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.

Score Reading: Misprints

A passage from the fugue of Franck’s Prelude, Fugue and Variation in B minor, op. 18 is quoted above. I believe it contains a rather serious misprint in the highlighted measure.

Misprints in musical scores can occur for a number of reasons: a slip of the copyist’s pen from autograph to 1st edition or to any subsequent edition, a copyist’s misinterpretation of the composer’s notation, misreading a clef, an editor’s decision, or in rare cases, a mistake on the part of the composer.

When the composer’s autograph is not available, how are we to know which edition to use? Can we trust so-called ‘urtext’ editions implicitly? Fortunately, two or more editions are available for most repertoire, although many performances are indeed based on a single source. It is also fortunate that misprints are extremely rare. What is unfortunate is that they can easily go undetected.

The alleged misprint in the Franck excerpt occurs in the soprano voice - the eighth note D should be a major 6th higher - B on the 3rd line. The evidence supporting this assertion is quite clear. In the measure in question, the soprano voice appears to re-enter, after a brief rest, with two additional connected statements of the characteristic 8th-note motive which is part of the fugue subject. [Actually, the previously existing soprano voice either becomes the alto, or it splits into two voices on the downbeat of the measure - notice the change in stem direction from the 1st to the 2nd measure of the system]. If the D is correct as it appears, this would be the only statement of the motive in the entire fugue which does not conform melodically to all its other appearances. There is more. The voice leading as it stands involves a pair of parallel unisons, again the only such occurrence - in this case of faulty counterpoint - in the fugue. Finally, the augmented 4th, D to G sharp, sounds disturbing, yet the piece is full of augmented and diminished intervals, both melodically and harmonically, which sound perfectly natural.

There are many instances in various editions of Franck’s organ music in which I believe there are misprints of this sort. As responsible musicians, we need to be on the lookout for this potential problem in our daily musical studies. This is especially true in the more complex chromatic styles and those of the 20th century, but we can never be too careful, whatever the style or composer.

Staff Notation: Clefs and Key Signatures

Most tonal music is notated with a key signature. It should be noted that ‘key’ and ‘key signature’ are not synonyms. F sharp major is a key; 6 sharps is a key signature. And most tonal music modulates from the home key and returns to it by the end of the piece. When the music moves to a secondary key, accidentals are inevitable, with special exception.

Let us use E flat major as a home key and consider its five diatonically related keys - F minor, G minor, A flat major, B flat major and C minor - in terms of the ‘accidental landscape’ when each of these secondary keys is in force: F minor - D flat, E natural; G minor - A natural, E natural, F sharp; A flat major - D flat; B flat major - A natural; C minor - A natural, B natural.

For minor keys, we shall use B minor, which like all minor keys, resides in a 9-note system including, in the case of B minor, the common accidentals G sharp and A sharp. Its related keys are D major, E minor, F sharp minor, G major and A major. For D major - this is the exception - accidentals disappear; E minor - C natural, D sharp; F sharp minor - G sharp, D sharp, E sharp; G major - C natural; A major - G sharp [and no A sharp].

An obvious conclusion can be drawn from this: as a musical score progresses, the music is not necessarily in the home key, or its attendant key signature, in every measure of the piece.

For your consideration: what are the clefs and key signature of the contrapuntal excerpt above? We can assume that the two clefs appear in order of register from bottom to top - bass, baritone, tenor, alto, mezzo soprano, soprano, treble. We should not assume, on the other hand, that the two clefs aren’t the same. There is more than one correct solution within these assumptions.

Score Reading: A Bach Autograph

There are many special features to be observed on the beautiful manuscript of Bach’s [Prelude and] Fugue in G minor, BWV 535 for organ, the opening page of which is shown above: 1] Bach notated his organ works on only two staves, usually with the soprano clef above the bass. 2] While the fugue is in G minor, the key signature contains only one flat. It was common practice in the Baroque period and earlier to notate music in the minor mode with a key signature of one flat less than we use today. This is known as the ‘Dorian’ key signature. Bach’s Toccata and Fugue in D minor [the so-called ‘Dorian’] has no flats in the key signature. Interestingly, in the Peters edition, the G minor fugue has a modern key signature while the Dorian adheres to the original. The one-flat key signature works as well for G minor as the modern two-flat version: Bach writes the flat symbol when E flat is required, and writes nothing when he needs E natural. In the modern signature, a natural sign needs to be written before E when that pitch occurs, but nothing is necessary when E flat is intended. It is a perfect illustration of the old saying ‘six of one, a half dozen of the other. 3] In the 4th measure, Bach rewrites the flat symbol in the 1st repeated group of 16th notes. This is the case in subsequent statements of the fugue’s subject in the home key of G minor and in several other instances throughout the piece. 4] Both the 1st and 2nd systems end with a half-measure, thus no bar line appears. 5] Two additional staff lines, rather than individual ledger lines, appear on the top staff toward the beginning of the 3rd system, and extra staff lines appear briefly in other places. 6] Bach often notates three voices on the upper staff alone, with crystal clarity. 7] The third entrance of the fugue subject, in the tenor, takes place on the 3rd beat of the 1st complete measure of the 2nd system, signifying an invisible shift of the bar line. The ‘displaced’ bar line shifts back to the notated downbeat when the bass voice enters in the last full measure of the 2nd system, where Bach writes in ‘Ped.’ The pedal begins a long rest in the last measure of the 3rd system, and does not return until the following page. 8] The prominent diminished 5th in the 2nd measure of the fugue subject is replaced by a perfect 5th later in the fugue, when the tonality shifts to the relative major.

Tonal Relationships: Transposition

The tonal organization of Schumann’s exquisitely beautiful song cycle, Dichterliebe, op. 48, is unique and quite special. Each of the 16 songs is in a different key, but never are two unrelated keys juxtaposed. The accompanying chart [1st column] indicates the succession of keys, starting in F sharp minor [1] and ending up in the closely related key of C sharp minor [16]. As the chart shows, this is not accomplished by any direct means, but rather, by an excursion first into keys with fewer sharps, followed by the two keys with no sharps or flats, on to keys with increasing numbers of flats, a jump from B flat major to its minor subdominant key of E flat minor [the only non-diatonic relationship in the cycle], on to C flat major - but written enharmonically as B major, and finally to both keys with signatures of 4 sharps.

Why does the title of this post refer to ‘transposition?’ Surely, we know that there exist editions of the lieder and chanson repertoire that are transposed, either up or down, from the original key. The reason for this is obvious: most vocalists have a specific range in which they sing comfortably, and much of the repertoire, in its original keys, does not always coincide with that range.

Two serious issues emerge: 1] is it of no concern to anyone that the altered keys possess entirely different characters than the originals? and 2] should pianists be expected to learn this repertoire in whatever key someone desires?

First things first. Vocal music is conceived by the composer in a specific tonality, the same as instrumental music. Schumann wrote his 2nd Symphony in C major - the same key as ‘Ich grolle nicht’ [no. 7]. His Piano Quintet is in E flat major - the same key as ‘Ein Jüngling liebt ein Mädchen’ [no. 11]. And the Violoncello Concerto is in A minor - the same key as ‘Und wüssten’s die Blumen’ [no. 8]. It is obvious that each key had a certain meaning to Schumann and to each of the master composers. With only rare exception, we don’t see transpositions of any of their instrumental music, so why the double standard? We don’t see transpositions of choral music either - imagine the ‘Dies Irae’ of the Verdi Requiem in E minor or the ‘Cum Sancto Spiritu’ of Bach's B minor Mass in E flat major? And we certainly don’t see transpositions of Mozart’s ‘Exultate, Jubilate’ down to D major for mezzo soprano, or worse yet, the operas.

As to the pianistic question: anyone who is a collaborative pianist knows that much of the lieder/chanson repertoire is as demanding technically as is chamber and solo piano music. Thus, for the same reasons that we wouldn’t suddenly decide to play Beethoven Sonatas or Chopin Ballades in the keys of our choice, we should not be called upon to participate in a distortion of the composer’s original intentions in vocal music, complete with potentially impossible technical challenges.

There is a much more troubling issue. In certain editions of Dichterliebe, for example, the ‘low’ key, there is a terrible distortion of the internal tonal architecture of the work. Referring once again to the chart, the center column indicates the interval down from the original key in which the transposed version appears. One would think that if a masterwork is to be transposed, at least the relative tonal structure should remain intact. Not in this case. Several of the resulting key relationships in certain editions are disturbing: D major moves to G minor [quite clumsily, in fact], B flat major is followed by F sharp minor, and C major goes to A major as well as the reverse. Also note that ‘Am leuchtenden Sommermorgen’ [no. 12] is only a minor 2nd lower than the original. Why bother? Schumann would probably be infuriated by all of this tampering, and would undoubtedly disapprove of the muddiness that some of the songs acquire in the lower register of the piano.

The most unfortunate aspect of all this is that the distortion of the tonal progression of Dichterliebe goes unnoticed by those who use faulty editions. I remember submitting a proposal to a ‘music theory society’ on the tonal organization of Dichterliebe, to be delivered at an all-Schubert/Schumann convention at which Dichterliebe was to be performed by a baritone. I was rejected because ‘the board decided that too many people applied from far away places’. I discovered later on - from the pianist who performed it - that my topic would have revealed that their performance was in fact a distortion and that my presentation would expose it. Well, doesn’t every fraud deserve a coverup?

My message here is not to attempt to put a stop to the practice of random transposition, but simply to encourage those who engage in this practice to know what they are doing. I shall never listen to Dichterliebe in any key other than the original, any more than I would listen to Brahms 4th Symphony in B flat minor.

Staff Notation: Clefs and Key Signatures

For the exercise in determining the clefs and key signature shown above, three assumptions can be made: 1) there aren’t necessarily three different clefs 2) the clefs are never ‘crossed’ 3) there is more than one correct solution.

Obviously, this is an imitative piece in three voices. Once the key is determined, consider these questions: 1) What is the range of all three voices? 2) What is the significance of the juxtaposition of the two consecutive sharp notes [dotted quarter to eighth] in measures 2, 3 and 4 in terms of conventional ‘scale’ nomenclature? 3] In which measures do complete triads - either in root position or inverted - occur as the result of the contrapuntal motion among the voices?

Score Reading: The Vocal Clefs

Like his contemporaries and predecessors, J. S. Bach used the soprano, alto and tenor clefs in all of his vocal compositions as well as in numerous instrumental works. The three ‘C’ clefs appear throughout the Cantatas, Masses, Passions and Motets. In the harpsichord and organ works, we encounter Bach’s use of soprano clef, not treble, in the right hand part. He also frequently wrote in the alto or tenor clefs for the inner voices in the organ music.

The first eight measures of a facsimile of the autograph of ‘Dir, dir, Jehova, will ich singen’, one of Bach’s hundreds of chorale harmonizations, is given above. Several features are worth noting. There is a large bow brace joining the four staves. Bar lines do not connect through the system. The key signatures for the soprano and bass voices involve pitches that are above their respective staves. Bach copied both lines of German text four times and assigned each pair of sentences a bow brace. The downward stems of half notes are drawn to the right of the note head. The eighth notes from measure 6 to 7 are beamed across the bar line. There is a thickening of ink in the tenor part in measure 5 and a few smudges above the tenor in measure 6. Not that it interferes in any way with the beauty of the autograph, it appears that the tool Bach used to create the 5-line staves was not calibrated properly: the first and fourth spaces are noticeably narrower than the two inner spaces on each staff. The staves, being hand drawn with the staff tool, are not always straight and parallel.

Structurally, there are many beautiful features. The eight measures are almost entirely diatonic: the only chromaticism is in measure 7 in the alto - a lower neighboring tone. With the exception of the subdominant harmony throughout measure 2 and on the last beat of measure 3, the excerpt is limited to tonic and dominant chords. A prominent motive, first appearing in the soprano in measure 1 and consisting of a quarter note followed by a neighboring tone figure connected to a chord tone skip in eighth notes, is restated in the a] bass - measure 2, b] soprano - measure 6, c] bass - measure 7, and d] tenor and bass - measure 5, a rhythmic variant, in parallel 3rds.

Harmonic Techniques: Voice Leading

The study of 4-part harmony is introduced in Lesson 7 of ‘Studies in Music Theory’ by James Harrison, Louis Martin and Myron Fink. A set of basic tools is established - conjunct voice leading using the tonic and dominant triads in root position, and the complete and incomplete forms of the root position dominant 7th chord. Rhythmic extensions of the tonic are also part of the initial vocabulary. With these resources and no more, it becomes apparent that it is possible to create a short harmonic piece that has a convincing musical shape. Lesson 8 then goes a few steps further by adding disjunct and composite voice leadings as well as rhythmic extensions of the dominant.

Two realizations of the same figured bass appear in the example above. The authors compare the two pieces, revealing that with an imaginative treatment of the available resources, a great deal can be accomplished. The first setting lacks any sense of direction or meaningful shape but is technically correct, while the second exhibits a beautiful pitch contour in the soprano voice, as well as more elegant shaping in the alto and tenor. The various rhythmic extensions make a world of difference at this or at any stage in the study of harmony. Also note that the bass line itself [identical in both versions] has an attractive contour, despite its restriction to only the tonic and dominant notes.

The examples are quoted by permission of the authors.

Staff Notation: Clefs and Key Signatures

Some questions for your consideration: 1] What are the clefs and possible key signature[s] of this three-part contrapuntal piece? 2] What is the harmonic basis for each measure? [example: F minor, root position; C# diminished, first inversion]. 3] Where does the greatest distance between any pair of voices occur? 4] The smallest? 5] Where do accented neighboring tones occur? 6] Where do consonant passing tones occur?

Staff Notation: Clefs

In Lesson 11 of ‘Studies in Music Theory’ by James Harrison, Louis Martin and Myron Fink, the alto clef is introduced. The lesson also includes a first glimpse at second species counterpoint, wherein the Cantus Firmus begins to appear consistently in the alto clef against treble or bass. The treble-alto and alto-bass combinations are favorable because in two part music, these pairs of vocal ranges produce a better overall balance.

A beautiful summary of the clefs that have been in use throughout common practice is given above. While not all of these clefs are currently in use, a responsible musician would need to be fluent in most of them in order to read complex scores more readily. The soprano clef facilitates reading instruments in A, while the mezzo soprano clef serves well in reading the English horn and the horn in F. The alto clef is the primary clef for the viola and alto trombone, and works well in reading instruments in D. Bassoon and violoncello parts often change to the tenor clef, the primary clef of the tenor trombone. The tenor clef is also used to read the B flat clarinet and trumpet. And the baritone clef is useful for reading the horn in G and the alto flute.

The next post will be [another] puzzle in determining the clefs and key signature of a three-voice texture.

The examples are quoted by permission of the authors.

Range Limitations: Chopin's Piano

The excerpt quoted above is from Chopin’s Ballade No. 3 in A flat major, op. 47, measures 33 - 36 [6/8 meter, Allegretto]. The entire passage, except for the last two notes in measure 36, is in C major, notwithstanding the key signature of 4 flats. Chopin has modulated to the diatonically unrelated key of the mediant major, or major III. A flat major and C major do have a relationship, however: they are both related to C minor. Also, the common tone C is in both keys. On the downbeat of measure 37, the music is back in A flat major.

What is particularly wonderful about this excerpt is that in the time span of exactly one measure - from the downbeat of m. 35 to the downbeat of m. 36 - Chopin traverses the complete range of the piano of his time. We should try to visualize a keyboard whose range is C1 to F7 - a total of 8 3/8" narrower than today’s 88-key range, and then imagine Chopin presiding over it and knowing that he can’t go any further down or up than its almost 6½-octave range would allow. Chopin probably didn’t give it a second thought. His magnificent oeuvre is a testament to how the range limitations of a musical instrument can be transformed into the most beautiful aesthetic and structural/design enhancements, but only in the hands of a genius.

There are some noteworthy dissonances in the excerpt: m. 33, beat 2 and again on the downbeat of m. 35 - F [RH] appoggiatura against E natural [LH]; m. 34, beat 1 - D natural [RH], also an appoggiatura; beat 2 - five of the seven white key pitches - from bass up - G, C, F, E and A. The logical explanation is: the F in the LH is an accented upper neighboring tone, while the A in the RH is an appoggiatura - all within the prevailing tonic harmony of C major. Chopin probably didn’t give any of this a second thought either.

Staff Notation: Clefs and Key Signatures

Some questions for your consideration: 1] What are the clefs and key signature of this short excerpt for piano? 2] How are the various chromatic elements explained? 3] What is striking about the upper melody with regard to intervallic inversion and motivic organization? 4] In which 'layer' of the upper melody does the primary structural line appear? 5] Who is the composer?

Staff Notation: Clefs and Key Signatures

Without clefs and key signatures, there would appear to be no basis for rationalizing music on the printed page. But would it be possible to determine which clefs and key signatures are in force without their actual inclusion in the score? I believe so.

Schubert wrote hundreds of dances for solo piano throughout his life. One of these miniature gems, an ‘Ecossaise’, appears above. We can assume that the clefs are either bass below treble, two trebles or two basses inasmuch as most two-staff music is written for either a keyboard instrument or the harp. Trying out the bass/treble combination first would reveal that the music is in one of these four keys: A flat major, A flat minor, A major or A minor. The two minor keys can be ruled out because they would require an accidental to indicate the leading tone at least. As for A flat major and A major, there is no evidence on the first system in support of either one, but on the second system, four accidentals appear - A natural, A flat, G flat and E natural - clearly revealing the tonality to be A flat major.

The three [not four] chromatic pitches in this piece are all structural: A natural is part of the dominant of ii, G flat is part of the dominant 7th of IV, and E natural belongs to the dominant of vi. The A flat is obviously a cancellation of the preceding A natural, but its inclusion here is appropriate even though the A natural occurs two measures earlier and in a different octave register.

This is obviously not a complex example. In subsequent posts, I will put up excerpts in two, three, four, five and more staves.

Upcoming posts: a Bach autograph, Transposition of Vocal Music, Music Critics, Fixed vs. Moveable Do, Rhythmic Grouping: Bar Line Displacement

Tonal Relationships: Related Keys and Modulation

Every major and minor key has 5 diatonically related keys. To illustrate, I am arbitrarily choosing the keys of A flat major and C sharp minor. For A flat major, the related keys are B flat minor, C minor, D flat major, E flat major and F minor. For C sharp minor, they are E major, F sharp minor, G sharp minor, A major and B major. Any two diatonically related keys either have the same key signature or a key signature with one sharp or flat more or less. Another type of key relationship is known as ‘parallel’, for example, B flat major and B flat minor. But this is not a diatonic relationship.

The 231-measure fugue from the Prelude and Fugue in E minor, BWV 548 is one of Bach’s longest. The formula given above would suggest that this fugue might visit the keys of G major, A minor, B minor, C major and D major. Every one of these keys indeed appears. In addition, however, there is an excursion, during the 113-measure middle section, to the unrelated key of F sharp minor. Bach achieves this goal by progressing from D major - a related key to F sharp minor - just before it. Thus, while E minor and F sharp minor are not closely related, D major is related to both of them.

Arriving at F sharp minor is done quite straightforwardly. It is the way in which Bach gets from F sharp minor back to related tonal areas that is remarkable. In the passage quoted above, measures 136-145, a continuous modulatory excursion takes place. Starting in F sharp minor, there is a motion to A major [related to F sharp minor], on to E minor [related to A minor, the parallel key of A major], G major [related], D minor [related to G minor, the parallel key of G major], F major [related to D minor], and C major [related]. The excerpt shows only upto the onset of G major. Bach has gone from F sharp minor to the remotest key of C major in only 10 measures by way of 5 intervening keys. Then from C major, the home key of E minor returns by way of a simple harmonic sequence.

Similar tonal excursions are found throughout the music of Bach.

Tonal Relationships: D flat minor

It is not often that we encounter the key of D flat minor, the key signature of which would be 8 flats and the relative major of which is F flat major. Composers generally use the enharmonic key of C sharp minor with a mere 4 sharps in its key signature. In fact, in the A flat major Ballade of Chopin, an entire passage [mm. 157-193] which is functionally in D flat minor is notated in the 4-sharp key signature. The relationship of D flat minor to the home key of A flat major is that of the minor subdominant, or ‘minor IV’. It is a relationship based on mode mixture - the use of the opposite mode within a larger structure.

In Schubert’s A flat major Impromptu, op. 142, no. 2, the middle section is in the subdominant key of D flat major. Within that section is a passage in D flat minor, the parallel minor of D flat major, quoted above. Schubert accomplishes this not by an enharmonic key signature change but by writing in the accidentals F flat and B double flat when those pitches are required.

The excerpt also contains a beautiful example of ornamental chromaticism: the D naturals and F naturals in the 3rd measure act as accented passing tones on the downbeat and neighboring tones on the 3rd beat, all within a 2-measure rhythmic extension of the dominant.

Range Limitations: Beethoven's Piano

The range of the piano increased during the creative life of Beethoven. His early works are limited to the same keyboard for which Mozart and Haydn composed - exactly five octaves from F1 to F6. By the end of his life, Beethoven wrote as low as C1 and as high as F7, an increase of a perfect 11th.

The two excerpts from the first movement [Presto, 2/2 meter] of Beethoven’s early [1796] Sonata in D major, op. 10, no. 3, above, illustrate a typical feature of sonata form: corresponding passages from the exposition and recapitulation are often not exact transpositions of each other. The range limitations of the keyboard, usually at the upper end, often determine the necessity to modify one of the two statements of particular material. In this piece, the first statement, in the dominant key [A major], stops ascending in the upper octave one measure before the cadence. Looking at the later statement, in the home key of D major, we see the top line ascending all the way to the tonic.

These observations raise additional questions. Did Beethoven compose ‘chronologically’, thus conceiving the exposition before the recapitulation, or did the entire movement, and the entire sonata, occur to him in a single moment of inspiration? Another question may be asked: why didn’t Beethoven revisit his earlier works later in life, when he could easily have reconstructed them to fit the increased range of the piano? And a final question: what are the other differences between the two passages?

Contrapuntal Techniques: Voice Crossing

A superb example of invertible counterpoint at the octave appears in Bach's monumental Fantasie [and Fugue] in G minor, BWV 542. Taking the two analogous passages quoted above, we see that in the first instance, in D minor, the soprano is a minor 6th above the alto. In the later statement, in G minor, these two voices start a major 3rd apart and are thus an inversion of the previous statement. The tenor is a literal transposition of the first statement, as is the pedal line.

Invertible counterpoint appears throughout the literature, especially during the Baroque era. But something quite fascinating takes place in this Fantasie regarding the voice leading at the cadences of the two excerpts. An additional voice appears [black square] toward the end of the 2nd measure in both cases. The tenor actually divides and becomes two independent voices [tenor 1 and tenor 2]. Now to the fascinating part: in the D minor statement, tenor 1 [B natural - up a major 6th from D below] crosses above the alto [G sharp - down a diminished 7th from F above] on the 4th beat. Both voices then proceed to A [unison] on the next downbeat. Needless to say, this voice crossing will have a bearing on how the organist plays the passage.

There is compelling evidence to support this assertion. Hint: it is directly connected to the process of inversion.

Comments are most welcome.

Rhythmic Grouping: Counting

When musicians count, we are doing more than just assigning a succession of increasing numbers to the beats. Counting is an expressive pursuit as well. The downbeat, or initial metric unit, is unique in that it serves as the rhythmic center of gravity and is less active than the ensuing metric units. Upbeats are distinguished by their pull to the next downbeat but are not emphasized unless specifically called for by the composer. In triple meters, the middle beat can vary in its intensity. And in quadruple meters, the third beat has a secondary emphasis, while the second beat is perhaps the least dynamic of all.

When a piece begins with an anacrusis, none of this changes. J. S. Bach’s magnificent chorale prelude, O Mensch, bewein’ dein’ Sünde gross, BWV 622, begins with a quarter-note anacrusis, establishing that the first 2-measure phrase ends on the third beat of measure 2. It then follows that each subsequent 2-measure phrase is identical in rhythmic organization.

I believe there is something unusual about the way the piece is notated. If we listen to it without knowing in advance that it is in 4/4 meter and that it begins with an anacrusis, how would we count along as we listen? Would we recite ‘4 & 1 & 2 & 3 &’ without giving it a second thought? I have tried this as I listen, and don’t feel it to be the proper inflection in the case of this chorale prelude. Instead, ‘! & 2 & 3 & 4 &’ feels right, as if there is no anacrusis.

Organists and others are most welcome to offer their comments.

Harmony and Meter

Two key aspects of musical organization, harmony and meter, may be viewed as interdependent elements in styles ranging from Medieval to Impressionism and beyond. Simply by listening to music, we sense that the right chords always fall in the right places. Think of ‘And the Glory of the Lord’ from Händel’s ‘Messiah’ for a familiar and powerful example.

In a discussion on this topic in their book, ‘Studies in Music Theory’, ACP, 1991, James Harrison, Louis Martin and Myron Fink state that ‘changes in harmony may produce the accentuation and differentiation needed to create metrical patterns.’ The harmonic scheme in G minor above is given as an illustration of how harmonic motion coincides with meter. H, M & F propose that ‘only one of the three metrical interpretations synchronizes with the harmony. In triple meter [Ex. b], chord changes always occur between the upbeat and downbeat: the sense of motion from V to I therefore reinforces the metrical accent. This type of organization, where harmonic changes have metrical prominence, is common in all styles.’ Included are two additional harmonic schemes, one in E major, the other in G minor, for which the proper meter is to be determined.

Harmony and meter are like color and time, respectively. Every masterpiece has its own balance of the two. For further investigation: can the interaction of harmony and meter be a basis for determining a composer’s style?

Example reproduced with permission of the authors.

Rhythmic Grouping: Rests

The term 'rhythmic grouping' or simply, 'grouping' describes the way in which notes, motives, phrases and larger units are organized in a specific composition.

In the opening of Symphony No. 4 by Brahms, quarter rests delineate each statement of a two-note motive. Four rhythmically equal gestures connect to form a single phrase. This is perhaps the simplest possible illustration of how rests are part of a rhythmic group, rather than separate from the group. There is no question that the violinists here will taper each half note into the ensuing rest, stopping the motion of the bow for the duration of the rest. A change of bow direction takes place during the rest as well.

Now on to the main point of this post: in my experience as a collaborative pianist/organist with singers and as an avid listener of lieder and opera, I am troubled by the fact that, most of the time, singers do not observe rests at the ends of rhythmic groups. The biggest names in vocal performance are just as remiss in this regard as the most amateur singer. What could possibly be the reason behind this disregard for the composers' markings?

Anyone who has sung in a chorus knows the hard work that goes into making all cutoffs perfectly together. Choral directors are constantly reminding the singers to watch especially at the ends of phrases - why? so that the sound turns into silence at a precise moment in time. One would think that highly trained 'professional' singers would take this wonderful structural aspect of the music more seriously, but they do not. I'm relatively certain that they are unaware of the problem.

All comments are welcome.

Music Terminology: Melodic Minor

One of the fundamental aspects of the study of music - terminology - is certainly a subject for debate. Research has revealed that terminology varies considerably from one college to another.

This is an invitation to those interested music professors to participate in a discussion on this topic. The term 'melodic minor' would be a good place to start as there appears to be a good deal of controversy about it.

The included excerpt is from Bach's French Overture in B minor for harpsichord. The music is obviously in F sharp minor at this point. As it is the general consensus that the minor mode consists of the 'natural', 'harmonic' and 'melodic' forms - with 'melodic' reverting to 'natural' for its possible descent - it appears that Bach's music presents a discrepancy in terminology.

Your comments and insights are most welcome.