Neutron - Revision history

Godtone: /* Candidate 1 */ note tuning constraints

2025-03-11T21:23:34Z

Candidate 1: note tuning constraints

← Older revision		Revision as of 21:23, 11 March 2025
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	One possibility is a generator around 30 cents. This generator can be chained both the positive and negative directions from the tonic 5 times without traversing the period, leading to a "complete" MOS of 77 tones, 5\|5(7) in UDP notation. [[neutron77-maybe\|Example 77-tone scale here]]. If it doesn't pan out to anything worthy of the original name, it could alternately be called "Lucky", "Jackpot", or "Fortune" due to the abundance of 7s in its construction and structure. Although given the problems stated below, maybe that's not so apposite.		One possibility is a generator around 30 cents. This generator can be chained both the positive and negative directions from the tonic 5 times without traversing the period, leading to a "complete" MOS of 77 tones, 5\|5(7) in UDP notation. [[neutron77-maybe\|Example 77-tone scale here]]. If it doesn't pan out to anything worthy of the original name, it could alternately be called "Lucky", "Jackpot", or "Fortune" due to the abundance of 7s in its construction and structure. Although given the problems stated below, maybe that's not so apposite.

	Upon study of this MOS, a curious pattern of "blind spots" emerges for certain harmonics, namely that certain pairs of intervals considered to be the "major" and "minor" of that limit have one interval tuned well but not the other. In the 5-limit, 6/5 has an very close representative, but 5/4 has to settle for one more than 8c away. Likewise in the 7-limit, where 7/6 is more out-of-tune than 9/7, although a bit less so than the 5s. 11 and 13 are tuned okay; higher harmonics aren't really represented. It is likely one would need a high complexity for an accurate tuning of 5 and 7.		Upon study of this MOS, a curious pattern of "blind spots" emerges for certain harmonics, namely that certain pairs of intervals considered to be the "major" and "minor" of that limit have one interval tuned well but not the other. In the 5-limit, 6/5 has an very close representative, but 5/4 has to settle for one more than 8c away. Likewise in the 7-limit, where 7/6 is more out-of-tune than 9/7, although a bit less so than the 5s. 11 and 13 are tuned okay; higher harmonics aren't really represented. It is likely one would need a high complexity for an accurate tuning of 5 and 7. Also, the damage of 3 must practically exactly cancel the damage of 13 in the opposite direction, because of the accuracy of ~39/32 = 2\7. Similarly, the damages on primes 3, 5 and 7 are constrained for a similar reason by ~128/105 = 2\7.

	{{todo\|expand\|review\|comment=More to come; contributions such as comma ideas, different generators, other useful modes/mappings with existing generators, etc. are welcome. I very obviously don't know what I'm doing.\|inline=1}}		{{todo\|expand\|review\|comment=More to come; contributions such as comma ideas, different generators, other useful modes/mappings with existing generators, etc. are welcome. I very obviously don't know what I'm doing.\|inline=1}}

BudjarnLambeth: +"For technical data see Mistismic temperaments#Neutron."

2024-12-05T09:57:13Z

+"For technical data see Mistismic temperaments#Neutron."

← Older revision		Revision as of 09:57, 5 December 2024
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			For technical data see [[Mistismic temperaments#Neutron]].

	=The Basic Scale, [[7edo\|7EDO]]=		=The Basic Scale, [[7edo\|7EDO]]=
	[[William Lynch]] gave the name "Neutron[7]" to [[7edo]] used as a "neutral diatonic" scale. While it can function just fine as a scale on its own, implicit in this designation is that 7edo represents the starting point for a temperament with 7 periods per octave, just as 3edo represents "[[Augmented]][3]" with 3 periods per octave.		[[William Lynch]] gave the name "Neutron[7]" to [[7edo]] used as a "neutral diatonic" scale. While it can function just fine as a scale on its own, implicit in this designation is that 7edo represents the starting point for a temperament with 7 periods per octave, just as 3edo represents "[[Augmented]][3]" with 3 periods per octave.

BudjarnLambeth: BudjarnLambeth moved page Neutron Temperament to Neutron: To confirm with article naming conventions

2024-09-19T03:24:03Z

BudjarnLambeth moved page Neutron Temperament to Neutron: To confirm with article naming conventions

← Older revision	Revision as of 03:24, 19 September 2024
(No difference)

BudjarnLambeth: Converted todo message to proper todo template

2024-09-19T03:22:05Z

Converted todo message to proper todo template

← Older revision		Revision as of 03:22, 19 September 2024
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	Upon study of this MOS, a curious pattern of "blind spots" emerges for certain harmonics, namely that certain pairs of intervals considered to be the "major" and "minor" of that limit have one interval tuned well but not the other. In the 5-limit, 6/5 has an very close representative, but 5/4 has to settle for one more than 8c away. Likewise in the 7-limit, where 7/6 is more out-of-tune than 9/7, although a bit less so than the 5s. 11 and 13 are tuned okay; higher harmonics aren't really represented. It is likely one would need a high complexity for an accurate tuning of 5 and 7.		Upon study of this MOS, a curious pattern of "blind spots" emerges for certain harmonics, namely that certain pairs of intervals considered to be the "major" and "minor" of that limit have one interval tuned well but not the other. In the 5-limit, 6/5 has an very close representative, but 5/4 has to settle for one more than 8c away. Likewise in the 7-limit, where 7/6 is more out-of-tune than 9/7, although a bit less so than the 5s. 11 and 13 are tuned okay; higher harmonics aren't really represented. It is likely one would need a high complexity for an accurate tuning of 5 and 7.

	~~<more~~ to come; contributions such as comma ideas, different generators, other useful modes/mappings with existing generators, etc. are welcome. I very obviously don't know what I'm doing.~~>~~		{{todo\|expand\|review\|comment=More to come; contributions such as comma ideas, different generators, other useful modes/mappings with existing generators, etc. are welcome. I very obviously don't know what I'm doing.\|inline=1}}

	[[Category:7edo]]		[[Category:7edo]]
	[[Category:diatonic]]		[[Category:diatonic]]
	[[Category:neutral]]		[[Category:neutral]]

Spt3125: formatting, category

2018-12-10T17:20:13Z

formatting, category

← Older revision		Revision as of 17:20, 10 December 2018
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	=The Basic Scale, [[7edo\|7EDO]]=		=The Basic Scale, [[7edo\|7EDO]]=
	William Lynch gave the name "Neutron[7]" to [[7edo~~\|7EDO~~]] used as a "neutral diatonic" scale. While it can function just fine as a scale on its own, implicit in this designation is that 7edo represents the starting point for a temperament with 7 periods per octave, just as 3edo represents "[[~~augmented\|~~Augmented]][3]" with 3 periods per octave.		[[William Lynch]] gave the name "Neutron[7]" to [[7edo]] used as a "neutral diatonic" scale. While it can function just fine as a scale on its own, implicit in this designation is that 7edo represents the starting point for a temperament with 7 periods per octave, just as 3edo represents "[[Augmented]][3]" with 3 periods per octave.

	=Building a Regular Temperament=		=Building a Regular Temperament=
	From this base, we can say that a prospective ~~Neutron Temperament~~ tempers out the difference between a stack of 7 intervals in the "greater neutral second" range and the octave. The simplest ratio that comes to mind is 11/10, and this gives us a comma of \|8 0 7 0 -7~~>~~, or 20000000/19487171 in ratio form. Being about 6 cents sharp, it's not a bad representation. Another advantage of starting from 7 notes is that a familiar "Halberstadt-like" keyboard arrangement could be constructed for such a temperament. That's just the period, however. The generator is the hard part.		From this base, we can say that a prospective neutron temperament tempers out the difference between a stack of 7 intervals in the "greater neutral second" range and the octave. The simplest ratio that comes to mind is 11/10, and this gives us a comma of {{Monzo\|8 0 7 0 -7}}, or 20000000/19487171 in ratio form. Being about 6 cents sharp, it's not a bad representation. Another advantage of starting from 7 notes is that a familiar "Halberstadt-like" keyboard arrangement could be constructed for such a temperament. That's just the period, however. The generator is the hard part.

	~~= =~~

	=Generator Investigations=		=Generator Investigations=

	==Candidate 1==		==Candidate 1==
	One possibility is a generator around 30 cents. This generator can be chained both the positive and negative directions from the tonic 5 times without traversing the period, leading to a "complete" MOS of 77 tones, 5\|5(7) in UDP notation. ~~See~~ [[neutron77-maybe\|here]]. If it doesn't pan out to anything worthy of the original name, it could alternately be called "Lucky", "Jackpot", or "Fortune" due to the abundance of 7s in its construction and structure. Although given the problems stated below, maybe that's not so apposite.		One possibility is a generator around 30 cents. This generator can be chained both the positive and negative directions from the tonic 5 times without traversing the period, leading to a "complete" MOS of 77 tones, 5\|5(7) in UDP notation. [[neutron77-maybe\|Example 77-tone scale here]]. If it doesn't pan out to anything worthy of the original name, it could alternately be called "Lucky", "Jackpot", or "Fortune" due to the abundance of 7s in its construction and structure. Although given the problems stated below, maybe that's not so apposite.

	Upon study of this MOS, a curious pattern of "blind spots" emerges for certain harmonics, namely that certain pairs of intervals considered to be the "major" and "minor" of that limit have one interval tuned well but not the other. In the 5-limit, 6/5 has an very close representative, but 5/4 has to settle for one more than 8c away. Likewise in the 7-limit, where 7/6 is more out-of-tune than 9/7, although a bit less so than the 5s. 11 and 13 are tuned okay; higher harmonics aren't really represented. It is likely one would need a high complexity for an accurate tuning of 5 and 7.		Upon study of this MOS, a curious pattern of "blind spots" emerges for certain harmonics, namely that certain pairs of intervals considered to be the "major" and "minor" of that limit have one interval tuned well but not the other. In the 5-limit, 6/5 has an very close representative, but 5/4 has to settle for one more than 8c away. Likewise in the 7-limit, where 7/6 is more out-of-tune than 9/7, although a bit less so than the 5s. 11 and 13 are tuned okay; higher harmonics aren't really represented. It is likely one would need a high complexity for an accurate tuning of 5 and 7.

	<more to come; contributions such as comma ideas, different generators, other useful modes/mappings with existing generators, etc. are welcome. I very obviously don't know what I'm doing.>		<more to come; contributions such as comma ideas, different generators, other useful modes/mappings with existing generators, etc. are welcome. I very obviously don't know what I'm doing.>
	[[Category:~~7_edo~~]]
			[[Category:7edo]]
	[[Category:diatonic]]		[[Category:diatonic]]
	[[Category:neutral]]		[[Category:neutral]]

Wikispaces>FREEZE at 00:00, 17 July 2018

2018-07-17T00:00:00Z

← Older revision		Revision as of 00:00, 17 July 2018
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	~~<h2>IMPORTED REVISION FROM WIKISPACES</h2>~~		=The Basic Scale, [[7edo\|7EDO]]=
	~~This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>~~		William Lynch gave the name "Neutron[7]" to [[7edo\|7EDO]] used as a "neutral diatonic" scale. While it can function just fine as a scale on its own, implicit in this designation is that 7edo represents the starting point for a temperament with 7 periods per octave, just as 3edo represents "[[augmented\|Augmented]][3]" with 3 periods per octave.
	~~: This revision was by author [[User:kai.lugheidh\|kai.lugheidh]] and made on <tt>2017-04-28 00:06:10 UTC</tt>.<br>~~
	~~: The original revision id was <tt>611666805</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>~~
	<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;white-space: pre-wrap ! important" class="old-revision-html">=The Basic Scale, [[7EDO]]=
	William Lynch gave the name "Neutron[7]" to [[7edo\|7EDO]] used as a "neutral diatonic" scale. While it can function just fine as a scale on its own, implicit in this designation is that 7edo represents the starting point for a temperament with 7 periods per octave, just as 3edo represents "[[Augmented]][3]" with 3 periods per octave.

	=Building a Regular Temperament=		=Building a Regular Temperament=
	From this base, we can say that a prospective Neutron Temperament tempers out the difference between a stack of 7 intervals in the "greater neutral second" range and the octave. The simplest ratio that comes to mind is 11/10, and this gives us a comma of \|8 0 7 0 -7>, or 20000000/19487171 in ratio form. Being about 6 cents sharp, it's not a bad representation. Another advantage of starting from 7 notes is that a familiar "Halberstadt-like" keyboard arrangement could be constructed for such a temperament. That's just the period, however. The generator is the hard part.		From this base, we can say that a prospective Neutron Temperament tempers out the difference between a stack of 7 intervals in the "greater neutral second" range and the octave. The simplest ratio that comes to mind is 11/10, and this gives us a comma of \|8 0 7 0 -7>, or 20000000/19487171 in ratio form. Being about 6 cents sharp, it's not a bad representation. Another advantage of starting from 7 notes is that a familiar "Halberstadt-like" keyboard arrangement could be constructed for such a temperament. That's just the period, however. The generator is the hard part.
	= =
	=Generator Investigations=		= =
	==Candidate 1==
	One possibility is a generator around 30 cents. This generator can be chained both the positive and negative directions from the tonic 5 times without traversing the period, leading to a "complete" MOS of 77 tones, 5\|5(7) in UDP notation. See [[~~xenharmonic/~~neutron77-maybe\|here]]. If it doesn't pan out to anything worthy of the original name, it could alternately be called "Lucky", "Jackpot", or "Fortune" due to the abundance of 7s in its construction and structure. Although given the problems stated below, maybe that's not so apposite.		=Generator Investigations=

			==Candidate 1==
			One possibility is a generator around 30 cents. This generator can be chained both the positive and negative directions from the tonic 5 times without traversing the period, leading to a "complete" MOS of 77 tones, 5\|5(7) in UDP notation. See [[neutron77-maybe\|here]]. If it doesn't pan out to anything worthy of the original name, it could alternately be called "Lucky", "Jackpot", or "Fortune" due to the abundance of 7s in its construction and structure. Although given the problems stated below, maybe that's not so apposite.

	Upon study of this MOS, a curious pattern of "blind spots" emerges for certain harmonics, namely that certain pairs of intervals considered to be the "major" and "minor" of that limit have one interval tuned well but not the other. In the 5-limit, 6/5 has an very close representative, but 5/4 has to settle for one more than 8c away. Likewise in the 7-limit, where 7/6 is more out-of-tune than 9/7, although a bit less so than the 5s. 11 and 13 are tuned okay; higher harmonics aren't really represented. It is likely one would need a high complexity for an accurate tuning of 5 and 7.		Upon study of this MOS, a curious pattern of "blind spots" emerges for certain harmonics, namely that certain pairs of intervals considered to be the "major" and "minor" of that limit have one interval tuned well but not the other. In the 5-limit, 6/5 has an very close representative, but 5/4 has to settle for one more than 8c away. Likewise in the 7-limit, where 7/6 is more out-of-tune than 9/7, although a bit less so than the 5s. 11 and 13 are tuned okay; higher harmonics aren't really represented. It is likely one would need a high complexity for an accurate tuning of 5 and 7.

	<more to come; contributions such as comma ideas, different generators, other useful modes/mappings with existing generators, etc. are welcome. I very obviously don't know what I'm doing.>~~</pre></div>~~		<more to come; contributions such as comma ideas, different generators, other useful modes/mappings with existing generators, etc. are welcome. I very obviously don't know what I'm doing.>
	~~<h4>Original HTML content~~:~~</h4>~~		[[Category:7_edo]]
	~~<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>Neutron Temperament</title></head><body><!-- ws:start:WikiTextHeadingRule:0:&lt;h1&gt; --><h1 id="toc0"><a name="The Basic Scale, 7EDO"></a><!-- ws:end:WikiTextHeadingRule:0 -->The Basic Scale, <a class="wiki_link" href="/7EDO">7EDO</a></h1>		[[Category:diatonic]]
	~~William Lynch gave the name &quot;Neutron~~[7]&quot; to <a class="wiki_link" href="/7edo">7EDO</a> used as a &quot;neutral diatonic&quot; scale. While it can function just fine as a scale on its own, implicit in this designation is that 7edo represents the starting point for a temperament with 7 periods per octave, just as 3edo represents &quot;<a class="wiki_link" href="/Augmented">Augmented</a>[~~3]&quot; with 3 periods per octave.<br />~~		[[Category:neutral]]
	~~<br />~~
	~~<!-- ws:start:WikiTextHeadingRule:2:&lt;h1&gt; --><h1 id="toc1"><a name="Building a Regular Temperament"></a><!-- ws~~:~~end:WikiTextHeadingRule:2 -->Building a Regular Temperament</h1>~~
	~~From this base, we can say that a prospective Neutron Temperament tempers out the difference between a stack of 7 intervals in the &quot;greater~~ neutral second&quot; range and the octave. The simplest ratio that comes to mind is 11/10, and this gives us a comma of \|8 0 7 0 -7&gt;, or 20000000/19487171 in ratio form. Being about 6 cents sharp, it's not a bad representation. Another advantage of starting from 7 notes is that a familiar &quot;Halberstadt-like&quot; keyboard arrangement could be constructed for such a temperament. That's just the period, however. The generator is the hard part.<br />
	~~<!-- ws:start:WikiTextHeadingRule:4:&lt;h1&gt; --><h1 id="toc2"><!-- ws:end:WikiTextHeadingRule:4 --> </h1>~~
	<!-- ws:start:WikiTextHeadingRule:6:&lt;h1&gt; --><h1 id="toc3"><a name="Generator Investigations"></a><!-- ws:end:WikiTextHeadingRule:6 -->Generator Investigations</h1>
	<!-- ws:start:WikiTextHeadingRule:8:&lt;h2&gt; --><h2 id="toc4"><a name="Generator Investigations-Candidate 1"></a><!-- ws:end:WikiTextHeadingRule:8 -->Candidate 1</h2>
	One possibility is a generator around 30 cents. This generator can be chained both the positive and negative directions from the tonic 5 times without traversing the period, leading to a &quot;complete&quot; MOS of 77 tones, 5\|5(7) in UDP notation. See <a class="wiki_link" href="http://xenharmonic.wikispaces.com/neutron77-maybe">here</a>. If it doesn't pan out to anything worthy of the original name, it could alternately be called &quot;Lucky&quot;, &quot;Jackpot&quot;, or &quot;Fortune&quot; due to the abundance of 7s in its construction and structure. Although given the problems stated below, maybe that's not so apposite.<br />
	~~<br />~~
	Upon study of this MOS, a curious pattern of &quot;blind spots&quot; emerges for certain harmonics, namely that certain pairs of intervals considered to be the &quot;major&quot; and &quot;minor&quot; of that limit have one interval tuned well but not the other. In the 5-limit, 6/5 has an very close representative, but 5/4 has to settle for one more than 8c away. Likewise in the 7-limit, where 7/6 is more out-of-tune than 9/7, although a bit less so than the 5s. 11 and 13 are tuned okay; higher harmonics aren't really represented. It is likely one would need a high complexity for an accurate tuning of 5 and 7.<br />
	~~<br />~~
	&lt;more to come; contributions such as comma ideas, different generators, other useful modes/mappings with existing generators, etc. are welcome. I very obviously don't know what I'm doing.&gt;</body></html></pre></div>

Wikispaces>kai.lugheidh: Imported revision 611666805 - Original comment:

2017-04-28T00:06:10Z

**Imported revision 611666805 - Original comment: **

← Older revision		Revision as of 00:06, 28 April 2017
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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:kai.lugheidh\|kai.lugheidh]] and made on <tt>2017-04-28 00:03:21 UTC</tt>.<br>		: This revision was by author [[User:kai.lugheidh\|kai.lugheidh]] and made on <tt>2017-04-28 00:06:10 UTC</tt>.<br>
	: The original revision id was <tt>~~611666703~~</tt>.<br>		: The original revision id was <tt>611666805</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 14:		Line 14:
	=Generator Investigations=		=Generator Investigations=
	==Candidate 1==		==Candidate 1==
	One possibility is a generator around 30 cents. This generator can be chained both the positive and negative directions from the tonic 5 times without traversing the period, leading to a "complete" MOS of 77 tones, 5\|5(7) in UDP notation. See [[~~http:/~~/neutron77-maybe~~.scl~~\|here]]. If it doesn't pan out to anything worthy of the original name, it could alternately be called "Lucky", "Jackpot", or "Fortune" due to the abundance of 7s in its construction and structure. Although given the problems stated below, maybe that's not so apposite.		One possibility is a generator around 30 cents. This generator can be chained both the positive and negative directions from the tonic 5 times without traversing the period, leading to a "complete" MOS of 77 tones, 5\|5(7) in UDP notation. See [[xenharmonic/neutron77-maybe\|here]]. If it doesn't pan out to anything worthy of the original name, it could alternately be called "Lucky", "Jackpot", or "Fortune" due to the abundance of 7s in its construction and structure. Although given the problems stated below, maybe that's not so apposite.

	Upon study of this MOS, a curious pattern of "blind spots" emerges for certain harmonics, namely that certain pairs of intervals considered to be the "major" and "minor" of that limit have one interval tuned well but not the other. In the 5-limit, 6/5 has an very close representative, but 5/4 has to settle for one more than 8c away. Likewise in the 7-limit, where 7/6 is more out-of-tune than 9/7, although a bit less so than the 5s. 11 and 13 are tuned okay; higher harmonics aren't really represented. It is likely one would need a high complexity for an accurate tuning of 5 and 7.		Upon study of this MOS, a curious pattern of "blind spots" emerges for certain harmonics, namely that certain pairs of intervals considered to be the "major" and "minor" of that limit have one interval tuned well but not the other. In the 5-limit, 6/5 has an very close representative, but 5/4 has to settle for one more than 8c away. Likewise in the 7-limit, where 7/6 is more out-of-tune than 9/7, although a bit less so than the 5s. 11 and 13 are tuned okay; higher harmonics aren't really represented. It is likely one would need a high complexity for an accurate tuning of 5 and 7.
Line 28:		Line 28:
	<!-- ws:start:WikiTextHeadingRule:6:&lt;h1&gt; --><h1 id="toc3"><a name="Generator Investigations"></a><!-- ws:end:WikiTextHeadingRule:6 -->Generator Investigations</h1>		<!-- ws:start:WikiTextHeadingRule:6:&lt;h1&gt; --><h1 id="toc3"><a name="Generator Investigations"></a><!-- ws:end:WikiTextHeadingRule:6 -->Generator Investigations</h1>
	<!-- ws:start:WikiTextHeadingRule:8:&lt;h2&gt; --><h2 id="toc4"><a name="Generator Investigations-Candidate 1"></a><!-- ws:end:WikiTextHeadingRule:8 -->Candidate 1</h2>		<!-- ws:start:WikiTextHeadingRule:8:&lt;h2&gt; --><h2 id="toc4"><a name="Generator Investigations-Candidate 1"></a><!-- ws:end:WikiTextHeadingRule:8 -->Candidate 1</h2>
	One possibility is a generator around 30 cents. This generator can be chained both the positive and negative directions from the tonic 5 times without traversing the period, leading to a &quot;complete&quot; MOS of 77 tones, 5\|5(7) in UDP notation. See <a class="~~wiki_link_ext~~" href="http://neutron77-maybe~~.scl" rel="nofollow~~">here</a>. If it doesn't pan out to anything worthy of the original name, it could alternately be called &quot;Lucky&quot;, &quot;Jackpot&quot;, or &quot;Fortune&quot; due to the abundance of 7s in its construction and structure. Although given the problems stated below, maybe that's not so apposite.<br />		One possibility is a generator around 30 cents. This generator can be chained both the positive and negative directions from the tonic 5 times without traversing the period, leading to a &quot;complete&quot; MOS of 77 tones, 5\|5(7) in UDP notation. See <a class="wiki_link" href="http://xenharmonic.wikispaces.com/neutron77-maybe">here</a>. If it doesn't pan out to anything worthy of the original name, it could alternately be called &quot;Lucky&quot;, &quot;Jackpot&quot;, or &quot;Fortune&quot; due to the abundance of 7s in its construction and structure. Although given the problems stated below, maybe that's not so apposite.<br />
	<br />		<br />
	Upon study of this MOS, a curious pattern of &quot;blind spots&quot; emerges for certain harmonics, namely that certain pairs of intervals considered to be the &quot;major&quot; and &quot;minor&quot; of that limit have one interval tuned well but not the other. In the 5-limit, 6/5 has an very close representative, but 5/4 has to settle for one more than 8c away. Likewise in the 7-limit, where 7/6 is more out-of-tune than 9/7, although a bit less so than the 5s. 11 and 13 are tuned okay; higher harmonics aren't really represented. It is likely one would need a high complexity for an accurate tuning of 5 and 7.<br />		Upon study of this MOS, a curious pattern of &quot;blind spots&quot; emerges for certain harmonics, namely that certain pairs of intervals considered to be the &quot;major&quot; and &quot;minor&quot; of that limit have one interval tuned well but not the other. In the 5-limit, 6/5 has an very close representative, but 5/4 has to settle for one more than 8c away. Likewise in the 7-limit, where 7/6 is more out-of-tune than 9/7, although a bit less so than the 5s. 11 and 13 are tuned okay; higher harmonics aren't really represented. It is likely one would need a high complexity for an accurate tuning of 5 and 7.<br />
	<br />		<br />
	&lt;more to come; contributions such as comma ideas, different generators, other useful modes/mappings with existing generators, etc. are welcome. I very obviously don't know what I'm doing.&gt;</body></html></pre></div>		&lt;more to come; contributions such as comma ideas, different generators, other useful modes/mappings with existing generators, etc. are welcome. I very obviously don't know what I'm doing.&gt;</body></html></pre></div>

Wikispaces>kai.lugheidh: Imported revision 611666703 - Original comment:

2017-04-28T00:03:21Z

**Imported revision 611666703 - Original comment: **

Wikispaces>kai.lugheidh: Imported revision 611666637 - Original comment:

2017-04-28T00:01:01Z

**Imported revision 611666637 - Original comment: **

@@ 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:k9assassin|k9assassin]] and made on <tt>2015-07-24 19:48:41 UTC</tt>.<br>
+: This revision was by author [[User:kai.lugheidh|kai.lugheidh]] and made on <tt>2017-04-28 00:01:01 UTC</tt>.<br>
-: The original revision id was <tt>555718591</tt>.<br>
+: The original revision id was <tt>611666637</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>
-<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;white-space: pre-wrap ! important" class="old-revision-html">See [[7edo|7 EDO]]. </pre></div>
+<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;white-space: pre-wrap ! important" class="old-revision-html">=The Basic Scale, [[7EDO]]=
 <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">&lt;html&gt;&lt;head&gt;&lt;title&gt;Neutron Temperament&lt;/title&gt;&lt;/head&gt;&lt;body&gt;See &lt;a class="wiki_link" href="/7edo"&gt;7 EDO&lt;/a&gt;.&lt;/body&gt;&lt;/html&gt;</pre></div>
+<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">&lt;html&gt;&lt;head&gt;&lt;title&gt;Neutron Temperament&lt;/title&gt;&lt;/head&gt;&lt;body&gt;&lt;!-- ws:start:WikiTextHeadingRule:0:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc0"&gt;&lt;a name="The Basic Scale, 7EDO"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:0 --&gt;The Basic Scale, &lt;a class="wiki_link" href="/7EDO"&gt;7EDO&lt;/a&gt;&lt;/h1&gt;

Wikispaces>k9assassin: Imported revision 555718591 - Original comment:

2015-07-24T19:48:41Z

**Imported revision 555718591 - Original comment: **

New page

<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:k9assassin|k9assassin]] and made on <tt>2015-07-24 19:48:41 UTC</tt>.<br>
: The original revision id was <tt>555718591</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>
<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;white-space: pre-wrap ! important" class="old-revision-html">See [[7edo|7 EDO]]. </pre></div>
<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>Neutron Temperament</title></head><body>See <a class="wiki_link" href="/7edo">7 EDO</a>.</body></html></pre></div>

← Older revision		Revision as of 00:03, 28 April 2017
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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:kai.lugheidh\|kai.lugheidh]] and made on <tt>2017-04-28 00:01:01 UTC</tt>.<br>		: This revision was by author [[User:kai.lugheidh\|kai.lugheidh]] and made on <tt>2017-04-28 00:03:21 UTC</tt>.<br>
	: The original revision id was <tt>~~611666637~~</tt>.<br>		: The original revision id was <tt>611666703</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>
	<h4>Original Wikitext content:</h4>		<h4>Original Wikitext 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;white-space: pre-wrap ! important" class="old-revision-html">=The Basic Scale, [[7EDO]]=		<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;white-space: pre-wrap ! important" class="old-revision-html">=The Basic Scale, [[7EDO]]=
	William Lynch gave the name "Neutron[7]" to [[7edo\|7EDO]] used as a "neutral diatonic" scale. While it can function just fine as a scale on its own, ~~implied~~ is that 7edo represents the starting point for a temperament with 7 periods per octave, just as ~~4edo~~ represents "[[~~Diminished~~]][4]" with 4 periods per octave.		William Lynch gave the name "Neutron[7]" to [[7edo\|7EDO]] used as a "neutral diatonic" scale. While it can function just fine as a scale on its own, implicit in this designation is that 7edo represents the starting point for a temperament with 7 periods per octave, just as 3edo represents "[[Augmented]][3]" with 3 periods per octave.

	=Building a Regular Temperament=		=Building a Regular Temperament=
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	<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>Neutron Temperament</title></head><body><!-- ws:start:WikiTextHeadingRule:0:&lt;h1&gt; --><h1 id="toc0"><a name="The Basic Scale, 7EDO"></a><!-- ws:end:WikiTextHeadingRule:0 -->The Basic Scale, <a class="wiki_link" href="/7EDO">7EDO</a></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>Neutron Temperament</title></head><body><!-- ws:start:WikiTextHeadingRule:0:&lt;h1&gt; --><h1 id="toc0"><a name="The Basic Scale, 7EDO"></a><!-- ws:end:WikiTextHeadingRule:0 -->The Basic Scale, <a class="wiki_link" href="/7EDO">7EDO</a></h1>
	William Lynch gave the name &quot;Neutron[7]&quot; to <a class="wiki_link" href="/7edo">7EDO</a> used as a &quot;neutral diatonic&quot; scale. While it can function just fine as a scale on its own, ~~implied~~ is that 7edo represents the starting point for a temperament with 7 periods per octave, just as ~~4edo~~ represents &quot;<a class="wiki_link" href="/~~Diminished~~">~~Diminished~~</a>[4]&quot; with 4 periods per octave.<br />		William Lynch gave the name &quot;Neutron[7]&quot; to <a class="wiki_link" href="/7edo">7EDO</a> used as a &quot;neutral diatonic&quot; scale. While it can function just fine as a scale on its own, implicit in this designation is that 7edo represents the starting point for a temperament with 7 periods per octave, just as 3edo represents &quot;<a class="wiki_link" href="/Augmented">Augmented</a>[3]&quot; with 3 periods per octave.<br />
	<br />		<br />
	<!-- ws:start:WikiTextHeadingRule:2:&lt;h1&gt; --><h1 id="toc1"><a name="Building a Regular Temperament"></a><!-- ws:end:WikiTextHeadingRule:2 -->Building a Regular Temperament</h1>		<!-- ws:start:WikiTextHeadingRule:2:&lt;h1&gt; --><h1 id="toc1"><a name="Building a Regular Temperament"></a><!-- ws:end:WikiTextHeadingRule:2 -->Building a Regular Temperament</h1>