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.

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.
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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)." 

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.

5-6 sequences
​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.

Further Reading
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:
Free Composition
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:
Unfoldings

In this post I examine the first cello suite by Johann Sebastian Bach using Schenkerian methodology. My research continues the endeavor begun by Dr. David Beach in his "Aspects of Unity in J.S. Bach's Partitas and Suites" (2005) using the tools and methodology created and enhanced by Dr. David Damschroder, which are demonstrated in his "Harmony in Schubert" (2010) and following publications. I proceed movement by movement, providing in-depth graphical analyses and commentary in an effort to identify deeper unifying traits of the movements and present a deeper reading of the suite as a whole.

Note: Since Weebly cannot include superscript or subscript please consider the first number to be above the second number in the figured bass descriptions. 

Prelude
The forty-two measures of this movement are split into two parts by a fermata, but are still through-composed; the first part, measures 1 through 222, contains the main harmonic movement of the Prelude; the second part, measures 223 through 42, prolongs the dominant and contains the tonic’s final return. A third-progression underlies the movement; the Kopfton ^3 arrives in the first measure accompanied by the tonic, ^2 arrives in measure 22 with the dominant, and ^1 arrives in measure 42 with the tonic.

The Prelude begins simply with an arpeggiation of the tonic and a lower neighboring ornamentation of the Kopfton ^3. In measures 1 through 4, the arpeggiation is accompanied by an inner voice ascent from D to G. This is accomplished by a rising diatonic scalar motion paired with a neighboring motion, in the form of 3-4-3, over a pedal tonic root. (Ex.1) When we consider these facets together we find a prolongational technique, that of 53 – 64 – 74 – 83, which will be used elsewhere in the movement and suite in modified forms.
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Measures 5 through 10 continue the harmonic movement barely begun in measures 1 through 4. In measures 5 and 8, we find the 6 phase of the tonic. Measures 6 and 9 contain a surging supertonic – an evolved form of the supertonic – which possesses a seventh and raised third. In measures 7 and 10, dominant chords complete the harmonic gesture begun in measure 1. This could be interpreted as a I6 – II#7 – V progression deployed twice in different configurations. (Ex. 2) But, in essence, what has been accomplished is a progression from the tonic through a surging supertonic to the dominant, and then a tonicization of the dominant by a similar progression. (Ex. 3)

Measures 11 through 14 seemingly forget the prior events and present a continuation of the tonic from measure 1 through 4 in the form of its 6 phase. There are two ways of perceiving these measures, which is essentially a composing-out of the tonic's 6 phase. The first interpretation is that measure 11 presents an evolved E chord, one possessing a raised third, a minor seventh, and a minor ninth. Measure 12 then is simply a IV chord of the tonic's 6 phase; measure 13 presents the dominant of the tonic's 6 phase with a seventh and resolves to the tonic's 6 phase in measure 14. (Ex. 4) The second interpretation is more fluid. The 6 phase of tonic is presented in measure 11, but only its seventh and raised third are potent; in measure 12 the raised third ascends and seventh descends. In measure 13, the fourth remains while the sixth ascends, by augmented second, to a raised seventh; in measure 14, the tension developed in the previous three measures is dispersed by an ascent of the raised seventh and descent of the fourth. What this reading entails is that measures 11 through 14 provide a second example of the prolongational effects of the 3-4-4-3 figuration found in measures 1 through 4; in this instance, the figuration being 7# - 64 - #74 – 83. (Ex. 5)

The second half of the Prelude could easily be considered an exercise in dominant prolongation. Measures 22 through 28 prolong the dominant through various voice leading configurations. In measures 22 through 24 the dominant is lead through its seventh to its minor ninth and back to its seventh before proceeding to a 64 configuration above the dominant pedal. Following the 64 is a dominant-like configuration which is highly dissonant, in that it possesses both a seventh and a ninth (the ninth here being volatile and quickly descending to the octave of the dominant).The dominant returns unadorned in measure 28.

​Following the circuitous voice leading that preceded measure 28, the following material of measures 29 through 31 falls effortlessly. Measures 29 through 31 contain a descending diatonic 7 - 64 sequence begun on D and descending diatonically to A. Measure 29 contains the model for the sequence; the D seventh chord, a major triad with a minor seventh, proceeds to its 64. Measure 30 contains two copies of this model; the first based on C and the second based on B. Measure 31 concludes the descent with a seventh chord based on A, which leads back to the dominant. At this point the dominant reasserts itself. (Ex. 8)

Measures 31 through 37 are much simpler. (Ex. 9) In measures 31 through 33, the dominant’s third, F#, is embellished by its upper and lower neighbors. In measures 33 through 37, alternation between varying presentations of the 64 and 53 figurations of the dominant are employed to ascend to and then descend from the D of measure 34. What is accomplished is a prolongation of the dominant in its 53 configuration.

Measures 37 through 42 present the two concluding gestures of the Prelude. The first gesture is a chromatic ascent, up the octave from the F at the beginning of measure 37 to the F# at the end of measure 38. The second gesture is the final iteration of the 3-4-4-3 figuration, here in the form of 53 – 64 – 54 – 73. This figuration is used to prepare the arrival of the final tonic and deep structural ^1. The arrival of ^1 and the tonic is enhanced by the dissonance of the 73 figuration which precedes it. (Ex. 10)

As has been shown, the 3-4-4-3 figuration plays an important role in the prolongation of tonic, the tonic’s 6 phase, and the dominant of this Prelude. It appears in measures 1 through 4 and measures 15 through 19, prolonging the tonic. It appears in a decidedly modified form in measures 11 through 14, prolonging the tonic’s 6 phase. At a lower middleground level, the dominant is held together by this figuration in measures 22 through 41.
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To take a broad view of the entire movement, the tonic is prolonged by its 6 phase and a return to its 5 phase in measure 19. A surging II arrives in measure 20 and leads to the dominant in measure 21. The dominant is prolonged from measure 22 through measure 41. The tonic and the deep structural ^1 arrive in measure 42 and conclude the Prelude. (Ex. 11)

​Allemande
In this movement Bach employs a great amount of repetition and again makes use of the 3-4-4-3 figuration. Bach prolongs the tonic and Kopfton ^3 through repetition of a I–II–V progression that is adorned by the 3-4-4-3 figuration. The deep structural chords do not appear until late in the movement.

Ex. 1 shows four possible prototypes of the tonic prolongation used in this movement. Ex. 1a is an example of harmonic movement that serves to prolong the Kopfton ^3. It possesses the characteristics of what is commonly considered a I–II–V7–I progression but should be considered simply a means of embellishing the tonic and Kopfton. Ex. 1b is a modified version of Ex. 1a with a surging II chord. Ex. 1c is a shortened prototype showing the A and D of Ex. 1a occurring simultaneously rather than successively. Ex. 1d demonstrates the essence of the preceding prototypes. Simple neighboring motion is what underlies the tonic’s various prolongations and gives rise to their different appearances. As is shown in Ex. 2, the repetition of the I–II–V progression happens six times before giving way to deeper harmonic movement.

​Ex. 3 shows the first iteration of the prolongation in measures 1 through 4. In this instance, I is adorned by its 6 phase, proceeds to II7 and V7, and returns to I.

​Measures 12 through 14 is the first iteration without tonic’s 6 phase. (Ex. 6) I proceeds directly to a surging II, which in turn leads to V. Measure 13’s II­#7 is emphasized by its breadth and inversion. It spans two octaves and is in second inversion. Also, the E and G at the beginning of the measure could be a 6 phase but with the addition of the rest of the measure we see that these tones are simply the fifth and seventh of a II chord.

​Measures 25 through 28 show the departure from the I–II–V progression repetition. (Ex. 10) IV’s 5 phase moves to its 6 phase through a sequence of two common sequence models. To put this sequence in context, the C chord moves to the A chord by tenths, passing over a B chord. The C chord of measure 26 is proceeds to its 6 phase, preparing the listener for a continued 5 – 6 sequence. The B7 chord of measure 27 does not confound this expectation, but the following E chord does. This descending 5 – 6 sequence becomes a 7 - 6­4 sequence. Continuing downwards, the 6 phase of IV is reached, which then proceeds to V.

Courante
The Courante, one of the suite’s longer movements, spans 42 measures. The tonic is prolonged for 29 measures and is followed by a subdominant, which branches out, its octave descending through its seventh to its 6 phase. The subdominant’s 6 phase gains a seventh and is followed by the movement’s deep structural dominant, which is prolonged for six measures and resolves to the tonic. (Ex. 1)

​Ex. 2 shows the first eight measures of the Courante’s tonic prolongation. The Kopfton ^5 of measure 1 gives way to a middleground third-progression in measure 2. ^2 arrives with the dominant, which is prolonged by a descending 5 – 6 sequence and a cadential 64 figuration.

​Ex. 3 shows the tonic’s continued prolongation. The form and goal of the prolongation is now clarified. Measure 1’s tonic’s goal is to gain the seventh of measure 29. This transformation is achieved by raising the bass from G through A to B. Each scale degree is embellished through various means. G’s embellishment was shown in Ex. 2. A’s prolongation is shown in Ex. 3. As can be seen, A is embellished by 64 figurations and a single descending 5 – 6 sequence.

​Ex. 4 shows the embellishment of B. Once the B is arrived at, a composing-out of the tonic chord in first inversion seems imminent. This is not the case because a dominant ninth-like chord initiates a tonicization of VI in measure 23. Note two facets of this passage. The first is that this tonicization contains the First Suite’s second statement of a supertonic with a lowered root (here a ♮II); the first occurred in measure 22 of the Allemande. The second is that the tonicization could serve as tonic’s 6 phase but, with C’s inclusion in measure 28, the passage is an unfurling of a 64 chord. This unfurling technique is used at a deeper level later in the suite in Minuet I.

​Ex. 5 shows the tonic prolongation’s end and the material which ends the Courante. Following the arrival of the tonic’s seventh, the subdominant is stated and its prolongation and embellishment is begun. The octave of the subdominant descends to the seventh in measure 34. This prepares the passage for ^2’s arrival in measure 35. The deep structural dominant of the Courante follows shortly afterwards and is prolonged by a 64 figuration and a descending 5 – 6 sequence.

Sarabande
​The tonic once again receives extensive prolongational treatment in this movement. Thrice the Kopfton ^3 is stated, ventured from, and returned to before the movement’s deeper harmonic material is reached. Ex. 1 shows the first statement to venture from the Kopfton. Bach uses the 3-4-4-3 figuration in the same form as he did in the first four measures of the Prelude. The surface-level figuration is different but the scalar ascent of the inner voice from D to G and the 3-4-4-3 adorning figuration are deployed in the exact same way. Also, to modern ears and certain modern forms of harmonic thought this example implies a I­–IV–V–I progression.

Minuet I
​Much like the Courante, the tonic prolongation in this movement ends with a descent to its seventh and is achieved through a scalar ascent at a deep structural level. Here again, the scalar ascent consists of G ascending through A to B. Adding to this, Bach uses a C in measure 16 to transform the E minor chord from a 6 phase chord into a component of an unfurled 64 chord, like he did in the Courante. Ex. 1 shows I’s prolongation by scalar ascent and 64-unfurling. Ex. 2 shows the manner of the 64’s unfurling. Ex. 3 shows the scalar ascension and 64 unfurling as they occur in measures 1 through 17.

​Once the tonic gains its seventh, in measure 17, it proceeds directly to the subdominant and its 6 phase. These are adorned by their sevenths and followed by the dominant. The dominant of this movement, in a way which is increasingly becoming characteristic of dominants in the first suite, is embellished by a 5 – 6 sequence. This sequence begins on D and leads to F#. The movement ends with a cadential 6­4 motion that leads to the final tonic and deep structural ^1. A graph of the entire movement is shown in Ex. 4.

Minuet II
In this movement Bach demonstrates the unifying effect of sequences on a tonal structure. In measures 1 through 8 a descending 5 – 6 sequence moves I to IV. This IV in turn has a 6 phase that proceeds to V, which is back-relating. (Ex. 1) Ex. 2 shows the reader that Bach is utilizing parallel tenths (a), adorned by 5 – 6 motions (b).

Gigue
​Broad gestures dominate this movement. The tonic, supertonic, and the dominant are all prolonged on a large scale. The tonic is embellished by neighboring motion, the supertonic by scalar thirds of a peculiar sort, and the dominant by both aforementioned techniques. The final tonic prolongation of measures 28 through 34 introduces parallel chord successions as a means of prolongation.

​Ex. 3 shows the prolongation of the tonic after the deep structural ^1 has been reached. A succession of chords in their 63 figuration move diatonically from a G chord through a D chord to an E chord. This E chord promptly falls to a D chord in 53 figuration, which is embellished by its 64. Following this is the final statement of the tonic and the deep structural ^1.