example, although the conventional 5/3 Major Sixth may be both close to the Tonic on the harmonic lattice as well as a local harmonic entropy minimum, but because it's combination of disconnectedness with the Tonic and close connection with the Serviant seeming proving to be a liability for those who seek to establish a decent sense of tonality, this consonance is thus best classified as an "Imperfect Consonance". However, dissonance, on account of its crucial function as a propulsive force for harmonic motion, is not to be dismissed- rather, it too should be split into two classes based on how they relate to the Tonic in terms of both Harmonic Entropy and Connectivity. For example the pitch related to the Tonic by an interval of 11/8- an interval which I call a "Paramajor 4th"- displays a high degree of Harmonic entropy relative to the Tonic- although less so that the pitches immediately surrounding it- on the flipside, it demonstrates a high degree of connectivity to the Tonic, lending to this interval being classified as an "Imperfect Dissonance". On the flipside, the 17/12 Tritone not only exhibits high degree of Harmonic Entropy, but is also disconnected from the Tonic, leading to its classification as a "Perfect Dissonance".

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	== Application ==		== Application ==

	In light of Connectivity Hypothesis and its implications, I propose we classify consonances according to not only their harmonic entropy, but also their connectivity. For example, the 3/2 Perfect 5th is both a harmonic entropy minima and has high connectivity with the Tonic, resulting in the 3/2 Perfect 5th being classified as a "Perfect Consonance". As another example, although the conventional 5/3 Major Sixth may be both close to the Tonic on the harmonic lattice as well as a local harmonic entropy minimum, but because it's combination of disconnectedness with the Tonic and close connection with the Serviant seeming proving to be a liability for those who seek to establish a decent sense of tonality, this consonance is thus best classified as an "Imperfect Consonance". However, dissonance, on account of its crucial function as a propulsive force for harmonic motion, is not to be dismissed- rather, it too should be split into two classes based on how they relate to the Tonic in terms of both Harmonic Entropy and Connectivity. For example the pitch related to the Tonic by an interval of 11/8- an interval which I call a "Paramajor 4th"- displays a high degree of Harmonic entropy relative to the Tonic- although less so that the pitches immediately surrounding it- on the flipside, it demonstrates a high degree of connectivity to the Tonic, lending to this interval being classified as an "Imperfect Dissonance". On the flipside, the 17/12 Tritone not only exhibits high degree of Harmonic Entropy, but is also disconnected from the Tonic, leading to its classification as a "Perfect Dissonance".		In light of the Connectivity Hypothesis and its implications, I propose we classify consonances according to not only their harmonic entropy, but also their connectivity. For example, the 3/2 Perfect 5th is both a harmonic entropy minima and has high connectivity with the Tonic, resulting in the 3/2 Perfect 5th being classified as a "Perfect Consonance". As another example, although the conventional 5/3 Major Sixth may be both close to the Tonic on the harmonic lattice as well as a local harmonic entropy minimum, but because it's combination of disconnectedness with the Tonic and close connection with the Serviant seeming proving to be a liability for those who seek to establish a decent sense of tonality, this consonance is thus best classified as an "Imperfect Consonance". However, dissonance, on account of its crucial function as a propulsive force for harmonic motion, is not to be dismissed- rather, it too should be split into two classes based on how they relate to the Tonic in terms of both Harmonic Entropy and Connectivity. For example the pitch related to the Tonic by an interval of 11/8- an interval which I call a "Paramajor 4th"- displays a high degree of Harmonic entropy relative to the Tonic- although less so that the pitches immediately surrounding it- on the flipside, it demonstrates a high degree of connectivity to the Tonic, lending to this interval being classified as an "Imperfect Dissonance". On the flipside, the 17/12 Tritone not only exhibits high degree of Harmonic Entropy, but is also disconnected from the Tonic, leading to its classification as a "Perfect Dissonance".