Perhaps the cruelest remark ever made about Berlioz came from Mendelssohn, who said that what was so Philistine about Berlioz was that “with all his efforts to go stark mad he never once succeeds.” Donald Francis Tovey, who quotes this in his essay on Berlioz’s Harold in Italy,1 comments that “from its own standpoint the criticism was neither unfriendly nor untrue.” (I feel sure that Berlioz would have found it unfriendly.) Mendelssohn, in fact, liked Berlioz personally. He considered the music “indifferent drivel, mere grunting, shouting and screaming back and forth,” but thought the composer himself a “friendly, quiet, meditative person” with an acute critical sense for everything except his own work, and he was depressed by the contrast.2
Mendelssohn wrote in 1831. Years of the kind of misunderstanding revealed in his comments must have eroded Berlioz’s friendly good nature. More than fifty years later Verdi wrote:
Berlioz was a poor, sick man who raged at everyone. He was greatly and subtly gifted. He had a real feeling for instrumentation, anticipated Wagner in many instrumental effects. (The Wagnerians won’t admit it, but it is true.) He had no moderation. He lacked the calm and what I may call the balance that produce complete works of art. He always went to extremes, even when he was doing admirable things.3
With all its recognition of Berlioz’s genius, this is disingenuous and ungracious, particularly in the way Verdi insists on Berlioz’s influence on Wagner without acknowledging his own debt, which was enormous, and not solely in the realm of instrumentation.4
Mendelssohn’s gibes show that Berlioz’s contemporaries were already aware how much of his romantic madness was only skin deep although he fought passionately for the cause of romanticism. He took up arms for Shakespeare, for Goethe’s Faust, Oriental exoticism, program music, the Swiss mountains with the lonely sound of shepherd’s pipes, the Gothic macabre, the projection of the ego in the work of art, as well as the artist as inspired lunatic—all the commonplace, intellectual bric-a-brac of the period, in fact. Berlioz’s eccentricities impressed almost everyone, as he hoped and expected, but it has taken more than a century to realize that it is not Berlioz’s oddity but his normalcy, his ordinariness that made him great.
In this he differed from a composer like Schumann, whose genius was tied to a profoundly eccentric sense of form and of polyphony. In spite of Schumann’s obstinate aspiration to aesthetic respectability through his symphonies, quartets, and sonatas, his short, fragmentary piano pieces and songs remain his most enduring achievement. Berlioz’s greatest work, most critics would now argue, is The Trojans, an opera on the most classical of all subjects and the most academic: Virgil’s Aeneid. Like Delacroix’s mural decorations for the National Assembly, Berlioz’s finest opera reconciles avant-grade technique with academic ideals. The Trojans is the musical equivalent of the grandes machines that the so-called pompiers displayed at the mid-century salons—a pretentious historical costume drama, life-size and imperturbably earnest. It is the only French grand opera since the works of Cherubini, Berlioz’s hated master, to be untouched by cheap melodrama and to attain the genuine seriousness of the high academic style.
In order to achieve this more conventional seriousness, Berlioz renounced some of his audacity. A comparison of the love music of the earlier Roméo et Juliette with the love duet in Act IV of The Trojans, “O nuit d’ivresse,” shows the later work, beautiful as it is, to be much closer to the music of Gounod (who did, indeed, admire this particular number). In The Musical Language of Berlioz, Julian Rushton writes:
Berlioz remarked of the love-duet in Act IV that the music “settled on this scene like a bird on ripe fruit,” yet it took him sixteen pages of sketches to get it right. If it seemed easy in retrospect it must have been because he enjoyed every moment of rigorous self-criticism.
Rushton is too kind. It is more probable that Berlioz was simply lying, as he often did about these matters. He wrote in his memoirs, for example, that he composed the fourth movement of the Fantastic Symphony in one night—and no doubt he did, as he merely copied it out from a work written a few years before, Les Francs-juges.
Criticism of Berlioz generally reveals a perfidy as insidious as the remarks of Mendelssohn. Debussy’s few allusions to Berlioz are typical in their ambiguity: “One can even say without irony that Berlioz was always the favorite musician of those who do not know much about music…. Professionals are still horrified at his harmonic liberties (they even would say his ‘clumsiness’) and the negligence of his form”;5 “Berlioz is an exception, a monster. He is not at all a musician; he gives the illusion of music with procedures borrowed from literature and painting.”6 It is possible but awkward to reconcile this with Debussy’s claim to venerate Berlioz, and his description of the Fantastic Symphony as “a feverish masterpiece of romantic ardor…, moving as a battle of the elements.”
These contradictions remain basic to the modern conception of Berlioz. There are, of course, the Berlioz idolaters, still in a minority, who hold passionately that he could do no wrong and that any other view is fed either by malice or a willful refusal to listen correctly. For other musicians, Berlioz remains a puzzling figure. The belief in the clumsiness of his harmony, the naiveté of his counterpoint, and the negligence of his forms has not been dissipated. Few contest his greatness: what is in question is his competence.
This is very odd: it is hard to see how Berlioz can be as great as we all believe him to be if he is as incompetent as so many think. Rushton deals with this problem head on. He may be counted as a Berlioz idolater, but a rational one; he does not dismiss the objections as simple misunderstandings, but attempts to account for them, while showing them to be fundamentally irrelevant by his analysis of Berlioz’s style. Along with the brilliant articles of 1971–1972 by Edward T. Cone in the regrettably short-lived Musical Newsletter, he has written the best and most persuasive justification of Berlioz’s work I have read.
The opposition to Berlioz in our time is a very powerful one and includes Boulez (“There are awkward harmonies in Berlioz that make one scream”) and Stravinsky (“Berlioz’s reputation as an orchestrator has always seemed highly suspect to me”). They do not deny his importance, but their objections are not simple to deal with. An easy answer, quoted by Rushton along with the above attacks, is provided by a letter of 1886 from Emmanuel Chabrier, the French composer most openly indebted to Berlioz:
Berlioz, a Frenchman above all (he wasn’t old-hat in his time) put variety, color, rhythm into La Damnation, Roméo, and L’Enfance du Christ—there isn’t any unity, people say—and I answer, Shit!
This is a possible approach to the Berlioz problem, and ultimately, I suppose, a practical one. It has the merit of recommending an immediate and workable course of action: the dismissal of all adverse criticism, and an enjoyment of the music for its evident merits, however these are to be defined.
The road taken by Rushton is a more arduous one: that of close, detailed technical analysis. It also can seem a more dubious road. In an otherwise favorable review of Rushton’s book, fellow idolater Hugh MacDonald writes pessimistically:
Thorough examination of every note in a score is inevitably the only way to study a work properly, but the conclusions are invariably the same as those with which one started out. Rushton digs endless pits for himself, with many tables extracting parametric readings (superbly printed) and the inevitable Schenkerian diagrams, but steps deftly across them by telling us what he knew all along, namely that Berlioz does not do what Bach or Mendelssohn would have done, though of course occasionally, indeed often, he does. The real intuitive processes in Berlioz’s mind remain remote, and presumably they always will if such comprehensive treatment as this does not uncover them.
The musical analyst can observe but he is impotent to explain or to judge.7
A telltale phrase here, “the inevitable Schenkerian diagrams,” betrays Mac-Donald: his conclusions will indeed invariably be the same as those with which he started out. MacDonald’s obscurantism, the belief that “the real intuitive processes in Berlioz’s mind remain remote, and presumably…always will,” arises from a misunderstanding of the nature of analysis—and by the suspect ontology of “the real [why real?] intuitive processes.” Insofar as Berlioz’s intuitive processes are embodied and expressed in the music, are active in the work, analysis will uncover them and make them less remote. All the finest Berlioz criticism, from Robert Schumann’s great essay on the Fantastic Symphony up to Cone and Rushton, has laid bare these forces before our eyes. Of course, if intuitive processes are essentially unknowable or “real,” that is, not a part of musical experience, analysis will not help us.
Analysis cannot, indeed, judge—although some analysts, including the greatest, like Schenker, feel that they have found a system of analysis which could do just this (a work that does not fit the system is automatically vicious). However, it provides the necessary material for judgment; by definition, it does not produce a synthesis. We might say that the proper synthesis of a “thorough examination of every note in a score” is either a performance or an act of listening. Like Alexis de Tocqueville before he set out to discover democracy in America, the analyst sets out knowing in advance what he wants to prove, and his analysis is determined by his thesis—but that does not mean that the thesis is not also transformed by his voyage, sometimes subtly, sometimes very radically indeed. This alteration in the initial thesis is the highest demand that one can make of analysis—not to make us change our minds by demonstration, but, by illumination, to change the nature and character of what we thought we knew.
Rushton is able to explode most of the critical commonplaces about Berlioz, while suggesting how they came into being. Berlioz’s alleged inability to write correct counterpoint is the easiest to dispose of. It is clear that, early in his career, he was a master of what is not after all a very difficult craft. Rushton perceptively observes that the strictness of the fugue in the last movement of the Fantastic Symphony is ironic: it must have appealed to the composer’s grim humor to portray a witches’ Sabbath by an absolutely correct academic fugue. Much of Berlioz’s polyphony, however, escapes from classical standards through his imaginative use of rhythm. His exploration of what he called intermittent sounds is an example. These are individual “sounds independent of the principal melody and of the accompanimental rhythm and separated from each other at expanding or contracting distances in proportions impossible to predict”—to quote Berlioz’s own description. (Rushton gives a beautiful example of this in the septet from The Trojans.) This technique of intermittent sounds not only cannot be subjected to laws of classical counterpoint, but is clearly developed against them. It also demands a basic classical texture on which the intermittent sounds are superimposed in order to realize their full effect. It is this double requirement of a classical system and an anticlassical subversion of it that makes it so hard to generalize about Berlioz’s achievement.
The strategy of Rushton’s book is relatively simple, although he employs it often with great subtlety. He subjects Berlioz’s music with more or less rigor to the kinds of analysis that have proven themselves most efficient with the German classical tradition from Bach to Schönberg (including Chopin, whom Schenker claimed as an honorary German); he marks the ways in which these analytical procedures fail to deal with Berlioz, or the ways in which the music fails to live up to classical expectations, and then he displays the extraordinary variety of musical ideas that appear in Berlioz’s work, hold the listener’s interest and make the apparent failure unimportant. This has been the basic tactic of the best Berlioz criticism, starting with Schumann’s famous essay of 1835. (It is curious, however, that the best criticism of Berlioz is always defensive.) Rushton himself sums up this approach:
It is true that Berlioz often does not reduce down to a cleanly classical Satz.8 This does not, however, invalidate reductive analysis, which reveals the positive as well as the negative qualities of the music. Such analysis even suggests why, from one point of view—a perfectly legitimate one—Berlioz’s music is curiously unsatisfying. But it has qualities which prevent dissatisfaction from modulating to boredom or disgust and which, rather, increase the appetite to experience each work again.
The one criticism of Berlioz that Rushton does not fully appreciate was made by Chopin, and is quoted from Delacroix’s diary of April 7, 1849.
[In Mozart]: Each of the parts has its own movement, which, while still according with the others, keeps on with its own melody and follows it perfectly; there is your counterpoint…. He [Chopin] told me that the custom now is to learn the harmonies before coming to counterpoint, that is to say, the succession of notes which lead to the harmonies. The harmonies of Berlioz are overlaid like a veneer; he fills in the intervals as best he can.
Chopin is attacking Berlioz’s education, along with most of the teaching of composition of his time. He insists that counterpoint must precede the study of harmony, or else the harmonic movement will have no inner life—it will be laid on from the outside, as he says, like a veneer.
Rushton writes well about Berlioz’s education, which he shows convincingly to have been much more professional and thorough than legend will have it, but he skims lightly over the relationship between counterpoint and harmony emphasized by Chopin—or shies away from it equivocally. Berlioz’s education started by his reading the official textbook of the Conservatoire on harmony by Charles Simon Catel, and continued with his studies at the Conservatoire under Anton Reicha. About Catel, Rushton says:
Catel states in his preface: “I have made it my object in this work to teach harmony by instilling the elements of counterpoint.” That part-writing comes before chords is a surprisingly modern, even Schenkerian, idea.
As we have seen from Chopin’s remarks, the idea of putting part-writing (counterpoint) before chords (harmony) is not a surprisingly modern idea—it is the oldfashioned way, and Chopin deplored its disappearance. From 1600 to 1800, instruction in composition started with counterpoint and it rarely went on to anything else. It was the late-eighteenth-century development of large harmonic areas, of modulation, in fact, that made the teaching of harmony independent of counterpoint. (It must be added that Catel’s declaration is only lip service to this old idea, and that you cannot learn the elements of counterpoint from his work.) The same stylistic development also gave Rameau’s theory of classifying chords by their roots9 an importance it did not have when it appeared in the early eighteenth century. Rameau’s theory became of central importance to musical education in early-nineteenth-century France.
When Rushton reaches the training Berlioz received from his teacher, he notes that Reicha emphasized the implicit relationship between melody and harmony in tonal music. He observes, however, that Reicha declared that he would treat melody independently of its relation to harmony, and adds:
In no time, however, he is discussing scales, modulations, and cadences, as the indispensable syntax of melody, together with intervals and durations. All he omits, therefore, is the contrapuntal realization of the harmony.
“All he omits” is everything that Chopin considered fundamental to music: the contrapuntal realization of the harmony.
I hope that a little simple technical explanation will be welcome here, to explain why Chopin’s claim of a failure on Berlioz’s part is partly true—and why that failure accounts for much that is powerful and original in Berlioz’s music. Until the nineteenth century, music education began with what is called species counterpoint. In this exercise, the student is given a simple phrase of long, even notes like a part of a Gregorian chant, called a cantus firmus, and is asked to write another phrase of long, even notes that could be played or sung with it. The first species is one note of the countermelody for one note of the cantus firmus: the different species then advance in rhythmic complexity, the last being a free rhythm against the original cantus firmus. The student advances from two voices to three-, four-, and five-part counterpoint.
The rules of species counterpoint are exceedingly simple: the countermelody must not make parallel octaves or fifths with the cantus, since that would be too much like a simple doubling of the original line; the countermelody must not often leap into a dissonance 10 and never out of it, but the dissonance must be approached and, above all, resolved in stepwise motion directly and simply to the nearest consonance—this last is a rule for making dissonant movement graceful and beautiful, and is central to all tonal music.
However, the role of counterpoint in tonal music has a double and conflicting aspect that is not always clearly understood. The rules of counterpoint apply not only to several voices but also, paradoxically, to simple unaccompanied melodies: the successive notes of a melody are conceived as dissonant or consonant to each other. A tune in C major itself defines the C-major triad, implies its own harmony as it goes along, and must end on one of the notes of its central triad. This is what enables Bach to write music for solo violin or cello, using for long stretches only a single unaccompanied line: the harmony is implicit in the melodic line. Everyone unconsciously imagines some of the notes as lasting, as being valid beyond the moment of sound, and providing the basic harmony. The other notes are heard as dissonances resolving into the basic harmonic movement according to the simple rules of species counterpoint. The subjection of a simple unaccompanied melody to the laws of species counterpoint is one reason why Chopin felt that study starts with counterpoint and only afterward considers harmony.
In classical terms—but not always for Berlioz—counterpoint has priority over harmony because the relations of consonance and dissonance that govern harmony and melody are derived, as we have seen, from counterpoint. The harmony of every phrase of tonal music is therefore determined by more than one factor—overdetermined, in fact, to use a term of psychoanalysis, since each one of these factors alone is conceived as a sufficient determination. These factors are the melody itself, which implies a specific harmonization, and the movement of each independent voice, which must approach and resolve its dissonances with ease and grace. As Chopin said to Delacroix, “each of the parts has its own movement, which, while still according with the others, keeps on with its own melody and follows it perfectly.” Every chord, every note of the harmony, therefore, is the result of conflicting forces: the demands of the melody (the harmony it implies played by itself) and the similar demands of the individual subordinate voices which make up the harmony, all subject to the same conventions.
Berlioz, as we have seen, was a master of academic counterpoint when the occasion suited him. In addition, he understood the harmonic implications of melody as well as anyone, and he worked them out with an imagination that equaled that of his greatest contemporaries, although only at rare moments was he as radical in harmony as Chopin or Wagner. It is easy for Rushton to refute the common reproach that Berlioz’s melodies do not carry, or imply, their own harmony, and he makes an astute observation:
In fact, most of Berlioz’s melodies have clear tonal and harmonic implications: some of these are fulfilled, others denied. But they are difficult to harmonize in an “ordinary” way, for rhythmic reasons. Classic and romantic melody usually implies harmonic motion of some consistency and smoothness; Berlioz’s aspiration to musical prose tends to resist such consistency.
Tonality is not simply a harmonic system, but a rhythmic one as well, as many theorists now realize—resolution of dissonance depends as much on rhythm as on anything else (this is how Schönberg is able to reconstruct the effect of dissonance and consonance rhythmically within a nontonal system). The originality of phrase structure in Berlioz is the basis for the astonishing idiosyncrasy of some of his harmonic progressions. In this, he is more modern than Chopin or Wagner, and clearly anticipates Debussy. After Rushton, no one will be able to deny both the sensitivity of Berlioz’s harmonizations and his ability to master academic counterpoint.
This, however, does not answer Chopin’s reproach. It is evident that Berlioz was not able instinctively to do both at once, to carry out the full implications of his melody through a contrapuntal web in which each inner strand has its own life. There are places in his music where the significance of the melody takes total precedence over contrapuntal decorum. At some but by no means all of these moments, an expressive aspect of the melody is realized with such intelligence that initial professional outrage is generally succeeded by admiration.
How did some composers succeed in escaping the bad effects of the degenerate educational system deplored by Chopin? Berlioz did not have, in his training, the necessary corrective that almost every other contemporary composer had from childhood: the Well-Tempered Keyboard of Johann Sebastian Bach. This was the basis of instruction at the piano. Through this work, Beethoven, Schumann, Mendelssohn, Chopin, Liszt, and more or less everybody else learned to play the piano. Even if their training in composition was theoretically defective (as Chopin claimed, and as most theorists today would agree), they learned the contrapuntal realization of harmony in a purely practical way, by playing Bach. For Chopin and many others, the Well-Tempered Keyboard was the foundation of all composition. It is impossible to overestimate the educational value of this work for the early nineteenth century. Berlioz, however, could not play the piano and he thought Bach was a bore. He played the guitar, the flageolet, and the kettledrums; and he loved Gluck.
It is interesting that Gluck was reproached, and still is, with the same inadequacies in counterpoint as Berlioz. What Berlioz learned from Gluck was a harmonization of melody for expressive purposes that violates the contrapuntal movement of the individual voices. (It is, as a practical matter, easier to explain Gluck by means of Berlioz than to understand Berlioz’s individuality as a derivation from his idol.) Berlioz often sets the climax of his melodies in relief with the most emphatic chord—a triad in root position, and often a tonic chord where the melody implies a dominant. The second phrase of the main theme, the idée fixe, of the Fantastic Symphony is famous for its shock to classical sensibilities: the melody clearly implies a dominant at its climax resolved by a tonic, and Berlioz anticipates the resolution by putting a tonic under the climactic note. He has his cake and eats it, too, as the sense of the dominant is so strong that it lasts through the substituted tonic, which gives a brightness to the climactic note that would make the “right” harmonization seem impossibly bland. All composers have at times exploited the ambiguous and surprising effect of a “wrong” harmonization but none with greater genius than Berlioz.
This effect, which sounds like a simple mistake when it does not come off, has often been ascribed to Berlioz’s guitar playing. Rushton demolishes this contention with great ease: all that can be admitted, perhaps, is that the guitar encourages thinking of harmony in blocks, while every pianist is physically aware through the muscles of the hand and arm of the movement of independent voices.
There is one instrumental effect that appears throughout orchestral music from 1770 to 1820 in which the wrong harmony—or wrong bass—is implied: that is, the use of the kettledrums. Only two timpani were generally available, and when Mozart and Beethoven needed a dramatic accent they had to choose one of two notes for the timpanist to hit. This was very often not the bass note of the chord; the trouble is, a kettledrum always sounds like a bass, even when it is playing higher than the cellos. Normally we eliminate the fact that the kettledrum is playing the wrong bass from our listening, just as we disregard wrong notes, coughs, and unnecessary acoustical phenomena—all this is partially filtered out of consciousness, although a vague sense of it remains. Beethoven is the first composer to exploit the “wrong note” effect of the timpani and Berlioz was the first critic to appreciate what he was up to. Rushton quotes a brilliant remark of Berlioz about the bridge to the last movement of Beethoven’s Symphony no. 5 in C Minor:
the A-flat chord…seems to introduce a new key; on the other hand isolated hammering of the timpani on C tends to preserve the ambiance of the original tonic. The ear hesitates…one cannot see the outcome of this harmonic mystery.
The history of progress in music runs from the composer who thinks wrong notes are funny, as in the polytonal cadences and the whole-tone scale in Mozart’s Musical Joke, to the composers like Debussy and Milhaud who employ them seriously.
I do not want to duplicate the nonsense of Berlioz’s enemies who said that he composed as a guitarist by claiming that he harmonized as a timpanist—although when he played the timpani he quite evidently relished a “wrong” note that gave emphasis to the climax. Nevertheless, one of Berlioz’s most individual characteristics, only remotely derived from Gluck, is that he harmonized for expressive accent. We have no technical word for this device: perhaps coloristic accent would do. Berlioz chose which inversion of the chord to use for its color, and many of the root positions that sound so awkward and that have no contrapuntal rationalization in his work can be justified expressively. The opening of “L’Absence” from Les Nuits d’été (see musical illustration on this page) creates a notorious shock, and not only to a pedant. The chord in the fourth bar is decidedly wrong: Berlioz resolves a dissonance with an ungainly leap by the bass into a root position. He needs both the poignancy of the austerely dissonant third bar, and the brightness of the fourth bar, the vibrance that the root position has and that the more correct and mellifluous sixth chord would not. He could not allow the fourth bar to be less brilliant in sonority than the first, which it repeats. One cannot correct Berlioz, as everyone from Schumann on has seen.
That does not mean that he always sounds right—at least not at first hearing. In spite of offering an alternative to the classical German system, he remains too close to it, and deviates from it too unpredictably for the music to satisfy at once. The first stanza of Marguerite’s romance from La Damnation de Faust sounds beautiful but a little awkward; the reappearance of the melody in the second stanza seems much less odd; and the third has become convincing, beautiful without any reservation, completely normal. I have found this true at each performance. Rushton writes of the “Song of the Brigands” from Lélio:
I do not wish to imply that any outlandish musical syntax can be justified by the effect if the musical result is actually incoherent, especially if the motivation is so trivial as the exaggerated depiction of an outlaw, or the purpose merely épater le bourgeois. There are other factors in Berlioz’s “Chanson de brigands” which make it cohere. One is obvious; the verse comes four times. The oddest happenings may seem to have been explained, when they have merely become familiar, and by verses 3 and 4 the harmonic chasm has become an expectation, duly fulfilled, the strongest possible aid to coherence.
This point, brilliant in its simplicity, reminds one of Humpty Dumpty: anything said three times is true. The substitution of repetition for logic is more than persuasive. It carries complete conviction for one’s experience of Berlioz. It seems to me absolutely valid, but disquieting. As Rushton has said, dissatisfaction with Berlioz always stimulates a desire to hear his work again. But it also suggests that the controversy about him may be permanent.
(This is the second of two articles.)
April 26, 1984
Essays in Musical Analysis, vol. 4 (London, 1936), p. 75. ↩
Quoted by Edward T. Cone in his edition of the Fantastic Symphony (Norton, 1971), p. 282. ↩
Letter to Opprandino Arrivabene, June 5, 1882, quoted in Letters of Composers, edited by Norman and Shrifte (Grosset and Dunlap, 1946). ↩
One small example may show the nature of Verdi’s borrowings: the opening of the fugue in the “Libera me” of the “Manzoni” Requiem marks the entrance of each new voice with an interjected dominant-tonic cadence in a crashing fortissimo, and this device comes directly from the “Ronde du Sabbat” in the last movement of the Fantastic Symphony. ↩
Review in Gil Blas, May 8, 1903. ↩
Interview in La Revue bleue, April 2, 1904. ↩
Times Literary Supplement, February 24, 1984, p. 187. ↩
The Satz, here, is the basic line—the underlying linear structure or skeleton—revealed by Schenkerian analysis. ↩
Every triad (a C-major chord, say) has three forms: a fundamental or root position, used for cadences, to end with; a first inversion, which is consonant and can be used for the resolution of dissonance; and a second inversion, which is dissonant and must be resolved. In counterpoint, the relation of consonance and dissonance is more important than the kinship of the three forms: that is, it is more important whether the chord must be resolved than whether it is C major or not. Each of these three forms has a different expressive color that comes from its function. ↩
Dissonance and consonance are simply defined as, respectively, intervals that need resolution, and intervals into which one can resolve. From the fifteenth century until the twentieth, unisons, thirds, fifths, sixths, and octaves are the only consonances (along with their extensions above the octave: i.e., tenths and twelfths being thirds and fifths at a greater distance). All other intervals are dissonant. ↩