Prime harmonic series - Revision history

BudjarnLambeth: Added to category "xenharmonic series"

2023-04-26T05:18:05Z

Added to category "xenharmonic series"

← Older revision		Revision as of 05:18, 26 April 2023
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	[[Category:Just intonation]]		[[Category:Just intonation]]
	[[Category:Prime]]		[[Category:Prime]]
			[[Category:Xenharmonic series]]

Fredg999 category edits: Moving from Category:Interval collection to Category:Lists of intervals using Cat-a-lot

2023-04-13T22:04:37Z

Moving from Category:Interval collection to Category:Lists of intervals using Cat-a-lot

← Older revision		Revision as of 22:04, 13 April 2023
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	[[Category:Harmonic series]]		[[Category:Harmonic series]]
	[[Category:~~Interval collection~~]]		[[Category:Lists of intervals]]
	[[Category:Just intonation]]		[[Category:Just intonation]]
	[[Category:Prime]]		[[Category:Prime]]

Fredg999 category edits: Removing from Category:Theory using Cat-a-lot

2023-03-05T05:32:47Z

Removing from Category:Theory using Cat-a-lot

← Older revision		Revision as of 05:32, 5 March 2023
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	[[Category:Just intonation]]		[[Category:Just intonation]]
	[[Category:Prime]]		[[Category:Prime]]
	~~[[Category:Theory]]~~

Fredg999: Categories

2021-08-26T16:37:16Z

Xenwolf: some cleanup: simplified some links and tables cells

2020-11-20T20:45:00Z

some cleanup: simplified some links and tables cells

Show changes

Xenwolf: Xenwolf moved page The Prime Harmonic Series to Prime harmonic series: Rule: only first letter capitalized. Reason: less typing when referenced

2020-06-12T07:50:53Z

Xenwolf moved page The Prime Harmonic Series to Prime harmonic series: Rule: only first letter capitalized. Reason: less typing when referenced

← Older revision	Revision as of 07:50, 12 June 2020
(No difference)

Cmloegcmluin at 23:52, 9 February 2020

2020-02-09T23:52:55Z

@@ Line 163: / Line 163: @@
 <span style="font-size: 90%;">Because the lowest partial is 17, there are no familiar lower prime limit intervals like octaves (2/1), fifths (3/2), thirds (5/4), etc. Nevertheless, some intervals between higher primes approximate the lower prime limit intervals (e.g. 61/31 is very close to an octave), without of course reproducing them exactly." [http://users.rcn.com/dante.interport//justguitar.html (original page source)]</span>
-<span style="font-size: 90%;">[http://www.youtube.com/watch?v=tP9iafbjlOw "Tarkovsky's Mirror" for prime guitar by Dante Rosati]</span>      [[Category:harmonic_series]]
+<span style="font-size: 90%;">[http://www.youtube.com/watch?v=tP9iafbjlOw "Tarkovsky's Mirror" for prime guitar by Dante Rosati]</span>
 [[Category:intervals]]
 [[Category:just]]
 [[Category:prime]]
 [[Category:theory]]

Wikispaces>FREEZE at 00:00, 17 July 2018

2018-07-17T00:00:00Z

Show changes

Wikispaces>kentpollard: Imported revision 411572958 - Original comment: Reverted to Jun 29, 2011 5:34 am: Reverted to remove spam

2013-03-03T14:26:41Z

**Imported revision 411572958 - Original comment: Reverted to Jun 29, 2011 5:34 am: Reverted to remove spam**

← Older revision		Revision as of 14:26, 3 March 2013
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	<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:~~guest~~\|~~guest~~]] and made on <tt>2013-03-03 14:24:37 UTC</tt>.<br>		: This revision was by author [[User:kentpollard\|kentpollard]] and made on <tt>2013-03-03 14:26:41 UTC</tt>.<br>
	: The original revision id was <tt>~~411572484~~</tt>.<br>		: The original revision id was <tt>411572958</tt>.<br>
	: The revision comment was: <tt></tt><br>		: The revision comment was: <tt>Reverted to Jun 29, 2011 5:34 am: Reverted to remove spam</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>
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	giving these step sizes:		giving these step sizes:

	\|\| 34/32		\|\| 34/32
	(17/16) \|\| 37/34 \|\| 38/37 \|\| 40/38		(17/16) \|\| 37/34 \|\| 38/37 \|\| 40/38
	(20/19) \|\| 44/40		(20/19) \|\| 44/40
	(11/10) \|\| 46/44		(11/10) \|\| 46/44
	(23/22) \|\| 48/46		(23/22) \|\| 48/46
	(24/23) \|\| 52/48		(24/23) \|\| 52/48
	(13/12) \|\| 56/52		(13/12) \|\| 56/52
	(14/13) \|\| 58/56		(14/13) \|\| 58/56
	(29/28) \|\| 62/58		(29/28) \|\| 62/58
	(31/29) \|\| 64/62		(31/29) \|\| 64/62
	(32/31) \|\|		(32/31) \|\|
	\|\| 104.96 \|\| 146.39 \|\| 46.17 \|\| 88.8 \|\| 165 \|\| 76.96 \|\| 73.68 \|\| 138.57 \|\| 128.3 \|\| 60.75 \|\| 115.46 \|\| 54.97 \|\|		\|\| 104.96 \|\| 146.39 \|\| 46.17 \|\| 88.8 \|\| 165 \|\| 76.96 \|\| 73.68 \|\| 138.57 \|\| 128.3 \|\| 60.75 \|\| 115.46 \|\| 54.97 \|\|
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	----		----

	Any segment of the prime harmonic series can be used "as is" as musical material.		Any segment of the prime harmonic series can be used "as is" as musical material.

	The step sizes of the series itself exhibit an interesting variety, including the phenomena of [[http://en.wikipedia.org/wiki/Twin_prime\|twin primes]] which provide for small steps which contrast with the wider steps elsewhere in the series:		The step sizes of the series itself exhibit an interesting variety, including the phenomena of [[http://en.wikipedia.org/wiki/Twin_prime\|twin primes]] which provide for small steps which contrast with the wider steps elsewhere in the series:
Line 83:		Line 83:
	<span style="font-size: 90%;">Because the lowest partial is 17, there are no familiar lower prime limit intervals like octaves (2/1), fifths (3/2), thirds (5/4), etc. Nevertheless, some intervals between higher primes approximate the lower prime limit intervals (e.g. 61/31 is very close to an octave), without of course reproducing them exactly." [[http://users.rcn.com/dante.interport//justguitar.html\|(original page source)]]</span>		<span style="font-size: 90%;">Because the lowest partial is 17, there are no familiar lower prime limit intervals like octaves (2/1), fifths (3/2), thirds (5/4), etc. Nevertheless, some intervals between higher primes approximate the lower prime limit intervals (e.g. 61/31 is very close to an octave), without of course reproducing them exactly." [[http://users.rcn.com/dante.interport//justguitar.html\|(original page source)]]</span>

	<span style="font-size: 90%;">~~////~~[[http://www.youtube.com/watch?v=tP9iafbjlOw\|"Tarkovsky's Mirror" for prime guitar by Dante Rosati]]~~////~~</span></pre></div>		<span style="font-size: 90%;">[[http://www.youtube.com/watch?v=tP9iafbjlOw\|"Tarkovsky's Mirror" for prime guitar by Dante Rosati]]</span></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>The Prime Harmonic Series</title></head><body>The <strong>acoustic prime harmonic series</strong> is similar to the set of <a class="wiki_link" href="/prime%20numbers">prime numbers</a>, except that it begins with 1, and skips 2 because of <a class="wiki_link" href="/octave%20equivalence">octave equivalence</a> : 1, 3, 5, 7, 11, 13 etc.<br />		<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>The Prime Harmonic Series</title></head><body>The <strong>acoustic prime harmonic series</strong> is similar to the set of <a class="wiki_link" href="/prime%20numbers">prime numbers</a>, except that it begins with 1, and skips 2 because of <a class="wiki_link" href="/octave%20equivalence">octave equivalence</a> : 1, 3, 5, 7, 11, 13 etc.<br />
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	<table class="wiki_table">		<table class="wiki_table">
	<tr>		<tr>
	<td>34/32<br />		<td>34/32 <br />
	(17/16)<br />		(17/16)<br />
	</td>		</td>
Line 250:		Line 250:
	(20/19)<br />		(20/19)<br />
	</td>		</td>
	<td>44/40<br />		<td>44/40 <br />
	(11/10)<br />		(11/10)<br />
	</td>		</td>
	<td>46/44<br />		<td>46/44 <br />
	(23/22)<br />		(23/22)<br />
	</td>		</td>
	<td>48/46<br />		<td>48/46 <br />
	(24/23)<br />		(24/23)<br />
	</td>		</td>
	<td>52/48<br />		<td>52/48 <br />
	(13/12)<br />		(13/12)<br />
	</td>		</td>
	<td>56/52<br />		<td>56/52 <br />
	(14/13)<br />		(14/13)<br />
	</td>		</td>
	<td>58/56<br />		<td>58/56 <br />
	(29/28)<br />		(29/28)<br />
	</td>		</td>
	<td>62/58<br />		<td>62/58 <br />
	(31/29)<br />		(31/29)<br />
	</td>		</td>
	<td>64/62<br />		<td>64/62 <br />
	(32/31)<br />		(32/31)<br />
	</td>		</td>
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	<hr />		<hr />
	<br />		<br />
	Any segment of the prime harmonic series can be used &quot;as is&quot; as musical material.<br />		Any segment of the prime harmonic series can be used &quot;as is&quot; as musical material. <br />
	<br />		<br />
	The step sizes of the series itself exhibit an interesting variety, including the phenomena of <a class="wiki_link_ext" href="http://en.wikipedia.org/wiki/Twin_prime" rel="nofollow">twin primes</a> which provide for small steps which contrast with the wider steps elsewhere in the series:<br />		The step sizes of the series itself exhibit an interesting variety, including the phenomena of <a class="wiki_link_ext" href="http://en.wikipedia.org/wiki/Twin_prime" rel="nofollow">twin primes</a> which provide for small steps which contrast with the wider steps elsewhere in the series:<br />

Wikispaces>guest: Imported revision 411572484 - Original comment:

2013-03-03T14:24:37Z

**Imported revision 411572484 - Original comment: **

← Older revision		Revision as of 14:24, 3 March 2013
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>~~2011~~-06-~~29 07~~:34:21 UTC</tt>.<br>		: This revision was by author [[User:guest\|guest]] and made on <tt>2013-03-03 14:24:37 UTC</tt>.<br>
	: The original revision id was <tt>~~239298801~~</tt>.<br>		: The original revision id was <tt>411572484</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 52:		Line 52:
	giving these step sizes:		giving these step sizes:

	\|\| 34/32		\|\| 34/32
	(17/16) \|\| 37/34 \|\| 38/37 \|\| 40/38		(17/16) \|\| 37/34 \|\| 38/37 \|\| 40/38
	(20/19) \|\| 44/40		(20/19) \|\| 44/40
	(11/10) \|\| 46/44		(11/10) \|\| 46/44
	(23/22) \|\| 48/46		(23/22) \|\| 48/46
	(24/23) \|\| 52/48		(24/23) \|\| 52/48
	(13/12) \|\| 56/52		(13/12) \|\| 56/52
	(14/13) \|\| 58/56		(14/13) \|\| 58/56
	(29/28) \|\| 62/58		(29/28) \|\| 62/58
	(31/29) \|\| 64/62		(31/29) \|\| 64/62
	(32/31) \|\|		(32/31) \|\|
	\|\| 104.96 \|\| 146.39 \|\| 46.17 \|\| 88.8 \|\| 165 \|\| 76.96 \|\| 73.68 \|\| 138.57 \|\| 128.3 \|\| 60.75 \|\| 115.46 \|\| 54.97 \|\|		\|\| 104.96 \|\| 146.39 \|\| 46.17 \|\| 88.8 \|\| 165 \|\| 76.96 \|\| 73.68 \|\| 138.57 \|\| 128.3 \|\| 60.75 \|\| 115.46 \|\| 54.97 \|\|
Line 67:		Line 67:
	----		----

	Any segment of the prime harmonic series can be used "as is" as musical material.		Any segment of the prime harmonic series can be used "as is" as musical material.

	The step sizes of the series itself exhibit an interesting variety, including the phenomena of [[http://en.wikipedia.org/wiki/Twin_prime\|twin primes]] which provide for small steps which contrast with the wider steps elsewhere in the series:		The step sizes of the series itself exhibit an interesting variety, including the phenomena of [[http://en.wikipedia.org/wiki/Twin_prime\|twin primes]] which provide for small steps which contrast with the wider steps elsewhere in the series:
Line 83:		Line 83:
	<span style="font-size: 90%;">Because the lowest partial is 17, there are no familiar lower prime limit intervals like octaves (2/1), fifths (3/2), thirds (5/4), etc. Nevertheless, some intervals between higher primes approximate the lower prime limit intervals (e.g. 61/31 is very close to an octave), without of course reproducing them exactly." [[http://users.rcn.com/dante.interport//justguitar.html\|(original page source)]]</span>		<span style="font-size: 90%;">Because the lowest partial is 17, there are no familiar lower prime limit intervals like octaves (2/1), fifths (3/2), thirds (5/4), etc. Nevertheless, some intervals between higher primes approximate the lower prime limit intervals (e.g. 61/31 is very close to an octave), without of course reproducing them exactly." [[http://users.rcn.com/dante.interport//justguitar.html\|(original page source)]]</span>

	<span style="font-size: 90%;">[[http://www.youtube.com/watch?v=tP9iafbjlOw\|"Tarkovsky's Mirror" for prime guitar by Dante Rosati]]</span></pre></div>		<span style="font-size: 90%;">////[[http://www.youtube.com/watch?v=tP9iafbjlOw\|"Tarkovsky's Mirror" for prime guitar by Dante Rosati]]////</span></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>The Prime Harmonic Series</title></head><body>The <strong>acoustic prime harmonic series</strong> is similar to the set of <a class="wiki_link" href="/prime%20numbers">prime numbers</a>, except that it begins with 1, and skips 2 because of <a class="wiki_link" href="/octave%20equivalence">octave equivalence</a> : 1, 3, 5, 7, 11, 13 etc.<br />		<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>The Prime Harmonic Series</title></head><body>The <strong>acoustic prime harmonic series</strong> is similar to the set of <a class="wiki_link" href="/prime%20numbers">prime numbers</a>, except that it begins with 1, and skips 2 because of <a class="wiki_link" href="/octave%20equivalence">octave equivalence</a> : 1, 3, 5, 7, 11, 13 etc.<br />
Line 240:		Line 240:
	<table class="wiki_table">		<table class="wiki_table">
	<tr>		<tr>
	<td>34/32 <br />		<td>34/32<br />
	(17/16)<br />		(17/16)<br />
	</td>		</td>
Line 250:		Line 250:
	(20/19)<br />		(20/19)<br />
	</td>		</td>
	<td>44/40 <br />		<td>44/40<br />
	(11/10)<br />		(11/10)<br />
	</td>		</td>
	<td>46/44 <br />		<td>46/44<br />
	(23/22)<br />		(23/22)<br />
	</td>		</td>
	<td>48/46 <br />		<td>48/46<br />
	(24/23)<br />		(24/23)<br />
	</td>		</td>
	<td>52/48 <br />		<td>52/48<br />
	(13/12)<br />		(13/12)<br />
	</td>		</td>
	<td>56/52 <br />		<td>56/52<br />
	(14/13)<br />		(14/13)<br />
	</td>		</td>
	<td>58/56 <br />		<td>58/56<br />
	(29/28)<br />		(29/28)<br />
	</td>		</td>
	<td>62/58 <br />		<td>62/58<br />
	(31/29)<br />		(31/29)<br />
	</td>		</td>
	<td>64/62 <br />		<td>64/62<br />
	(32/31)<br />		(32/31)<br />
	</td>		</td>
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	<hr />		<hr />
	<br />		<br />
	Any segment of the prime harmonic series can be used &quot;as is&quot; as musical material. <br />		Any segment of the prime harmonic series can be used &quot;as is&quot; as musical material.<br />
	<br />		<br />
	The step sizes of the series itself exhibit an interesting variety, including the phenomena of <a class="wiki_link_ext" href="http://en.wikipedia.org/wiki/Twin_prime" rel="nofollow">twin primes</a> which provide for small steps which contrast with the wider steps elsewhere in the series:<br />		The step sizes of the series itself exhibit an interesting variety, including the phenomena of <a class="wiki_link_ext" href="http://en.wikipedia.org/wiki/Twin_prime" rel="nofollow">twin primes</a> which provide for small steps which contrast with the wider steps elsewhere in the series:<br />

← Older revision		Revision as of 16:37, 26 August 2021
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	[[Category:Harmonic series]]		[[Category:Harmonic series]]
	[[Category:~~Intervals~~]]		[[Category:Interval collection]]
	[[Category:Just]]		[[Category:Just intonation]]
	[[Category:Prime]]		[[Category:Prime]]
	[[Category:Theory]]		[[Category:Theory]]