Chains of suspensions

Because a resolution is a consonance, it can serve as the preparation of the next suspension: over a bass descending by step, each 7–6 resolution becomes the seventh against the next bass note, and the device renews itself for as long as the bass keeps walking. A chain converts the strictest dissonance discipline into an engine of continuity — the classic sequence of the strict style, and the 4–3 chains the same way over a bass falling in fifths.

Chains cover harmonic ground — several bars from one arrival to another — without new material: the same figure, a step lower each time, fills the space with continuous motion instead of separate decisions. They extend a sequence, whether the bass walks down by step under a run of 7–6s or falls by fifths under 4–3s, both constant in fugal episodes and partimento realizations. Because each resolution is already a consonance, the chain costs nothing in dissonance treatment, and can run for as many links as the plan requires.

• Breaking the stepwise descent partway through the chain — a leap in the bass, or a change of direction — which stops each resolution from lining up as the next preparation.
• Rearticulating the resolution instead of tying it over into the next suspension, which turns a bound chain into separately struck notes and loses its continuous line.
• Letting parallel fifths or octaves creep in between the two voices from one link to the next, the standard hazard of any sequence repeated without a check at each step.
• Extending the chain past the point the harmonic plan calls for, so the sequence arrives somewhere the phrase never intended to go.
• Mixing 7–6 and 4–3 links within a single descent, when the bass motion each pattern assumes — stepwise for the 7–6, by fifths for the 4–3 — has already committed the passage.

• Johann Joseph Fux, Gradus ad Parnassum (1725), Liber secundus, fourth species (successive ligatures) — The species practises the ties in succession, each resolution preparing the next.
• Ebenezer Prout, Harmony: Its Theory and Practice (1889), The chapter on suspensions — Chains treated as the sequential extension of the single case.
• George Frideric Handel, Thoroughbass and composition lessons for Princess Anne (1724), The thoroughbass lessons, suspension-chain exercises — Handel drills exactly these chains at the keyboard for his royal pupil.