Periods and generators: Difference between revisions

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<h2>IMPORTED REVISION FROM WIKISPACES</h2>

This is an imported revision from Wikispaces. The revision metadata is included below for reference:

: This revision was by author [[User:~~mbattaglia1~~|~~mbattaglia1~~]] and made on <tt>~~2011~~-09-~~19 00~~:06:54 UTC</tt>.

: This revision was by author [[User:guest|guest]] and made on <tt>2012-11-23 21:26:43 UTC</tt>.

: The original revision id was <tt>~~255469366~~</tt>.

: The original revision id was <tt>385427630</tt>.

: The revision comment was: <tt></tt>

The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.

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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.

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: (...) - C0 - D0 - E0 - F0 - G0 - A0 - B0 - C1 - D1 - E1 - F1 - G1 - A1 - B1 - C1 - (...). In this case, the generator at which the scale is repeated is given the special name of **period**.

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: (...) - C0 - D0 - E0 - F0 - G0 - A0 - B0 - C1 - D1 - E1 - F1 - G1 - A1 - B1 - C2 - (...). In this case, the generator at which the scale is repeated is given the special name of **period**.

Hence, in the above example, the Pythagorean diatonic scale is generated by two different intervals, which are the 3/2 and the 2/1, and the 2/1 is the period.

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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.

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: (...) - C0 - D0 - E0 - F0 - G0 - A0 - B0 - C1 - D1 - E1 - F1 - G1 - A1 - B1 - C1 - (...). In this case, the generator at which the scale is repeated is given the special name of period.

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: (...) - C0 - D0 - E0 - F0 - G0 - A0 - B0 - C1 - D1 - E1 - F1 - G1 - A1 - B1 - C2 - (...). In this case, the generator at which the scale is repeated is given the special name of period.

Hence, in the above example, the Pythagorean diatonic scale is generated by two different intervals, which are the 3/2 and the 2/1, and the 2/1 is the period.

@@ Line 1: / Line 1: @@
 <h2>IMPORTED REVISION FROM WIKISPACES</h2>
 This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>
-: This revision was by author [[User:mbattaglia1|mbattaglia1]] and made on <tt>2011-09-19 00:06:54 UTC</tt>.<br>
+: This revision was by author [[User:guest|guest]] and made on <tt>2012-11-23 21:26:43 UTC</tt>.<br>
-: The original revision id was <tt>255469366</tt>.<br>
+: The original revision id was <tt>385427630</tt>.<br>
 : The revision comment was: <tt></tt><br>
 The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.<br>
@@ Line 21: / Line 21: @@
 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.
-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: (...) - C0 - D0 - E0 - F0 - G0 - A0 - B0 - C1 - D1 - E1 - F1 - G1 - A1 - B1 - C1 - (...). In this case, the generator at which the scale is repeated is given the special name of **period**.
+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: (...) - C0 - D0 - E0 - F0 - G0 - A0 - B0 - C1 - D1 - E1 - F1 - G1 - A1 - B1 - C2 - (...). In this case, the generator at which the scale is repeated is given the special name of **period**.
 Hence, in the above example, the Pythagorean diatonic scale is generated by two different intervals, which are the 3/2 and the 2/1, and the 2/1 is the period.
@@ Line 57: / Line 57: @@
   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.&lt;br /&gt;
 &lt;br /&gt;
-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: (...) - C0 - D0 - E0 - F0 - G0 - A0 - B0 - C1 - D1 - E1 - F1 - G1 - A1 - B1 - C1 - (...). In this case, the generator at which the scale is repeated is given the special name of &lt;strong&gt;period&lt;/strong&gt;.&lt;br /&gt;
+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: (...) - C0 - D0 - E0 - F0 - G0 - A0 - B0 - C1 - D1 - E1 - F1 - G1 - A1 - B1 - C2 - (...). In this case, the generator at which the scale is repeated is given the special name of &lt;strong&gt;period&lt;/strong&gt;.&lt;br /&gt;
 &lt;br /&gt;
 Hence, in the above example, the Pythagorean diatonic scale is generated by two different intervals, which are the 3/2 and the 2/1, and the 2/1 is the period.&lt;br /&gt;