User:Aura/Aura's Ideas of Consonance

Introduction

Just about every musician these days is acquainted with the idea of "Consonance" and "Dissonance". However, as has been noted- there are difference concepts of "Consonance" and "Dissonance". This page is for exploring my particular concepts of "Consonance" and "Dissonance".

Connectivity

To me, the exact nature of consonance is determined by the confluence of the minimum harmonic entropy and another factor which I refer to as "connectivity". 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", and the resulting consonance is thus best classified as an "Imperfect Consonance". This is part of why the 5-limit Major and Minor thirds are not entirely equivalent in terms of their consonance, and 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 doesn't appear in the bass. It should be noted that the utonal equivalent of a virtual fundamental *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. However, when such a minor triad is built on the tonic from the bass upwards, this virtual-fundamental-analog is not of the same pitch class as the Tonic- a fact which lends itself to a weakened sense of tonality in bass-up minor keys, and very likely of the reasons for Major being preferred over Minor in the first place. Furthermore, this same issue of disconnectedness plagues the otherwise pleasant-sounding 5/3 major sixth- as stated on my page on diatonic scales. It may be close to the Tonic on the harmonic lattice, but it's combination of disconnectedness with the Tonic and close connection with the Serviant proves to be a liability for those who seek to establish a decent sense of tonality in their chosen key, for reasons which I shall explain below.

Connectivity Ranks

In order to illustrate why disconnectedness is such a liability, I shall first have rank the various types of harmonies based on their odd-limit as well as their prime-limit- assigning ranks as I go.

Proximal Harmonies

This family of harmonic relationships is the only one further broken down into various classes due to these harmonies having the most intimate relationships with the fundamental- which most naturally doubles as the Tonic.

Pitch Class Prime - This is the class to which the Tonic itself- as well as all pitches related to it by 2-limit harmonies- belong. This is the case in light of how pitches related to the Tonic by powers of two naturally seem to our hearing to be the same as the Tonic in ways that other primes don't.

Diatonic Prime - This is the class to which 3-limit and 5-limit harmonies belong on account of their key functions in just diatonic and just chromatic music. In particular, the first 3-limit pitches give rise to the Dominant and Serviant harmonies, with the exact role of each of these harmonies being determined by your chosen tonality's direction of construction.