(musTh 212) Rhythm and Meter Assignment Number 2

Due Monday, 2/27/12.

Exercises from Chapter 6 of the Kostka (pp. 122 – 124):

• Part A, 3 and 4
• Part B, 1 – 5

For the questions about polytempo in Part A, the equation and explanations from the tempo modulation post will be all you need to solve for all the tempi in question 3. For question 4, the wording is a little confusing. Here are some hints:

• 4a: first find the quarter note tempo of half = 96. Then treat the triplet eighth and the sixteenth note as the same rhythmic value (they equal each other from old to new). The new tempo will be slower than the old quarter note tempo (but faster than the old half note tempo).
• 4b: focus on the common denominator rhythmic value between the dotted half note and the half note tied to an eighth note. If you plug and chug you are likely to end up with a faster tempo, but realize that if the new shorter duration equals the old longer duration, then the tempo is slowing down.** Adjust your ratio accordingly; the answer is a whole number, and slower than the original tempo.
• 4c: the same is true of this ratio. What used to take x units now takes x+1. The new tempo is slower than the previous tempo.**

**Consider a two simple examples:

• The tempo is quarter = 120.
• To change to the new tempo, an old eighth note now equals a triplet eighth note. It used to take two subdivisions to complete one beat, but now it takes three subdivisions of the same length to complete one beat. Therefore, the tempo is slowing down.
• 120(2/3) = 80. The old grouping was two (eighth notes); the new grouping is three (triplet eighth notes, that are the same duration as the old eighth note).
• The tempo is quarter = 120.
• The old half note equals the new quarter note. The old grouping is four eighth notes and the new grouping is two eighth notes, but the eighth notes are note equal across tempi. What took two beats now takes one beat, which is twice as long as the old beat 120(1/2)=60. Remember, if the old duration is equal to a new duration of shorter rhythmic value, then the tempo is slowing down. Adjust your ratio accordingly.