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| <h2>IMPORTED REVISION FROM WIKISPACES</h2>
| | For technical data see [[Mistismic temperaments#Neutron]]. |
| This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>
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| : This revision was by author [[User:kai.lugheidh|kai.lugheidh]] and made on <tt>2017-04-28 00:06:10 UTC</tt>.<br>
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| : The original revision id was <tt>611666805</tt>.<br>
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| : The revision comment was: <tt></tt><br>
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| The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.<br>
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| <h4>Original Wikitext content:</h4>
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| <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]]=
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| 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.
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| =Building a Regular Temperament= | | =The Basic Scale, [[7edo|7EDO]]= |
| 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.
| | [[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. |
| = =
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| =Generator Investigations=
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| ==Candidate 1==
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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. 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.
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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.
| | =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 {{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. |
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| <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>
| | =Generator Investigations= |
| <h4>Original HTML content:</h4>
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| <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>
| | ==Candidate 1== |
| 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 />
| | 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. |
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| <!-- 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>
| | 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. |
| 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 />
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| <!-- ws:start:WikiTextHeadingRule:4:&lt;h1&gt; --><h1 id="toc2"><!-- ws:end:WikiTextHeadingRule:4 --> </h1>
| | {{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}} |
| <!-- ws:start:WikiTextHeadingRule:6:&lt;h1&gt; --><h1 id="toc3"><a name="Generator Investigations"></a><!-- ws:end:WikiTextHeadingRule:6 -->Generator Investigations</h1>
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| <!-- ws:start:WikiTextHeadingRule:8:&lt;h2&gt; --><h2 id="toc4"><a name="Generator Investigations-Candidate 1"></a><!-- ws:end:WikiTextHeadingRule:8 -->Candidate 1</h2>
| | [[Category:7edo]] |
| 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 />
| | [[Category:diatonic]] |
| <br />
| | [[Category:neutral]] |
| 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 /> | |
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| &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>
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