Theory 149 007 Lecture September 3rd, 2025 - Interval & Figured Bass Essentials

Interval hearing and warm-up

Use an easier interval in the opposite direction to hear the interval clearly when given a hard one.
Complement to an octave: if an interval is difficult, find the interval in the other direction that, together with the hard interval, spans an octave.
Example principle: down a seventh is the same as up a second; seconds are easy to hear because they’re nearby.
Move to diatonic intervals: focus on major/minor between scale degrees in major and harmonic minor.
Practice in Do-based (C) context; switch between major and harmonic minor as needed.

Sing diatonic intervals between scale degrees 1 and others; emphasize easy-to-hear relationships.
When solving, aim for the simplest, closest interval that fits the direction you’re using.

Tactus (primary pulse): the layer you tap/conduct to.
Subdivisions rise above tactus; levels above tactus are hypermetric levels.
Dot diagram exercise: visualize metric levels from tactus upward; identify how the music subdivides (duple vs triple) and where the top dividers sit.
Useful terms: tactus, hypermetric levels.

Assign dots to the layer corresponding to the primary pulse (tactus).
Determine how far the music subdivides below that, i.e., the lowest note value reached.
Identify hypermetric levels above tactus; determine whether subdivisions are mostly duple with occasional triple (as in the Mozart minuets).
Use the diagram to infer how many metric layers the piece articulates and where the emphasis falls.

Figured bass labels the size of intervals above the bass, not inversions or root-first harmonic analysis.
Intervals above the bass are counted by lines/spaces; key signature determines exact pitches.
Notation describes any simultaneity, not just triads/seventh chords.
Full figuration vs abbreviations: memorize common shorthand.

Five-three (5-3) can be abbreviated to 5; often assumed as 5-3 if nothing else is shown.
Six-three (6-3) can be abbreviated to 6 (sometimes 3 also used, depending on context).
Six-four (6-4) usually kept in full form; rarely abbreviated.
Seven-five-three (7-5-3) abbreviated to 7.
Six-five-three (6-5-3) abbreviated to 6-5.
These are read as a bass note with upper intervals; never think of them strictly as traditional inversions.

The key signature determines exact pitch spelling for the figures (which notes above bass to play).
When a chromatic (non-diatonic) note appears, add the accidental to the right of the figure (e.g., 2 with sharp: 2♯).
A slash through a number (e.g., ⟨2 with a slash⟩) can indicate a sharp without writing the symbol explicitly.
Doublings: typically avoid doubling in figures; only include necessary notes above the bass.

Chromatic alteration is indicated by accidentals attached to the figures; relates to notes outside the key signature.
There isn’t a universal slash for flats across all contexts, but slashes for sharps are common; in practice, follow the instructor’s notation guide.

You can label any simultaneity with figures, not just conventional triads/seventh chords.
In Bach chorales, figures often reflect the same harmonic thinking as Roman-numeral analysis but with a key-signature-aware notation.
The exercise often involves applying figures to a Bach chorale to capture chromatic harmonies.

Key terms: tactus, hypermetric levels, dot diagram, figured bass, full figuration, abbreviations (5-3, 6-3, 6-4, 7-5-3, 6-5-3).
Rules: biggest number on top; abbreviations summarize the full figuration; always consider key signature when realizing figures.
Practical mindset: treat figured bass as a practical keyboard-improv aid, not just a theoretical chord label.

Prepare to sing Bach chorale with figures under the bass line, in a chosen tempo, using the taught abbreviations and chromatic adjustments.