Theory 139 Laboratory September 9th, 2025 - Music Theory: Intervals, Triads, and Key Signatures

Intervals

• Definition: the distance between two notes.
• Size: number of scale steps; e.g., from scale degree 1 to 3 is a 2-step size and is called a 3rd. In general, size = the nth interval (2nd, 3rd, 4th, …).
• Quality: how large the interval is within the context of the scale (major, minor, perfect, etc.).
• Semitone mapping (common cases):
  • Major second = $2$ semitones, Minor second = $1$ semitone
  • Major third = $4$ semitones, Minor third = $3$ semitones
  • Perfect fourth = $5$ semitones, Perfect fifth = $7$ semitones
• Consonance vs. dissonance (Western classical context):
  • Consonant = stable
  • Dissonant = unstable and requires resolution
• Special note on the fourth: can be consonant musically in some contexts and dissonant in harmony; resolution depends on context.

Triads

• Definition: a chord built by stacking notes in thirds.
• Tonic triad: built on scale degree 1 with notes $1!\,3!\,5$.
• Inversions (by bass note):
  • Root position: root in the bass (labels: I, etc.).
  • First inversion: third in the bass (labels: I⁶).
  • Second inversion: fifth in the bass (labels: I⁶⁄⁴).
• Factors vs. members: triad = 3 members (root, third, fifth).
• Key point: all inversions share the same pitches (the same triad), just rearranged.
• Roman numeral idea vs. figured bass history: two traditions exist; use whichever your course emphasizes, but the essential is the bass note defines the inversion.

Aural recognition and practice (triads)

• Activity 1: listen to a triad, identify the interval heard relative to the bass/presentation.
• Activity 2: hear an interval described in words (e.g., major third) and sing it back, linking terminology to sound.
• Purpose: connect abstract terminology with embodied sound and scale-degree relationships.

Key signatures and identification

• Two quick tricks:
  • Sharps: the key is the last sharp plus a half step. Example: last sharp is $F\sharp$; half step above is $G$, so key = G major.
  • Flats: the key is the second-to-last flat. Example: key with two flats (Bb, Eb) has second-to-last flat = Bb, so key = Bb major.
• Quick list (common example references):
  • 5 sharps → $B\text{ major}$
  • 6 sharps → $F\sharp\text{ major}$
  • 7 sharps → $C\sharp\text{ major}$
  • 5 flats → $B\flat\text{ major}$
  • 6 flats → $G\flat\text{ major}$
  • 7 flats → $C\flat\text{ major}$
• Scale degree one (tonic) follows from the key signature.
• Practical tip: for most singing tasks, the actual key matters less than relative pitch; focus on interval relationships and relative pitch.

Quick practice reminders from today’s session

• Ensure you specify both the size and the quality when naming intervals (e.g., $2\text{ (size)}\; \text{and}\; \text{Major}$ for a major second).
• For minor intervals, apply the correct diacritic/notation as your course requires; this is checked in grading.
• When identifying keys, use the last sharp (or second-to-last flat) rule and know the tonic note of the key.
• If you’re uncertain, practice with scale-degree planning (1–7) and sing through the intervals and triads in your target keys.
• If you want to earn back points, you can reach out to review a portion of homework and discuss possible partial credit opportunities.

Key takeaways for quick recall

• Interval = distance between two notes; size = scale steps; quality = major/minor/perfect.
• Consonance is stable; dissonance is unstable and resolves.
• A triad = 3 notes stacked in thirds; tonic triad = 1–3–5; inversions shift which note is in the bass (I, I⁶, I⁶⁄⁴).
• Key signatures: last sharp + half step → major key; second-to-last flat → major key; memorize the common sharp/flat keys listed above.
• Aural skills drills link terminology to sound via listening and singing exercises.