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.