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.

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.

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.