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| <h2>IMPORTED REVISION FROM WIKISPACES</h2>
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| This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br> | | This page contains an archived discussion between [[Chris Vaisvil]] and [[Mike Battaglia]] about [[just intonation subgroup]]s and [[regular temperament]]s. |
| : This revision was by author [[User:vaisvil|vaisvil]] and made on <tt>2012-11-01 21:37:38 UTC</tt>.<br>
| | <pre> |
| : The original revision id was <tt>378510076</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> | |
| <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">On Thu, Nov 1, 2012 at 9:10 PM, Chris Vaisvil <[[@mailto:chrisvaisvil%40gmail.com|[email protected]]]> | |
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| wrote:
| | > For certain, no. I could only guess that subgroups are actually harmonic series prime limits. |
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| | Subgroups expand the concept of a prime limit. For instance, say you want the 7-limit, but you don't care about prime 5; you just want primes 2, 3, and 7. So that's the 2.3.7 subgroup. Or say that you want the 7-limit, but you don't care about 3/1 but you do care about 9/1. Then that's the 2.5.7.9 subgroup. Or, say that you want primes 2 and 3, and the composite interval 7/5; that's the 2.3.7/5 subgroup. The rule for any subgroup is that if you multiply or divide intervals, that's also in the subgroup. So for the 2.3.7 subgroup, 7*3 = 21/1 is in the subgroup, as is 7/(2*3) = 7/6. And for the 2.3.7/5 subgroup, 2/(7/5 * 7/5) = 50/49 is in the subgroup, and so on. They're infinite lattices of intervals. |
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| > For certain, no. I could only guess that subgroups are actually harmonic
| | 11-EDO happens to be a decent temperament for the 2.7.9.11 subgroup. |
| > series prime limits.
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| Subgroups expand the concept of a prime limit. For instance, say you
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| want the 7-limit, but you don't care about prime 5; you just want
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| primes 2, 3, and 7. So that's the 2.3.7 subgroup. Or say that you want
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| the 7-limit, but you don't care about 3/1 but you do care about 9/1.
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| Then that's the 2.5.7.9 subgroup. Or, say that you want primes 2 and
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| 3, and the composite interval 7/5; that's the 2.3.7/5 subgroup.
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| The rule for any subgroup is that if you multiply or divide intervals,
| | -Mike |
| that's also in the subgroup. So for the 2.3.7 subgroup, 7*3 = 21/1 is
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| in the subgroup, as is 7/(2*3) = 7/6. And for the 2.3.7/5 subgroup,
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| 2/(7/5 * 7/5) = 50/49 is in the subgroup, and so on. They're infinite
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| lattices of intervals.
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| 11-EDO happens to be a decent temperament for the 2.7.9.11 subgroup. | | Anyway, you asked about figuring out what steps in 11-EDO approximate what intervals. So if 11-EDO supports the 2.7.9.11 subgroup, I can just give you the mappings for 2/1, 7/1, 9/1, and 11/1, and you can mix and match them to get what intervals you want, right. So for instance, 2/1 is 11 steps, 7/1 is 31 steps, 9/1 is 35 steps, and 11/1 is 38 steps. So then 11/9 is 38-35 = 3 steps. That should be enough information for you to get all the intervals. |
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| -Mike | | -Mike |
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| Anyway, you asked about figuring out what steps in 11-EDO approximate
| | OK, so rather than write all of that out in English, though, we can just use a simple notation. So if 2/1 is 11 steps, 7/1 is 31 steps, 9/1 is 35 steps, and 11/1 is 38 steps, then we can just condense all that as follows: |
| what intervals. So if 11-EDO supports the 2.7.9.11 subgroup, I can
| | |
| just give you the mappings for 2/1, 7/1, 9/1, and 11/1, and you can
| | <11 31 35 38| |
| mix and match them to get what intervals you want, right. So for
| | |
| instance, 2/1 is 11 steps, 7/1 is 31 steps, 9/1 is 35 steps, and 11/1
| | where it's understood in this particular case that the coefficients represent how many steps map to 2/1, 7/1, 9/1 and 11/1, respectively. This is called a val, and this is why we use them; so we can figure out how many steps every interval maps to. So 9/7 in the above case is 35-31 = 4 steps. |
| is 38 steps. So then 11/9 is 38-35 = 3 steps. That should be enough | | |
| information for you to get all the intervals.
| | -Mike</pre> |
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| | == See also == |
| | * [[Equal-step tuning/Jake's tips]] (contains another archived discussion with Chris Vaisil) |
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| -Mike
| | [[Category:Guides]] |
| <span style="color: #ffffff; display: block;">__._,_.___</span></pre></div>
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| <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>n00b page</title></head><body>On Thu, Nov 1, 2012 at 9:10 PM, Chris Vaisvil &lt;<a class="wiki_link" href="http://mailto.wikispaces.com/chrisvaisvil%2540gmail.com" target="_blank">[email protected]</a>&gt;<br /> | |
| <br />
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| wrote:<br />
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| <br />
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| &gt;<br />
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| <br />
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| <ul class="quotelist"><li>For certain, no. I could only guess that subgroups are actually harmonic</li><li>series prime limits.</li></ul>Subgroups expand the concept of a prime limit. For instance, say you<br />
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| want the 7-limit, but you don't care about prime 5; you just want<br />
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| primes 2, 3, and 7. So that's the 2.3.7 subgroup. Or say that you want<br />
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| the 7-limit, but you don't care about 3/1 but you do care about 9/1.<br />
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| Then that's the 2.5.7.9 subgroup. Or, say that you want primes 2 and<br />
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| 3, and the composite interval 7/5; that's the 2.3.7/5 subgroup.<br />
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| <br />
| |
| The rule for any subgroup is that if you multiply or divide intervals,<br />
| |
| that's also in the subgroup. So for the 2.3.7 subgroup, 7*3 = 21/1 is<br />
| |
| in the subgroup, as is 7/(2*3) = 7/6. And for the 2.3.7/5 subgroup,<br />
| |
| 2/(7/5 * 7/5) = 50/49 is in the subgroup, and so on. They're infinite<br />
| |
| lattices of intervals.<br />
| |
| <br />
| |
| 11-EDO happens to be a decent temperament for the 2.7.9.11 subgroup.<br />
| |
| <br />
| |
| -Mike<br />
| |
| <br />
| |
| Anyway, you asked about figuring out what steps in 11-EDO approximate<br />
| |
| what intervals. So if 11-EDO supports the 2.7.9.11 subgroup, I can<br />
| |
| just give you the mappings for 2/1, 7/1, 9/1, and 11/1, and you can<br />
| |
| mix and match them to get what intervals you want, right. So for<br />
| |
| instance, 2/1 is 11 steps, 7/1 is 31 steps, 9/1 is 35 steps, and 11/1<br />
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| is 38 steps. So then 11/9 is 38-35 = 3 steps. That should be enough<br />
| |
| information for you to get all the intervals.<br />
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| <br />
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| -Mike<br />
| |
| <span style="color: #ffffff; display: block;"><u>._,_.</u>_</span></body></html></pre></div>
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