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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 octave? 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?