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atterns in J.S. Bach

rade Level: High School; Type: Mathematics

bjective:

etermine the mathematical patterns in JS Bach’s two movement preludes and

gues.

esearch Question:

Is there a mathematical pattern in these compositions?

Does the ratio of treble notes to bass notes in a measure repeat itself?

Does the total number of notes in a measure repeat itself in a predictable

 way?

his experiment does demand a certain level of musical and mathematical

nowledge. It's also helpful to know how to set up a spreadsheet in Excel or similar program.

aterials:

Computer with Excel, or comparable program installed

Johann Sebastian Bach, Complete Preludes and Fugue for Organ. Bach’s Notebook for Anna Magdelina

can also be used.

xperimental Procedure:

1. Identify the measure numbers in your sheet music by counting them off and labeling them: measure #1,

measure #2, and so forth

2. Set up your spreadsheet. There should be a row for every measure and a column for the number of bassnotes, treble notes and pedal lines, as well as a column for the ratio of treble notes to bass notes, the ratio

of treble notes to pedal lines, and the ratio of bass notes to pedal lines. Be advised, there are no pedal

lines in the Notebook for Anna Magdalena.

3. Count the number of treble notes, bass notes and pedal lines in every measure. Enter this data on your

data sheet.

4. Create three bar graphs showing a) the number of treble notes per meausure, b) the number of bass

notes per measure and c) the ratio between the two.

5. Examine the graph to determine a pattern. For example, is a measure with 16 treble notes more likely to be

followed with a measure of 4 notes? Record your findings.

6. Examine the pedal lines as a function of the number of treble notes and as a function of the number of bass

notes. Record what pattern, if any, you observe.

erms/Concepts: treble notes, bass notes, pedal lines, ratio, function, repeating sequences