The Chromatic Fourth during Four Centuries of Music.
This is a fine and fascinating book on a subject which, as far as I am aware, has never previously been treated, even though the chromatic fourth, its meanings and uses, has been part of musical general knowledge for as long as I can remember. Many, then, will not be greatly surprised by what they read here, though it is good to have the evidence gathered together in one place. As Peter Williams says - with great honesty - others may well find examples that he has not discovered; indeed, in one way this piece of work is dangerous, for it makes one listen for chromatic fourths all over the place. But that, of course, is a measure of the book's success.
Williams at all stages gives both the pros and cons of the argument with great fairness. He is right to emphasize the importance of D minor to the chromatic fourth, for the pitches involved when that key is used in early music are all viable in mean-tone tuning. One is, however, bound to question whether such niceties about accurate tuning hold good for the lute (and other instruments with frets - see p. 58), since here the distance between, say, G and G[sharp] is no different from that between G and A[flat], G and C[sharp], F and F[sharp], A and B[flat] or D and E[flat]: the lowest semitone is bound to be the same size on each string. For these instruments the distinction between small and large semitones clearly breaks down. Williams is right historically, however, for composers through the centuries have very often associated the motif with D minor.
Williams is right, too, to draw attention to the function of the chromatic fourth in helping to emphasize a settled tonality by throwing the latter's diatonic nature into relief. As he says, such a use might occur just before the end of a movement (he often refers to the spectacular example in the coda of the first movement of Beethoven's Ninth Symphony), but equally the feature will often set up a sonata-form retransition (especially when used in descending form). Perhaps the reasons for this could have been explored more fully. The chromatic tetrachord contains the essence of both major and minor tonalities in any particular key (it is a combination of 'melodic-' and 'harmonic-minor'), and its outer notes emphasize the tonic and dominant of the key: the [flat]VI-V movement is the ideal preparation for a dominant pedal, and is often used to set up the overall progression [flat]VI-V-I. The chromatic nature of the bass, when it uses the outline of a fourth, can summarize the tonal fluidity of the foregoing development section, and act, as Williams says, to throw the settled nature of the forthcoming tonality into relief. In a sense, then, the [flat]VI can act rather like an inverted leading note. (The first movement of Schubert's String Quintet in C does not use quite enough notes to get listed in this book, though I cannot resist quoting the mouth-watering 'wrong-key' preparation for the second subject and the chromatic slide that connects it to the start of the new key, simultaneously throwing the new and settled tonality into relief and drawing attention to the third-related scheme of keys. If the relationship had been the conventional tonic-dominant one, Schubert might well have introduced a chromatic fourth at some point, rather than this major third.)
The [flat]VI-V at the bottom of the descending fourth has another fascination for composers in that it implies a Phrygian cadence, and such an obviously modal characteristic has resonances of the antique. The references to the chromatic fourth that Williams points out in Verdi's Requiem might well, then, have been related back to the opening bars of the work, in which the descending A-G-F-E, unharmonized at first, gives rise to a Phrygian cadence that is presumably intended to evoke ancient liturgical music. In fact, the position of the descending chromatic fourth as a logical development of the descending diatonic tetrachord, even though it is mentioned in passing, might well have been explored further. In a book of this size there is no space to investigate everything in depth; but there is much here that can lead others to make their own explorations. There would be some sense, for instance, in tracing both back to the basses used as ostinatos for improvisation (the formula that begins with d-c-d-A, for example). This progression is only one stage removed from the ordinary descending tetrachord, and the connection with pieces based on grounds - Williams frequently mentions the use of the chromatic fourth for passacaglias etc. - is strong in all three types (improvisatory bass, descending tetrachord and chromatic fourth).
Such a derivation might also have taken in the examples which are very nearly full uses of the chromatic fourth, though Williams could object that he had to draw the line somewhere. Nevertheless, Byrd's 'Ave rerum corpus' provides a well-known early example, for its opening phrase uses g'-f[sharp]' (in the topmost part), then f[natural]-e[flat]-d in the bass; only e[natural] is missing from the chromatic fourth, and Byrd continues to use tetrachords (though not chromatic ones) at various points later in the piece (indeed, the opening bass line is only one stage removed from quoting Dowland's Lachrimae theme, and the rest of the piece is virtually a meditation on that shape). Clearly the Affekt here - a notion that Williams explores intensively and well - gives rise to the use of the formula in Byrd's motel.
But, as Williams says, the Affekt, so striking in music before the nineteenth century, can become dulled when composers treat the feature as an 'off the peg' formula: perhaps we could have heard more about the harmonic reasons why the cadence so beloved of Mendelssohn et al. came about. The 'relaxed' nature of tonal motion towards the subdominant led to a flattening of the seventh above the tonic at final cadences, and thus to a digression towards a plagal cadence; combined with this is a liking for the minor chord on the subdominant (which, when the home tonality is major, provides more colour than the normal major chord on IV) - and there is a liking, too, for progressions in which the major chord on IV shifts to the minor. Given these factors, the use of the descending chromatic fourth as part of a final progression becomes almost inevitable. How different, though, is this thoughtless use of the conventional formula from the dynamic, vital and lively use of it in the Prelude of Bach's 'Weimar' Prelude and Fugue in C, BWV 545, in both its opening and closing bars.
Solmization can partly explain some of the features that Williams isolates in the early part of the book. The chromatic fugue subject by Frescobaldi (which history books love to quote) given as Ex. 2.6 is surely the result of writing a conventional chromatic fourth but with the first couple of notes after the initial tonic rising instead of falling; and in Ex. 1.4 the conventional solmization of the vowels la, mi and sol in 'Calami so-' as fa and sol in the hard hexachord (resulting in C and D) with an unexpected major third between them (C[sharp], which can only be solmized as mi) readily explains the chromaticism of the subject.
This is a finely presented, well-produced book: there are just three minor slips ('occurring' is misspelt on page 18; the Palestrina madrigal mentioned on page 35 has 'abi' for 'ahi'; and 'Timor et tremor' is not a Te Deum (p. 51), despite containing the words 'non confundar in aeternum'). The book is copiously illustrated and - all round - is a great joy.