SHOSYS ACADEMY 14 LESSON: Criteria Of Consonance And Dissonance
Kelvin Sholar
1 Introduction To The Blog Series
This series of lessons and tests incorporates an easy music appreciation curriculum for adult beginners who are remote learning, or are self-taught. Lessons are posted on Mondays while Tests are posted on Saturdays. For more in depth and private guidance, I offer personal instruction by Zoom (Personal Meeting ID 8522954569) – for 1 dollar a minute. Time schedules range from a minimum of 30 minutes to a maximum of 60 minutes. Email me at [email protected] to set up personal instruction. I accept payments and cash gifts by Cash App ($KelvinSholar), Zelle ([email protected]) or Paypal (paypal.me/kelvinsholar).
2 Revisiting The Tree Of Knowledge
In Lesson 13, we learned about classifying performance media and techniques. In this Lesson, we will learn about criteria of consonance and dissonance. This knowledge resides in the Ways branch (1.20) of the Tree of Knowledge (1.00), at the sixth leaf from the left (1.24) – Criteria. In “Taxonomy Of Educational Objectives”, Benjamin Bloom describes Knowledge of criteria as: “Knowledge of the criteria by which facts, principles, opinions, and conduct are tested or judged” (Bloom 72). In this context, criteria means a principle or a standard by which one can decide something.
2.1 CRITERIA OF CONSONANCE AND DISSONANCE
Music is both a science and an art. As a science, we are concerned with the physical properties of sound and how they relate to psychical properties. As an art, we are concerned with music as a medium of pleasure and beauty. Thus, we seek to learn the standards by which music is decided to be pleasurable or beautiful, consonant or dissonant.
Instead of pleasure and beauty in music, Roger Kamien describes consonance and dissonance in terms of stability and instability, or restful and tense respectively: “A tone combination that is stable is called a consonance. Consonances are points of arrival, rest, and resolution. A tone combination that is unstable is called a dissonance. Its tension demands an onward motion to a stable chord. Dissonant chords are “active”; traditionally they have been considered harsh and have expressed pain, grief, and conflict” (Kamien 41).
Kamien also describes the motion from dissonance to consonance as a resolution. He adds: “When this resolution is delayed or accomplished in unexpected ways, a feeling of drama, suspense, or surprise is created. In this way a composer plays with the listener’s sense of expectation” (Kamien 41).
Sir James Jeans writes about criteria in music as an art: “To say the same thing in another way, the aim of music is to weave the elementary sounds we have been discussing into combinations and sequences which give pleasure to the brain through the ear. As between two pieces of music both of which give pleasure in a high degree, only the artist can decide which gives most, but the scientist can explain why some give no pleasure at all. He cannot explain why we find Bach specially pleasurable, but he can explain why we find the cat music specially painful. And this brings us to the subject of the present chapter why is it that some combinations of sounds are agreeable to the ear, while others are disagreeable?” (Jeans 152).
Roger Penrose writes that the first Western scientist to address the problem of criteria in music was Pythagoras of Samos. In addition to applying applying mathematical proof to problems of physics, Pythagoras thought that arithmetical concepts governed the actions of the world (Penrose 10). According to legend, Pythagoras noticed that “that the most beautiful harmonies produced by lyres or flutes corresponded to the simplest fractional ratios between the lengths of vibrating strings or pipes. He is said to have introduced the ‘Pythagorean scale’, the numerical ratios of what we now know to be frequencies determining the principal intervals on which Western music is essentially based” (Penrose 10). This is what I will call Pythagoras’ theory of consonance.
Pythagoras’ theory of consonance implies that intervals can be ordered by increasing dissonance (or decreasing consonance); this means that the more that we find large numbers, the least consonant the interval is (Jeans 154):
- unison = 1:1
- octave = 2:1
- fifth = 3:2
- fourth = 4:3
- major third = 5:4
- minor sixth = 5:3
- minor third = 6:5
- major sixth = 8:5
- second = 9:8
A major problem with Pythagoras’ theory is the assumption that all musicians hear the same ways, and that all cultures use the same tuning systems and performance media in their music.
Beyond measuring the consonance that is inherent in intervals, Leonard Euler attempted to measure the consonance that is inherent in chords. According to Sir James Jeans: “His plan was to express the frequency ratio of the chord in question by the smallest numbers possible, and then to find the smallest number into which all these could be divided exactly. This last number, he thought, gave a measure of the dissonance of the chord. For example,the frequency ratio of the notes of the common chord CEGc’ is 4:5:6:8. The measure of dissonance is accordingly 120, since this is the smallest number of which 4, 5, 6 and 8 are all factors” (Jeans 154).
A problem with Euler’s theory is that other chords with the same frequency ratio are not considered equally consonant. For example, the chord CEGB has the frequency ratio 8:10:12:15; hence the dissonance is 120, but the chord does not have the same level of dissonance as CEGc’ (i.e. 4:5:6:8).
3 Bibliography
Bloom, B. S.; Engelhart, M. D.; Furst, E. J.; Hill, W. H.; Krathwohl, D. R. Taxonomy Of Educational Objectives: The Classification Of Educational Goals. Handbook I: Cognitive Domain. New York: David McKay Company, 1956
Jeans, Sir. James. Science And Music, Cambridge: Cambridge University Press, 1937
Kamien, Roger. Music: An Appreciation. New York: McGraw-Hill Education, 2018
Penrose, Sir. Roger. The Road To Reality. London: Random House, 2004