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Problem 6) Let's consider another way we might arrive at different tunings for enharmonic equivalents. We will think of tunings where 11 P5 are equal,

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Problem 6) Let's consider another way we might arrive at different tunings for enharmonic equivalents. We will think of tunings where 11 P5 are equal, and one is different (usually a badlytuned \"wolf\"). We can avoid the wolf if we think of the circle of fths as a spiral, since note names never repeat: there is no \"circle\" that must \"close\" to 8400 cents. Note that your cents values should be kept between 0 and 1200: shift by whole octaves, as needed... a) Start at C and go up 7 P5, all just. What is the note name, properly spelled, and what is the cents value relative to C 'F b) Start at C and go down 5 P5, all just. What is the note name, properly spelled, and what is the cents value relative to C? c) If you did a) and b) correctly, you should get two different tunings for dierentlynamed enhar monic equivalents. Which is sharper, the note with the sharp in the name, or the note with the at? (Older violin nger charts often make this distinction!) d) In 1/4comma meantone tuning, 11 of the P5 are equal, but atter than just. Ignore the wolf, and use the \"common\" P5 size for meantone in place of the just value, and redo parts a), b), c). What is the main \"big picture\" difference? e) In parts a), b), we kept correct spelling and also avoided using the Wolf P5 cents value. Now, go down 5 P5 from C, but this time make the P5 below E\" be the usual Pythagorean wolf, and also misspell (only) this P5 as going down from Eb to Giff. Now, what does the answer to b) become, both name and tuning in cents? HINT: this time, +7 P5 and 5 P5 should agree, since it is a real 12noteperoctave tuning, unlike the nonrepeating spiral with ALL Just P5

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