Consonance and dissonance
In 1940, Ernst Krenek published a classification system in his book Studies in Counterpoint that ranked chords from 1 to 6 based on their internal consonance. A C major triad received the lowest rank of 1 because it contained three consonant intervals. A chord containing C, D, and B received a higher rank of 6 due to its inclusion of sharp dissonances like the minor second between C and D. This ranking illustrates how music theory treats these concepts as mutually exclusive categories that form a structural gradation rather than simple opposites. German composer Paul Hindemith once stated that for over a thousand years, definitions of these terms had varied without complete explanation. Modern listeners often associate consonance with sweetness and pleasantness while linking dissonance to harshness or unacceptability. However, this perception depends heavily on familiarity and musical expertise within specific cultural contexts. The distinction forms a gradation ranging from the most consonant sounds to the most dissonant ones. In casual discourse, the two concepts define each other by mutual exclusion where one is simply what the other is not.
When two pure sine waves play together at frequencies close to each other, people perceive maximum dissonance if those frequencies fall within a critical band. For low frequencies, this critical band can be as wide as a minor third interval. At high frequencies, the same band narrows to approximately a minor second. Amplitude fluctuations describe variations in sound signal strength relative to a reference point and result from wave interference patterns. If fluctuation rates stay below filter bandwidth, listeners hear beating or roughness as loudness changes. When fluctuation rates increase beyond filter limits, complex tones emerge without obvious beating sensations. Neural firing supplies data for pattern matching between separately analyzed partials and best-fit harmonic templates. Purely harmonic tones cause neural firing exactly with the period of the pure tone itself. Dissonance sensation arises from the brain's response to unusual or rare sound perceptions entering the ears. An EEG pattern known as P300/P3b emerges when listening to such oddball events causing slight stress in the listener. This biological mechanism explains why certain intervals feel more consonant while others feel dissonant regardless of cultural training.
Ancient Greek theorists used the term symphonos to describe intervals like the fourth, fifth, octave and their doublings. Aristoxenus applied this terminology to Pythagorean tuning where ratios of 4:3, 3:2 and 2:1 were directly tunable. Boethius wrote in the sixth century that consonance represents blending high sounds with low ones arriving sweetly at the ears. He described dissonance as harsh percussion of two mixed sounds creating unhappy effects. Hucbald of Saint Amand later defined six consonances including unison, octave, fifth, fourth, double octave and octave plus fifth. Johannes de Garlandia classified perfect consonances as unisons and octaves while median consonances included fourths and fifths. Medieval music treated minor sevenths and major ninths as harmonic consonances because they correctly reproduced interval ratios of the harmonic series. These intervals softened bad effects through resonant units characteristic of contemporary musics. Thirds and sixths received severe tempering from pure ratios and usually functioned as dissonances requiring resolution into complete cadences. The concept evolved differently across centuries before reaching modern understanding of these musical relationships.
Johann Sebastian Bach inserted an unexpected B natural over the final chord of his St Matthew Passion before melting into a C minor cadence. John Eliot Gardiner heard this moment as an almost excruciating reminder of Christ's betrayal and crucifixion. Albert Schweitzer noted that Cantata BWV 54 begins with an alarming seventh chord meant to depict horror of sin's curse. Gillies Whittaker observed that thirty-two continuo quavers in four bars support only four consonances while twelve others contain five different notes. Joseph Haydn composed Symphony No. 82 containing barbaric strength dissonances succeeded by delicate Mozartean grace passages. Wolfgang Amadeus Mozart wrote the Dissonance Quartet K465 opening with passing dissonances on bar three beats. Philip Radcliffe described a passage from Piano Concerto No. 21 as remarkably poignant with surprisingly sharp dissonances. Eric Blom claimed Mozart's hearers sat up due to daring modernities creating suppressed discomfort feelings. Ludwig van Beethoven opened Symphony No. 9 finale with a startling discord inserting B flat into D minor chords. Roger Scruton referenced Wagner's description of this chord introducing huge Schreckensfanfare or horror fanfare elements.
Igor Stravinsky premiered The Rite of Spring Sacrificial Dance excerpt in 1913 receiving immediate attention for its rhythmic complexity. Gustav Mahler composed an unfinished Tenth Symphony Adagio opening with diminished nineteenth harmonies containing nine different pitches. Richard Taruskin analyzed these chords as searingly dissonant dominant harmonies potentially unprecedented even for Guido Adler. Henry Cowell viewed tone clusters as using higher and higher overtones within early twentieth century American composition. George Russell published his Lydian Chromatic Concept of Tonal Organization in 1953 presenting alternative views widely adopted by jazz musicians. Dan Haerle released The Jazz Language in 1980 extending harmonic consonance ideas to alter Paul Hindemith's Series 2 gradation table. Haerle placed the minor ninth as most dissonant interval more dissonant than previously considered octave equivalent minor seconds. He promoted tritone from most dissonant position to one slightly less consonant than perfect fourths and fifths. These theories returned to medieval considerations where intervals correctly reproducing mathematical ratios remained truly non-dissonant regardless of traditional rules. Musicians effectively promoted major ninths and minor sevenths to legitimate harmonic consonance status through four-note chord fabrics.
Bosnian ganga singing explores buzzing sounds creating attractive musical timbre through slight roughness elements. Indian tambura drones stylize improvisations on Middle Eastern mijwiz instruments producing similar acoustic characteristics. Indonesian gamelan traditions consider beating phenomena desirable parts of overall sound production requiring specialized instrument construction. Anonymous XIII allowed two or three successive imperfect consonances while Johannes de Garlandia permitted three, four or more combinations. Adam von Fulda wrote that modern composers do not prohibit sequences exceeding ancient limits of three or four imperfect consonances. The regola delle terze e seste required imperfect consonances resolve to perfect ones via half-step progressions in single voices. Full cadential consonances of fourths, fifths and octaves need not target resolution beat-to-beat within certain time spans. Minor sevenths and major ninths moved directly to octaves forthwith while sixths transitioned into fifths or minor sevenths. These structural choices created succession of non-consonant sonorities limited only by next cadence points. Different tuning systems compared to modern times produced varying perceptions of interval acceptability across global musical traditions.
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Common questions
What classification system did Ernst Krenek publish in 1940 to rank chords by consonance?
Ernst Krenek published a classification system in his book Studies in Counterpoint that ranked chords from 1 to 6 based on their internal consonance. A C major triad received the lowest rank of 1 because it contained three consonant intervals while a chord containing C, D, and B received a higher rank of 6 due to its inclusion of sharp dissonances like the minor second between C and D.
How does the brain process dissonance according to EEG patterns described in the text?
Dissonance sensation arises from the brain's response to unusual or rare sound perceptions entering the ears. An EEG pattern known as P300/P3b emerges when listening to such oddball events causing slight stress in the listener which explains why certain intervals feel more consonant while others feel dissonant regardless of cultural training.
Which ancient Greek theorists used the term symphonos to describe specific musical intervals?
Ancient Greek theorists used the term symphonos to describe intervals like the fourth, fifth, octave and their doublings. Aristoxenus applied this terminology to Pythagorean tuning where ratios of 4:3, 3:2 and 2:1 were directly tunable.
What historical examples illustrate the use of dissonance in classical compositions by Bach and Beethoven?
Johann Sebastian Bach inserted an unexpected B natural over the final chord of his St Matthew Passion before melting into a C minor cadence. Ludwig van Beethoven opened Symphony No. 9 finale with a startling discord inserting B flat into D minor chords.
How did Dan Haerle alter Paul Hindemith's Series 2 gradation table regarding interval dissonance?
Dan Haerle released The Jazz Language in 1980 extending harmonic consonance ideas to alter Paul Hindemith's Series 2 gradation table. He placed the minor ninth as most dissonant interval more dissonant than previously considered octave equivalent minor seconds while promoting tritone from most dissonant position to one slightly less consonant than perfect fourths and fifths.