833 Cent Golden Scale (Bohlen) - Revision history

BudjarnLambeth: Moved from category "golden" to "golden ratio"

2023-04-28T09:25:53Z

Moved from category "golden" to "golden ratio"

← Older revision		Revision as of 09:25, 28 April 2023
Line 45:		Line 45:

	[[Category:7-tone scales]]		[[Category:7-tone scales]]
	[[Category:Golden]]		[[Category:Golden ratio]]
	[[Category:Nonoctave]]		[[Category:Nonoctave]]
	[[Category:Bohlen]]		[[Category:Bohlen]]
	[[Category:Listen]]		[[Category:Listen]]

Fredg999 category edits: Moving from Category:7-note scales to Category:7-tone scales using Cat-a-lot

2022-02-26T18:19:52Z

Moving from Category:7-note scales to Category:7-tone scales using Cat-a-lot

← Older revision		Revision as of 18:19, 26 February 2022
Line 44:		Line 44:
	* [http://www.huygens-fokker.org/bpsite/833cent.html ''An 833 Cents Scale - An experiment on harmony''] (Bohlen's original article)		* [http://www.huygens-fokker.org/bpsite/833cent.html ''An 833 Cents Scale - An experiment on harmony''] (Bohlen's original article)

	[[Category:7-~~note~~ scales]]		[[Category:7-tone scales]]
	[[Category:Golden]]		[[Category:Golden]]
	[[Category:Nonoctave]]		[[Category:Nonoctave]]
	[[Category:Bohlen]]		[[Category:Bohlen]]
	[[Category:Listen]]		[[Category:Listen]]

Fredg999: Recategorization, improved markup, moved external link to the end

2021-08-05T15:39:08Z

Recategorization, improved markup, moved external link to the end

← Older revision		Revision as of 15:39, 5 August 2021
Line 1:		Line 1:
	~~=The 833 Cent Golden Scale (~~Heinz Bohlen)=		Heinz Bohlen's '''833 Cents Scale''' is a combination-tone-based scale which repeats at the interval of the [[golden ratio]] (φ = 1.618...).
	'''~~Golden~~ Scale: a combination-tone-based scale which repeats at the interval of the ~~Golden Ratio,~~ 1.618...~~'''~~

	~~See Bohlen's own site for the full story: http://www.huygens-fokker.org/bpsite/833cent.html~~		== Theory ==

	There are seven ~~'''~~unequal steps~~'''~~ in the Golden Scale, for starters:		There are seven unequal steps in the Golden Scale, for starters:

	: 99.27 - 136.50 - 131.14 - 99.27 - 131.14 - 136.50 - 99.27		: 99.27 - 136.50 - 131.14 - 99.27 - 131.14 - 136.50 - 99.27
Line 12:		Line 11:
	: 99.27 - 235.77 - 366.91 - 466.18 - 597.32 - 733.82 - 833.09		: 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 Hz. You have 55, 89, 144, 233, 377, 610, 987, 1597 Hz and so on. These frequencies 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 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 Hz. You have 55, 89, 144, 233, 377, 610, 987, 1597 Hz and so on. These frequencies 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.
Line 38:		Line 37:
	-Dave G.		-Dave G.

			== Music ==
			* ''[[:File:GR_Symphony_A.mp3\|Gr Symphony A]]'' by [[David_Guillot\|David Guillot]] ([https://soundcloud.com/dmguillotine/gr-symphony Listen on SoundCloud])
			* ''833c by Bohlen scale improv'' by [[Yin Bell]] ([https://soundcloud.com/yinbell/833c-bp-scale-improv Listen on SoundCloud])

	==~~Music~~==		== External links ==
	~~''[~~[:~~File:GR_Symphony_A~~.~~mp3\|"Gr Symphony A"]]~~'' ~~by [[David_Guillot\|David Guillot]~~]		* [http://www.huygens-fokker.org/bpsite/833cent.html ''An 833 Cents Scale - An experiment on harmony''] (Bohlen's original article)

			[[Category:7-note scales]]
			[[Category:Golden]]
			[[Category:Nonoctave]]
	[[Category:Bohlen]]		[[Category:Bohlen]]
	[[Category:~~golden]]~~		[[Category:Listen]]
	~~[[Category:golden_ratio]]~~
	~~[[Category:listen]]~~
	~~[[Category:ratio]]~~
	~~[[Category:scale~~]]

Spt3125: formatting, category

2018-12-10T16:49:19Z

formatting, category

← Older revision		Revision as of 16:49, 10 December 2018
Line 1:		Line 1:
	=The 833 Cent Golden Scale (Heinz Bohlen)=		=The 833 Cent Golden Scale (Heinz Bohlen)=

	'''Golden Scale: a combination-tone-based scale which repeats at the interval of the Golden Ratio, 1.618...'''		'''Golden Scale: a combination-tone-based scale which repeats at the interval of the Golden Ratio, 1.618...'''

	See Bohlen's own site for the full story.		See Bohlen's own site for the full story: http://www.huygens-fokker.org/bpsite/833cent.html

	~~[http~~:~~//www.huygens-fokker.org/bpsite/833cent.html~~ http://www.huygens-fokker.org/bpsite/833cent.html]

	There are seven '''unequal steps''' in the Golden Scale, for starters:		There are seven '''unequal steps''' in the Golden Scale, for starters:

	99.27 - 136.50 - 131.14 - 99.27 - 131.14 - 136.50 - 99.27		: 99.27 - 136.50 - 131.14 - 99.27 - 131.14 - 136.50 - 99.27

	Which means these are the cent-intervals in the scale before it repeats:		Which means these are the cent-intervals in the scale before it repeats:

	99.27 - 235.77 - 366.91 - 466.18 - 597.32 - 733.82 - 833.09		: 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 "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 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 Hz. You have 55, 89, 144, 233, 377, 610, 987, 1597 Hz and so on. These frequencies 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:		The scale has its own harmonious triads, based on three crucial intervals:

	a. the Golden Ratio or GR, 833.09 ~~cents~~		: a. the Golden Ratio or GR, 833.09 cents

	~~b. the Inversion of the GR, or GRI, 366.91~~ cents

	c. the ~~difference~~ of ~~these two~~, or ~~GRD~~, ~~466~~.18 cents		: b. the Inversion of the GR, or GRI, 366.91 cents

	~~A Root - GRI - GR chord has a more "minor" sound~~,		: c. the difference of these two, or GRD, 466.18 cents

	whereas a Root - GRD - GR chord has a more "major" sound.		A Root - GRI - GR chord has a more "minor" sound, whereas a Root - GRD - GR chord has a more "major" sound.

	A combination of these is the GRID chord, with a dissonance in the middle, which uses inversion to compress a 4-note GR stack into the range of a single GR interval.		A combination of these is the GRID chord, with a dissonance in the middle, which uses inversion to compress a 4-note GR stack into the range of a single GR interval.
Line 35:		Line 30:
	The octave or pseudo-octave occurs at every tenth step of the scale. Perfect fifths appear sometimes too; if you know the scale well enough, you can use traditional harmony within its boundaries. Bohlen describes the variety of intervals that happen at different points in the scale, variable depending on which scale degree you're starting from.		The octave or pseudo-octave occurs at every tenth step of the scale. Perfect fifths appear sometimes too; if you know the scale well enough, you can use traditional harmony within its boundaries. Bohlen describes the variety of intervals that happen at different points in the scale, variable depending on which scale degree you're starting from.

	~~36-EDO~~ provides suitable tempered approximations of the intervals in the Golden Scale. It afford us the ability to compose in the GR scale and/or the traditional Western tonality.		[[36edo]] provides suitable tempered approximations of the intervals in the Golden Scale. It afford us the ability to compose in the GR scale and/or the traditional Western tonality.

	~~[[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/

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

	But there is much still to be discovered with this tuning system. Combination tone harmony opens some interesting doors. The tuning is of course in need of its own theory, something I've been working on for the past year and a half. If you have any interest in the scale, please contact me at [mailto:dmguillot@gmail.com dmguillot@gmail.com] - thanks!		But there is much still to be discovered with this tuning system. Combination tone harmony opens some interesting doors. The tuning is of course in need of its own theory, something I've been working on for the past year and a half. If you have any interest in the scale, please contact me at [mailto:dmguillot@gmail.com dmguillot@gmail.com] - thanks!
Line 47:		Line 38:
	-Dave G.		-Dave G.

	~~'''Musical Example:'''~~

	''[[:File:GR_Symphony_A.mp3\|"Gr Symphony A"]]'' by [[David_Guillot\|David Guillot]] ~~[[Category:833]]~~		==Music==
			''[[:File:GR_Symphony_A.mp3\|"Gr Symphony A"]]'' by [[David_Guillot\|David Guillot]]

	[[Category:Bohlen]]		[[Category:Bohlen]]
	[[Category:golden]]		[[Category:golden]]

Wikispaces>FREEZE at 00:00, 17 July 2018

2018-07-17T00:00:00Z

Show changes

Wikispaces>JosephRuhf: Imported revision 602523412 - Original comment:

2016-12-19T20:21:52Z

**Imported revision 602523412 - Original comment: **

← Older revision		Revision as of 20:21, 19 December 2016
Line 1:		Line 1:
	<h2>IMPORTED REVISION FROM WIKISPACES</h2>		<h2>IMPORTED REVISION FROM WIKISPACES</h2>
	This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>		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>		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>		<h4>Original Wikitext content:</h4>
Line 19:		Line 19:
	99.27 - 235.77 - 366.91 - 466.18 - 597.32 - 733.82 - 833.09		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 "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:		The scale has its own harmonious triads, based on three crucial intervals:
Line 38:		Line 38:
	[[xenharmonic/36edo\|https://xenharmonic.wikispaces.com/36edo]]		[[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/]]		[[http://www.huygens-fokker.org/bpsite/]]

Line 61:		Line 61:
	99.27 - 235.77 - 366.91 - 466.18 - 597.32 - 733.82 - 833.09<br />		99.27 - 235.77 - 366.91 - 466.18 - 597.32 - 733.82 - 833.09<br />
	<br />		<br />
	<strong>833.09 is the cents value of the Golden Ratio</strong>, 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. <br />		<strong>833.09 is the cents value of the Golden Ratio</strong>, 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.<br />
	<br />		<br />
	<br />		<br />
	The scale is designed to take advantage of the naturally occurring mathematical concept of <strong>combination tones</strong> 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.<br />		The scale is designed to take advantage of the naturally occurring mathematical concept of <strong>combination tones</strong> 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.<br />
	<br />		<br />
	The scale has its own harmonious triads, based on three crucial intervals:<br />		The scale has its own harmonious triads, based on three crucial intervals:<br />
Line 80:		Line 80:
	<a class="wiki_link" href="http://xenharmonic.wikispaces.com/36edo">https://xenharmonic.wikispaces.com/36edo</a><br />		<a class="wiki_link" href="http://xenharmonic.wikispaces.com/36edo">https://xenharmonic.wikispaces.com/36edo</a><br />
	<br />		<br />
	<strong>Again, </strong>the best authority on the scale is Bohlen himself:<br />		<strong>Again,</strong> the best authority on the scale is Bohlen himself:<br />
	<a class="wiki_link_ext" href="http://www.huygens-fokker.org/bpsite/" rel="nofollow">http://www.huygens-fokker.org/bpsite/</a><br />		<a class="wiki_link_ext" href="http://www.huygens-fokker.org/bpsite/" rel="nofollow">http://www.huygens-fokker.org/bpsite/</a><br />
	<br />		<br />

Wikispaces>xenwolf: Imported revision 388402046 - Original comment: I hope that's ok for you, Dave?

2012-12-03T03:19:51Z

**Imported revision 388402046 - Original comment: I hope that's ok for you, Dave?**

← Older revision		Revision as of 03:19, 3 December 2012
Line 1:		Line 1:
	<h2>IMPORTED REVISION FROM WIKISPACES</h2>		<h2>IMPORTED REVISION FROM WIKISPACES</h2>
	This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>		This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>
	: This revision was by author [[User:~~keenanpepper~~\|~~keenanpepper~~]] and made on <tt>2012-10-~~26 13~~:10:50 UTC</tt>.<br>		: This revision was by author [[User:xenwolf\|xenwolf]] and made on <tt>2012-12-03 03:19:51 UTC</tt>.<br>
	: The original revision id was <tt>~~376758350~~</tt>.<br>		: The original revision id was <tt>388402046</tt>.<br>
	: The revision comment was: <tt></tt><br>		: The revision comment was: <tt>I hope that's ok for you, Dave?</tt><br>
	The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.<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>		<h4>Original Wikitext content:</h4>
Line 46:		Line 46:

	Musical Example:		Musical Example:
	//[[file:xenharmonic/GR Symphony A.mp3\|"Gr Symphony A"]]//</pre></div>		//[[file:xenharmonic/GR Symphony A.mp3\|"Gr Symphony A"]]// by [[David Guillot]]</pre></div>
	<h4>Original HTML content:</h4>		<h4>Original HTML content:</h4>
	<div style="width:100%; max-height:400pt; overflow:auto; background-color:#f8f9fa; border: 1px solid #eaecf0; padding:0em"><pre style="margin:0px;border:none;background:none;word-wrap:break-word;width:200%;white-space: pre-wrap ! important" class="old-revision-html"><html><head><title>833 Cent Golden Scale (Bohlen)</title></head><body><!-- ws:start:WikiTextHeadingRule:0:&lt;h1&gt; --><h1 id="toc0"><a name="The 833 Cent Golden Scale (Heinz Bohlen)"></a><!-- ws:end:WikiTextHeadingRule:0 -->The 833 Cent Golden Scale (Heinz Bohlen)</h1>		<div style="width:100%; max-height:400pt; overflow:auto; background-color:#f8f9fa; border: 1px solid #eaecf0; padding:0em"><pre style="margin:0px;border:none;background:none;word-wrap:break-word;width:200%;white-space: pre-wrap ! important" class="old-revision-html"><html><head><title>833 Cent Golden Scale (Bohlen)</title></head><body><!-- ws:start:WikiTextHeadingRule:0:&lt;h1&gt; --><h1 id="toc0"><a name="The 833 Cent Golden Scale (Heinz Bohlen)"></a><!-- ws:end:WikiTextHeadingRule:0 -->The 833 Cent Golden Scale (Heinz Bohlen)</h1>
Line 83:		Line 83:
	<a class="wiki_link_ext" href="http://www.huygens-fokker.org/bpsite/" rel="nofollow">http://www.huygens-fokker.org/bpsite/</a><br />		<a class="wiki_link_ext" href="http://www.huygens-fokker.org/bpsite/" rel="nofollow">http://www.huygens-fokker.org/bpsite/</a><br />
	<br />		<br />
	But there is much still to be discovered with this tuning system. Combination tone harmony opens some interesting doors. The tuning is of course in need of its own theory, something I've been working on for the past year and a half. If you have any interest in the scale, please contact me at <!-- ws:start:WikiTextUrlEmailRule:45:dmguillot@gmail.com --><a class="wiki_link_ext" href="mailto:dmguillot@gmail.com" rel="nofollow">dmguillot@gmail.com</a><!-- ws:end:WikiTextUrlEmailRule:45 --> - thanks!<br />		But there is much still to be discovered with this tuning system. Combination tone harmony opens some interesting doors. The tuning is of course in need of its own theory, something I've been working on for the past year and a half. If you have any interest in the scale, please contact me at <!-- ws:start:WikiTextUrlEmailRule:46:dmguillot@gmail.com --><a class="wiki_link_ext" href="mailto:dmguillot@gmail.com" rel="nofollow">dmguillot@gmail.com</a><!-- ws:end:WikiTextUrlEmailRule:46 --> - thanks!<br />
	<br />		<br />
	-Dave G.<br />		-Dave G.<br />
	<br />		<br />
	<strong>Musical Example:</strong><br />		<strong>Musical Example:</strong><br />
	<em><a href="http://xenharmonic.wikispaces.com/file/view/GR%20Symphony%20A.mp3/370837078/GR%20Symphony%20A.mp3" onclick="ws.common.trackFileLink('http://xenharmonic.wikispaces.com/file/view/GR%20Symphony%20A.mp3/370837078/GR%20Symphony%20A.mp3');">&quot;Gr Symphony A&quot;</a></em></body></html></pre></div>		<em><a href="http://xenharmonic.wikispaces.com/file/view/GR%20Symphony%20A.mp3/370837078/GR%20Symphony%20A.mp3" onclick="ws.common.trackFileLink('http://xenharmonic.wikispaces.com/file/view/GR%20Symphony%20A.mp3/370837078/GR%20Symphony%20A.mp3');">&quot;Gr Symphony A&quot;</a></em> by <a class="wiki_link" href="/David%20Guillot">David Guillot</a></body></html></pre></div>

Wikispaces>keenanpepper: Imported revision 376758350 - Original comment:

2012-10-26T13:10:50Z

**Imported revision 376758350 - Original comment: **

Show changes

Wikispaces>dmGuillotine: Imported revision 371263022 - Original comment:

2012-10-08T18:22:54Z

**Imported revision 371263022 - Original comment: **

← Older revision		Revision as of 18:22, 8 October 2012
Line 1:		Line 1:
	<h2>IMPORTED REVISION FROM WIKISPACES</h2>		<h2>IMPORTED REVISION FROM WIKISPACES</h2>
	This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>		This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>
	: This revision was by author [[User:dmGuillotine\|dmGuillotine]] and made on <tt>2012-10-~~07 13~~:05:38 UTC</tt>.<br>		: This revision was by author [[User:dmGuillotine\|dmGuillotine]] and made on <tt>2012-10-08 18:22:54 UTC</tt>.<br>
	: The original revision id was <tt>~~370891878~~</tt>.<br>		: The original revision id was <tt>371263022</tt>.<br>
	: The revision comment was: <tt></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>		The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.<br>
Line 16:		Line 16:


	<span style="background-color: #ffffff;">Which means these are the intervals in the scale before it repeats:</span>		<span style="background-color: #ffffff;">Which means these are the cent-intervals in the scale before it repeats:</span>
	<span style="background-color: #ffffff;">99.27 - 235.77 - 366.91 - 466.18 - 597.32 - 733.82 - 833.09</span>		<span style="background-color: #ffffff;">99.27 - 235.77 - 366.91 - 466.18 - 597.32 - 733.82 - 833.09</span>

Line 58:		Line 58:
	<br />		<br />
	<br />		<br />
	<span style="background-color: #ffffff;">Which means these are the intervals in the scale before it repeats:</span><br />		<span style="background-color: #ffffff;">Which means these are the cent-intervals in the scale before it repeats:</span><br />
	<span style="background-color: #ffffff;">99.27 - 235.77 - 366.91 - 466.18 - 597.32 - 733.82 - 833.09</span><br />		<span style="background-color: #ffffff;">99.27 - 235.77 - 366.91 - 466.18 - 597.32 - 733.82 - 833.09</span><br />
	<br />		<br />

Wikispaces>dmGuillotine: Imported revision 370891878 - Original comment:

2012-10-07T13:05:38Z

**Imported revision 370891878 - Original comment: **

← Older revision		Revision as of 13:05, 7 October 2012
Line 1:		Line 1:
	<h2>IMPORTED REVISION FROM WIKISPACES</h2>		<h2>IMPORTED REVISION FROM WIKISPACES</h2>
	This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>		This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>
	: This revision was by author [[User:dmGuillotine\|dmGuillotine]] and made on <tt>2012-10-07 03:23:58 UTC</tt>.<br>		: This revision was by author [[User:dmGuillotine\|dmGuillotine]] and made on <tt>2012-10-07 13:05:38 UTC</tt>.<br>
	: The original revision id was <tt>~~370837192~~</tt>.<br>		: The original revision id was <tt>370891878</tt>.<br>
	: The revision comment was: <tt></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>		The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.<br>
Line 34:		Line 34:

	<span style="background-color: #ffffff;">The octave or pseudo-octave occurs at every tenth step of the scale. Perfect fifths appear sometimes too; if you know the scale well enough, you can use traditional harmony within its boundaries. Bohlen describes the variety of intervals that happen at different points in the scale, variable depending on which scale degree you're starting from.</span>		<span style="background-color: #ffffff;">The octave or pseudo-octave occurs at every tenth step of the scale. Perfect fifths appear sometimes too; if you know the scale well enough, you can use traditional harmony within its boundaries. Bohlen describes the variety of intervals that happen at different points in the scale, variable depending on which scale degree you're starting from.</span>

			36-EDO provides suitable tempered approximations of the intervals in the Golden Scale. It afford us the ability to compose in the GR scale and/or the traditional Western tonality.
			[[xenharmonic/36edo\|https://xenharmonic.wikispaces.com/36edo]]

	<span style="background-color: #ffffff;">Again, </span>the best authority on the scale is Bohlen himself:		<span style="background-color: #ffffff;">Again, </span>the best authority on the scale is Bohlen himself:
Line 73:		Line 76:
	<br />		<br />
	<span style="background-color: #ffffff;">The octave or pseudo-octave occurs at every tenth step of the scale. Perfect fifths appear sometimes too; if you know the scale well enough, you can use traditional harmony within its boundaries. Bohlen describes the variety of intervals that happen at different points in the scale, variable depending on which scale degree you're starting from.</span><br />		<span style="background-color: #ffffff;">The octave or pseudo-octave occurs at every tenth step of the scale. Perfect fifths appear sometimes too; if you know the scale well enough, you can use traditional harmony within its boundaries. Bohlen describes the variety of intervals that happen at different points in the scale, variable depending on which scale degree you're starting from.</span><br />
			<br />
			36-EDO provides suitable tempered approximations of the intervals in the Golden Scale. It afford us the ability to compose in the GR scale and/or the traditional Western tonality.<br />
			<a class="wiki_link" href="http://xenharmonic.wikispaces.com/36edo">https://xenharmonic.wikispaces.com/36edo</a><br />
	<br />		<br />
	<strong><span style="background-color: #ffffff;">Again, </span></strong>the best authority on the scale is Bohlen himself:<br />		<strong><span style="background-color: #ffffff;">Again, </span></strong>the best authority on the scale is Bohlen himself:<br />
	<a class="wiki_link_ext" href="http://www.huygens-fokker.org/bpsite/" rel="nofollow">http://www.huygens-fokker.org/bpsite/</a><br />		<a class="wiki_link_ext" href="http://www.huygens-fokker.org/bpsite/" rel="nofollow">http://www.huygens-fokker.org/bpsite/</a><br />
	<br />		<br />
	But there is much still to be discovered with this tuning system. Combination tone harmony opens some interesting doors. The tuning is of course in need of its own theory, something I've been working on for the past year and a half. If you have any interest in the scale, please contact me at <!-- ws:start:WikiTextUrlEmailRule:69:dmguillot@gmail.com --><a class="wiki_link_ext" href="mailto:dmguillot@gmail.com" rel="nofollow">dmguillot@gmail.com</a><!-- ws:end:WikiTextUrlEmailRule:69 --> - thanks!<br />		But there is much still to be discovered with this tuning system. Combination tone harmony opens some interesting doors. The tuning is of course in need of its own theory, something I've been working on for the past year and a half. If you have any interest in the scale, please contact me at <!-- ws:start:WikiTextUrlEmailRule:73:dmguillot@gmail.com --><a class="wiki_link_ext" href="mailto:dmguillot@gmail.com" rel="nofollow">dmguillot@gmail.com</a><!-- ws:end:WikiTextUrlEmailRule:73 --> - thanks!<br />
	<br />		<br />
	-Dave G.<br />		-Dave G.<br />

833 Cent Golden Scale (Bohlen) - Revision history

BudjarnLambeth: Moved from category "golden" to "golden ratio"

Fredg999 category edits: Moving from Category:7-note scales to Category:7-tone scales using Cat-a-lot

Fredg999: Recategorization, improved markup, moved external link to the end

Spt3125: formatting, category

Wikispaces>FREEZE at 00:00, 17 July 2018

Wikispaces>JosephRuhf: **Imported revision 602523412 - Original comment: **

Wikispaces>xenwolf: **Imported revision 388402046 - Original comment: I hope that's ok for you, Dave?**

Wikispaces>keenanpepper: **Imported revision 376758350 - Original comment: **

Wikispaces>dmGuillotine: **Imported revision 371263022 - Original comment: **

Wikispaces>dmGuillotine: **Imported revision 370891878 - Original comment: **

Wikispaces>JosephRuhf: Imported revision 602523412 - Original comment:

Wikispaces>xenwolf: Imported revision 388402046 - Original comment: I hope that's ok for you, Dave?

Wikispaces>keenanpepper: Imported revision 376758350 - Original comment:

Wikispaces>dmGuillotine: Imported revision 371263022 - Original comment:

Wikispaces>dmGuillotine: Imported revision 370891878 - Original comment: