Harmonic Intervals: From Strict Counterpoint to Modern Harmony

Over the years, the dualities of tension and resolution, along with consonance and dissonance, became a spectrum that constitutes various degrees of tension. In strict counterpoint, the harmonic intervals of a unison, 3rd, 5th, 6th, and octave were considered consonant, while the 2nd and 7th were considered dissonant. The 4th was classified as consonant only if formed between upper voices, but dissonant if formed with the bass. Augmented and diminished intervals were considered dissonant. Each of the above dissonances required proper preparation and resolution.

Gradually, with the transition to free counterpoint, composers took liberties to break these conventions. The 7th and the 4th (with the bass) began to be used freely, and the appoggiatura made preparation unnecessary. Over time, unresolved dissonances became common, and a modern concept of degrees of consonance and dissonance emerged: open consonances (octave and perfect 5th), soft consonances (3rds and 6ths), mild dissonances (major 2nd and minor 7th), and sharp dissonances (minor 2nd and major 7th).

The character of the perfect 4th (as consonant or dissonant) and the tritone (as neutral or restless) depends on context. The tritone can sound neutral in chromatic surroundings but restless in diatonic ones, while the perfect 4th can sound consonant within a dissonant context, and vice versa. This allows composers to control the percentage of consonance or dissonance within a phrase (linear) or chord (vertical). Crescendos and diminuendos of intervallic tension (open to sharp and vice versa) can be written and the tension of a single chord can be calculated and varied to be harsh, smooth or anything in between, much like a painter mixing colors.

Selected Bibliography

• Fux, Johann Joseph. The Study of Counterpoint: From Johann Joseph Fux's Gradus Ad Parnassum. Translated and edited by Alfred Mann. New York: W. W. Norton & Company, 1965.

• Hindemith, Paul. The Craft of Musical Composition. Revised Edition. Translated by Arthur Mendel. New York: Associated Music Publishers, 1945.

• Persichetti, Vincent. Twentieth-Century Harmony: Creative Aspects and Practice. New York: W. W. Norton & Company, 1961.