MUSIC THEORY FUNDAMENTALS - Chapter 10, Exercise 2 Solution
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Inserting a ii-V-I Progression

PROBLEM
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This piece's whole 8-bar harmonic plan is I-IV-V-V | I-IV-V-I. Rewrite
it to use a ii-V-I progression (Chapter 8) somewhere within the
consequent phrase instead of the plain IV-V-I, and name the new chord
you introduced along with its Roman numeral.

SOLUTION
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The consequent phrase (bars 5-8) currently reads: I - IV - V - I
(C major - F major - G major - C major).

To insert a real ii-V-I progression, replace the IV chord in bar 6 with
the ii chord instead, keeping bars 7-8 (V-I) unchanged:

    Bar 5: C major (I)   -  unchanged
    Bar 6: D minor (ii)  -  changed from F major (IV)
    Bar 7: G major (V)   -  unchanged
    Bar 8: C major (I)   -  unchanged

D minor is Chapter 7's own real ii chord in C major (built on the 2nd
scale degree, D, per the chapter's own diatonic-chord derivation).

ANSWER: The new chord introduced is D minor (ii), replacing F major (IV)
in bar 6. The consequent phrase's own new harmonic plan becomes
I-ii-V-I instead of I-IV-V-I.

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WHY THIS WORKS AS AN ANSWER

Both ii and IV are real, valid predominant-function chords leading
naturally into V - Chapter 7's own diatonic-chord table confirms D minor
(ii) is available in C major alongside F major (IV) - so this
substitution stays fully within the key while giving the phrase the
smoother, real jazz-associated ii-V-I motion Chapter 8 specifically
named as one of the most common progressions across nearly all Western
popular music, not just jazz.