Comparison of mode notation systems: Difference between revisions
Wikispaces>jdfreivald **Imported revision 581133883 - Original comment: ** |
Wikispaces>jdfreivald **Imported revision 581134437 - Original comment: ** |
||
| Line 1: | Line 1: | ||
<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 11:54:35 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>581134437</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 310: | Line 310: | ||
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.) | 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. | Let's try something harder: the rank-3 scale [[http://x31eq.com/cgi-bin/scala.cgi?ets=12_31_22&limit=11&tuning=po|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. | ||
NOTE: NO collapsing genchains. NO generator knowledge needed. No mapping knowledge (or indeed mapping at all) required. Extensible to higher ranks without problems. It doesn't matter whether the scale is a temperament at all. | NOTE: NO collapsing genchains. NO generator knowledge needed. No mapping knowledge (or indeed mapping at all) required. Extensible to higher ranks without problems. It doesn't matter whether the scale is a temperament at all. | ||
=Request for admins= | |||
Admins: Please delete the blank page at http://xenharmonic.wikispaces.com/Modal+Notation+by+Genchain+Position | Admins: Please delete the blank page at http://xenharmonic.wikispaces.com/Modal+Notation+by+Genchain+Position | ||
| Line 321: | Line 320: | ||
<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>Naming Rank-2 Scales</title></head><body><!-- ws:start:WikiTextHeadingRule:0:&lt;h1&gt; --><h1 id="toc0"><!-- ws:end:WikiTextHeadingRule:0 --> </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>Naming Rank-2 Scales</title></head><body><!-- ws:start:WikiTextHeadingRule:0:&lt;h1&gt; --><h1 id="toc0"><!-- ws:end:WikiTextHeadingRule:0 --> </h1> | ||
<!-- ws:start:WikiTextTocRule: | <!-- ws:start:WikiTextTocRule:30:&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:30 --><!-- ws:start:WikiTextTocRule:31: --><div style="margin-left: 1em;"><a href="#toc0"> </a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:31 --><!-- ws:start:WikiTextTocRule:32: --><div style="margin-left: 1em;"><a href="#Kite Giedraitis method">Kite Giedraitis method</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:32 --><!-- ws:start:WikiTextTocRule:33: --><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: | <!-- ws:end:WikiTextTocRule:33 --><!-- ws:start:WikiTextTocRule:34: --><div style="margin-left: 2em;"><a href="#Kite Giedraitis method-MODMOS scales">MODMOS scales</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:34 --><!-- ws:start:WikiTextTocRule:35: --><div style="margin-left: 2em;"><a href="#Kite Giedraitis method-Fractional-octave periods">Fractional-octave periods</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:35 --><!-- ws:start:WikiTextTocRule:36: --><div style="margin-left: 2em;"><a href="#Kite Giedraitis method-Non-MOS non-MODMOS scales">Non-MOS non-MODMOS scales</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:36 --><!-- ws:start:WikiTextTocRule:37: --><div style="margin-left: 2em;"><a href="#Kite Giedraitis method-Explanation / Rationale">Explanation / Rationale</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:37 --><!-- ws:start:WikiTextTocRule:38: --><div style="margin-left: 3em;"><a href="#Kite Giedraitis method-Explanation / Rationale-Why not number the modes in the order they occur in the scale?">Why not number the modes in the order they occur in the scale?</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:38 --><!-- ws:start:WikiTextTocRule:39: --><div style="margin-left: 3em;"><a href="#Kite Giedraitis method-Explanation / Rationale-Why make an exception for 3/2 vs 4/3 as the generator?">Why make an exception for 3/2 vs 4/3 as the generator?</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:39 --><!-- ws:start:WikiTextTocRule:40: --><div style="margin-left: 3em;"><a href="#Kite Giedraitis method-Explanation / Rationale-Then why not always choose the larger of the two generators?">Then why not always choose the larger of the two generators?</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:40 --><!-- ws:start:WikiTextTocRule:41: --><div style="margin-left: 3em;"><a href="#Kite Giedraitis method-Explanation / Rationale-Why not always choose the chroma-positive generator?">Why not always choose the chroma-positive generator?</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:41 --><!-- ws:start:WikiTextTocRule:42: --><div style="margin-left: 3em;"><a href="#Kite Giedraitis method-Explanation / Rationale-Why not just use UDP notation?">Why not just use UDP notation?</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:42 --><!-- ws:start:WikiTextTocRule:43: --><div style="margin-left: 1em;"><a href="#Jake Freivald method">Jake Freivald method</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:43 --><!-- ws:start:WikiTextTocRule:44: --><div style="margin-left: 2em;"><a href="#Jake Freivald method-Extending to non-MOS">Extending to non-MOS</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:44 --><!-- ws:start:WikiTextTocRule:45: --><div style="margin-left: 1em;"><a href="#Request for admins">Request for admins</a></div> | ||
< | <!-- ws:end:WikiTextTocRule:45 --><!-- ws:start:WikiTextTocRule:46: --></div> | ||
<!-- ws:end:WikiTextTocRule:46 --><!-- 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-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> | <!-- 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> | ||
<br /> | <br /> | ||
| Line 917: | Line 917: | ||
<br /> | <br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule:6:&lt;h2&gt; --><h2 id="toc3"><a name="Kite Giedraitis method-MODMOS scales"></a><!-- ws:end:WikiTextHeadingRule:6 --><!-- ws:start:WikiTextAnchorRule: | <!-- ws:start:WikiTextHeadingRule:6:&lt;h2&gt; --><h2 id="toc3"><a name="Kite Giedraitis method-MODMOS scales"></a><!-- ws:end:WikiTextHeadingRule:6 --><!-- ws:start:WikiTextAnchorRule:47:&lt;img src=&quot;/i/anchor.gif&quot; class=&quot;WikiAnchor&quot; alt=&quot;Anchor&quot; id=&quot;wikitext@@anchor@@How to name rank-2 scales-MODMOS scales&quot; title=&quot;Anchor: How to name rank-2 scales-MODMOS scales&quot;/&gt; --><a name="How to name rank-2 scales-MODMOS scales"></a><!-- ws:end:WikiTextAnchorRule:47 --><strong><u>MODMOS scales</u></strong></h2> | ||
To find a <a class="wiki_link" href="/MODMOS%20Scales">MODMOS</a> scale's name, start with the genchain for the scale, which will always have gaps. Compact it into a chain without gaps by altering one or more notes. If there is more than one way to do this, the way that alters as few notes as possible is generally preferable. Determine the mode number from the <u>compacted</u> genchain. <em>[This may change]</em> For example, for harmonic minor, A is the 4th note of the uncompacted genchain, but the 5th note of the compacted one. This is so that two notes an aug or dim fifth apart will have adjacent mode numbers. Just like A and E are adjacent, Ab and E are too. In other words, determining the mode number from the scale degree remains fifth-based.<br /> | To find a <a class="wiki_link" href="/MODMOS%20Scales">MODMOS</a> scale's name, start with the genchain for the scale, which will always have gaps. Compact it into a chain without gaps by altering one or more notes. If there is more than one way to do this, the way that alters as few notes as possible is generally preferable. Determine the mode number from the <u>compacted</u> genchain. <em>[This may change]</em> For example, for harmonic minor, A is the 4th note of the uncompacted genchain, but the 5th note of the compacted one. This is so that two notes an aug or dim fifth apart will have adjacent mode numbers. Just like A and E are adjacent, Ab and E are too. In other words, determining the mode number from the scale degree remains fifth-based.<br /> | ||
<br /> | <br /> | ||
| Line 1,108: | Line 1,108: | ||
<br /> | <br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule:8:&lt;h2&gt; --><h2 id="toc4"><a name="Kite Giedraitis method-Fractional-octave periods"></a><!-- ws:end:WikiTextHeadingRule:8 --><!-- ws:start:WikiTextAnchorRule: | <!-- ws:start:WikiTextHeadingRule:8:&lt;h2&gt; --><h2 id="toc4"><a name="Kite Giedraitis method-Fractional-octave periods"></a><!-- ws:end:WikiTextHeadingRule:8 --><!-- ws:start:WikiTextAnchorRule:48:&lt;img src=&quot;/i/anchor.gif&quot; class=&quot;WikiAnchor&quot; alt=&quot;Anchor&quot; id=&quot;wikitext@@anchor@@How to name rank-2 scales-Fractional-octave periods&quot; title=&quot;Anchor: How to name rank-2 scales-Fractional-octave periods&quot;/&gt; --><a name="How to name rank-2 scales-Fractional-octave periods"></a><!-- ws:end:WikiTextAnchorRule:48 --><strong><u>Fractional-octave periods</u></strong></h2> | ||
Fractional-period rank-2 temperaments have multiple genchains running in parallel. For example, shrutal[10] might look like this:<br /> | Fractional-period rank-2 temperaments have multiple genchains running in parallel. For example, shrutal[10] might look like this:<br /> | ||
Eb -- Bb -- F --- C --- G<br /> | Eb -- Bb -- F --- C --- G<br /> | ||
| Line 1,319: | Line 1,319: | ||
<br /> | <br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule:10:&lt;h2&gt; --><h2 id="toc5"><a name="Kite Giedraitis method-Non-MOS non-MODMOS scales"></a><!-- ws:end:WikiTextHeadingRule:10 --><!-- ws:start:WikiTextAnchorRule: | <!-- ws:start:WikiTextHeadingRule:10:&lt;h2&gt; --><h2 id="toc5"><a name="Kite Giedraitis method-Non-MOS non-MODMOS scales"></a><!-- ws:end:WikiTextHeadingRule:10 --><!-- ws:start:WikiTextAnchorRule:49:&lt;img src=&quot;/i/anchor.gif&quot; class=&quot;WikiAnchor&quot; alt=&quot;Anchor&quot; id=&quot;wikitext@@anchor@@How to name rank-2 scales-Non-MOS scales&quot; title=&quot;Anchor: How to name rank-2 scales-Non-MOS scales&quot;/&gt; --><a name="How to name rank-2 scales-Non-MOS scales"></a><!-- ws:end:WikiTextAnchorRule:49 --><strong><u>Non-MOS non-MODMOS scales</u></strong></h2> | ||
Compact the genchain to remove any gaps via alterations. The mode number is derived from the compacted genchain. Examples:<br /> | Compact the genchain to remove any gaps via alterations. The mode number is derived from the compacted genchain. Examples:<br /> | ||
<br /> | <br /> | ||
| Line 1,338: | Line 1,338: | ||
<br /> | <br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule:12:&lt;h2&gt; --><h2 id="toc6"><a name="Kite Giedraitis method-Explanation / Rationale"></a><!-- ws:end:WikiTextHeadingRule:12 --><!-- ws:start:WikiTextAnchorRule: | <!-- ws:start:WikiTextHeadingRule:12:&lt;h2&gt; --><h2 id="toc6"><a name="Kite Giedraitis method-Explanation / Rationale"></a><!-- ws:end:WikiTextHeadingRule:12 --><!-- ws:start:WikiTextAnchorRule:50:&lt;img src=&quot;/i/anchor.gif&quot; class=&quot;WikiAnchor&quot; alt=&quot;Anchor&quot; id=&quot;wikitext@@anchor@@How to name rank-2 scales-Non-MOS scales&quot; title=&quot;Anchor: How to name rank-2 scales-Non-MOS scales&quot;/&gt; --><a name="How to name rank-2 scales-Non-MOS scales"></a><!-- ws:end:WikiTextAnchorRule:50 --><u>Explanation / Rationale</u></h2> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule:14:&lt;h3&gt; --><h3 id="toc7"><a name="Kite Giedraitis method-Explanation / Rationale-Why not number the modes in the order they occur in the scale?"></a><!-- ws:end:WikiTextHeadingRule:14 --><strong><u>Why not number the modes in the order they occur in the scale?</u></strong></h3> | <!-- ws:start:WikiTextHeadingRule:14:&lt;h3&gt; --><h3 id="toc7"><a name="Kite Giedraitis method-Explanation / Rationale-Why not number the modes in the order they occur in the scale?"></a><!-- ws:end:WikiTextHeadingRule:14 --><strong><u>Why not number the modes in the order they occur in the scale?</u></strong></h3> | ||
| Line 1,625: | Line 1,625: | ||
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 /> | 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. | Let's try something harder: the rank-3 scale <a class="wiki_link_ext" href="http://x31eq.com/cgi-bin/scala.cgi?ets=12_31_22&amp;limit=11&amp;tuning=po" rel="nofollow">minerva[12],</a> 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 /> | ||
<br /> | <br /> | ||
NOTE: NO collapsing genchains. NO generator knowledge needed. No mapping knowledge (or indeed mapping at all) required. Extensible to higher ranks without problems. It doesn't matter whether the scale is a temperament at all.<br /> | NOTE: NO collapsing genchains. NO generator knowledge needed. No mapping knowledge (or indeed mapping at all) required. Extensible to higher ranks without problems. It doesn't matter whether the scale is a temperament at all.<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule:28:&lt;h1&gt; --><h1 id="toc14"><a name="Request for admins"></a><!-- ws:end:WikiTextHeadingRule:28 -->Request for admins</h1> | |||
<br /> | <br /> | ||
Admins: Please delete the blank page at <!-- ws:start:WikiTextUrlRule: | Admins: Please delete the blank page at <!-- ws:start:WikiTextUrlRule:1752:http://xenharmonic.wikispaces.com/Modal+Notation+by+Genchain+Position --><a href="http://xenharmonic.wikispaces.com/Modal+Notation+by+Genchain+Position">http://xenharmonic.wikispaces.com/Modal+Notation+by+Genchain+Position</a><!-- ws:end:WikiTextUrlRule:1752 --><br /> | ||
<span style="display: block; height: 1px; left: 0px; overflow: hidden; position: absolute; top: 4019.5px; width: 1px;"><span style="background-color: #f6f7f8; color: #141823; font-family: helvetica,arial,sans-serif; font-size: 12px; line-height: 16.08px;"><strong><span style="color: #3b5998;"><a class="wiki_link_ext" href="https://www.facebook.com/kite.giedraitis?fref=ufi" rel="nofollow">Giedraitis</a></span></strong> <span class="UFICommentBody">Been</span></span></span></body></html></pre></div> | <span style="display: block; height: 1px; left: 0px; overflow: hidden; position: absolute; top: 4019.5px; width: 1px;"><span style="background-color: #f6f7f8; color: #141823; font-family: helvetica,arial,sans-serif; font-size: 12px; line-height: 16.08px;"><strong><span style="color: #3b5998;"><a class="wiki_link_ext" href="https://www.facebook.com/kite.giedraitis?fref=ufi" rel="nofollow">Giedraitis</a></span></strong> <span class="UFICommentBody">Been</span></span></span></body></html></pre></div> | ||