Comparison of mode notation systems: Difference between revisions
Wikispaces>jdfreivald **Imported revision 581132177 - 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:jdfreivald|jdfreivald]] and made on <tt>2016-04-25 11: | : This revision was by author [[User:jdfreivald|jdfreivald]] and made on <tt>2016-04-25 11:51:30 UTC</tt>.<br> | ||
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[[toc]] | [[toc]] | ||
=__**Kite** Giedraitis method__= | =__**Kite** Giedraitis method__= | ||
==__<span style="font-size: 1.3em; line-height: 1.5;"> | ==__<span style="font-size: 1.3em; line-height: 1.5;">Proposed method of naming all possible rank-2 scales</span>__== | ||
**This page is a work in progress...** | **This page is a work in progress...** | ||
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None of these scales have had a problem that I'm about to address and resolve. To wit: | None of these scales have had a problem that I'm about to address and resolve. To wit: | ||
Let's pick a rank-3 scale: 1/1 - 9/8 - 5/4 - 4/3 - 3/2 - 5/3 - 15/8 - 2/1. (Note that this is not a temperament at all.) That's LMsLMLs. With three L's and only two M's and s's, L has to go first. But there are no larger or smaller clusters of L's! They only come one at a time. So let's pick the mode that has the longest string of non-L's to go first. (That pushes the last L out as far as it will go.) | Let's pick a rank-3 scale: 1/1 - 9/8 - 5/4 - 4/3 - 3/2 - 5/3 - 15/8 - 2/1. (Note that this is not a temperament at all.) That's LMsLMLs. With three L's and only two M's and s's, L has to go first. But there are no larger or smaller clusters of L's! They only come one at a time. So let's pick the mode that has the longest string of non-L's to go first. (That pushes the last L out as far as it will go.) This gives us LMsLMLs, which is our original scale, which is also a convenient touchpoint, in my opinion. | ||
This also works for Kite's question about meantone[8], which is LMsMLLML. There are more L's than any other step size, so the scale has to start with L. The L's are in equal clusters of two, so there's no obvious way to pick which one goes first: mode 1 must start with LL. So let's pick the mode that has the longest string of non-L's to go after that first LL: Mode 1 of meantone[8] is LLMsMLLM. (That's C - D - E - F - F# - G - A - B - C, or something like it.) | This also works for Kite's question about meantone[8], which is LMsMLLML. There are more L's than any other step size, so the scale has to start with L. The L's are in equal clusters of two, so there's no obvious way to pick which one goes first: mode 1 must start with LL. So let's again pick the mode that has the longest string of non-L's to go after that first LL: Mode 1 of meantone[8] is LLMsMLLM. (That's C - D - E - F - F# - G - A - B - C, or something like it.) | ||
Let's try something harder: the rank-3 scale minerva[12], which I found through Graham's temperament finder.* Since there are four step sizes, I'm going to label them LMms, where the capital M is larger than the small m. With steps of 113, 113, 87, 113, 87, 99, 113, 87, 113, 87, 113, and 73, that's LLmLmMLmLmLs, 6L+1M+4m+1s. L has to go first. There's a cluster of two L's in the string, and I push that as close to the end as possible: LmMLmLmLsLLm. Graham is showing mode 10 of this scale in his temperament finder. | Let's try something harder: the rank-3 scale minerva[12], which I found through Graham's temperament finder.* Since there are four step sizes, I'm going to label them LMms, where the capital M is larger than the small m. With steps of 113, 113, 87, 113, 87, 99, 113, 87, 113, 87, 113, and 73, that's LLmLmMLmLmLs, 6L+1M+4m+1s. L has to go first. There's a cluster of two L's in the string, and I push that as close to the end as possible: LmMLmLmLsLLm. Graham is showing mode 10 of this scale in his temperament finder. | ||
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<!-- ws:start:WikiTextTocRule:28:&lt;img id=&quot;wikitext@@toc@@normal&quot; class=&quot;WikiMedia WikiMediaToc&quot; title=&quot;Table of Contents&quot; src=&quot;/site/embedthumbnail/toc/normal?w=225&amp;h=100&quot;/&gt; --><div id="toc"><h1 class="nopad">Table of Contents</h1><!-- ws:end:WikiTextTocRule:28 --><!-- ws:start:WikiTextTocRule:29: --><div style="margin-left: 1em;"><a href="#toc0"> </a></div> | <!-- ws:start:WikiTextTocRule:28:&lt;img id=&quot;wikitext@@toc@@normal&quot; class=&quot;WikiMedia WikiMediaToc&quot; title=&quot;Table of Contents&quot; src=&quot;/site/embedthumbnail/toc/normal?w=225&amp;h=100&quot;/&gt; --><div id="toc"><h1 class="nopad">Table of Contents</h1><!-- ws:end:WikiTextTocRule:28 --><!-- ws:start:WikiTextTocRule:29: --><div style="margin-left: 1em;"><a href="#toc0"> </a></div> | ||
<!-- ws:end:WikiTextTocRule:29 --><!-- ws:start:WikiTextTocRule:30: --><div style="margin-left: 1em;"><a href="#Kite Giedraitis method">Kite Giedraitis method</a></div> | <!-- ws:end:WikiTextTocRule:29 --><!-- ws:start:WikiTextTocRule:30: --><div style="margin-left: 1em;"><a href="#Kite Giedraitis method">Kite Giedraitis method</a></div> | ||
<!-- ws:end:WikiTextTocRule:30 --><!-- ws:start:WikiTextTocRule:31: --><div style="margin-left: 2em;"><a href="#Kite Giedraitis method- | <!-- ws:end:WikiTextTocRule:30 --><!-- ws:start:WikiTextTocRule:31: --><div style="margin-left: 2em;"><a href="#Kite Giedraitis method-Proposed method of naming all possible rank-2 scales">Proposed method of naming all possible rank-2 scales</a></div> | ||
<!-- ws:end:WikiTextTocRule:31 --><!-- ws:start:WikiTextTocRule:32: --><div style="margin-left: 2em;"><a href="#Kite Giedraitis method-MODMOS scales">MODMOS scales</a></div> | <!-- ws:end:WikiTextTocRule:31 --><!-- ws:start:WikiTextTocRule:32: --><div style="margin-left: 2em;"><a href="#Kite Giedraitis method-MODMOS scales">MODMOS scales</a></div> | ||
<!-- ws:end:WikiTextTocRule:32 --><!-- ws:start:WikiTextTocRule:33: --><div style="margin-left: 2em;"><a href="#Kite Giedraitis method-Fractional-octave periods">Fractional-octave periods</a></div> | <!-- ws:end:WikiTextTocRule:32 --><!-- ws:start:WikiTextTocRule:33: --><div style="margin-left: 2em;"><a href="#Kite Giedraitis method-Fractional-octave periods">Fractional-octave periods</a></div> | ||
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<!-- ws:end:WikiTextTocRule:43 --><!-- ws:start:WikiTextHeadingRule:2:&lt;h1&gt; --><h1 id="toc1"><a name="Kite Giedraitis method"></a><!-- ws:end:WikiTextHeadingRule:2 --><u><strong>Kite</strong> Giedraitis method</u></h1> | <!-- ws:end:WikiTextTocRule:43 --><!-- ws:start:WikiTextHeadingRule:2:&lt;h1&gt; --><h1 id="toc1"><a name="Kite Giedraitis method"></a><!-- ws:end:WikiTextHeadingRule:2 --><u><strong>Kite</strong> Giedraitis method</u></h1> | ||
<!-- ws:start:WikiTextHeadingRule:4:&lt;h2&gt; --><h2 id="toc2"><a name="Kite Giedraitis method- | <!-- ws:start:WikiTextHeadingRule:4:&lt;h2&gt; --><h2 id="toc2"><a name="Kite Giedraitis method-Proposed method of naming all possible rank-2 scales"></a><!-- ws:end:WikiTextHeadingRule:4 --><u><span style="font-size: 1.3em; line-height: 1.5;">Proposed method of naming all possible rank-2 scales</span></u></h2> | ||
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<strong>This page is a work in progress...</strong><br /> | <strong>This page is a work in progress...</strong><br /> | ||
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None of these scales have had a problem that I'm about to address and resolve. To wit:<br /> | None of these scales have had a problem that I'm about to address and resolve. To wit:<br /> | ||
<br /> | <br /> | ||
Let's pick a rank-3 scale: 1/1 - 9/8 - 5/4 - 4/3 - 3/2 - 5/3 - 15/8 - 2/1. (Note that this is not a temperament at all.) That's LMsLMLs. With three L's and only two M's and s's, L has to go first. But there are no larger or smaller clusters of L's! They only come one at a time. So let's pick the mode that has the longest string of non-L's to go first. (That pushes the last L out as far as it will go.)<br /> | Let's pick a rank-3 scale: 1/1 - 9/8 - 5/4 - 4/3 - 3/2 - 5/3 - 15/8 - 2/1. (Note that this is not a temperament at all.) That's LMsLMLs. With three L's and only two M's and s's, L has to go first. But there are no larger or smaller clusters of L's! They only come one at a time. So let's pick the mode that has the longest string of non-L's to go first. (That pushes the last L out as far as it will go.) This gives us LMsLMLs, which is our original scale, which is also a convenient touchpoint, in my opinion.<br /> | ||
<br /> | <br /> | ||
This also works for Kite's question about meantone[8], which is LMsMLLML. There are more L's than any other step size, so the scale has to start with L. The L's are in equal clusters of two, so there's no obvious way to pick which one goes first: mode 1 must start with LL. So let's pick the mode that has the longest string of non-L's to go after that first LL: Mode 1 of meantone[8] is LLMsMLLM. (That's C - D - E - F - F# - G - A - B - C, or something like it.)<br /> | This also works for Kite's question about meantone[8], which is LMsMLLML. There are more L's than any other step size, so the scale has to start with L. The L's are in equal clusters of two, so there's no obvious way to pick which one goes first: mode 1 must start with LL. So let's again pick the mode that has the longest string of non-L's to go after that first LL: Mode 1 of meantone[8] is LLMsMLLM. (That's C - D - E - F - F# - G - A - B - C, or something like it.)<br /> | ||
<br /> | <br /> | ||
Let's try something harder: the rank-3 scale minerva[12], which I found through Graham's temperament finder.* Since there are four step sizes, I'm going to label them LMms, where the capital M is larger than the small m. With steps of 113, 113, 87, 113, 87, 99, 113, 87, 113, 87, 113, and 73, that's LLmLmMLmLmLs, 6L+1M+4m+1s. L has to go first. There's a cluster of two L's in the string, and I push that as close to the end as possible: LmMLmLmLsLLm. Graham is showing mode 10 of this scale in his temperament finder.<br /> | Let's try something harder: the rank-3 scale minerva[12], which I found through Graham's temperament finder.* Since there are four step sizes, I'm going to label them LMms, where the capital M is larger than the small m. With steps of 113, 113, 87, 113, 87, 99, 113, 87, 113, 87, 113, and 73, that's LLmLmMLmLmLs, 6L+1M+4m+1s. L has to go first. There's a cluster of two L's in the string, and I push that as close to the end as possible: LmMLmLmLsLLm. Graham is showing mode 10 of this scale in his temperament finder.<br /> | ||