Voice-leading for Roots - a P4 Apart

Author: Kari Jo Douglas
Lesson Plan:

Lesson Plan Title: Part Writing for Roots a Fourth Apart

Concept / Topic To Teach: How to write four-part harmony between two chords whose roots are a perfect fourth (or the inverted perfect fifth) apart.

Standards Addressed: Students must be able to write four-part harmony according to tonal harmony conventions as covered on the National AP Music Theory Exam.

General Goal(s): Given two chords with the roots a perfect fourth (or its inversion) apart, students will be able to demonstrate the use of three different methods.

Specific Objectives: Students will be able to identify the common tone between chords and analyze the bass movement of two chords. Using this information they will be able to demonstrate each of the following three methods:

    1) keep the common tone, move remaining upper two voices in parallel motion with the fourth (or opposite the fifth) in the bass;
    2) move all three remaining upper voices in similar motion in leaps no greater than a major third and in the direction opposite the fourth (or with the fifth);
    3) keep the common tone between chords, move the voice containing the third of the first chord to the third of the second chord, and move the remaining voice by step to complete the chord.

Required Materials: Blank staff paper and pencil

Anticipatory Set (Lead-In):

    Writing four-part harmony for chords with their roots a perfect fourth apart can be made very simple by choosing one of three methods and simply "plugging the notes into it".

Step-By-Step Procedures:

  1. Start with two notes that are a perfect fourth apart: C and F.
  2. Ask the students to spell the two chords: CEG and FAC.
  3. Ask them what note is common to both chords: C.
  4. Circle that note in both chord spellings.
  5. On the board, realize the C chord by filling in the upper three voices with CEG (making sure to follow proper tonal harmony conventions, i.e., not having more than an octave between adjacent voices and making sure to double the root, and use all members of the chord).


  • Circle the note in the first chord that is common to both chords. For example, if the alto voice has a C, circle the C in the alto voice. Have the students copy the same note in the same voice for the second chord. Point out that they have just "kept the common tone" between the two chords.
  • Next, have them analyze the bass notes. Does the C in the first chord go up a fourth to F in the second chord or does it go down a fifth to F in the second chord? In this first method, the two remaining upper voices need to move by step in parallel motion in the same direction as the fourth in the bass or in the opposite direction as the fifth in the bass. The students should discover that the two remaining voices (soprano and tenor) should move up by step.
  • Have them check the finished product: do both chords have all members present? Is the root doubled? Are there any parallel 5ths or 8ves? Is there a spacing error (more than an octave between adjacent voices except the bass)? They should find that the second chord is perfectly written. Play the two chords for them on the piano.


  • Repeat steps 1-5 above. Point out that they will not keep the common tone in method two, but that it is still important to be aware of it.
  • Have them analyze the bass notes as they did in Method 1. In Method 2 the upper three voices need to move in similar direction opposite the fourth or with the fifth. If the C in the bass moves up to F, then the upper three voices should move up to the nearest chord tone of the second chord (all leaps will be no larger than a major 3rd). If the C in the bass moves down to F, then the upper three voices will still move up (with the fourth, opposite the fifth).
  • Go back to * and have them analyze the two chords.


  • Repeat steps 1-5 above.
  • Point out that they will again be keeping the common tone.
  • Have them copy the C in the upper voices into the C in the second chord (if the C is in the alto in the first chord, it should be repeated in the second chord).
  • Ask them what the third of the first chord is: E.
  • Ask them what the third of the second chord is: A.
  • Ask them which voice contains the third of the first chord. The voice that contains the third of the first chord should leap to the third of the second chord: if the tenor has the E in the first chord, the tenor should have the A in the second chord. When this voice leaps, it is important to make sure that it does not "leap" out of its range. The remaining upper voice will move by step to complete the spelling of the chord with the root doubled (in our example the remaining voice will move by step from a G in the first chord to an F in the second chord). This method is most likely to create a spacing error.
  • Have students make sure that they have not written more than an octave between soprano and alto or between alto and tenor. They may have to change the leaping direction of the voice carrying the third.

Plan For Independent Practice: Give students bass notes a fourth or fifth apart and have them write the upper three voices using all three methods for each bass line. Working in small groups of 2 or 3 may be very helpful in practicing this new tool. Examples of bass lines: F-C; C-G; G-D; D-A; A-E; E-B (and the inversion of each).

Closure (Reflect Anticipatory Set): Plugging notes into one of these three methods can make four-part writing simpler for roots a P4th apart.

Assessment Based On Objectives: Given a bass line, have students write the upper three voices using each of the three methods and identifying the method used.

Adaptations (For Students With Learning Disabilities): Teach method 1 only as it is the most common and can be used most frequently.

Extensions (For Gifted Students): Have the students connect the bass lines above into one continuous progression and identify the methods between chords.

Possible Connections To Other Subjects: Music always has a mathematical connection.