Some more features

In this section, we are going through beethoven_n03_1.mscx to bring the previous content all together and to talk about some special cases:

• melodies in the bass

• bass arpeggios

• advanced use of applied chord notation

• organ and pedal points

• unisono

• augmented sixth and ninth chords

At this point of the tutorial you’re already familiar with all the important principles of the DCML harmonic annotation standard, so you’re invited to challenge the suggested solutions: Try to guess the reasoning behind the suggested solutions and check whether it is consistent throughout the examples. Where you have reasons to suggest a better solution, you are more than welcome to share and discuss it with us on our issue tracker either by inserting MuseScore 3 shots (Tools -> Image Capture) or by uploading the MuseScore file as attachment to your issue.

Melodies in the bass

To get into the piece, please annotate the first 13 measures after deciding on harmonic pace and phrasing for this Allegro con brio.

First movement of Beethoven’s Piano Sonata no. 3, mm. 1–13, annotated

How did it go? There isn’t an aweful lot of choice when it comes to harmonic rhythm and phrasing, is there?

Things to note

• In mm. 10 & 11 the melody in the bass causes I64 tonic inversions. Please be aware that quite often, when the melody is in the bass, it is the next higher voice that perceptually takes over the bass function which is decisive for the chord inversion. Here, however, the inversions seem plausible.

• The first label in m. 12 is actually spelled correctly, V(64#0), but displayed incorrectly. No worries. However, you would have all reason to be surprised why it’s #0 and not V(#764). For an explanation, please check Replacement of the root by its lower neighbour below.

Bass arpeggios

Let’s continue, please annotate mm. 13-20.

First movement of Beethoven’s Piano Sonata no. 3, mm. 13–20, annotated

So the annotator decided to express the bass arpeggios as chord inversions. This can hardly be wrong, naturally, but depending on the context, in similar cases one might want to express the whole as a single harmonic entity, e.g. as a single I in this case. If that was your solution: great!

So what did you do to mm. 15-16? Parallel thirds are a classical case of under-determined triads, which the annotator reflected by notating alternatives. At first it looks as if a fauxbourdon was the first solution and step-wise descending root position triads the alternative. But the chords V and I reveal that they probably rather had a regola dell’ottava harmonization in mind—which has of course a lot of overlap with fauxbourdon. Annotation, here, actually is inventing a third voice so theoretically someone could find an excuse to assume a chain of suspensions here. Or someone who feels very uncomfortable with assuming could mark missing chord tones by writing viio(-5) vi(-5)... or V6(-1) IV(-1)....

Let’s take it to the medial caesura…

First movement of Beethoven’s Piano Sonata no. 3, mm. 21–26, annotated

In the introduction of the section you read the word “pedal point” but this pedal here is not one that we annotate. Rather, it remains implicit in the chord progression.

Please check whether you also put the phrase ending on beat 1 of m. 25 because it is a great example of how the phrase annotation syntax “works”: The } marks the structural ending and what follows in this case is just surplus momentum.

Advanced use of applied chord notation

Please try annotating mm. 27-42 in the key of V. Below, it will become clearer why.

First movement of Beethoven’s Piano Sonata no. 3, mm. 27–42, annotated

So how do you stay in the same local key but still express the equivalence of mm. 27–32 and mm. 33–38? Well, maybe you guessed from the heading: The “applied chord notation” / can be used to a wider extent than is maybe common. Note how the second system is just a copy of the first one with /v appended to all labels; up to m. 38 where we have reached another fifth above, /ii. The resulting V2/V/v and V2/iv/v are fine because they fulfill this specific purpose, namely displaying the recursive borrowing of chords from other keys.

In m. 42 you were probably wondering about some special syntax for augmented sixth chords and indeed, we have It6, Ger6, and Fr6 in our repertoire.

Why V and not v? And why not change the local keys?

The answer to this legitimate question will be much clearer when looking a bit ahead, but before that, let us look at another feature:

Organ Points

Our organ point annotation uses square brackets []. Just as our phrase annotations with curly brackets {}, the completeness of opening and closing brackets is a constant source of errors and needs to be handled with care.

Most organ points stand on a dominant V[V .... V] or on a tonic I[I .... I] with the dots representing other harmonies. In difference to phrase annotations, the square brackets cannot stand alone: They always need to come in conjunction with a chord label. The opening [ separates the scale degree of the pedal note from the first harmony over the pedal note, whereas the closing ] always needs to be the last element of a chord label (which, in return, always precedes a potential cadence and/or phrase label). But see for yourself:

First movement of Beethoven’s Piano Sonata no. 3, mm. 43–48, with organ point syntax

Now looking at the bigger picture of mm. 27–48, we see more clearly what the annotator probably had in mind (and where at least one reviewer did not object): By changing the local key in m. 27, the beginning of the second tableau in the expected key of V has been marked and the overarching harmonic outline of the section, {i v ii V7 i V/V V}, has been made visible. This analytical decision results in a soothing tonal plan, too:

If you want, you can do the G major section mm. 47–68 but there is nothing new or challenging for this tutorial to discuss, so let’s have a look at what to do with

Unisono passages

Please annotate the ending of the exposition, starting from m. 69.

First movement of Beethoven’s Piano Sonata no. 3, mm. 27–42, annotated

The annotator in this example followed the general guideline to infer which chords are being horizontalized. In such cases, annotators often account for ambiguity by writing labels including two alternatives, separated by a dash (not in this example, though).

Advanced use of chord tone replacement

General principles

In a previous section we introduced the syntax for replacement of the chord tones 1, 3, and 5 from above, namely through the combinations 2, b2, v#2 , 4, b4, v#4, 6, b6, v#6 within parentheses following the chord inversion. The digits preceded by a sharp require the symbol v because without it they would be assumed to replace the chord tone above. Similarly, ^2, ^b2, #2, ^4, ^b4, #4, ^6, ^b6, #6 are used to indicate replacement of chord tones 3, 5, and 7 from below.

Note

Remember that the accidentals depend on the local major or (natural) minor scale.

Replacement of a chord tone’s octave doubling

The same principles apply when the chord tone in question is present, but replaced in one of the octaves above, in form of the digits 9, 11, and 13. For example in the case of the so-called “Chopin chord” which is commonly said to be a “dominant seventh chord add 13”: We would express that as V7(13) to make it clear that the chordal fifth is actually present and the suspension (at least) a ninth apart.

The same logic can be applied to added notes, for example to express a difference between V7(+6) (dissonance is a second) and V7(+13).

Ninth chords

To give the most prominent example of ninth chords, dominant ninth chords are expressed as

• V7(9), V7(b9), V7(v#9) if the ninth is considered to replace an octave doubling of the root;

• V7(^9), V7(^b9), V7(#9) if the ninth is considered to replace an octave doubling of the chordal third;

• V7(+b9), V7(+9), V7(+#9) if the ninth is considered as an added note.

Replacement of the root by its lower neighbour

For root replacement we needed to introduce a special case: Following the above logic, replacement of the lowest root (1) in the chord should be expressed through through 0 and #0 (leading tone in a minor scale). However, to not overstretch annotator’s departure from inveterate annotation practices, we have it commonly expressed as 7 or #7 (which, logically, would express replacement of an octave doubling of the root). Therefore 0 and 7 are equivalent in nearly all cases, the exception being root position chords, where the root is in the bass: Here, 0 is required to differentiate from replacement of an octave doubling (7). The following examples, hopefully, will not leave any doubts:

DCML syntax for replacement of the chordal root in the bass vs. in other voices.

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In case you wondered: v7, vb7 are theoretically possible but only in debatable cases where a sixth above the root could be considered to be a chord tone. At present, this would—if ever stretching the concept of root pretty far—theoretically be the case for the augmented sixth chords Fr6, Ger6, and It6.

End of the tutorial

Thank you for making it to the end! In case you managed to read and internalize all sections, congratulations, you are now in the position to Once more the invitation to state problems you might have had in our issue tracker.

Missing sections

• augmented sixth chords