Dr. B Music Theory Lesson 3 (Intervals, Consonance vs. Dissonance)

Inversions of Intervals

Understanding Interval Categories

• The discussion begins with the classification of intervals into two main categories: perfect, augmented, and diminished (0s).

• The first category includes unison, fourths, fifths, and octaves; these can only be classified as perfect or diminished.

• The second category consists of seconds, thirds, sixths, and sevenths; these can be major, minor, augmented, or diminished (36s).

Inverting Intervals

• When inverting an interval (e.g., C to G), the bottom note becomes the top note and vice versa. This changes a perfect fifth into a perfect fourth if C is in the G Major scale (73s).

• Every interval has its inversion; for example, a perfect fourth inverted returns to a perfect fifth (145s).

Characteristics of Perfect Intervals

• Perfect intervals remain unchanged when inverted; they always stay perfect regardless of their position (170s).

Augmented and Diminished Intervals

• An augmented interval will become diminished upon inversion. For instance, E to B♯ is an augmented fifth that turns into a diminished fourth when inverted (211s).

• Conversely, all diminished intervals become augmented when inverted. For example: A to D♭ is a diminished fourth that becomes an augmented fifth upon inversion (290s).

Mathematical Relationships in Inversions

• The sum of the numbers representing intervals equals nine: this rule applies across various types of intervals including seconds and thirds.

• Example: A major third becomes a minor sixth upon inversion because 3 + 6 = 9 (402s).

• Major intervals turn into minor ones when inverted and vice versa (483s).

Consonance vs Dissonance

Defining Harmonic Intervals

• Harmonic intervals are those heard simultaneously compared to melodic intervals which are played sequentially.

Cultural Perception of Consonance

Understanding Acoustic Perception and Harmony in Music

The Nature of Sound and Overtones

• Human perception of consonance and dissonance is fundamentally acoustic, based on the overtone series, which is universal across cultures.

• When a pitch is heard (e.g., C), it includes overtones that vibrate sympathetically above the fundamental note, contributing to the unique sound of different instruments.

• Instruments playing the same pitch produce different sounds due to varying intensities in their overtone series, akin to an EQ setting on a stereo.

• The first few overtones include an octave above (first overtone), a perfect fifth (second overtone), followed by another octave and major third, illustrating the natural structure of sound.

Consonance vs. Dissonance

• The perfect octave is considered consonant; however, perceptions of "good" sound are subjective and culturally influenced.

• Major triads form the foundation of harmony because they naturally occur within the overtone series, highlighting a scientific basis for musical structures rather than purely cultural ones.

• Dissonant intervals such as sevenths and seconds are consistently perceived as dissonant; augmented or diminished intervals also fall into this category.

The Complexity of Intervals

• The fourth interval's perception can vary between consonant or dissonant depending on its context within the overtone series.

• A fourth interval may seem consonant when low in the overtone series but can be perceived as dissonant if positioned incorrectly relative to a base note.

Tension and Relaxation in Music

• Contextual placement affects how intervals like fourths are perceived; for example, C to F can create tension if not resolved properly.

• A 4-3 suspension illustrates how certain notes create tension that resolves into consonance when played correctly within harmonic contexts.

Compositional Techniques

• Dissonance represents tension while consonance signifies relaxation; these concepts are more nuanced than simply labeling sounds as good or bad.