THE ETHOS OF THE
Comparisons are, by their very nature,
delusive. Still, I would like to venture the following — comparative —
statement: classical harmony is to modal harmony what a geocentric world
concept is to a heliocentric one. Let us arrange the tone set of the Jupiter
Symphony in a circle of fifths. In a traditional representation, the
tonic – C – will be placed at the top of the fifth-circle, in the center
of symmetry of the system.
However, earlier we came to the conclusion
and one glance at a piano keyboard (with the white and black keys) will
make us understand that the axis of symmetry of the C major scale
is not C... but D (or Ab),
in relation to which every note of the C major scale has a symmetrical
counterpart both upward and down. Of course, C major, with its zero key
signature, occupies a special place in our system of musical notation.
Moreover, as we can see on the second diagram below, F major with 1 flat
and E minor with 1 sharp (or B major with 5 sharps and Bb
minor with 5 flats ) are symmetrical opposites in relation to a D center
Wouldn’t it be more appropriate, in a
depiction of the circle of fifths, to place the D at the top of the system
and the Ab at the bottom?
We would thus illustrate the actual relationship between the notes:
Now let us replace the preceding fifths
with their corresponding keys. In the upper half of the circle,
the chords F major and D minor, as well as G major and E minor belong to
the scale of C major (or A minor). Similarly, the chords Db
major and Bb minor, as well
as B major and Ab (G#)
minor all belong to the Gb
(F#) major and Eb
minor scales in the lower half of the circle. (See on next
The relative C major and A minor keys
rest on the same notes and (as it appears from Fig. 216
on p. 114) have
The symmetry thus obtained remains flawless
even when the major triads are replaced by their parallel minor triads,
and vice versa (for example, D minor and G major by D major and G minor
D major and G minor will still occupy
symmetrical positions in relation to the D center). The above figure will
henceforth be referred to as the basic formula of our system.
the basic formula
of our chapter
The subject of our study will be Verdi’s
Carlos (we must be satisfied with a sketchy summary only, as a detailed
analysis would require a separate volume).
According to our basic formula the symmetrical
is B minor.
Is it not striking that the opera begins
in Bb major — with 2 flats,
and ends in B minor — with 2 sharps? Or, why is it that in the nocturnal
garden scene the settling effect of the F major terzett is followed
by Eboli’s E minor revenge-aria? And why is the effect so convincing?
As has been seen,
F major’s mirror is E minor.
The dramatic turning-point of the dialogue
between Posa and Filippo: Filippo’s confession in F minor, is likewise
preceded by an E major play with ’colours’. The thought of Carlos’
’salvation’ in Ab major
(Eboli’s aria) and Carlos’ ’fall’ in C# minor
display a similar relationship (see our basic formula). Following Posa’s
Db major farewell,
the revolution breaks out — strikingly enough — in Ab
minor: in this system the counterpart of
is Ab minor.
The clue to this tonal riddle comes from
Verdi himself (he places, so to speak, the clue into our hands). The KEY-SENTENCE
is sung by the ’Monk’ (whose disguise of anonymity conceals Charles V bound
for the monastery). The first half of this sentence is about ’world cares’,
the second half about ’heavenly consolation’. The Cb
major tonality representing earthly concerns is
contrasted with the Bb minor
tonality denoting heavenly affairs. The mirror image of Cb
major is (as can be seen in our basic formula) Bb
Incidentally, it was Verdi in his late
works who brought this system to the highest perfection. If we were to
classify (to ’catalogue’) the scales and themes of Don Carlos, we
would discover not only the special meaning of each key, but also the multidimensional
between the keys. Let us take as an example a D minor triad, which has
the following characteristics:
|symmetrical counterpart (in our basic formula):
|complementary (annihilating) key:
|parallel major (with the same name):
|polar major key (with a difference of 6 accidentals):
|it is the modal dominant of
Therefore, the meaning of a chord changes
according to its relation with another harmony. In the case of counterpoles,
a difference of plus 6 = minus 6 key signatures equalize, compensate one
another — thus, these necessarily imply the existence of common traits.
The upper and lower halves (or left and right halves) of our basic formula
also conceal surprising symbols.
Each of the tables below represents a
specific tonal relation and, more important still, one of ’content’. Any
one of the 24 keys can form 23 direct relations with the rest of the possible
keys. Moreover, one is also led to realize that second- and third-degree
relations perforce produce identical results — indeed, they
even reinforce each other! In other terms, should we only know the ’meaning’
of 23 keys, we could deduct the meaning of the unknown 24th key from these
Hence it follows that the system holds
true only if every dimension is verified and confirmed by the work’s dramaturgical
content or poetical meaning. Our ’serial’ study — our musical ’Rubik cube’
— as it appears in the tabulation below, is based on the five-act version
Don Carlos, 1886 (Ricordi Edition, 1982). The tonic is C major.
||the center of the ’physical’ world, firm ground, the
image of tangible reality, natural light (its condition of existence is
||the center of the supernatural world (the Church), the
basic key of spiritual existence: the temple of Religion, stability and
||the basic formula for ’expression’, it has an emotional
charge (its dynamics and tension is most often created by the course of
music in ’time’).
||the conveyor of mystical experiences, frequently expressing
the loneliness caused by remoteness (religiosity cherishing feelings and
illusions): yearning for eternity, longing to get away to another world
(as Carlos’ appearance in the Court Scene in Act II).
||dark passion, despair, emotional revolt, opposition to
the existing world order.
||the forlorn hope of redemption, unrelievable and incurable
heart-ache (e.g. the beginning of Act II).
||serenity - caused by the ’senses’ (good taste, love of
beauty, acceptance of all that is good and noble), enthusiasm: the delusion
of the Veil Song (’the eye winks through the veil on the face of beautiful
ladies’), just as Posa’s sensual manoeuvre (his A major romance in the
Court Scene of Act II).
||humanity, benign sympathy and understanding (the reflection
not of active life but of contemplation), intellectual and human dignity,
spiritual wisdom, friendship.
||living force, vital impulse; desire for action, direct
effect, often success.
||’fulfilment’ through love - or through redeeming death
(without any connotation of direct action or militant deed).
||visible greatness and strength, predominance of will,
heavy Royal splendour, external festive pomp (Auto-da-fé Scene).
||if E major is the image of strength, Bb
major is that of beauty (occasionally, glitter of mundane finery which
adheres to external beauty and stems from the senses), attractiveness caused
by direct ’impression’.
||failure in one’s vocation; setback, fiasco, defeat suffered
in social life.
||ill fate caused by outside violence (e.g. violent death):
Eboli’s fall, Posa’s funeral music, the breaking of Elisabeth’s resistance
||elevation: through physical weightlessness, bodilessness,
the cessation of constraints (e.g. social constraints).
||active elevation: through a transcendental (religious)
experience; some-times sacred anger: a sense of calling (with signs of
aggressiveness in the case of the Grand Inquisitor).
||shadow effect produced by an active force (the dark colour
appears in the form of an effective and shaping force), it may also be
the image of hard-won calm.
||human worries, renunciation of the vanity of this world
or resignation; the burden of bodily existence (e.g. the Cb
major farewell duet).
||a result achieved by volitional factors (in spite of
something), or an advantage obtained through rank (birth, privilege, cleverness,
skil-fulness); courtly manners belong here as well.
||heroism at the cost of self-sacrifice, hymnic unfolding.
||inward brooding, self-doubts, inclination for self-torture:
the predominance of psychical aspects.
||events determined not by human intervention but by ’destiny’
and law; unavoidable and unimpressionable - fateful - events (in a milder
form: the fixed order of courtly etiquette).
||annihilation - dead point: stemming from the absence
of driving forces; deadly and unconscious dream (Filippo’s aria).
||annihilation through ’burning’ - turbulence, riot and
destructive instincts (cf. revolution scene).
THE SYMMETRICAL CORRESPONDENCES OF
||the primary experience of existence, the visible world
(perceivable with the senses).
||the elemental manifestation of passion.
||longing for the unattainable, yearning for mystical experiences:
ancient and heroic, distant and mysterious - like the ancient Tasso-songs.
||faith as certainty: belief in God and spiritual existence.
||positive and immediate effect, the spontaneous (active)
manifestation of will and consciousness.
||passive quietude, inclination to melancholy, the silence
of annihilation and destruction.
||the overthrow of the existing world order: upheaval,
revolution, destructive forces.
||happiness (or even happy death), the ’art’ of ultimate
love: emotional nobility and superiority.
||natural gravitation, intellectual depth or deep calm;
often a shadow effect that reinforces a subsequent light-effect.
||physical weightlessness - or flight from reality (the
latter will be found in the form of spiritual drunkenness as well, as in
Eboli’s vow for revenge in the garden scene).
||transcendental elevation, the ecstasy of the soul.
||the giving up of worldly thoughts - through renunciation.
||blind passion, a feverish state: fanatic vehemence, challenge
and burst of fury (see "L’ora fatale" preparing the finale of the Fontainebleau
||elation, rapture, devotedness, intellectual elevation.
||spiritual harmony, goodwill and warmth, sympathy (sharing
the worries of others), service for mankind.
||spiritual sorrow and anguish: heart-sore; an emotional
state of suffering (even the weight of an anathema).
||failure (ill-success), frustration, unfulfilled desires,
defeat (conflict with the law or with social conventions).
||meeting with success (e.g. a successful appearance at
court), advance-ment and good fortune in social life; triumph over one’s
self or over others.
||an unselfish act, sacrifice raised to a ritual degree:
the peremptory call of humanism - which one must even be willing to die
for (see the Peace Song in the Auto-da-fé Scene).
||violence exerted upon others, falling victim to arbitrariness,
tragedy inflicted by tyranny - deep mourning.
||self-torment or qualms of conscience, introversion; pensiveness,
endless worry, self-reproach.
||the external signs of Power: artificial light, pomp;
energy and vitality (also in the form of an excessive test of strength).
||the magic of beauty (’external’ beauty), experience radiating
happiness, festive cheerfulness, love of live.
||a climate of tragedy: the constraining force of a coercive
external power, predestination: as ’written in the stars’; inescapable
destiny or strictly regulated order (e.g. the strict rules of etiquette).
Actually, our traditional method of notation
also reflects the above principles (see the basic formula). Those keys
in which the number of sharps and flats is identical occupy a symmetrical
position in the system.
RELATIONS BETWEEN PARALLEL KEYS
In the case of parallel major and minor keys one of the
two keys always belongs to a family of ’natural’ keys, and the other to
one of ’modified’ keys. C major, for example, differs from C minor in that
the natural DO-MI-SO chord is altered to DO-MA-SO.
||static force; self-evident, popular naturalness.
||rebellious defiance, furious temper, obsessed and vehement,
uncontrollable and capable of anything.
||hope, life-force, self-consciousness; desire for action,
success (the art of getting on).
||humiliation, miscarriage, social disgrace (loss of honour,
||victory over somebody: the rising above the commonplace,
or the rising above the instincts.
||passivity, the lack or total exhaustion of life forces,
oblivion, the longing for a dream; fatigue caused by excessive burden.
||elevated spirits - where the voice has an ’impressionistic’
||passion or expressiveness - where the voice has an ’emotional’
||size and weightiness: the power of the masses, luxury,
heavy pomp, spectacular ceremony, authority (massive, weighty forces).
||incorporeal hovering, weightlessness, aerial quality
(but also a ’raised’ and edged voice).
||the sphere of worldly concerns, self-surrender, passive
acceptance of the unavoidable, reconciliation with destiny.
||inappellable and severe power (higher authority) that
cannot be shunned; in another form: the shackles of convention and court-manners.
||the temple of everlasting life.
||the misery of earthly existence.
||fulfilled desire - salvation.
||a broken existence (physical death and mourning).
||redemption - through self-denial: absolution.
||perdition, burning out - by way of self-destruction;
turbulence: rebellion against order.
||exalted thoughts: love and compassion with belief in
mankind, friendly devotedness.
||mystery, foreignness, longing to be elsewhere, loneliness.
||alluring power, force of attraction (as a vehicle of
a refined outward appearance); vain beauty or loveliness that arouses desire;
the joy of feast and celebration (cf. the Royal Hunt).
||the appeal of the afterlife: irrational desires.
||well-deserved repose after a time of worries and troubles,
profoundity of ideas and thoughts.
||spiritual conflict and pensiveness, inner motivation.
RELATIONS IN CONTENT BETWEEN SUBSTITUTE
|C major and E minor:
||materiality and immateriality (often in the form of ’spiritual
drunkenness’ as well).
|G major and B minor:
||the Beginning and the End: openness and restriction -
the latter exposed to fate or courtly etiquette. (Awakening to consciousness
and tragic end.)
|D major and F#
||cheerfulness and sorrow (the glitter and the bitterness
of courtly life).
|A major and C#
||sensual attraction and its breaking down (e.g. Posa’s
personal charms and his fall).
|E major and Ab
||greatness and decay; domination and revolution.
|B major and Eb
||earthly and heavenly philosophy; the renunciation of
mundane desires and the magic of faith.
and Bb minor:
||static tranquility and high aspirations (in an extreme
case a militant sense of calling, as in the scene of the Grand Inquisitor).
and F minor:
||redemption and remorse; sensual satisfaction and masochistic
and C minor:
||the hymnic and the angry word; constructive and destructive
and G minor:
||dignity and indignity, human warmth and a state of being
and D minor:
||impression and expression; physical beauty and spiritual
agony; love of life and depression.
|F major and A minor:
||profoundity of ideas and spontaneous passion; the dark
and light side of the soul; gravitation caused by seriousness and the rising
RELATIONS IN CONTENT BETWEEN COMPLEMENTARY
|C major and Ab
||existence and non-existence.
|G major and Eb
||sense of reality and imagination; self-consciousness
and intuition; physical well-being and the longing for the hereafter.
|D major and Bb
||persistent attachment to life and sacred sense of calling;
this-worldly and other-worldly language (may figure as the contrast between
courtly lustre and the ’sacred wrath’).
|A major and F minor:
||confidence and doubt; external serenity and inner conflict.
|E major and C minor:
||power and the challenge of power.
|B major and G minor:
||resignation and excitement.
and D minor:
||the eternal order of theology and the longing for non-existence.
and A minor:
||passive release (looseness) and active reaction; emotional
elevation and passion.
and E minor:
||awareness of one’s vocation and intoxication: controlled
and uncontrolled action (may also be the contrast between devotion and
and B minor:
||man-centered and fate-centered world; the opposition
between the personal and the impersonal (humanity and inhumanity).
and F# minor:
||poetry of glaring light and of the night; happiness and
|F major and C#
||profoundity of thoughts and senseless violence.
POLAR MAJOR AND MINOR CHORDS
The major and minor keys displaying a difference of 6
accidentals reflect the same contrast, in terms of content, as the pole–counterpole
relations. These correspondences may be found in our first tabulation —
if the connections below are considered:
TONIC chords reflect static motionlessness. This applies
not only to the tonal pillars of C major (and A minor), or F#
major (and Eb minor), but
to the variations of these as well:
|the positive A major and Eb
major (of LA- DI- MI principle) and
|the negative C minor and F# minor (of DO-MA-SO
are also characterized by the fact that they cannot be
further developed — there is no way out of them.
DOMINANT keys differ from tonic ones by the ’active’ force
they exert (complying with the principles of the axis system). This is
|E major became the symbol of Power,
the symbol of Beauty,
|G major the symbol of Life force,
the symbol of Happiness.
The dominant minor chords can engender a rise, like the
E minor and Bb minor keys,
but a violent and tragic turn as well, like C# minor and G minor.
SUBDOMINANT chords function in a similar manner:
|D major represents nobleness and dignity,
|F major represents calm and seriousness,
|B major represents spiritual peace.
The minor subdominant chords are distinguished
by their passivity:
|D minor is the key of sleep and nonexistence,
is the key of annihilating turbulence,
|B minor is the key of defenselessness,
|F minor is the key of doubt.
NATURAL AND MODIFIED KEYS
The upper half of our basic formula (p.
114) makes up the diatonic scale (7-degree scale). The diatonic scale
contains six perfect triads:
|C major and A minor have a zero key signature,
|G major and E minor have one sharp,
|F major and D minor have one flat.
This is to say:
|the ’highest’ minor : E minor and
|the ’lowest’ major: F major
are in fact
|the positive substitute chord of the C major tonic,
|the negative substitute chord of the A minor tonic.
All of the above applies to the lower half of our basic
formula as well (in which case F#=DO).
If we change the ’gender’ of the keys, that is, if we
substitute a minor key for its parallel major and a major key for its parallel
minor, we may note that all ’natural’ thoughts correspond to unmodified
and ’stimulated’ emotional states to modified ones.
Even in Eboli’s revenge melody, E minor is associated
with ’natural’ (i.e. instinctive) emotions — while E major radiates an
’artificial’, intensified light (Auto-da-fé Scene). In the
same way, Ab minor denotes
self-destruction, but Ab major
suggest a heroic sacrifice at the cost of one’s own life (as in the finale
of Eboli’s aria or in the Peace Song of the Auto-da-fé Scene).
UPPER AND LOWER SPHERES
The system is ’closed’. The upper and lower halves of
our basic formula are mirror reflections of one another. This means that,
for instance, F# minor is dialectically related
not only to F# major — but to the C major tonic as well.
In the first case we perceive it as a DO-MA-SO chord, expressing ’despair’
— as in Elisabeth’s heart-rending lament ("Ben lo sapete...") after the
chest has been forced open. But in relation to the C major tonic, ’F#
minor’ represents the most immaterial harmony to be found in Verdi’s music:
that is why we sense the FI-LA-DI formula — Elisabeth’s F# minor
melody — as being so "immacolata" (as indicated in the libretto).
Symbolically speaking, the upper and the lower halves
of our basic formula relate to each other as the empirical Aristotelian
world to the Platonic one — to the world of Ideas.
THE POTENTIALITIES OF THE AXIS SYSTEM
A similar ’dictionary’ may be compiled from the relations
between relative major and minor keys — or what is even more fascinating,
those between axis-related major or minor keys. Let us cite only
one example here.
The cheerful Bb
major of the Royal Hunt in Act I is transformed into Db
major: into a love-scene. (If Bb
major is a DO-MI-SO tonic, then the Db
major must be interpreted as MA major!) — In Act II, too, the finest
moments of the Carlos—Elisabeth duet are marked by a Bb
turn. In the nocturnal garden scene it is just the opposite what happens:
Carlos and Eboli – hidden behind masks – declare their ’love’ to each other
but at the moment of unmasking, we immediately return to
According to the classical definition, the major triad
consists of the 3 closest overtones of a basic note — while the minor triad
is made up of the 3 closest basic notes of a common overtone:
This alone helps us understand why C
major represents the external (visible) world and F minor the
internal (invisible) one. Using the above principle as a new basis, we
may discover a new dimension of our tonal system (which also corresponds
to the ’Western’ and ’Eastern’ ways of thinking):
||major and F
||the empirical and the psychical world (C-center).
||major and C
||affirmation and denial (G-center).
||major and G
||bright cheerfulness and dark passion (D-center).
||major and D
||wakefulness and sleep.
||major and A
||impersonal greatness and personal feeling.
||major and E
||immobility and desire to act.
||major and B
||spiritual haven of refuge and blind fate.
||major and F#
||fulfilment and longing (Db
= C# center).
||major and C#
||unfolding and failure (Ab
= G# center).
||major and Ab
||constructive (humane) and destructive forces.
||major and Eb
||sense of beauty and sadness.
||major and Bb
||low and high