Download Music Theory 171 Questions on Chapters 3A, 3B and 3C 3A

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Music Theory 171
Questions on Chapters 3A, 3B and 3C
3A Pythagorean Ratios
1. Briefly summarize the arithmetic mean and the harmonic mean and indicate
which intervals are created by each mean.
2. What does this say about the relationship between the fifth, the fourth and the
3. What is created between the fifth and the fourth, and what is its ratio?
4. The notes of the major, minor, Phrygian and Middle Eastern tetrachords and listed
on this page. Transpose them to the key of D and write the names of the notes for
the four tetrachords, beginning on D.
5. Briefly summarize the relationship between the irrational number derived from
the unit triangle (both sides equal to 1) and the interval of the tritone.
3B Pythagorean Scales
1. How can Pentatonic scales be seen as being derived from perfect fifths above and
below a central tone?
2. Note the ratios of the pentatonic scale. We have covered the octave (1:1), fifth
(3:2), fourth (4:3) and whole tone (9:8). The other inverval discovered here is the
minor seventh from D to C. How is it derived?
3. How can the Dorian mode be seen to be derived from fifths above and below the
central D tone?
4. Read through the remainder of this page and summarize the issue regarding the
fact that two Pythagorean semitones does not equal on Pythagorean whole tone.
3C Just Intonataion
1. Give a reading of this page and answer this one question: What is the ratio of the
major and minor third based on Just Intonation, and why did this become the
preferred method of intonation?