Periods and generators: Difference between revisions

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== Introduction to periods ==

In the case of the above example, the addition of 2/1 as a second prime interval will allow us the additional degree of freedom needed to turn the Pythagorean chain of fifths into the Pythagorean diatonic scale. The operation to do so is trivial: simply take seven consecutive fifths out of the chain, and then reduce each note to the octave. In this case, we obtain 0 → 204 → 408 → 498 → 702 → 906 → 1110 cents, which in diatonic notation spells C-D-E-F-G-A-B.

In the case of the above example, the addition of 2/1 as a second prime interval will allow us the additional degree of freedom needed to turn the Pythagorean chain of fifths into the Pythagorean diatonic scale. The operation to do so is trivial: simply take seven consecutive fifths out of the chain, and then reduce each note to the octave. In this case, we obtain {{dash|0, 204, 408, 498, 702, 906, 1110|s=space|d=rarr}} cents, which in diatonic notation spells {{dash|C-D-E-F-G-A-B}|s=thin|d=med}}.

If we so wish, we can take this resulting pattern and tile it ad infinitum along this new chain of octave generators, copying and pasting it every time a new octave appears. If we do, we obtain an infinitely-repeating periodic scale: {{dash|(...), C0, D0, E0, F0, G0, A0, B0, C1, D1, E1, F1, G1, A1, B1, C2, (...)|s=thin|d=med}}. In this case, the generator at which the scale is repeated is given the special name of '''period'''.

@@ Line 20: / Line 20: @@
 == Introduction to periods ==
-In the case of the above example, the addition of 2/1 as a second prime interval will allow us the additional degree of freedom needed to turn the Pythagorean chain of fifths into the Pythagorean diatonic scale. The operation to do so is trivial: simply take seven consecutive fifths out of the chain, and then reduce each note to the octave. In this case, we obtain 0 → 204 → 408 → 498 → 702 → 906 → 1110 cents, which in diatonic notation spells C-D-E-F-G-A-B.
+In the case of the above example, the addition of 2/1 as a second prime interval will allow us the additional degree of freedom needed to turn the Pythagorean chain of fifths into the Pythagorean diatonic scale. The operation to do so is trivial: simply take seven consecutive fifths out of the chain, and then reduce each note to the octave. In this case, we obtain {{dash|0, 204, 408, 498, 702, 906, 1110|s=space|d=rarr}} cents, which in diatonic notation spells {{dash|C-D-E-F-G-A-B}|s=thin|d=med}}.
 If we so wish, we can take this resulting pattern and tile it ad infinitum along this new chain of octave generators, copying and pasting it every time a new octave appears. If we do, we obtain an infinitely-repeating periodic scale: {{dash|(...), C0, D0, E0, F0, G0, A0, B0, C1, D1, E1, F1, G1, A1, B1, C2, (...)|s=thin|d=med}}. In this case, the generator at which the scale is repeated is given the special name of '''period'''.