Terminology and nomenclature in musical analysis are tricky things. There are many ways to talk about, write about, and model music. There are many ways of labeling chords and talking about structure. What works for a gigging musician who needs to have a massive repertoire at their disposal at a moments notice won't work for a composer that needs to craft an original idiom. Similarly, what works for a Jazz musician will have parallels in Metal and Baroque music, but will need to be tweaked to be useful.
No analytic framework, no matter how piercing, can cover all bases or be useful to all people. In analysis, we gather the tools needed to explore the music we love. If we hear a harmony or chord progression that interests us and want to know how it works, we figure out a way to model it. Analytic terminology is useful to me in how well it models the music I'm exploring. If I want to learn about J.S. Bach's harmonic methods, I study the texts he gave his students to work through (In this case, his Precepts and Principles of Thorough-bass, which is out of print, but still available through public and university libraries), or other teaching works like the Well-tempered Clavier and Inventions and Sinfonias.
This is not to say that an analytic framework can't have widespread applications. I have found that Schenkerian analysis, which at its core is a way of considering how tonality flexes during a composition and how these flexes are grounded on fundamental structures, is applicable to Pop music, folk music, method books for beginning musicians, etc. I apply these concepts to many genres, in an effort to make connections between different kinds of music.
A piece that can be heard as solidly grounded in a tonality can be analyzed in terms of that tonality. A basic example of this is Roman Numeral chord nomanclature, I-IV-V-I. This method of chord labeling shows that every chord is evaluated around the tonic (I) and the tonality it implies. For example, in BWV 1007's prelude, there isn't a collection of pitches which strays too far from the confines of diatonic G Major. The furthest away we get is the A9 chord of m. 26 and this is seemingly a momentary intensification to spice things up. Doing this allows the reader/listener to keep in mind the relationship between whatever moment they're thinking about, where they began, and the relationship of both these to what follows.
In some forms of tonal analysis, hierarchy is important; Some pitches carry greater weight in the listener's mind than others. This concept is implicit in basic tonal fundamentals. The Tonic is what grounds a piece but for a sense of completion, the dominant is often necessary; anything else seems less resolute. It would be interesting to explore the etymology of terms such as these, but to paraphrase, there needs to be a potent, "dominating" force to make the return of the tonic more pleasing. It is a very basic form of variety.
There are two types of tonal progressions: Harmonic and Sequential - To establish a tonality, harmonic progressions are used. To destabilize a tonality, sequential progressions are used. This is an oversimplification made to introduce these ideas, but I find that this is generally the case. What constitutes a harmonic progression? The succession of a tonic-functioning chord to a predominant-functioning chord, to a dominant-functioning chord that ends on a tonic-functioning chord. My favorite way of explaining this is that tonal harmony is based on two mantras: I - II - V - I and I - IV - V - I.
These progressions can be heard as a abstract basis for most progressions. The examples above shouldn't be considered a rigid schemata of how progressions must act and should be seen as abstractions of how we often find music to flow. Each one of these chords is composed-out in free composition (the actual act of writing music that people want to listen to), so the examples above depict abstract chord "spaces" as well as simple foundational progressions. The most common ways of composing-out these chord spaces is as follows:
The 5 and 6 connected by a line indicates a 5 phase of a chord moving to its 6 phase. I find this notation useful in showing the close relationship between one chord (the 5 phase) and a chord who's root is a third lower (the 6 phase); this can be a major or minor third lower. Please examine my explanation of 5-6 sequences later in this post for further clarification of 5 phases and 6 phases.
Here the mantras are even more embellished:
When a chord possesses non-diatonic chord tones, like the VI chord of the first example and the II chord of the second example above, I refer to these chords as surging. The reason for this descriptor is because, to my ear, the chords sound more powerful and often come directly from their diatonic counterparts. This term, in my vocabulary, takes the place of a secondary dominant or secondary leading tone chord. Like most of my current terminology, I have borrowed this term from the writings and teachings of David Damschroder. I would recommend anyone looking for a deeper perspective on anything I've written to read some of the works I've listed in the further readings section at the end of this post.
When a series of chords can be found to not be related to these progressions they are often sequences. The most common sequences are the circle of fifths, the 5-6 sequence, and the circle of thirds. It is important to keep in mind that most music has voice leading of some sort and musicians don't use the same progressions and sequences in the same way; they spice them up by using different inversions, raising or lowering different parts of chords, and adding sevenths, ninths, elevenths, and thirteenths. Which leads me to the quote found at the beginning of Heinrich Schenker's Free Composition, "Semper idem sed non eodum modo (Always the same, but not always in the same way)."
I, II, III, IV, V, VI, VII - Roman numerals are an often-used tool in harmonic analysis. They signify a diatonic triad built on the scale step to which they correspond. Sometimes uppercase and lowercase Roman numerals are used to show chord quality, but I find that this complicates my analyses and makes the composing-out of harmonies difficult to discern. Most musicians I know understand that the supertonic is minor in Major and diminished in Minor; there isn't a real need for all sorts of peripheral notation.
Showing change in a Roman numeral's root tone - In order to clearly show the characteristics of a harmony that is non-diatonic, I simply add an accidental to the left of the Roman numeral to show a change in the root of the triad, as is the case for the ♭II chord (also called the "Neapolitan" chord).
Showing change in a Roman numeral's characteristics - If a chord differs from the diatonic state of a tonality, I show its slight modifications with Arabic numerals to the right of the Roman numeral. A good example of this when making comparisons between the common progression, I - II - V - I and what many would label I - V/V - V - I. I would label the latter I - II♯ - V - I. This allows the reader to quickly see the relation between the chords in both progressions, that the second chords of both progressions are built on scale step II, the supertonic, and lead to V, the dominant. This practice becomes especially useful when augmented sixth chords come into play, as they can be seen as types of II chords (although many will argue they are types of IV chords).
Inversions - you may have noticed that the standard inversion notation is relatively scarce; that of 6, 6/3, and 6/4. I don't use these, unless it illuminates voiceleading in sections of extended prolongation. In the example above you will see that the first example employs a II chord in first inversion. This, like the lack of uppercase and lowercase in my usage of numerals, is because the reader, having read any theory text, will understand that the chord is in an inversion just by seeing it. If the inversion of a chord is subjected to prolongation, it is then that I would use figured bass to show what is happening. See my analysis of the first cello suite's prelude for examples of this practice. For a greater example, see Heinrich Schenker's analysis of the first prelude of the Well-Tempered Clavier's first book, which is found in his Five Graphic Analyses.
Showing sequences - The notation of sequences, in my experience, hasn't been nailed down yet. I define a sequence as a sequence of chords that begins with two chords, which serve as a model to be copied, whose characteristics are repeated at different, relatively consistent intervals for as long as the composer deems necessary. This is a vague definition, which allows it to be applied widely. I label sequences by their root, no matter their inversion. To label the chords, I use the letter of their root, upper-cased for major chords, lower-cased for minor chords, upper-cased with a small addition symbol to the upper-right for augmented chords (which are rare in sequences, but possible), and lower-cased with a small circle to the upper-right for diminished. A simple example of this is the diatonic circle of fifths (the first example below) when compared to a circle of fifths who's chords are all major (the second example below).
One note on that last example; I have seen a passage such as this analyzed V/V/V/V/V/V, etc. This seems, to me, to be much less useful than simply stating the root of the chord and figuring its relation to its surrounding chords.
Besides the aforementioned circle of fifths, there are two other generic sequences; the 5-6 sequence and the circle of thirds.
The 5-6 sequence is a method of moving from one scale step to the one above or below without causing parallel fifths. The 5 of the 5-6 sequence denotes the fifth between the bass of the chord and the fifth of the chord; the 6 denotes the sixth between the bass of the chord and the sixth.
In essence, only one note needs to move. This pattern becomes a sequence, like the circle of fifths, through repetition.
To increase the strength of the sequence, all that is necessary is to make both the 5 phase and the 6 phase major.
the 5-6 sequence can ascend and descend. An example of the sequence descending in the minuet II of BWV 1007:
The circle of thirds is a sequence I find infrequently, so I won't say much about it here. A generic example of this sequence is as follows:
These are some of the texts I found most helpful on this subject. I hope that someone finds this selection useful.
Selected texts by Heinrich Schenker:
Counterpoint, Vol. 1 and 2
J.S. Bach's Chromatic Fantasy and Fugue
Selected texts by David Damschroder:
Thinking about Harmony
Harmony in Schubert
Harmony in Mozart and Haydn
Harmony in Chopin
Schubert, Chromaticism, and the Ascending 5–6 Sequence (in Journal of Music Theory, 50/2)
Schenker, Schubert, and the Subtonic Chord (in Gamut, 3/1)
Selected works by Carl Schachter: