15edo: 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:guest|guest]] and made on <tt>2010-02-19 06:15:39 UTC</tt>.

: This revision was by author [[User:guest|guest]] and made on <tt>2010-02-19 06:24:12 UTC</tt>.

: The original revision id was <tt>~~121498917~~</tt>.

: The original revision id was <tt>121499631</tt>.

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

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15-edo is a 7-limit tuning because of the amount of septimal intervals, but it does contain 11-limit intervals.

15-edo has been labeled a "Porcupine" temperament by Paul Erlich, which has stuck ever since. The name comes from a piece called the "Mizarian Porcupine Overture" by Herman Miller. It also falls into the ~~catagory~~ of kleisma tunings along with 53 and 19.

15-edo has been labeled a "Porcupine" temperament, by Paul Erlich, which has stuck ever since. The name comes from a piece called the "Mizarian Porcupine Overture" by Herman Miller. It also falls into the category of kleisma tunings along with 53 and 19.

from //wikipedia//:

""In music, 15 equal temperament, called 15-TET, 15-EDO, or 15-ET, is the tempered scale derived by dividing the octave into 15 equal steps. Each step represents a frequency ratio of 2 1/15, or 80 cents. Because 15 factors into 3 times 5, it can be seen as being made up of three scales of 5 equal divisions of the octave. 15-ET matches the 11:8 and 16:11 ratios, and does not match the 7:5 or 10:7 tritone."

Additional notes:

In the 15-edo system, major thirds cannot be divided perfectly into two, and coupled with the lack of a standard tritone, this tuning at first can be disorienting. However, because the guitar can be tuned symmetrically, from E to e (6th to 1st strings) unlike the 12-tone system on guitars, the learning curve is very manageable. All chords look the same modualted anywhere, and minor arpeggios are vertically stacked, making them very easy to play. 15-tone may be a promising start for anyone interested in superior harmony and xenharmony, a manageable number of tones, and the sonic fingerprint of multiples of 5-edo. .

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15-edo is a 7-limit tuning because of the amount of septimal intervals, but it does contain 11-limit intervals.

15-edo has been labeled a &quot;Porcupine&quot; temperament by Paul Erlich, which has stuck ever since. The name comes from a piece called the &quot;Mizarian Porcupine Overture&quot; by Herman Miller. It also falls into the ~~catagory~~ of kleisma tunings along with 53 and 19.

15-edo has been labeled a &quot;Porcupine&quot; temperament, by Paul Erlich, which has stuck ever since. The name comes from a piece called the &quot;Mizarian Porcupine Overture&quot; by Herman Miller. It also falls into the category of kleisma tunings along with 53 and 19.

from wikipedia:

&quot;&quot;In music, 15 equal temperament, called 15-TET, 15-EDO, or 15-ET, is the tempered scale derived by dividing the octave into 15 equal steps. Each step represents a frequency ratio of 2 1/15, or 80 cents. Because 15 factors into 3 times 5, it can be seen as being made up of three scales of 5 equal divisions of the octave. 15-ET matches the 11:8 and 16:11 ratios, and does not match the 7:5 or 10:7 tritone.&quot;

Additional notes:

In the 15-edo system, major thirds cannot be divided perfectly into two, and coupled with the lack of a standard tritone, this tuning at first can be disorienting. However, because the guitar can be tuned symmetrically, from E to e (6th to 1st strings) unlike the 12-tone system on guitars, the learning curve is very manageable. All chords look the same modualted anywhere, and minor arpeggios are vertically stacked, making them very easy to play. 15-tone may be a promising start for anyone interested in superior harmony and xenharmony, a manageable number of tones, and the sonic fingerprint of multiples of 5-edo. .

@@ 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:guest|guest]] and made on <tt>2010-02-19 06:15:39 UTC</tt>.<br>
+: This revision was by author [[User:guest|guest]] and made on <tt>2010-02-19 06:24:12 UTC</tt>.<br>
-: The original revision id was <tt>121498917</tt>.<br>
+: The original revision id was <tt>121499631</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 9: / Line 9: @@
 -edo is a 7-limit tuning because of the amount of septimal intervals, but it does contain 11-limit intervals.
--edo has been labeled a "Porcupine" temperament by Paul Erlich, which has stuck ever since. The name comes from a piece called the "Mizarian Porcupine Overture" by Herman Miller. It also falls into the catagory of kleisma tunings along with 53 and 19.
+-edo has been labeled a "Porcupine" temperament, by Paul Erlich, which has stuck ever since. The name comes from a piece called the "Mizarian Porcupine Overture" by Herman Miller. It also falls into the category of kleisma tunings along with 53 and 19.
+from //wikipedia//:
 ""In music, 15 equal temperament, called 15-TET, 15-EDO, or 15-ET, is the tempered scale derived by dividing the octave into 15 equal steps. Each step represents a frequency ratio of 2 1/15, or 80 cents. Because 15 factors into 3 times 5, it can be seen as being made up of three scales of 5 equal divisions of the octave. 15-ET matches the 11:8 and 16:11 ratios, and does not match the 7:5 or 10:7 tritone."
+Additional notes:
+In the 15-edo system, major thirds cannot be divided perfectly into two, and coupled with the lack of a standard tritone, this tuning at first can be disorienting. However, because the guitar can be tuned symmetrically, from E to e (6th to 1st strings) unlike the 12-tone system on guitars, the learning curve is very manageable. All chords look the same modualted anywhere, and minor arpeggios are vertically stacked, making them very easy to play. 15-tone may be a promising start for anyone interested in superior harmony and xenharmony, a manageable number of tones, and the sonic fingerprint of multiples of 5-edo. .
@@ Line 36: / Line 41: @@
   &lt;br /&gt;
 -edo is a 7-limit tuning because of the amount of septimal intervals, but it does contain 11-limit intervals.&lt;br /&gt;
--edo has been labeled a &amp;quot;Porcupine&amp;quot; temperament by Paul Erlich, which has stuck ever since. The name comes from a piece called the &amp;quot;Mizarian Porcupine Overture&amp;quot; by Herman Miller. It also falls into the catagory of kleisma tunings along with 53 and 19.&lt;br /&gt;
+-edo has been labeled a &amp;quot;Porcupine&amp;quot; temperament, by Paul Erlich, which has stuck ever since. The name comes from a piece called the &amp;quot;Mizarian Porcupine Overture&amp;quot; by Herman Miller. It also falls into the category of kleisma tunings along with 53 and 19.&lt;br /&gt;
 &lt;br /&gt;
+from &lt;em&gt;wikipedia&lt;/em&gt;:&lt;br /&gt;
 &amp;quot;&amp;quot;In music, 15 equal temperament, called 15-TET, 15-EDO, or 15-ET, is the tempered scale derived by dividing the octave into 15 equal steps. Each step represents a frequency ratio of 2 1/15, or 80 cents. Because 15 factors into 3 times 5, it can be seen as being made up of three scales of 5 equal divisions of the octave. 15-ET matches the 11:8 and 16:11 ratios, and does not match the 7:5 or 10:7 tritone.&amp;quot;&lt;br /&gt;
+&lt;br /&gt;
+Additional notes:&lt;br /&gt;
+&lt;br /&gt;
+In the 15-edo system, major thirds cannot be divided perfectly into two, and coupled with the lack of a standard tritone, this tuning at first can be disorienting. However, because the guitar can be tuned symmetrically, from E to e (6th to 1st strings) unlike the 12-tone system on guitars, the learning curve is very manageable. All chords look the same modualted anywhere, and minor arpeggios are vertically stacked, making them very easy to play. 15-tone may be a promising start for anyone interested in superior harmony and xenharmony, a manageable number of tones, and the sonic fingerprint of multiples of 5-edo. .&lt;br /&gt;
 &lt;br /&gt;
 &lt;br /&gt;