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

Line 39:

=== Implications ===

If such a hierarchy indeed exists, its existence would be consistent with the observation that when the 45th harmonic, a note with only a Medial Harmonic connection with the Tonic, is placed next to the 48th, the center of tonality seems to shift towards the 3rd harmonic and other members of its pitch class. It would also be consistent with my own observation that 8/5 Minor Third- the Contramediant in both Harmonic Major and Harmonic Minor- seems to have the effect of fostering a stronger sense of tonality than does the 5/3 ~~Major Third or even the 27/16~~ Major Third- an observation which explains the comments of [http://tonalcentre.org/Harmonicma.html Andy Milne] in regards to the Harmonic Major scale. Furthermore, the the disconnect between the conventional 5/3 Major Third and the Tonic seems to provide the grounds for the believability of George Russell's [https://en.wikipedia.org/wiki/Lydian_Chromatic_Concept_of_Tonal_Organization concept of Lydian as the center of tonal gravity] insofar as one uses Ptolemy's Intense Diatonic scale as the standard for Ionian mode. Furthermore, it would explain why the 5-limit Major and Minor thirds are not entirely equivalent in terms of their consonance, and it would additionally imply that the properties of a minor triad built on the Tonic from the bass-up lend themselves to a weakened sense of tonality in bass-up minor keys, which in turn might explain the reasons for Major being preferred over Minor in the first place.

If such a hierarchy indeed exists, its existence would be consistent with the observation that when the 45th harmonic, a note with only a Medial Harmonic connection with the Tonic, is placed next to the 48th, the center of tonality seems to shift towards the 3rd harmonic and other members of its pitch class. It would also be consistent with my own observation that 8/5 Minor Third- the Contramediant in both Harmonic Major and Harmonic Minor- seems to have the effect of fostering a stronger sense of tonality than does the 5/3 Major Third- an observation which explains the comments of [http://tonalcentre.org/Harmonicma.html Andy Milne] in regards to the Harmonic Major scale. Furthermore, the the disconnect between the conventional 5/3 Major Third and the Tonic seems to provide the grounds for the believability of George Russell's [https://en.wikipedia.org/wiki/Lydian_Chromatic_Concept_of_Tonal_Organization concept of Lydian as the center of tonal gravity] insofar as one uses Ptolemy's Intense Diatonic scale as the standard for Ionian mode. Furthermore, it would explain why the 5-limit Major and Minor thirds are not entirely equivalent in terms of their consonance, and it would additionally imply that the properties of a minor triad built on the Tonic from the bass-up lend themselves to a weakened sense of tonality in bass-up minor keys, which in turn might explain the reasons for Major being preferred over Minor in the first place.

== 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".

@@ Line 39: / Line 39: @@
 === Implications ===
-If such a hierarchy indeed exists, its existence would be consistent with the observation that when the 45th harmonic, a note with only a Medial Harmonic connection with the Tonic, is placed next to the 48th, the center of tonality seems to shift towards the 3rd harmonic and other members of its pitch class.  It would also be consistent with my own observation that 8/5 Minor Third- the Contramediant in both Harmonic Major and Harmonic Minor- seems to have the effect of fostering a stronger sense of tonality than does the 5/3 Major Third or even the 27/16 Major Third- an observation which explains the comments of [http://tonalcentre.org/Harmonicma.html Andy Milne] in regards to the Harmonic Major scale.  Furthermore, the the disconnect between the conventional 5/3 Major Third and the Tonic seems to provide the grounds for the believability of George Russell's [https://en.wikipedia.org/wiki/Lydian_Chromatic_Concept_of_Tonal_Organization concept of Lydian as the center of tonal gravity] insofar as one uses Ptolemy's Intense Diatonic scale as the standard for Ionian mode.  Furthermore, it would explain why the 5-limit Major and Minor thirds are not entirely equivalent in terms of their consonance, and it would additionally imply that the properties of a minor triad built on the Tonic from the bass-up lend themselves to a weakened sense of tonality in bass-up minor keys, which in turn might explain the reasons for Major being preferred over Minor in the first place.
+If such a hierarchy indeed exists, its existence would be consistent with the observation that when the 45th harmonic, a note with only a Medial Harmonic connection with the Tonic, is placed next to the 48th, the center of tonality seems to shift towards the 3rd harmonic and other members of its pitch class.  It would also be consistent with my own observation that 8/5 Minor Third- the Contramediant in both Harmonic Major and Harmonic Minor- seems to have the effect of fostering a stronger sense of tonality than does the 5/3 Major Third- an observation which explains the comments of [http://tonalcentre.org/Harmonicma.html Andy Milne] in regards to the Harmonic Major scale.  Furthermore, the the disconnect between the conventional 5/3 Major Third and the Tonic seems to provide the grounds for the believability of George Russell's [https://en.wikipedia.org/wiki/Lydian_Chromatic_Concept_of_Tonal_Organization concept of Lydian as the center of tonal gravity] insofar as one uses Ptolemy's Intense Diatonic scale as the standard for Ionian mode.  Furthermore, it would explain why the 5-limit Major and Minor thirds are not entirely equivalent in terms of their consonance, and it would additionally imply that the properties of a minor triad built on the Tonic from the bass-up lend themselves to a weakened sense of tonality in bass-up minor keys, which in turn might explain the reasons for Major being preferred over Minor in the first place.
 == 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".