Here are the six common chords of the diatonic scale. The triad on the
7th degree or "leading-note" (B) is a discord, and is therefore not
given here.
Now, in the 16th century it was neither necessary nor desirable that
chords should be grouped exclusively in this way. The relation between
tonic, dominant and subdominant must necessarily appear at the final
close, and in a lesser degree at subordinate points of repose; but,
where no harmonies were dwelt on as stable and independent entities
except the major and minor triads and their first inversions, a scheme
in which these were confined to the illustration of their most
elementary relationship would be intolerably monotonous. It is therefore
neither surprising nor a sign of archaism that the tonality of modal
music is from the modern point of view often very indefinite. On the
contrary, the distinction between masterpieces and inferior works in the
16th century is nowhere more evident than in the expressive power of
modal tonality, alike where it resembles and where it differs from
modern. Nor is it too much to say that that expressive power is based on
the modern sense of key, and that a description of modal tonality in
terms of modern key will accurately represent the harmonic art of
Palestrina and the other supreme masters, though it will have almost as
little in common with 16th-century theory and inferior 16th-century
practice as it has with modern custom. We must conceive modal harmony
and tonality as a scheme in which voices move independently and
melodiously in a scale capable of bearing the three chords of the tonic,
dominant and subdominant, besides three other minor triads, but not
under such restrictions of symmetrical rhythm and melodic design as will
necessitate a confinement to schemes in which these three cardinal
chords occupy a central position. The only stipulation is that the
relationship of at least two cardinal chords shall appear at every full
close. At other points the character and drift of the harmony is
determined by quite a different principle--namely, that, the scale being
conceived as indefinitely extended, the voices are agreed in selecting a
particular section of it, the position of which determines not only the
melodic character of each part but also the harmonic character of the
whole, according to its greater or less remoteness from the scale in
which major cardinal chords occupy a central position. Historically
these modes were derived, with various errors and changes, from the
purely melodic modes of the Greeks. Aesthetically they are systems of
modern tonality adapted to conditions in which the range of harmony was
the smallest possible, and the necessity for what we may conveniently
call a clear and solid key-perspective incomparably slighter than that
for variety within so narrow a range. We may thus regard modal harmony
as an essentially modern scheme, presented to us in cross-sections of
various degrees of obliquity, and modified at every close so as either
to take us to a point of view in which we see the harmony symmetrically
(as in those modes[5] of which the final chord is normally major, namely
the Ionian, which is practically our major scale, the Mixolydian and the
Lydian, which last is almost invariably turned into Ionian by the
systematic flattening of its 4th degree) or else to transform the mode
itself so that its own notes are flattened and sharpened into suitable
final chords (as is necessary in those modes of which the triad on the
final is normally minor, namely, the Dorian, Phrygian and Aeolian). In
this way we may describe Mixolydian tonality as a harmonic scheme in
which the keys of G major and C major are so combined that sometimes we
feel that we are listening to harmony in C major that is disposed to
overbalance towards the dominant, and sometimes that we are in G major
with a pronounced leaning towards the subdominant. In the Dorian mode
our sensations of tonality are more confused. We seem to be wandering
through all the key-relationships of a minor tonic without defining
anything, until at the final close the harmonies gather strength and
bring us, perhaps with poetic surprise, to a close in D with a major
chord. In the Phrygian mode the difficulty in forming the final close is
such that classical Phrygian compositions actually end in what we feel
to be a half-close, an impression which is by the great masters rendered
perfectly artistic by the strong feeling that all such parts of the
composition as do not owe their expression to the variety and
inconstancy of their harmonic drift are on the dominant of A minor.
It cannot be too strongly insisted that the expression of modal music is
a permanent artistic fact. Its refinements may be crowded out by the
later tonality, in which the much greater variety of fixed chords needs
a much more rigid harmonic scheme to control it, but they can never be
falsified. And when Beethoven in his last "Bagatelle" raises the 6th of
a minor scale for the pleasure he takes in an unexpectedly bright major
chord; or when, in the _Incarnatus_ of his _Mass in D_, he makes a free
use of the Dorian scale, he is actuated by precisely the same harmonic
and aesthetic motives as those of the wonderful opening of Palestrina's
eight-part _Stabat Mater_; just as in the Lydian figured chorale in his
_A minor Quartet_ he carries out the principle of harmonic variety, as
produceable by an oblique melodic scale, with a thoroughness from which
Palestrina himself would have shrunk. (We have noted that in
16th-century music the Lydian mode is almost invariably Ionicized.)
[Illustration: Ex. 7. Suspension.]
[Illustration: No. 8. Passing Notes.]
[Illustration: Ex. 9.]
III. _Modern Harmony and Tonality._--In the harmonic system of
Palestrina only two kinds of discord are possible, namely, _suspensions_
and _passing-notes_. The principle of the suspension is that while parts
are moving from one concord to another one of the parts remains behind,
so as to create a discord at the moment when the other parts proceed.
The suspended part then goes on to its concordant note, which must lie
on an adjacent (and in most cases a lower) degree of the scale.
Passing-notes are produced transiently by the motion of a part up or
down the scale while other parts remain stationary. The possibilities of
these two devices can be worked out logically so as to produce
combinations of extreme harshness. And, when combined with the rules
which laid on the performers the responsibility for modifying the strict
scale of the mode in order to form satisfactory closes and avoid melodic
harshness, they sometimes gave rise to combinations which the clearest
artistic intellects of the 16th century perceived as incompatible with
the modal style. For example, in a passage written thus the singer of
the lower part would be obliged to flatten his B in order to avoid the
ugly "tritone" between F and B, while the other singer would be hardly
less likely on the spur of the moment to sharpen his G under the
impression that he was making a close; and thus one of the most complex
and characteristically modern discords, that of the augmented 6th, did
frequently occur in 16th-century performances, and was not always
regarded as a blunder. But if the technical principles of 16th-century
discord left much to the good taste of composers and singers, they
nevertheless in conjunction with that good taste severely restricted the
resources of harmony; for, whatever the variety and artificiality of the
discords admitted by them, they all had this in common, that every
discord was transient and could only arise as a phenomenon of delay in
the movement of one or more parts smoothly along the scale ("in conjunct
motion") or of a more rapid motion up and down the scale in which none
but the rigorously concordant first and last notes received any
emphasis. No doubt there were many licenses (such as the
"changing-note") which introduced discords by skip, or on the strong
beat without preparation, but these were all as natural as they were
illogical. They were artistic as intelligible accidents, precisely like
those which make language idiomatic, such as "attraction of the
relative" in Greek. But when Monteverde and his fellow monodists tried
experiments with unprepared discords, they opened up possibilities far
too vast to be organized by them or by the next three generations. We
have elsewhere compared the difference between early and modern harmony
with that between classical Greek, which is absolutely literal and
concrete in expression, and modern English, which is saturated with
metaphors and abstractions. We may go further and say that a
16th-century discord, with its preparation and resolution, is, on a very
small scale, like a simile, in which both the figure and its
interpretation are given, whereas modern discord is like the metaphor,
in which the figure is a substitute for and not an addition to the
plain statement. It is not surprising that the sudden opening up of the
whole possibilities of modern harmony at the end of the 16th century at
first produced a chaos of style.
Another feature of the harmonic revolution arose from the new habit of
supporting a single voice on chords played by an instrument. This,
together with the use of discords in a new sense, drew attention to the
chords as things in themselves and not as moments of greater or less
repose in a flux of independent melodies. This was as valuable an
addition to musical thought and expression as the free use of abstract
terms is in literature, but it had precisely the same dangers, and has
until recent times vitiated harmonic theory and divorced it from the
modest observation of the practice of great masters. When, early in the
18th century, Rameau devoted much of his best energy to the elaboration
of a theory of harmony, his field of observation was a series of
experiments begun in chaos and resolved, not as yet in a great art, but
in a system of conventions, for the contemporary art of Bach and Handel
was beyond the scope of contemporary theory. He showed great analytical
genius and sense of tonality in his development of the notion of the
"fundamental bass," and it is rather to his credit than otherwise that
he did not emphasize the distinction between discords on the dominant
and those on other degrees of the scale. But his system, with all
subsequent improvements, refutations and repairs only led to that bane
of 19th-century theory and source of what may be called the journalese
of harmonic style, according to which every chord (no matter how
obviously artificial and transient) must be regarded, so to speak, as a
literal fact for which a root and a scientific connexion with the
natural harmonic series must at all cost be found. Some modern theorists
have, however, gone too far in denying the existence of harmonic roots
altogether, and certainly it is neither scientific nor artistic to
regard the coincidence of the major triad with the first five notes of
the harmonic series as merely accidental. It is not likely that the
dominant 7th owes all its naturalness to a resemblance to the flat 7th
of the harmonic series, which is too far out of tune even to pass for an
augmented 6th. But the dominant major 9th certainly gains in
sonorousness from its coincidence with the 9th harmonic, and many cases
in music could be found where the dominant 7th itself would gain from
being so far flattened as to add coincidence with a natural harmonic to
its musical significance as an unprepared discord (see, for example the
"native wood-notes wild" of the distant huntsmen in the second act of
_Tristan und Isolde_, where also the 9th and 11th are involved, and,
moreover, on horns, of which the natural scale is the harmonic series
itself). If the distinction between "essential" and "unessential"
discords is, in the light of history and common sense, a difference only
in degree, it is thus none the less of great aesthetic importance.
Arithmetic and acoustics show that in proportion as musical harmony
emphasizes combinations belonging to the lower region of the harmonic
series the effect will be sonorous and natural; but common sense,
history and aesthetics also show that the interaction of melody, harmony
and rhythm must produce a host of combinations which acoustics alone
cannot possibly explain. These facts are amply competent to explain
themselves. To describe them in detail is beyond the scope of the
present article, but a few examples from different periods are given at
the end in musical type.
IV. _The Minor Mode._--When the predecessors of Bach and Handel had
succeeded in establishing a key-system able to bear the weight of free
discord, that key-system took two forms, in both of which the three
chords of tonic, dominant and subdominant occupied cardinal points. In
the one form the tonic chord was natural, that is to say, major. In the
other form the tonic chord was artificial, that is to say, minor. In the
minor mode so firm is the position of the tonic and dominant (the
dominant chord always being major) that it is no longer necessary, as in
the 16th century, to conclude with a major chord, although it long
remained a frequent practice, rather because of the inherent beauty and
surprise of the effect than because of any mere survival of ancient
customs, at least where great masters are concerned. (This final major
chord is known as the _Tierce de Picardie_.) The effect of the minor
mode is thus normally plaintive because it centres round the artificial
concord instead of the natural; and, though the keynote bears this minor
artificial triad, the ear nevertheless has an expectation (which may be
intensified into a powerful emotional effect) that the final conclusion
of the harmonic scheme may brighten out into the more sonorous harmonic
system of major chords. Let us once more recall those ecclesiastical
modes of which the 3rd degree is normally minor. We have seen how they
may be regarded as the more oblique of the various cross-sections of the
16th-century harmonic scheme. Now, the modern minor mode is too firmly
rooted in its minor tonic chord for the 16th-century feeling of an
oblique harmonic scheme to be of more than secondary importance, though
that feeling survives, as the discussion of key-relationships will show
us. But it is constantly thrust into the background by the new
possibility that the minor tonic chord with its attendant minor
harmonies may give place to the major system round the same tonic, and
by the certainty that if any change is made at the conclusion of the
work it will be upon the same tonic and not have reference to some other
harmonic centre. In other words, a major and minor key on the same tonic
are felt as identical in everything but expression (a point in which the
Tonic Sol Fa system, as hitherto practised, with its identification of
the minor key with its "relative" instead of its tonic major, shows a
most unfortunate confusion of thought). The characteristics of the major
and minor modes may of course be modified by many artistic
considerations, and it would be as absurd to develop this account into a
scheme of pigeon-holed passions as to do the same for the equally
obvious and closely parallel fact that in drama a constant source of
pathos is the placing of our sympathies in an oblique relation to the
natural sequence of events or to the more universal issues of the
subject.
V. _Key-Relationships._--On the modern sense of the identity of the
tonic in major and minor rests the whole distinctive character of modern
harmony, and the whole key-system of the classical composers. The
masters of the 16th century naturally found it necessary to make full
closes much more frequently than would be desirable if the only possible
close was that on the final of the mode. They therefore formed closes on
other notes, but they formed them on these exactly as on a final. Thus,
a close on the second degree of the Ionian mode was identical with a
Dorian final close. The notes, other than the final, on which closes
could be made were called _modulations_. And what between the three
"regular modulations" (known as the dominant, mediant, and participant)
and the "conceded modulations," of which two were generally admitted in
each mode simply in the interests of variety, a composer was at liberty
to form a full close on any note which did not involve too many
extraneous sharps or flats for its correct accomplishment. But there was
a great difference between modal and modern conceptions of modulation.
We have said that the close on the second degree of the Ionian mode was
Dorian, but such a modulation was not regarded as a visit paid to the
Dorian mode, but merely as the formation of a momentary point of repose
on the second degree of the Ionian mode. When therefore it is said that
the modulations of 16th-century music are "purposeless and shifting,"
the criticism implies a purpose in change of key which is wholly
irrelevant. The modal composers' purpose lay in purely local
relationships of harmony, in various degrees of refinement which are
often crowded out of the larger and more coarse-grained scheme of modern
harmony, but which modern harmony is perfectly capable of employing in
precisely the same sense whenever it has leisure.
Modulation, in the modern sense of the term, is a different thing. The
modern sense of tonality is so firm, and modern designs so large, that
it is desirable that different portions of a composition should be
arranged round different harmonic centres or keys, and moreover that the
relation between these keys and the primary key should be felt, and the
whole design should at last return to the primary key, to remain there
with such emphasis and proportion as shall leave upon the mind the
impression that the whole is in the primary key and that the foreign
keys have been as artistically grouped around it as its own local
harmonies. The true principles on which keys are related proved so
elastic in the hands of Beethoven that their results utterly outstripped
the earlier theory which adhered desperately to the limitations of the
16th century; and so vast is the range of key which Beethoven is able to
organize in a convincing scheme of relationship, that even modern
theory, dazzled by the true harmonic possibilities, is apt to come to
the conclusion, more lame and impotent than any ancient pedantry, that
all keys are equally related. A vague conception, dubbed "the unity of
the chromatic scale," is thus made to explain away the whole beauty and
power of Wagner's no less than Beethoven's harmonic system. We have not
space to dispute the matter here, and it must suffice to state
dogmatically and statistically the classical facts of key-relationship,
including those which Beethoven established as normal possibilities on
the suggestion of Haydn, in whose works they appear as special effects.
a. _Direct Relationships._--The first principle on which two keys are
considered to be related is a strengthening of that which determined the
so-called modulations of the 16th-century modes. Two keys are directly
related when the tonic chord of the one is among the common chords of
the other. Thus, D minor is related to C major because the tonic chord
of D minor is the common chord on the supertonic of C (see Ex. 6). In
the same way the four other related keys to C major are E minor the
mediant, F major the subdominant, G major the dominant and A minor the
submediant.
[Illustration: Ex. 10.]
This last key-relationship is sometimes called the "relative" minor,
partly because it is usually expressed by the same key-signature as the
tonic, but probably more justifiably because it is the point of view
from which to reckon the key-relationships of the minor tonic. If we
take the minor scale in its "harmonic" form (i.e. the form deducible
from its chords of minor tonic, minor subdominant and major dominant,
without regard to the exigencies of melody in concession to which the
"melodic" minor scale raises the 6th in ascent and flattens the 7th in
descent), we shall find it impossible to build a common chord upon its
mediant (Ex. 10). But we have seen that A minor is related to C major;
therefore it is absurd to suppose that C major is not related to A
minor. Clearly then we must deduce some of the relationships of a minor
tonic as the converse of those of a major tonic. Thus we may read Ex. 6
backwards and reason as follows: A minor is the submediant of C major;
therefore C major is the mediant or relative major of A minor. D minor
is the supertonic of C major; therefore C major is related to D minor
and may be called its flat 7th. Taking A minor as our standard key, G
major is then the flat 7th to A minor. The remaining major keys (C major
to E minor = F major to A minor) may be traced directly as well as
conversely; and the subdominant, being minor, does not involve an appeal
to the major scale at all. But with the dominant we find the curious
fact that while the dominant _chord_ of a minor key is major it is
impossible to regard the major dominant _key_ as directly related to the
minor tonic, since it does not contain the minor tonic chord at all;
e.g. the only chord of A in E major is A major. But the dominant minor
key contains the tonic chord of the primary minor key clearly enough as
subdominant, and therefore when we modulate from a minor tonic to a
minor dominant we feel that we have a direct key-relationship and have
not lost touch with our tonic. Thus in the minor mode modulation to the
dominant key is, though frequent and necessary, a much more uphill
process than in the major mode, because the naturally major dominant
chord has first to be contradicted. On the other hand, a contrast
between minor tonic and major dominant key is very difficult to work on
a large scale (as, for example, in the complementary key for second
subjects of sonata movements) because, while the major dominant key
behaves as if not directly related to the minor tonic, it also gives a
curious sensation of being merely _on_ the dominant instead of _in_ it;
and thus we find that in the few classical examples of a dominant major
second subject in a minor sonata-movement the second subject either
relapses into the dominant minor, as in Beethoven's _Kreutzer Sonata_
and the finale of Brahms's _Third Symphony_, or begins in it, as in the
first movement of Brahms's _Fourth Symphony_.
The effect of a modulation to a related key obviously depends upon the
change of meaning in the chords common to both keys, and also in the new
chords introduced. Thus, in modulating to the dominant we invest the
brightest chord of our first key with the finality and importance of a
tonic; our original tonic chord becomes comparatively soft in its new
position as subdominant; and a new dominant chord arises, surpassing in
brilliance the old dominant (now tonic) as that surpassed the primary
tonic. Again, in modulating to the subdominant the softest chord of the
primary key becomes tonic, the old tonic is comparatively bright, and a
new and softer subdominant chord appears. We have seen the peculiarities
of modulation to the dominant from a minor tonic, and it follows from
them that modulation from a minor tonic to the subdominant involves the
beautiful effect of a momentary conversion of the primary tonic chord to
major, the poetic and often dramatically ironical power of which is
manifested at the conclusion of more than half the finest classical slow
movements in minor keys, from Bach's E[flat] minor Prelude in the first
book of the _Forty-eight_ to the slow movement of Brahms's _G major
String Quintet_, Op. 111.
The effect of the remaining key-relationships involves contrasts between
major and minor mode; but it is otherwise far less defined, since the
primary tonic chord does not occupy a cardinal position in the second
key. These key-relationships are most important from a minor tonic, as
the change from minor to major is more vivid than the reverse change.
The smoothest changes are those to "relative" minor, "relative" major (C
to A minor; C minor to E[flat]); and mediant minor and submediant major
(C to E minor; C minor to A[flat]). The change from major tonic to
supertonic minor is extremely natural on a small scale, i.e. within the
compass of a single melody, as may be seen in countless openings of
classical sonatas. But on a large scale the identity of primary dominant
with secondary subdominant confuses the harmonic perspective, and
accordingly in classical music the supertonic minor appears neither in
the second subjects of first movements nor as the key for middle
movements.[6] But since the key-relationships of a minor tonic are at
once more obscure harmonically and more vivid in contrast, we find that
the converse key-relationship of the flat 7th, though somewhat bold and
archaic in effect on a small scale, has once or twice been given organic
function on a large scale in classical movements of exceptionally
fantastic character, of which the three great examples are the ghostly
slow movement of Beethoven's _D major Trio, Op. 70_, No. 1, the scherzo
of his _Ninth Symphony_, and the finale of Brahms's _D minor Violin
Sonata_ (where, however, the C major theme soon passes permanently into
the more orthodox dominant minor).
Thus far we have the set of key-relationships universally recognized
since the major and minor modes were established, a relationship based
entirely on the place of the primary tonic chord in the second key. It
only remains for us to protest against the orthodox description of the
five related keys as being the "relative" minor or major and the
dominant and subdominant with their "relative" minors or majors; a
conception which expresses the fallacious assumption that keys which are
related to the same key are related to one another, and which thereby
implies that all keys are equally related and that classical composers
were fools. It cannot be too strongly insisted that there is no
foundation for key-relationship except through a tonic, and that it is
through the tonic that the most distant keys have always been connected
by every composer with a wide range of modulation, from Haydn to Brahms
and (with due allowance for the conditions of his musical drama) Wagner.
b. _Indirect Relationships._--So strong is the identity of the tonic
in major and minor mode that Haydn and Mozart had no scruple in
annexing, with certain reservations, the key-relationships of either as
an addition to those of the other. The smoothness of Mozart's style
makes him prefer to annex the key-relationships of the tonic minor (e.g.
C major to A[flat], the submediant of C minor), because the primary
tonic note is in the second key, although its chord is transformed. His
range of thought does not allow him to use these keys otherwise than
episodically; but he certainly does not treat them as chaotically remote
by confining them to rapid modulations in the development-portions of
his movements. They occur characteristically as beautiful purple patches
before or during his second subjects. Haydn, with his mastery of
rational paradox, takes every opportunity, in his later works, of using
all possible indirect key-relationships in the choice of key for slow
movements and for the trios of minuets. By using them thus sectionally
(i.e. so as not to involve the organic connecting links necessary for
the complementary keys of second subjects) he gives himself a free hand;
and he rather prefers those keys which are obtained by transforming the
minor relationships of a major primary key (e.g. C to A major instead of
A minor). These relationships are of great brilliance and also of some
remoteness of effect, since the primary tonic note, as well as its
chord, disappears entirely. Haydn also obtains extreme contrasts by
changing both modes (e.g. C minor to A major, as in the _G minor
Quartet, Op. 72_, No 6, where the slow movement is in E major), and
indeed there is not one key-contrast known to Beethoven and Brahms which
Haydn does not use with complete sense of its meaning, though his art
admits it only as a surprise.
Beethoven rationalized every step in the whole possible range of
key-relationship by such harmonic means as are described in the article
BEETHOVEN. Haydn's favourite key-relationships he used for the
complementary key in first movements; and he at once discovered that the
use of the major mediant as complementary key to a major tonic implied
at all events just as much suggestion of the submediant major in the
recapitulation as would not keep the latter half of the movement for too
long out of the tonic. The converse is not the case, and where Beethoven
uses the submediant major as complementary key in a major first movement
he does not subsequently introduce the still more remote and brilliant
mediant in the recapitulation. The function of the complementary key is
that of contrast and vividness, so that if the key is to be remote it is
as well that it should be brilliant rather than sombre; and accordingly
the easier key-relationships obtainable through transforming the tonic
into minor do not appear as complementary keys until Beethoven's latest
and most subtle works, as the _Quartet in B[flat], Op. 130_ (where we
again note that the flat submediant of the exposition is temporarily
answered by the flat mediant of the recapitulation).
c. _Artificial Key-relationships._--Early in the history of the minor
mode it was discovered that the lower tetrachord could be very
effectively and naturally altered so as to resemble the upper (thus
producing the scale C D[flat] E[natural] F, G A[flat] B[natural] C).
This produces a flat supertonic (the chord of which is generally
presented in its first inversion, and is known as the Neapolitan 6th,
from its characteristic use in the works of the Neapolitan school which
did so much to establish modern tonality) and its origin, as just
described, often impels it to resolve on a major tonic chord.
Consequently it exists in the minor mode as a phenomenon not much more
artificial than the mode itself; and although the keys it thus connects
are extremely remote, and the effect of their connexion very surprising,
the connexion is none the less real, whether from a major or a minor
tonic, and is a crucial test of a composer's sense of key-perspective.
Thus Philipp Emanuel Bach in a spirit of mere caprice puts the charming
little slow movement of his _D major Symphony_ into E[flat] and
obliterates all real relationship by chaotic operatic connecting links.
Haydn's greatest pianoforte sonata (which, being probably his last, is
of course No. 1 in most editions) is in E[flat], and its slow movement
is in F[natural] major (= F[flat]). That key had already appeared, with
surprising effect, in the wanderings of the development of the first
movement. No attempt is made to indicate its connexion with E[flat]; and
the finale begins in E[flat], but its first bar is unharmonized and
starts on the one note which most contradicts E[natural] and least
prepares the mind for E[flat]. The immediate repetition of the opening
phrase a step higher on the normal supertonic strikes the note which the
opening had contradicted, and thus shows its function in the main key
without in the least degree explaining away the paradoxical effect of
the key of the slow movement. Brahms's _Violoncello Sonata Op. 99_, is
in F; a prominent episode in the development of the first movement is in
E[sharp] minor (= G[flat]), thus preparing the mind for the slow
movement, which is in F[sharp] major (= G[flat]), with a central episode
in F minor. The scherzo is in F minor, and begins on the dominant. Thus
if we play its first chord immediately after the last chord of the slow
movement we have exactly that extreme position of flat supertonic
followed by dominant which is a favourite form of cadence in Wagner, who
can even convey its meaning by its mere bass without any harmonies
(_Walkure_, Act 3, Scene 2: "Was jetzt du bist, das sage dir selbst").
Converse harmonic relationships are, as we have seen, always weaker than
their direct forms. And thus the relation of C major to B major or minor
(as shown in the central episode of the slow movement just mentioned) is
rare. Still more rare is the obtaining of indirect artificial
relationships, of which the episode in the first movement just mentioned
is an illustration in so far as it enhances the effect of the slow
movement, but is inconclusive in so far as it is episodic. For with
remote key-relationships everything depends upon whether they are used
with what may be called cardinal function (like complementary keys) or
not. Even a near key may occur in the course of wandering modulations
without producing any effect of relationship at all, and this should
always be borne in mind whenever we accumulate statistics from classical
music.
d. _Contrary and Unconnected Keys._--There remain only two pairs of
keys that classical music has not brought into connexion, a circumstance
which has co-operated with the utter vagueness of orthodox theories on
the subject to confirm the conventionally progressive critic in his
conviction that all modulations are alike. We have seen how the effect
of modulation from major tonic to minor supertonic is, on a large scale,
obscured by the identity of the primary dominant with the secondary
subdominant, though the one chord is major and the other minor. Now when
the supertonic becomes major this difference no longer obviates the
confusion, and modulation from C major to D major, though extremely
easy, is of so bewildering effect that it is used by classical composers
only in moments of intensely dramatic surprise, as, for example, in the
recapitulation of the first subject of Beethoven's _Eroica Symphony_,
and the last variation (or coda) of the slow movement of his _Trio in
B[flat], Op. 97._ And in both cases the balance is restored by the
converse (and equally if not more contradictory) modulation between
major tonic and major flat 7th, though in the slow movement of the
_B[flat] Trio_ the latter is represented only by its dominant chord
which is "enharmonically" resolved into quite another key. The frequent
attempts made by easy-going innovators to treat these key-contrasts on
another footing than that of paradox, dramatic surprise or hesitation,
only show a deficient sense of tonality, which must also mean an
inability to see the intensely powerful effect of the true use of such
modulations in classical music, an effect which is entirely independent
of any ability to formulate a theory to explain it.[7] There now
remains only one pair of keys that have never been related, namely,
those that (whether major or minor) are at the distance of a tritone
4th. In the first place they are unrelated because there is no means of
putting any form of a tonic chord of F[sharp] into any form of the key
of C, or vice versa; and in the second place because it is impossible to
tell which of two precisely opposite keys the second key may be (e.g. we
have no means of knowing that a direct modulation from C to F[sharp] is
not from C to G[flat], which is exactly the same distance in the
opposite direction). And this brings us to the only remaining subjects
of importance in the science and art of harmony, namely, those of the
tempered scale, enharmonic ambiguity and just intonation. Before
proceeding we subjoin a table of all the key-relationships from major
and minor tonics, representing the degrees by capital Roman figures when
the second key is major and small figures when minor. Thus I represents
tonic major, iv represents subdominant minor, and so on. A flat or a
sharp after the figure indicates that the normal degree of the standard
scale has been lowered or raised a semitone, even when in any particular
pair of keys it would not be expressed by a flat or a sharp. Thus
vi[flat] would, from the tonic of B[flat] major, express the position of
the slow movement of Beethoven's _Sonata, Op. 106_, which is written in
F[sharp] minor since G[flat] minor is beyond the practical limits of
notation.