(tonal serialism)

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 note

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:

Fig. 215

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 page.)

The relative C major and A minor keys rest on the same notes and (as it appears from Fig. 216 on p. 114) have identical weight!

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 respectively; 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.

Fig. 216

the basic formula
of our chapter

The subject of our study will be Verdi’s Don 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 counterpart of 

Bb major 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 

Db major 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 minor:

Fig. 217

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 relationships between the keys. Let us take as an example a D minor triad, which has the following characteristics:

symmetrical counterpart (in our basic formula): G major
counterpole: Ab minor
relative major: F major
substitute key: Bb major
complementary (annihilating) key: F# major
parallel major (with the same name): D major
polar major key (with a difference of 6 accidentals): B major 
functional meaning:  subdominant
it is the modal dominant of  E, etc.

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 relations.

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 of Don Carlos, 1886 (Ricordi Edition, 1982). The tonic is C major.


C major: the center of the ’physical’ world, firm ground, the image of tangible reality, natural light (its condition of existence is musical ’space’). 
F# major: the center of the supernatural world (the Church), the basic key of spiritual existence: the temple of Religion, stability and immovability.

A minor: 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’).
Eb minor: 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).

C minor: dark passion, despair, emotional revolt, opposition to the existing world order.
F# minor: the forlorn hope of redemption, unrelievable and incurable heart-ache (e.g. the beginning of Act II).

A major: 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).
Eb major: humanity, benign sympathy and understanding (the reflection not of active life but of contemplation), intellectual and human dignity, spiritual wisdom, friendship.

G major: living force, vital impulse; desire for action, direct effect, often success.
Db major: ’fulfilment’ through love - or through redeeming death (without any connotation of direct action or militant deed).

E major: visible greatness and strength, predominance of will, heavy Royal splendour, external festive pomp (Auto-da-fé Scene).
Bb major: 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’.

G minor: failure in one’s vocation; setback, fiasco, defeat suffered in social life.
C# minor: ill fate caused by outside violence (e.g. violent death): Eboli’s fall, Posa’s funeral music, the breaking of Elisabeth’s resistance (Act V).

E minor: elevation: through physical weightlessness, bodilessness, the cessation of constraints (e.g. social constraints).
Bb minor: 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).

F major: 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.
B major: human worries, renunciation of the vanity of this world or resignation; the burden of bodily existence (e.g. the Cb major farewell duet).

D major: 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.
Ab major: heroism at the cost of self-sacrifice, hymnic unfolding.

F minor: inward brooding, self-doubts, inclination for self-torture: the predominance of psychical aspects.
B minor: 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).

D minor: annihilation - dead point: stemming from the absence of driving forces; deadly and unconscious dream (Filippo’s aria).
Ab minor: annihilation through ’burning’ - turbulence, riot and destructive instincts (cf. revolution scene).



C major: the primary experience of existence, the visible world (perceivable with the senses).
A minor: the elemental manifestation of passion.

Eb minor: longing for the unattainable, yearning for mystical experiences: ancient and heroic, distant and mysterious - like the ancient Tasso-songs.
F# major: faith as certainty: belief in God and spiritual existence.

G major: positive and immediate effect, the spontaneous (active) manifestation of will and consciousness.
D minor: passive quietude, inclination to melancholy, the silence of annihilation and destruction.

Ab minor: the overthrow of the existing world order: upheaval, revolution, destructive forces.
Db major: happiness (or even happy death), the ’art’ of ultimate love: emotional nobility and superiority.

F major: natural gravitation, intellectual depth or deep calm; often a shadow effect that reinforces a subsequent light-effect.
E minor: 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).

Bb minor: transcendental elevation, the ecstasy of the soul.
B major: the giving up of worldly thoughts - through renunciation.

C minor: blind passion, a feverish state: fanatic vehemence, challenge and burst of fury (see "L’ora fatale" preparing the finale of the Fontainebleau scene).
A major: elation, rapture, devotedness, intellectual elevation.

Eb major: spiritual harmony, goodwill and warmth, sympathy (sharing the worries of others), service for mankind.
F# minor: spiritual sorrow and anguish: heart-sore; an emotional state of suffering (even the weight of an anathema).

G minor: failure (ill-success), frustration, unfulfilled desires, defeat (conflict with the law or with social conventions).
D major: 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.

Ab major: 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).
C# minor: violence exerted upon others, falling victim to arbitrariness, tragedy inflicted by tyranny - deep mourning.

F minor: self-torment or qualms of conscience, introversion; pensiveness, endless worry, self-reproach.
E major: the external signs of Power: artificial light, pomp; energy and vitality (also in the form of an excessive test of strength).

Bb major: the magic of beauty (’external’ beauty), experience radiating happiness, festive cheerfulness, love of live.
B minor: 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.


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.

C major: static force; self-evident, popular naturalness.
C minor: rebellious defiance, furious temper, obsessed and vehement, uncontrollable and capable of anything.

G major: hope, life-force, self-consciousness; desire for action, success (the art of getting on).
G minor: humiliation, miscarriage, social disgrace (loss of honour, abasement, branding).

D major: victory over somebody: the rising above the commonplace, or the rising above the instincts.
D minor: passivity, the lack or total exhaustion of life forces, oblivion, the longing for a dream; fatigue caused by excessive burden.

A major: elevated spirits - where the voice has an ’impressionistic’ colouration.
A minor: passion or expressiveness - where the voice has an ’emotional’ quality.

E major: size and weightiness: the power of the masses, luxury, heavy pomp, spectacular ceremony, authority (massive, weighty forces).
E minor: incorporeal hovering, weightlessness, aerial quality (but also a ’raised’ and edged voice).

B major: the sphere of worldly concerns, self-surrender, passive acceptance of the unavoidable, reconciliation with destiny.
B minor: inappellable and severe power (higher authority) that cannot be shunned; in another form: the shackles of convention and court-manners.

F# major: the temple of everlasting life.
F# minor: the misery of earthly existence.

Db major: fulfilled desire - salvation.
C# minor: a broken existence (physical death and mourning).

Ab major: redemption - through self-denial: absolution.
Ab minor: perdition, burning out - by way of self-destruction; turbulence: rebellion against order.

Eb major: exalted thoughts: love and compassion with belief in mankind, friendly devotedness.
Eb minor: mystery, foreignness, longing to be elsewhere, loneliness.

Bb major: 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).
Bb minor: the appeal of the afterlife: irrational desires.

F major: well-deserved repose after a time of worries and troubles, profoundity of ideas and thoughts.
F minor: spiritual conflict and pensiveness, inner motivation.




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# minor: cheerfulness and sorrow (the glitter and the bitterness of courtly life).

A major and C# minor: sensual attraction and its breaking down (e.g. Posa’s personal charms and his fall).

E major and Ab minor: greatness and decay; domination and revolution.

B major and Eb minor: earthly and heavenly philosophy; the renunciation of mundane desires and the magic of faith.

F# major 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).

Db major and F minor: redemption and remorse; sensual satisfaction and masochistic tendencies.

Ab major and C minor: the hymnic and the angry word; constructive and destructive instincts.

Eb major and G minor: dignity and indignity, human warmth and a state of being outcast.

Bb major 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 of emotions.




C major and Ab minor: existence and non-existence.

G major and Eb minor: sense of reality and imagination; self-consciousness and intuition; physical well-being and the longing for the hereafter.

D major and Bb minor: 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.

F# major and D minor: the eternal order of theology and the longing for non-existence.

Db major and A minor: passive release (looseness) and active reaction; emotional elevation and passion.

Ab major and E minor: awareness of one’s vocation and intoxication: controlled and uncontrolled action (may also be the contrast between devotion and revenge).

Eb major and B minor: man-centered and fate-centered world; the opposition between the personal and the impersonal (humanity and inhumanity).

Bb major and  F# minor: poetry of glaring light and of the night; happiness and death-wish.

F major and  C# minor: profoundity of thoughts and senseless violence.



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 principle)

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 how

E major became the symbol of Power,
Bb major the symbol of Beauty,
G major the symbol of Life force,
Db major 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:

Ab major represents self-sacrifice,
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,
Ab minor is the key of annihilating turbulence,
B minor is the key of defenselessness,
F minor is the key of doubt.



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 keys 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).


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.


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 majorDb major 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 in Db major; but at the moment of unmasking, we immediately return to Bb major!


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:

Fig. 218

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):

C major and F minor: the empirical and the psychical world (C-center).
G major and C minor: affirmation and denial (G-center).
D major and G minor: bright cheerfulness and dark passion (D-center).
A major and D minor: wakefulness and sleep.
E major and A minor: impersonal greatness and personal feeling.
B major and E minor: immobility and desire to act.
F# major and B minor: spiritual haven of refuge and blind fate.
Db major and F# minor: fulfilment and longing (Db = C# center).
Ab major and C# minor: unfolding and failure (Ab = G# center).
Eb major and Ab minor: constructive (humane) and destructive forces.
Bb major and Eb minor: sense of beauty and sadness.
F major and Bb minor: low and high