# Unit 2: Intervals This study guide summarizes the Unit 2 concepts from the provided photos. It is a paraphrased review, not a transcription of the textbook. ## Core Idea An interval measures the distance between two tones. Intervals can appear melodically, when tones sound one after another, or harmonically, when tones sound together. Unit 2 treats intervals as both naming tools and musical forces: their size, quality, inversion, consonance or dissonance, and scale-degree context all affect how they behave. ## Numerical Size and Quality The numerical size of an interval comes from counting letter names inclusively: C to E is a third because C-D-E spans three letter names. Quality describes the specific size within that number: major, minor, perfect, augmented, or diminished. The practical method is: - Find the interval number by counting letter names. - Compare the upper note to the note that would occur in the major scale built on the lower note. - For unisons, fourths, fifths, and octaves, use perfect as the basic form. - For seconds, thirds, sixths, and sevenths, use major/minor as the basic pair. - Enlarging a perfect or major interval by a chromatic half step makes it augmented. - Narrowing a perfect or minor interval by a chromatic half step makes it diminished. When constructing an interval below a given note, determine the required letter name first, then adjust accidentals to get the correct quality. ## Compound Intervals Compound intervals are larger than an octave. Because of octave equivalence, they often function like their simple equivalents: - A ninth functions like an expanded second. - A tenth functions like an expanded third. - A twelfth functions like an expanded fifth. - A fifteenth functions like an expanded octave. For the purposes of this unit, ninths and tenths are the most important compound names. ## Interval Inversion Inversion moves one tone of a simple interval by octave so that the lower tone becomes the upper tone, or the upper tone becomes the lower tone. The numbers of an interval and its inversion add to 9: | Interval | Inversion | | --- | --- | | 1 | 8 | | 2 | 7 | | 3 | 6 | | 4 | 5 | | 5 | 4 | | 6 | 3 | | 7 | 2 | | 8 | 1 | Qualities invert as follows: - Perfect remains perfect. - Major becomes minor. - Minor becomes major. - Augmented becomes diminished. - Diminished becomes augmented. ## Overtones Most musical sounds are composite sounds: a perceived fundamental pitch is accompanied by quieter component vibrations called overtones or partials. The overtone series begins with the fundamental, then the octave, fifth, next octave, major third, and so on. The series helps explain why octaves, fifths, and thirds have special importance in tonal music, though it does not explain the whole tonal system by itself. ## Consonance and Dissonance Consonant intervals sound relatively stable. Dissonant intervals sound active, tense, or in need of directed motion. Consonant intervals: - Perfect unison - Perfect octave - Perfect fifth - Perfect fourth in some contexts - Major and minor thirds - Major and minor sixths Dissonant intervals: - All seconds - All sevenths - Augmented and diminished intervals - Perfect fourth in some contexts Perfect consonances are unisons, octaves, and fifths. Imperfect consonances are major/minor thirds and major/minor sixths. Perfect consonances are especially strong at points of articulation, while imperfect consonances are more fluid and often support motion between structural points. ## The Special Case of the Fourth The perfect fourth is context-dependent. It is consonant when it clearly functions as an inversion of a fifth or as part of a stable arpeggiated sonority. It is dissonant when it appears above the bass or in a two-voice setting where it wants to resolve to a third. ## Dissonance and Activity The active scale degrees from Unit 1 connect directly to dissonance. In a simple tonal setting, scale degrees 1, 3, and 5 are mutually consonant because they form the tonic triad. Active tones such as 2, 4, 6, and 7 often create dissonances against the tonic-triad tones. Dissonances become musically useful when they are tied to stepwise motion: passing tones, neighboring tones, and other active tones create tension that is directed toward a consonant goal. ## Intervals in a Key Intervals do not behave only by abstract size and quality. Their scale-degree content matters. Each scale degree forms a distinctive pattern of intervals with the other degrees of the key, which contributes to its tonal character. In major, the diminished fifth occurs between scale degrees 7 and 4, and the augmented fourth occurs between 4 and 7. Because both notes have strong tendencies, this interval has a powerful drive toward resolution: - Diminished fifth tends to contract to a third. - Augmented fourth tends to expand to a sixth. This tritone is key-defining in major because a specific diatonic tritone occurs in only one major key. In natural minor, the corresponding diminished fifth and augmented fourth resolve to scale degrees 3 and 5. These tones belong to the tonic triad, but the resolution does not define the minor tonic as strongly because it can suggest the relative major. ## Chromatic Dissonances in Minor Harmonic and melodic minor introduce additional augmented and diminished intervals. The diminished seventh and augmented second are especially important: they are dissonant, tend toward resolution, and can strongly clarify the tonic when raised scale degree 7 points to 1. ## Enharmonic Equivalence Enharmonically equivalent intervals may sound the same on an equal-tempered instrument but are spelled and understood differently. For example, an augmented fourth and diminished fifth may share the same sounding distance, but their notation implies different scale degrees and different resolutions. ## Memory Targets - Construct and identify intervals by number and quality. - Know which interval numbers are perfect-type and which are major/minor-type. - Know compound interval equivalents, especially ninths and tenths. - Memorize inversion pairs and quality changes. - Know the basic overtone series through at least the eighth partial. - Classify consonances and dissonances. - Explain why the perfect fourth is context-dependent. - Understand how the tritone resolves in major and why it helps define key. - Recognize that enharmonic spelling affects tonal meaning and resolution.