Score Reading: Misprints

In Franck’s magnificent E major Chorale, there is an obvious blotch in certain editions which appears right next to the tenor voice of a 4-part texture (see dark blue square, upper left example). Whatever the genesis of the blotch, it has led to what I believe are incorrect performances of the passage.

The blotch clearly includes a large, somewhat circular shape, attached to what appears to be the note B in the space above the bass staff. If the B is indeed the composer’s intention, then it must be observed that 1) the lower right corner of the note head is missing, 2) a fifth, non-doubling voice has suddenly been added to the texture, and 3) the added note results in a dissonant 9 - 8 combination with the accented passing tone C sharp in the soprano, thus significantly changing the sonority of the chord.

If we look at the analogous passage later in the piece, with pedals added, we see that the B is not present. Its absence, however, has nothing to do with the added pedal line: the pedal line is simply an octave doubling of the lowest voice in the manuals.

The only sensible conclusion is that the B is part of the smudge. The middle and lower examples on the left show the large part of the blotch, and then the entire blotch, removed. Why does this problem go undetected? The answer is straightforward. The B is indeed possible - after all, it is the root of the prevailing harmony, the B dominant 7th chord. But why would Franck vary the harmony, by omitting the B, in only one instance throughout the course of the later passage, while what is happening in the music in the first place - in the later passage - is a registrational and textural variant of the initial statement?

The stained glass window, lower right, is part of a large panorama on the back wall of St. James the Apostle Church in Carmel, New York. Visit my website - Gallery of Stained Glass Art - at robertfertitta.org.

Score Reading: Clefs and Key Signatures

These questions pertain to the 10-measure instrumental excerpt shown above:

• What are the clefs and key signature?
• What is the rhythmic grouping?
• What is the significance of each of the chromaticisms?
• Where do the following nonharmonic tones occur and what types of dissonance result: accented neighboring tone (on 2 metrical levels)? articulated suspension?
• What is the harmonic organization of the piece, specifically, the chords and cadences?
• What tempo is appropriate for this Adagio?

Tonal Relationships: Key Signatures

In Studies in Music Theory by Harrison, Martin and Fink, it is not until Lesson 6 that the term ‘key signature’ is even mentioned, and it is not until Lesson 15 that the discussion of this topic is completed. In Lesson 6, the authors state: ‘The word key refers to a specific transposition of the major or minor tonal system; it accordingly implies the identification of a tonal center. One speaks of the ‘key of C major,’ or the ‘key of A minor’. The term key signature, therefore, is misleading: there is nothing in the one-flat symbol, for example, that specifically indicates F major or D minor. Signatures do imply ‘families’ of tonal systems, however.’

The illustration above is a composite of examples from Lessons 14 and 15. It shows the typical approach to key signature notation: the sharps in increasing numbers of accidentals from 1 to 7, and the same for the flat keys. C major and A minor are not included. Each family (or pair) of tonalities is indicated directly below its key signature.

Traditional thinking is that there are 24 keys - 12 major and their relative minors, in other words, a major and a minor key for each of the 12 chromatic pitches. This is not the complete picture, however. The illustration shows 14 major and 14 minor keys, to which we add the keys of C major and A minor, for a total of 30 keys. What therefore is the explanation for this discrepancy? The answer obviously lies in the three pairs of keys that are duplicated by their enharmonic equivalents: 5 sharps/7 flats, 6 sharps/6 flats, and 7 sharps/5 flats.

A frequently asked question arises: why do the keys of 7 sharps - C sharp major and A sharp minor, and 7 flats - C flat major and A flat minor exist? Wouldn’t it be just as expedient to use their enharmonic keys instead - D flat major, B flat minor, B major and G sharp minor, respectively - with only 5 accidentals in the signature? [The vast majority of instances do, in fact, appear in the 5 sharp or flat keys]. The answer centers around the concept that every key is part of a spectrum of 6 diatonically related keys. Let us consider C major as a ‘home’ key. To derive the 5 related keys, we simply name the key with the same key signature as C major, the 2 keys with 1 sharp more [or 1 flat less], and the 2 keys with 1 flat more [or 1 sharp less]. The resulting family of keys is: C major - A minor - G major - E minor - F major - D minor. Using A minor as the home key, the outcome is the same as that of C major, owing to the fact that C major and A minor share a key signature.

Taking traditional thinking a step further, it should be observed that, because each of the 4 keys with 7 sharps or flats in their key signatures have a set of 5 diatonically related keys of their own, there exist yet 4 additional keys. These 4 keys do not have key signatures, but rather, they appear within pieces as secondary to the home key. They are G sharp major and E sharp minor [8 sharps, diatonically related to C sharp major and A sharp minor], and F flat major and D flat minor [8 flats, diatonically related to C flat major and A flat minor]. To go one step further, there are actually examples in the literature written in keys with more than 8 sharps or flats.

Where are some of the famous places the ‘8-sharp’ and ‘8-flat’ keys appear? G sharp major and E sharp minor: Bach, Das Wohltempierte Klavier, both C sharp major fugues; G sharp major: Chopin, 1st Piano Concerto, 2nd movement; F flat major: Schubert, Moments Musicaux, No. 4; D flat minor: Schubert, Impromptu in A flat major, op. 142, no. 2. For an example of a key with 9 sharps, we refer again to the Chopin slow movement [E major]: when G sharp major modulates to its dominant, the result is D sharp major.

The example is quoted by permission of the authors.

Staff Notation: Clefs and Key Signatures

Some issues regarding the above excerpt for your consideration: 1] What are the clefs and key signature? 2] Which contrapuntal technique is freely used? 3] Which harmonic device appears from the beginning to the downbeat of measure 3?

Rhythmic Grouping: Asymmetry

The excerpt quoted above is the third and final verse of Schubert’s song, ‘Heidenröslein’ (The Wild Rosebud), 2/4 meter. The 3 verses of 16 measures each are identical, except, of course, for the text. In the autograph, Schubert wrote the music out only once, with the first verse of the poetry under the vocal line, while the text for verses 2 and 3 appears below the music in block form.

By far, the most typical rhythmic grouping for a 16-measure musical unit is (8 + 8), with each 8-measure phrase subdividing into (4 + 4). Perfect balance, proportion and symmetry operate within these parameters. [See the previous post - ‘Rhythmic Grouping: Symmetry’ - April 4, 2008].

The rhythmic grouping of ‘Heidenröslein’ is asymmetrical: [4 + 6 + 6], subdivided as [(2 + 2)] + [(2 + 2) + 2] + [(2 + 2) + 2]. The asymmetry exists on 2 levels: there are 3, not 2 (or 4) phrases, and the second and third phrases are expanded by way of a 2-measure extension. Clearly, the structure of the text has everything to do with the asymmetry of the music.

Other structural features of the song are worth noting: 1] a modulation to the dominant key takes place from measure 5 to 12; 2] there is a beautiful array of nonharmonic tones in the vocal line, including appoggiatura, passing tone, accented passing tone [on 2 different metrical levels], escaped tone, and accented neighboring tone; 3] strong dissonances occur in measure 9 between the vocal part and the top note of the piano part; 4] the highest note, G5, occurs in the vocal line of the following measures: 4 - root of the tonic, 10 - 7th of the dominant 7th of D major, 12 - root of the tonic, and 13 - 5th of the IV chord.

Rhythmic Grouping: Symmetry

Mozart wrote the Minuet, K. 6 quoted above, when he was 7 years old. It exhibits a tonal organization which is typical of the period: a modulation to the dominant key [measure 5 through 8], balanced by a return to C major immediately after the first double bar. In addition to the structural chromaticism involved in the modulation, there are 4 instances of ornamental chromaticism: C sharp [m.2] and D sharp [m.4] are accented passing tones; D sharp [m.6] and G sharp [m.14] are passing tones. This miniature binary piece also exemplifies perfect symmetry of phrase organization: [(2 + 2) + 4] + [(2 + 2) + 4]. As both 8-measure groups are to be played twice, the Minuet is 32 measures in length.

Studies in Music Theory by Harrison, Martin and Fink, states that ‘Rhythmic grouping occurs when a series of durations coalesces into a single musical unit. Phrases are rhythmic groups, discrete units of connected musical motion that are demarcated by clear beginnings and endings. We distinguish between phrase groupings [which end in a cadence and a convincing point of arrival] and subphrase groupings [shorter groups within phrases]. Caesuras, where breaths may be taken, define the limits of rhythmic groups. Rhythmic groups frequently end with a rest or relatively long note value.’

The symmetry of the grouping of the Minuet lies in the nearly exact rhythmic repetition of the first 8-measure phrase in the second half. Within each phrase are two 4-measure subphrases, the first of which has an internal grouping of (2 + 2) and the second of which is a single connected group. Thus, caesuras occur at the ends of measures 2, 4, 8, 10, 12 and 16, and [perfect authentic] cadences occur only in measures 8 and 16.

A question for further investigation: aside from tonality, what are the differences between the 2 phrases?

In the next post, asymmetrical rhythmic grouping will be the focus.

The example is quoted with the permission of the authors.

Staff Notation: Clefs and Key Signatures

The excerpt - in 3/4 meter - shown above is obviously for 3 instruments. The top line repeats a 1-measure motive, while the voice notated on the middle staff moves along in a continuous dotted rhythm. The lowest instrument plays a two-measure figure punctuated by a quarter rest.

For your consideration: 1] What are the clefs and key signature of the excerpt? 2] Where during the course of the 6-measures do complete triads occur on the beat? incomplete ones? 3] What is the significance of the chromaticism?

I am most interested in finding out different musicians’ methodologies in deriving the solution, so do write me a comment explaining your rationale if you have a moment.