5 Ámbito de la entrega y variantes de la cama
16.1 Protección del medio ambiente
At least since Classical Antiquity, music theorists have tried to explain the behavior of melodies by appealing to some concept of mode or scale. Ancient Greek music theory developed a system of eight modes, a corrupt version of which was transmitted into West-ern music theory during the Middle Ages in order to classify plain-chants. Medieval theorists adopted this system for several reasons.8 For one thing, performers needed an effective way to proceed from one chant to another; this was of paramount importance in singing antiphons and psalms. For another, performers needed a way to learn and teach the enormous repertory of chants that appear throughout the liturgical year; grouping them into families pro-vided one way to do this. For some theorists, the impetus may have been purely academic—to widen the frontiers of knowledge. What-ever their motivation, Medieval theorists generally used four crite-ria to explain such classification schemes: final; range or ambitus;
species of fourth, fifth, and octave; and reciting tone. Although these explanations worked for many chants, they were not always completely accurate; in some cases, chants were even rewritten to fit with theoretical norms; in others, recalcitrant chants were ignored completely. Theorists sometimes compensated for other anomalies by discussing irregular or imperfect modes.
By the turn of the sixteenth century, however, theorists ran into problems when they tried to extend their system of modal classifi-cation to polyphonic music. At first, they classified pieces accord-ing to the mode of the tenor; but as they tried to be more specific, the difficulties soon multiplied. Some of them stemmed from the fact that individual strands of the polyphony had different finals
and different ranges, whereas others stemmed from the fact that each line was constrained by a growing sense of triadicity. Even today, the task of explaining mode in polyphony remains one of the thorniest problems in contemporary music scholarship.
The problems of applying melodic categories to harmonic systems multiply when we try to use major and minor scales to explain tonal music written from the Common-Practice Period. Certainly, there has been no shortage of attempts to do so. Many music theory textbooks claim that the properties of functional triadic tonality derive from those of diatonic scales. According to William J. Mitchell, for exam-ple, “[T]he major and minor scales, which form the basis of this study of harmony, are diatonic.”9 Similarly, Edward Aldwell and Carl Schachter claim that “[f]rom the time of the ancient Greeks through the nineteenth century, most Western art music was based on dia-tonic scales.”10 Scholarly publications have likewise promoted this point of view. For example, Pieter van den Toorn has remarked:
Tonality is viewed here in its more restricted sense as a hierarchic system of pitch relations based on the diatonic major scale (the C scale) . . . the his-torical development of which can be traced from the beginning of the seven-teenth century to the end of the nineseven-teenth.11
Or, to quote Richard Taruskin:
Just as we get our sense of Mozart’s C major not only from his use of the “C scale on C” but also from the way the “black keys” are related hierarchically to the tones of the scale, so, if we are able to conceive of the octatonic col-lection as a tonality, we must be able to account for the use of the “other”
four tones in relation to it.12
Taruskin adds that, in Mozart’s case, “even the simplest minuet or sonatina movement will contain tones foreign to the C scale that defines its key.”13
But what does Taruskin really mean when he says that Mozart’s C major is referable to the “C scale on C”? How does this scale define the key of C major? How are the chromatic notes in Mozart’s simplest minuet or sonatina related hierarchically to the members of this scale? Are these “wrong” notes really intrusions of some other scale type? Do the properties of the tonal system really depend on those of major and minor scales?
As it happens, there are good reasons to be cautious about answering these questions. Even on an intuitive level, we know that scale membership is neither necessary nor sufficient for deter-mining the tonality of a passage or piece (see figure 4.1, Scale mem-bership and tonality). It is easy, for example, to imagine how a key might be defined by progressions that do not contain every note of the relevant scale. Take, for example, the progression I–V–I in fig-ure 4.1a; this passage clearly lacks two members of the C-major scale—4 and
6. Similarly, the mere presence of a given scale need not guarantee that a passage is “in” the corresponding key. As shown in figure 4.1b, a passage built exclusively from the notes of a C-major scale might actually be in A Aeolian, D Dorian, E Phry-gian, and so forth.
To complicate matters further, we can also establish a tonality using progressions built from pitches outside the diatonic collection.
Figures 4.1c and 4.1d give some simple cases in point. Figure 4.1c shows a short progression in D minor. Here, the opening chords move from I to VI6and back via VIIo7to I5, while the final cadence tonicizes D by the familiar succession VII6–I. The progression con-tains several interesting chromaticisms. The B (m. 1) is a simple mixture. The A (m. 3) seems to imply a local tonicization of C (VII), though the leading tone is immediately raised to tonicize D.
Meanwhile, in figure 4.1d, we find a progression from the tonic of E to the dominant of F. This motion is achieved by a common-tone progression onto a diminished-seventh sonority in m. 2. The chro-matic tones D and F in this sonority are both mixtures. The B(⫽A) and D in m. 2 then appear as tonicizations; they inflect the subsequent V$5 of F in m. 3.
These last two examples show very clearly that tonality does not simply depend on the presence of the “right” notes, but rather on the fact that particular notes appear in the “right” order accord-ing to some general laws of tonal voice leadaccord-ing and harmony.
Figures 4.1c and d are particularly telling in this regard; although both passages are tonal, neither is referable to the appropriate dia-tonic scale. Figure 4.1c is not built exclusively from the notes of a D-minor scale and figure 4.1d is not derivable from an E-major scale. In both cases, the passages are built exclusively from the notes of the octatonic scale shown in figure 4.1e.
Figure 4.1. Scale membership and tonality.