Just intonation subgroup/Mike's tips: Difference between revisions
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Wikispaces>vaisvil **Imported revision 378510076 - Original comment: ** |
Wikispaces>vaisvil **Imported revision 378515792 - Original comment: ** |
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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:vaisvil|vaisvil]] and made on <tt>2012-11-01 | : This revision was by author [[User:vaisvil|vaisvil]] and made on <tt>2012-11-01 22:01:06 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>378515792</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">On Thu, Nov 1, 2012 at 9:10 PM, Chris Vaisvil <[[@mailto | <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]]]> | ||
wrote: | wrote: | ||
| Line 38: | Line 38: | ||
is 38 steps. So then 11/9 is 38-35 = 3 steps. That should be enough | is 38 steps. So then 11/9 is 38-35 = 3 steps. That should be enough | ||
information for you to get all the intervals. | information for you to get all the intervals. | ||
-Mike | |||
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: | |||
<11 31 35 38| | |||
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. | |||
-Mike | -Mike | ||
| Line 72: | Line 87: | ||
is 38 steps. So then 11/9 is 38-35 = 3 steps. That should be enough<br /> | 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 /> | information for you to get all the intervals.<br /> | ||
<br /> | |||
-Mike<br /> | |||
<br /> | |||
OK, so rather than write all of that out in English, though, we can<br /> | |||
just use a simple notation. So if 2/1 is 11 steps, 7/1 is 31 steps,<br /> | |||
9/1 is 35 steps, and 11/1 is 38 steps, then we can just condense all<br /> | |||
that as follows:<br /> | |||
<br /> | |||
&lt;11 31 35 38|<br /> | |||
<br /> | |||
where it's understood in this particular case that the coefficients<br /> | |||
represent how many steps map to 2/1, 7/1, 9/1 and 11/1, respectively.<br /> | |||
This is called a val, and this is why we use them; so we can figure<br /> | |||
out how many steps every interval maps to. So 9/7 in the above case is<br /> | |||
35-31 = 4 steps.<br /> | |||
<br /> | <br /> | ||
-Mike<br /> | -Mike<br /> | ||
<span style="color: #ffffff; display: block;"><u>._,_.</u>_</span></body></html></pre></div> | <span style="color: #ffffff; display: block;"><u>._,_.</u>_</span></body></html></pre></div> | ||
Revision as of 22:01, 1 November 2012
IMPORTED REVISION FROM WIKISPACES
This is an imported revision from Wikispaces. The revision metadata is included below for reference:
- This revision was by author vaisvil and made on 2012-11-01 22:01:06 UTC.
- The original revision id was 378515792.
- The revision comment was:
The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.
Original Wikitext content:
On Thu, Nov 1, 2012 at 9:10 PM, Chris Vaisvil <[[@mailto/chrisvaisvil%40gmail.com|[email protected]]]> wrote: > > For certain, no. I could only guess that subgroups are actually harmonic > series prime limits. 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. 11-EDO happens to be a decent temperament for the 2.7.9.11 subgroup. -Mike 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. -Mike 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: <11 31 35 38| 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. -Mike <span style="color: #ffffff; display: block;">__._,_.___</span>
Original HTML content:
<html><head><title>n00b page</title></head><body>On Thu, Nov 1, 2012 at 9:10 PM, Chris Vaisvil <<a class="wiki_link" href="http://mailto.wikispaces.com/chrisvaisvil%2540gmail.com" target="_blank">[email protected]</a>><br /> <br /> wrote:<br /> <br /> ><br /> <br /> <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 /> want the 7-limit, but you don't care about prime 5; you just want<br /> primes 2, 3, and 7. So that's the 2.3.7 subgroup. Or say that you want<br /> the 7-limit, but you don't care about 3/1 but you do care about 9/1.<br /> Then that's the 2.5.7.9 subgroup. Or, say that you want primes 2 and<br /> 3, and the composite interval 7/5; that's the 2.3.7/5 subgroup.<br /> <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 /> 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 /> <br /> -Mike<br /> <br /> OK, so rather than write all of that out in English, though, we can<br /> just use a simple notation. So if 2/1 is 11 steps, 7/1 is 31 steps,<br /> 9/1 is 35 steps, and 11/1 is 38 steps, then we can just condense all<br /> that as follows:<br /> <br /> <11 31 35 38|<br /> <br /> where it's understood in this particular case that the coefficients<br /> represent how many steps map to 2/1, 7/1, 9/1 and 11/1, respectively.<br /> This is called a val, and this is why we use them; so we can figure<br /> out how many steps every interval maps to. So 9/7 in the above case is<br /> 35-31 = 4 steps.<br /> <br /> -Mike<br /> <span style="color: #ffffff; display: block;"><u>._,_.</u>_</span></body></html>