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1.4 Fourth Species — Suspension and Fiber Color

Definition. Fourth species introduces two new resources:

  • Suspensions: a note from the previous chord-zone is held into the new chord-zone, becoming a non-chord tone, then resolved by step to a chord tone.
  • Fiber inversions: motion through the fiber bundle (changing inversional state without changing the orbit).

What this teaches. Fourth species teaches rhythmic displacement and registral elaboration. The suspension is the cleanest expression of the OTH leading-interval-pair: a held note becomes dissonant against the new chord, then resolves by single semitone to a chord tone. The fiber inversion teaches the student to use registral motion as a temporal event, not just a static voicing choice.

Setup. A chord-graph path of 4-8 chords, with the added voice playing one note per chord-zone but with the note tied (or repeated) across the bar line into the next chord-zone, where it becomes the suspension. Alternatively, fiber inversions are inserted between consecutive base-space chords.

Step-by-step procedure for suspensions

  1. Identify candidate suspension moments. Look at each chord-graph edge in the cantus firmus. The voice that moves in the cantus firmus is changing by one semitone. If the added voice can be held on the old note of that voice into the new chord, the held note becomes a suspension (a non-chord tone in the new chord) and resolves by single semitone to the new note.

  2. Write the suspension. The added voice plays the chord tone on the “downbeat” of chord N. The voice holds (ties) into chord N+1. On the second beat of chord N+1, the voice resolves by single semitone to a chord tone of chord N+1.

  3. Resolve down (or up) by step. OTH suspensions can resolve in either direction. The choice depends on whether the resolving voice is following a tritone-expanding (d5 → P5) or A5-contracting (A5 → P5) motion.

  4. Stack suspensions for stretto effects. Multiple voices can have suspensions in different chord-zones, creating overlapping resolutions.

Step-by-step procedure for fiber inversions

  1. Identify a chord-zone in the cantus firmus. Pick a chord that you want to elaborate registrally without changing its harmonic identity.

  2. Compute the chord’s fiber positions. Each chord in B has 4 inversional positions in the fiber bundle E. Use the music-theory MCP to find them, or compute by Tymoczko inversion. The four positions are spaced 12 semitones apart (the L1 law).

  3. Choose a fiber position to move to. Typically, move “up” in the fiber by one inversion step — e.g., from voicing [C2-G2-D3-A3] to [G2-D3-A3-C4] (rotating the lowest voice up an octave to become the highest).

  4. Notate the fiber inversion. Within the chord-zone, write a transition from the base voicing to the fiber-inverted voicing. The pitch material of the chord is unchanged; only the registral distribution changes.

  5. Use fiber inversions for color, not function. A fiber inversion does not progress the harmonic narrative — it elaborates the current chord’s registral character. Use sparingly; the listener interprets fiber inversion as a texture event, not a harmonic event.

Worked example — Suspension

Cantus firmus: chord 1 (Q777, voice 4 = A3) → chord 2 (Q877, voice 4 = Bb3). Single-edge transition: A→Bb in voice 4.

Added voice (soprano, in fourth species):

Chord 1: A4 (chord tone of Q777)
Chord 2: A4 sustained (held over from chord 1, becomes non-chord tone) → Bb4 (resolution by single semitone)

The A4 across the chord boundary is the suspension: it was a chord tone of chord 1 but is non-chord-tone in chord 2 (Q877 = {C,D,G,Bb}, no A). It resolves by ascending semitone to Bb4 (a chord tone of chord 2). The resolution mirrors the cantus firmus’s own A→Bb edge — this is the leading-interval-pair in its purest form: two voices each moving A → Bb across the chord boundary, in different octaves.

Common errors in fourth species

  1. Unprepared suspensions. A suspension must be a chord tone of the previous chord. If you start a held note that wasn’t a chord tone before, it’s not a suspension — it’s just a held non-chord tone.

  2. Resolving in the wrong direction. Suspensions in OTH should resolve by single semitone to a chord tone of the new chord. If you resolve by a leap, you’ve abandoned the suspension figure.

  3. Fiber inversion treated as harmonic event. The fiber operates on color, not function. Using a fiber inversion to “modulate” or “resolve” misuses the device. It is a textural variation, not a harmonic move.

  4. Stacked suspensions creating cluster dissonance. When two voices both have suspensions over the same chord, the held non-chord tones can stack into dissonant clusters. Plan resolutions in different beats so each suspension can be heard distinctly.