I.e. the era of the tonal system from 1650 to 1900.
At the level of individual bars and beats, we can assign an annotation of Roman numerals:
The Roman numerals are below, the guitar-like chord symbols are above. We use Roman numerals to make the same analysis for any minor or major mode, regardless of its tonic pitch.
In which sense are Roman numerals "real", do we hear them? Are they the actual structure of the piece or are they some esoteric concepts helping us to make sense of a complete noise and chaos?
On a picture above, every red-circled note doesn't belong to any of the chord pitches. That is, all other notes belong to a local chord. That is, out of all 12 pitch classes, for every beat or several beats a composer selects exactly 3 or 4 and tries to locally shape all melodic and textural lines using that pre-selected pitch classes. This helps a composer to tell a story both in motives/texture (using rhythm, melodic direction, rests etc.) and simultaneous story about the progression of chords.
As chords build in thirds, we can reorder seven pitch classes as 1-3-5-7-2-4-6 and have a better visualization of a chord line:
All red-circled notes are not random. They are all classified, and we can annotated them in different colours:
Or in even more classes:
Alternatively, for every given chord we can assign twelve colors to all pitch classes relative to it (eg. in a rainbow order). We hope to see more of [0, 4, 7] colors for major chords (red, bright green, blue) and [0, 3, 7] colors (red, yellow, blue) for minor chords:
Chords in turn can be colored in a rainbow order. Also, the score can be represented as a piano roll rather than a music sheet:
At the lowest level, we can then ask, which chords are followed by which ones? Are there any patterns?
To do that, we first need to annotate a corpus of scores - say, all piano sonatas by Mozart. Then we can build a chord transition matrix:
We can compare these matrices between different composers to find differences in their languages:
The same idea can be expressed in a graph. Though, theoretical, there may be several origins of that graph. Ideally, you'd get a graph from a statistical computations on an annotated corpus. If no encompassing corpus is available yet, you can build a graph from your memories as a classically trained musician or by summarizing several theory books:
We can group several edges by an interval between the roots of its chords:
Then, we can go beyond two-chord pairs and speak of popular progressions of several chords:
A complete piece has a hierarchical structure with several levels, with each level using the structures one level below:
- level 1 (usually 4 bars long): antecedent, consequent, presentation, continuation, extended cadential phrase
- level 2 (usually 8 bars long): period, sentence, hybrid theme
- level 3: small ternary form, small binary form, subordinate theme, retransition, coda
- level 4: exposition, development, capitulation, menuet
- level 5, highest level of a movement: rondo, sonata-allegro, menuet and trio, theme with variations, concerto
This can be drawn separate from the score as a tree:
I'm using a language of Caplin who published an outstanding study book, where he draws the some levels of that structure over countless examples from Haydn, Mozart and Beethoven. (The fewer composers you take into your theory, the better your theory works to describe them.)
There are other theories for the same material, three of them debate in a single book
We can also overlay that structure above a music score:
We can compare relative lengths of those structures across a set of pieces:
We can also want to write a program that computationally does some parsing, and so we may design a formal theory of tonal syntax. Though it may lack some creative reading of an intentional composer's ambiguity by a theorist.
If we are dissatisfied with an ambiguity and fuzziness when defining high level structures, we may get to a level of cadences. At least they do exist for sure, and we can study their statistical probabilities:
https://mtosmt.org/issues/mto.22.28.1/mto.22.28.1.reenan.html
A common practice piece usually progress through a set of keys. For every piece of that period we have a music sheet. It gives us some information: through key signature we can understand the mid-level division into keys.
Local modulations aren't usually notated - we may see more sharps and flats inside the score, but not as a key signature change. We can apply a rough statistical technique to get some (not very accurate) approximation of local tonalities throughout the piece (paper):
(Mind that wavescapes are a novel take on keyscapes)
Also, at the very local level there's a "tonicization vs. modulation" dichotomy:
