800 023 Mathematics for Decision Making [Campbell] Music/Dance Problems

No Homework will be collected, but you should look at the following problems

A piece of music with a 5/4 time signature is to be played at 120 beats per minute. How many measures per minute is that? How long will a beat last? How long will a measure last?
A piece of music with a 3/4 time signature is to be played with 40 measures per minute. How many beats per minute is that? How long will a half note last? How long will a quarter note last? How long will an eighth note last? How long will a sixteenth note last?
a piece of music with a 2/2 time signature has 20 measures. If you want it to last 15 seconds, how many beats per minute should you play? How many measures per minute? What should be the duration of a quarter note?
A piece of music has the rhythm SQQSQ. If you want to represent this in a single measure with a S:Q ratio of 2:1, what time signature should you use? If you want to represent this in a single measure with a S:Q ratio of 3:1, what time signature should you use? If you want to represent this in a single measure with a S:Q ratio of 3:2, what time signature should you use? [use sixteenth notes for the beat]
between which octaves is the fifth harmonic? Between which octaves is the fiftieth harmonic?
Between which harmonics is five fifths above the fundamental? between which octaves is five fifths above the fundamental? Between which harmonics is a second above a third above a fourth above a fifth above a sixth above a seventh? Between which octaves is a second above a third above a fourth above a fifth above a sixth above a seventh?
Which is the lowest harmonic of the fundamental which is a harmonic of both a second and a seventh? Which is the lowest harmonic of the fundamental which is a harmonic of both a third and a sixth?
Which notes must be sharped or flatted to obtain an E major scale (the whole/half step sequence of the white keys starting with C, but starting with E)? Which notes must be sharped or flatted to obtain an E minor scale (the whole/half step sequence of the white keys starting with A, but starting with E)?
Which notes must be sharped or flatted to obtain a Neapolitan minor scale starting with C (the whole/half step sequence HWWWH(3/2)H)?
For the sequence of notes ABECGBD, give a repetition, an inversion, a retrogression, a translation, and a cycling.
How would you represent ladies 2 an 4 exchanging places and ladies 1 and 3 not moving in cycle (parentheses) notation? Lady 1 going to 2, 2 to 4, and 4 to 1, and 3 remaining in place?
What is the result of (13)(24) followed by (12)(34)? (124)(3) followed by (1)(243)? (124)(3) followed by (124)(3)?
What is the inverse of (1)(24)(3)? of (124)(3)?
What would return the women home after (124)(3) followed by (1)(243)? after (124)(3) followed by (124)(3)?
Which forms of symmetry restrict the center between two partners to a point? a line? the entire dance floor?
What is the impact of imposing multiple symmetries?
How can one transition from one symmetry to another (without a transition which is not a symmetry)?
What is possible in two dimensional dance viewed in two dimensions (with the planes coinciding) that is not possible in one dimensional dance viewed in one dimensional dance (with the lines coinciding)? What is further possible in three dimensional dance viewed in three dimensions?
What is the difference between two dimensional motion viewed in a plane which intersects the motion in a line containing the viewer and one dimensional motion and viewing for which the lines coincide? Is the increased motion dimension or viewing dimension responsible for the difference?
With one dimension for viewing and one dimension for dance, what is the difference between the viewing and dance lines coinciding versus intersecting in a single point? With one dimension for viewing and two dimensions for dance, what is the difference between the viewing line lying in the dance plane versus intersecting in a single point? With three dimensional viewing, what is the difference between the viewer being in versus not being in the line of one dimensional dance motion? With three dimensional viewing, what is the difference between the viewer being in versus not being in the plane of two dimensional dance motion?

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