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The most simple, basic definition of tonality is the relationship between pitches. All music, with the exception of atonal, twelve tone and perhaps polytonal music display some degree of tonality. Medieval music has tonal center and often resolves on the parent tone of a given mode, what was referred to as the final.
1 Answer. Well, tonality just means music that is organized around a central tone, generally called the tonic. Most people who use the term tonality also implicitly assume some sort of hierarchy of chordal functions, which are (as the question notes) based on the location within an (asymmetric) scale. Functional tonality (or functional harmony ...
Like many words, tonality can mean different things depending on the context. For example, tonal is typically contrasted with modal to describe music that plays by the rules of the "common practice" that arose in the 17th century and began to break down in the 19th. However, the concept of tonality can also be useful in modal contexts.
The first sense of the word 'tonality' just means, in general, 'the types of harmonic relationships and motions' in a piece of music. If this is the sense of the word 'tonality' that you mean, then we can say that a key is a way to describe the tonality of a piece of music from the perspective of the major/minor system.
The Oxford Companion to Music, ed. Alison Latham (Oxford University Press, 2002). Key. (1) The quality of a musical passage or composition that causes it to be sensed as gravitating towards a particular note, called the key note or the tonic. One therefore speaks of a piece as being in C major or minor. See Tonality.
The definition of 'Tonality' By following the links that are mentioned in the question you will see a strong tendency to hold on to a certain definition of the terminus 'Tonality' that is expressed e.g. by Andrew in his wonderful and spot-on answer to the question about the difference between tonality and modality.
Some, for instance, separate "tonal" music from "modal" music, while others still view modal music as being tonal. But it may be important to note that two historical theorists, Fétis and Choron, announced "the beginning of tonality" at the appearance of a dominant-seventh chord in a piece by Monteverdi around 1590.
However, in my experience the word was used somewhat flexibly to describe any harmonic structure, express or implied, including a single stacked chord, an agglomeration of notes, (a chord fitting the definition of standard practice chord) and also perhaps even including other combinations of notes which, though not fitting the definition of a ...
"Tonality" usually means (warning, over-simplified definition!) whether a piece is in a major or minor key. That has nothing much to do with "timber", or even with "timbre". – user19146
Tonality is a system of composition (or the theory describing it), and one aspect of Tonal music (that is, music following Tonality) is that there is a pitch center. Non-Tonal music — music composed outside the system of Tonality — can still have a pitch center, though it needn't. Atonal music is composed to avoid the sense of pitch center.