833 Cent Golden Scale (Bohlen): 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:~~xenwolf~~|~~xenwolf~~]] and made on <tt>~~2012~~-12-~~03 03~~:19:51 UTC</tt>.

: This revision was by author [[User:JosephRuhf|JosephRuhf]] and made on <tt>2016-12-19 20:21:52 UTC</tt>.

: The original revision id was <tt>~~388402046~~</tt>.

: The original revision id was <tt>602523412</tt>.

: The revision comment was: <tt>~~I hope that's ok for you, Dave?~~</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.

<h4>Original Wikitext content:</h4>

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99.27 - 235.77 - 366.91 - 466.18 - 597.32 - 733.82 - 833.09

**833.09 is the cents value of the Golden Ratio**, on which the scale is based and at which point the scale step pattern repeats. Octaves do occur in this scale but only incidentally; many octaves are out of tune, and the scale is not an octave-repeating scale.

The scale is designed to take advantage of the naturally occurring mathematical concept of **combination tones** in order to create a whole different breed of consonant harmony. The interval of the Golden Ratio has the peculiar quality of combining harmoniously with itself when stacked. Consider the Fibonacci Sequence, and say we're starting on A 55. You have 55, 89, 144, 233, 377, 610, 987, 1597 and so on. These hz values are all related intrinsically by combination, and the ratios of each adjacent pitch are extremely close to the Golden Ratio. So likewise, when any number of Golden intervals are stacked you get a stable, sonorous sound which could be considered "consonant." For this reason the scale repeats at the GR and not the octave; the harmony is built around the GR and its properties. The scale is designed so that no matter what step of the scale you're ~~one~~, if you go up seven steps you'll arrive at a perfect GR.

The scale is designed to take advantage of the naturally occurring mathematical concept of **combination tones** in order to create a whole different breed of consonant harmony. The interval of the Golden Ratio has the peculiar quality of combining harmoniously with itself when stacked. Consider the Fibonacci Sequence, and say we're starting on A 55. You have 55, 89, 144, 233, 377, 610, 987, 1597 and so on. These hz values are all related intrinsically by combination, and the ratios of each adjacent pitch are extremely close to the Golden Ratio. So likewise, when any number of Golden intervals are stacked you get a stable, sonorous sound which could be considered "consonant." For this reason the scale repeats at the GR and not the octave; the harmony is built around the GR and its properties. The scale is designed so that no matter what step of the scale you're on, if you go up seven steps you'll arrive at a perfect GR.

The scale has its own harmonious triads, based on three crucial intervals:

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[[xenharmonic/36edo|https://xenharmonic.wikispaces.com/36edo]]

**Again, **the best authority on the scale is Bohlen himself:

**Again,** the best authority on the scale is Bohlen himself:

[[http://www.huygens-fokker.org/bpsite/]]

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99.27 - 235.77 - 366.91 - 466.18 - 597.32 - 733.82 - 833.09

833.09 is the cents value of the Golden Ratio, on which the scale is based and at which point the scale step pattern repeats. Octaves do occur in this scale but only incidentally; many octaves are out of tune, and the scale is not an octave-repeating scale.

833.09 is the cents value of the Golden Ratio, on which the scale is based and at which point the scale step pattern repeats. Octaves do occur in this scale but only incidentally; many octaves are out of tune, and the scale is not an octave-repeating scale.

The scale is designed to take advantage of the naturally occurring mathematical concept of combination tones in order to create a whole different breed of consonant harmony. The interval of the Golden Ratio has the peculiar quality of combining harmoniously with itself when stacked. Consider the Fibonacci Sequence, and say we're starting on A 55. You have 55, 89, 144, 233, 377, 610, 987, 1597 and so on. These hz values are all related intrinsically by combination, and the ratios of each adjacent pitch are extremely close to the Golden Ratio. So likewise, when any number of Golden intervals are stacked you get a stable, sonorous sound which could be considered &quot;consonant.&quot; For this reason the scale repeats at the GR and not the octave; the harmony is built around the GR and its properties. The scale is designed so that no matter what step of the scale you're ~~one~~, if you go up seven steps you'll arrive at a perfect GR.

The scale is designed to take advantage of the naturally occurring mathematical concept of combination tones in order to create a whole different breed of consonant harmony. The interval of the Golden Ratio has the peculiar quality of combining harmoniously with itself when stacked. Consider the Fibonacci Sequence, and say we're starting on A 55. You have 55, 89, 144, 233, 377, 610, 987, 1597 and so on. These hz values are all related intrinsically by combination, and the ratios of each adjacent pitch are extremely close to the Golden Ratio. So likewise, when any number of Golden intervals are stacked you get a stable, sonorous sound which could be considered &quot;consonant.&quot; For this reason the scale repeats at the GR and not the octave; the harmony is built around the GR and its properties. The scale is designed so that no matter what step of the scale you're on, if you go up seven steps you'll arrive at a perfect GR.

The scale has its own harmonious triads, based on three crucial intervals:

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<a class="wiki_link" href="http://xenharmonic.wikispaces.com/36edo">https://xenharmonic.wikispaces.com/36edo</a>

Again, the best authority on the scale is Bohlen himself:

Again, the best authority on the scale is Bohlen himself:

<a class="wiki_link_ext" href="http://www.huygens-fokker.org/bpsite/" rel="nofollow">http://www.huygens-fokker.org/bpsite/</a>

@@ 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:xenwolf|xenwolf]] and made on <tt>2012-12-03 03:19:51 UTC</tt>.<br>
+: This revision was by author [[User:JosephRuhf|JosephRuhf]] and made on <tt>2016-12-19 20:21:52 UTC</tt>.<br>
-: The original revision id was <tt>388402046</tt>.<br>
+: The original revision id was <tt>602523412</tt>.<br>
-: The revision comment was: <tt>I hope that's ok for you, Dave?</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>
 <h4>Original Wikitext content:</h4>
@@ Line 19: / Line 19: @@
 .27 - 235.77 - 366.91 - 466.18 - 597.32 - 733.82 - 833.09
 **833.09 is the cents value of the Golden Ratio**, on which the scale is based and at which point the scale step pattern repeats. Octaves do occur in this scale but only incidentally; many octaves are out of tune, and the scale is not an octave-repeating scale.
-The scale is designed to take advantage of the naturally occurring mathematical concept of **combination tones** in order to create a whole different breed of consonant harmony. The interval of the Golden Ratio has the peculiar quality of combining harmoniously with itself when stacked. Consider the Fibonacci Sequence, and say we're starting on A 55. You have 55, 89, 144, 233, 377, 610, 987, 1597 and so on. These hz values are all related intrinsically by combination, and the ratios of each adjacent pitch are extremely close to the Golden Ratio. So likewise, when any number of Golden intervals are stacked you get a stable, sonorous sound which could be considered "consonant." For this reason the scale repeats at the GR and not the octave; the harmony is built around the GR and its properties. The scale is designed so that no matter what step of the scale you're one, if you go up seven steps you'll arrive at a perfect GR.
+The scale is designed to take advantage of the naturally occurring mathematical concept of **combination tones** in order to create a whole different breed of consonant harmony. The interval of the Golden Ratio has the peculiar quality of combining harmoniously with itself when stacked. Consider the Fibonacci Sequence, and say we're starting on A 55. You have 55, 89, 144, 233, 377, 610, 987, 1597 and so on. These hz values are all related intrinsically by combination, and the ratios of each adjacent pitch are extremely close to the Golden Ratio. So likewise, when any number of Golden intervals are stacked you get a stable, sonorous sound which could be considered "consonant." For this reason the scale repeats at the GR and not the octave; the harmony is built around the GR and its properties. The scale is designed so that no matter what step of the scale you're on, if you go up seven steps you'll arrive at a perfect GR.
 The scale has its own harmonious triads, based on three crucial intervals:
@@ Line 38: / Line 38: @@
 [[xenharmonic/36edo|https://xenharmonic.wikispaces.com/36edo]]
-**Again, **the best authority on the scale is Bohlen himself:
+**Again,** the best authority on the scale is Bohlen himself:
 [[http://www.huygens-fokker.org/bpsite/]]
@@ Line 61: / Line 61: @@
 .27 - 235.77 - 366.91 - 466.18 - 597.32 - 733.82 - 833.09&lt;br /&gt;
 &lt;br /&gt;
-&lt;strong&gt;833.09 is the cents value of the Golden Ratio&lt;/strong&gt;, on which the scale is based and at which point the scale step pattern repeats. Octaves do occur in this scale but only incidentally; many octaves are out of tune, and the scale is not an octave-repeating scale. &lt;br /&gt;
+&lt;strong&gt;833.09 is the cents value of the Golden Ratio&lt;/strong&gt;, on which the scale is based and at which point the scale step pattern repeats. Octaves do occur in this scale but only incidentally; many octaves are out of tune, and the scale is not an octave-repeating scale.&lt;br /&gt;
 &lt;br /&gt;
 &lt;br /&gt;
-The scale is designed to take advantage of the naturally occurring mathematical concept of &lt;strong&gt;combination tones&lt;/strong&gt; in order to create a whole different breed of consonant harmony. The interval of the Golden Ratio has the peculiar quality of combining harmoniously with itself when stacked. Consider the Fibonacci Sequence, and say we're starting on A 55. You have 55, 89, 144, 233, 377, 610, 987, 1597 and so on. These hz values are all related intrinsically by combination, and the ratios of each adjacent pitch are extremely close to the Golden Ratio. So likewise, when any number of Golden intervals are stacked you get a stable, sonorous sound which could be considered &amp;quot;consonant.&amp;quot; For this reason the scale repeats at the GR and not the octave; the harmony is built around the GR and its properties. The scale is designed so that no matter what step of the scale you're one, if you go up seven steps you'll arrive at a perfect GR.&lt;br /&gt;
+The scale is designed to take advantage of the naturally occurring mathematical concept of &lt;strong&gt;combination tones&lt;/strong&gt; in order to create a whole different breed of consonant harmony. The interval of the Golden Ratio has the peculiar quality of combining harmoniously with itself when stacked. Consider the Fibonacci Sequence, and say we're starting on A 55. You have 55, 89, 144, 233, 377, 610, 987, 1597 and so on. These hz values are all related intrinsically by combination, and the ratios of each adjacent pitch are extremely close to the Golden Ratio. So likewise, when any number of Golden intervals are stacked you get a stable, sonorous sound which could be considered &amp;quot;consonant.&amp;quot; For this reason the scale repeats at the GR and not the octave; the harmony is built around the GR and its properties. The scale is designed so that no matter what step of the scale you're on, if you go up seven steps you'll arrive at a perfect GR.&lt;br /&gt;
 &lt;br /&gt;
 The scale has its own harmonious triads, based on three crucial intervals:&lt;br /&gt;
@@ Line 80: / Line 80: @@
 &lt;a class="wiki_link" href="http://xenharmonic.wikispaces.com/36edo"&gt;https://xenharmonic.wikispaces.com/36edo&lt;/a&gt;&lt;br /&gt;
 &lt;br /&gt;
-&lt;strong&gt;Again, &lt;/strong&gt;the best authority on the scale is Bohlen himself:&lt;br /&gt;
+&lt;strong&gt;Again,&lt;/strong&gt; the best authority on the scale is Bohlen himself:&lt;br /&gt;
 &lt;a class="wiki_link_ext" href="http://www.huygens-fokker.org/bpsite/" rel="nofollow"&gt;http://www.huygens-fokker.org/bpsite/&lt;/a&gt;&lt;br /&gt;
 &lt;br /&gt;