Sound Reasoning
Table of Contents
Part II: Hearing Harmony
18.1 Hearing Harmony: What is Harmony?
18.2 Harmony in Western Music
18.3 Expressing Harmony
18.4 Listening Gallery: Expressing Harmony
18.5 Harmonic Rhythm
18.6 Listening Gallery: Harmonic Rhythm
18.7 Cadences
18.8 Listening Gallery: Cadences
18.9 The Tonic
18.10 Circular and Linear Progressions
18.11 Listening Gallery: Circular and Linear Progressions
18.12 The Major-minor Contrast
18.13 Modes and Scales
18.14 Hearing the Mode
18.15 Listening Gallery: Hearing the Mode
18.16 Tonic, Mode and Key
18.17 Listening Gallery: Tonic, Mode and Key
18.18 Music Within a Key
18.19 Listening Gallery: Music Within a Key
18.20 Postponed Closure
18.21 Listening Gallery: Postponing Closure
18.22 Chromaticism
18.23 Listening Gallery: Chromaticism
18.24 Dissonance
18.25 Leaving the Key
18.26 Harmonic Distance
18.27 Modulation
18.28 Harmonic Goals
18.29 The Return to the Tonic
18.30 Final Closure
18.31 Listening Gallery: Final Closure
18.32 Reharmonizing a Melody
18.33 Listening Gallery: Reharmonizing a Melody
18.34 Conclusion
18.26 Harmonic Distance
The first element of a modulation is the distance traveled. What does that mean in musical terms?
The primary measure of relatedness between keys is the number of notes shared in common: The greater the overlap, the more closely related the keys. Each Major key contains seven notes: Thus, the greatest possible overlap is six notes. Because there are twelve pitches in the chromatic scale, the minimum overlap is two notes (five distinct for each key plus two shared=all twelve pitches of the chromatic scale.)
In the West, hearing and vision are often correlated: For instance, we speak of pitches as “high” and “low” and of melodies “rising” and “falling.” This cross-domain mapping is not universal: As ethnomusicologists have shown, to the ancient Greeks, pitches were “sharp” or “heavy,” in Bali they are “small” or “large,” to the Saya people of the Amazon “young” and “old.” In Zimbabawe, what we call low pitches are “crocodiles,” whereas high ones are “those who follow crocodiles.” (Eitan and Timmers, “Beethoven’s last piano sonatas and those who follow crocodiles,” 9th International Conference on Music Perception and Cognition, 2006).
To Western ears, our musical-spatial framework is so ingrained, it is hard to realize it is only a cultural metaphor: To us. the piccolo is “above” the tuba, the singer “reaches” for her high note and voices may move in “parallel” or “contrary motion.”
While individual pitches are aligned on a vertical plane—up and down–keys tend to be “visualized” on a horizontal plane — near and far. Closely related keys are perceived as ”neighboring,” whereas those that are not are perceived as “distant.”
For instance, the pitches B and C lie very close together:
Meanwhile, there is a wider interval between C and G:
With respect to keys, however, the opposite is true: Because the keys of C-Major and G-Major share six notes in common, they are perceived as neighboring.
Meanwhile, C-Major and B-Major—which share only 2 of 7 notes—are heard as far apart.
The circle of fifths is an iconic diagram of keys arrayed in circle, like the face of a clock: The more notes two keys share in common, the closer they lie on the circle.
Circle of Fifths
Each Major key is paired with the minor one whose “natural” form shares the same scale: For instance, the keys of C-Major and a-natural minor share exactly the same seven pitches. These are called the relative Major and minor, because their pitch content is so closely related.
The circle of fifths is the primary way of visualizing harmonic distance. It is common to speak of “traveling” around the circle. Note that, just as with the twelve-hour time cycle, twelve steps around the circle of fifths returns you to your starting point.