Comparison of mode notation systems: Difference between revisions
Wikispaces>TallKite **Imported revision 580965979 - Original comment: ** |
Wikispaces>TallKite **Imported revision 580966291 - 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:TallKite|TallKite]] and made on <tt>2016-04-23 03: | : This revision was by author [[User:TallKite|TallKite]] and made on <tt>2016-04-23 03:31:42 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>580966291</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">Mode numbers | <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">**Mode numbers** provide a way to name MOS, MODMOS and even non-MOS rank-2 scales and modes systematically. Like [[xenharmonic/Modal UDP notation|Modal UDP notation]], it starts with the convention of using //some-temperament-name//[//some-number//] to create a generator-chain, and adds a way to number each mode uniquely. For example, here are all the modes of Meantone[7], using ~3/2 as the generator: | ||
|| old scale name || new scale name || Ls pattern || example on white keys || genchain || | || old scale name || new scale name || Ls pattern || example on white keys || genchain || | ||
|| Lydian || 1st Meantone[7] || LLLs LLs || F G A B C D E F || __**F**__ C G D A E B || | || Lydian || 1st Meantone[7] || LLLs LLs || F G A B C D E F || __**F**__ C G D A E B || | ||
| Line 16: | Line 16: | ||
|| Locrian || 7th Meantone[7] || sLLs LLL || B C D E F G A B || F C G D A E __**B**__ || | || Locrian || 7th Meantone[7] || sLLs LLL || B C D E F G A B || F C G D A E __**B**__ || | ||
These [[MOSScales|MOS scales]] are formed from a segment of the [[periods and generators|generator-chain]], or genchain. The first note in the genchain is the tonic of mode #1, the 2nd note is the tonic of mode #2, etc., somewhat analogous to harmonica positions. 4th Meantone[7] is spoken as "fourth meantone heptatonic". If in D, as above, it would be "D fourth meantone heptatonic". | These [[MOSScales|MOS scales]] are formed from a segment of the [[periods and generators|generator-chain]], or genchain. The first note in the genchain is the tonic of mode #1, the 2nd note is the tonic of mode #2, etc., somewhat analogous to harmonica positions. 4th Meantone[7] is spoken as "fourth meantone heptatonic" or possibly "fourth meantone seven". If in D, as above, it would be "D fourth meantone heptatonic". | ||
The same seven modes, all with C as the tonic, to illustrate the difference between modes. Similar modes are grouped together. The modes proceed from sharper (Lydian) to flatter (Locrian). | The same seven modes, all with C as the tonic, to illustrate the difference between modes. Similar modes are grouped together. The modes proceed from sharper (Lydian) to flatter (Locrian). | ||
| Line 111: | Line 111: | ||
|| 5th Shrutal[10] || Lssss-Lssss || C D Eb E F F# Ab A Bb B C || Ab Eb Bb F __**C**__ || D A E B F# || | || 5th Shrutal[10] || Lssss-Lssss || C D Eb E F F# Ab A Bb B C || Ab Eb Bb F __**C**__ || D A E B F# || | ||
There are only two Blackwood[10] modes. The period is a fifth-octave = 240¢. The generator is 5/4 = 386¢. L = 146¢ and s = 94¢. There are five short genchains. Ups and downs are used to distinguish between 5/4 and 2\5, in order to avoid duplicate note names. | There are only two Blackwood[10] modes. The period is a fifth-octave = 240¢. The generator is a just 5/4 = 386¢. L = 146¢ and s = 94¢. There are five short genchains. Ups and downs are used to distinguish between 5/4 and 2\5, in order to avoid duplicate note names. | ||
|| scale name || Ls pattern || example in C || 1st chain || 2nd chain || 3rd chain || 4th chain || 5th chain || | || scale name || Ls pattern || example in C || 1st chain || 2nd chain || 3rd chain || 4th chain || 5th chain || | ||
|| 1st Blackwood[10] || LsLsLs LsLs || C C#v D Ev F F#v G Av A Bv C ||= __**C**__ Ev || D F#v || F Av || G Bv || A C#v || | || 1st Blackwood[10] || LsLsLs LsLs || C C#v D Ev F F#v G Av A Bv C ||= __**C**__ Ev || D F#v || F Av || G Bv || A C#v || | ||
| Line 129: | Line 129: | ||
==__Explanation / Rationale__== | ==[[#How to name rank-2 scales-Non-MOS scales]]__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?__**=== | ||
| Line 141: | Line 141: | ||
"The syntonic temperament is a system of musical tuning in which the frequency ratio of each musical interval is a product of powers of an octave and a tempered perfect __**fifth**__." -- [[https://en.wikipedia.org/wiki/Syntonic_temperament|en.wikipedia.org/wiki/Syntonic_temperament]] | "The syntonic temperament is a system of musical tuning in which the frequency ratio of each musical interval is a product of powers of an octave and a tempered perfect __**fifth**__." -- [[https://en.wikipedia.org/wiki/Syntonic_temperament|en.wikipedia.org/wiki/Syntonic_temperament]] | ||
"Meantone is constructed the same way as Pythagorean tuning, as a stack of perfect __**fifths**__" -- | "Meantone is constructed the same way as Pythagorean tuning, as a stack of perfect __**fifths**__." -- | ||
[[https://en.wikipedia.org/wiki/Meantone_temperament|en.wikipedia.org/wiki/Meantone_temperament]] | [[https://en.wikipedia.org/wiki/Meantone_temperament|en.wikipedia.org/wiki/Meantone_temperament]] | ||
| Line 149: | Line 149: | ||
===__**Then why not always choose the larger of the two generators?**__=== | ===__**Then why not always choose the larger of the two generators?**__=== | ||
Because the interval arithmetic is easier with smaller intervals. It's easier to | Because the interval arithmetic is easier with smaller intervals. It's easier to add up stacked 2nds than stacked 7ths. Also, when the generator is a 2nd, the genchain is often identical to the scale, simplifying mode numbering. (See Porcupine[7] above.) | ||
===__Why not always choose the chroma-positive generator?__=== | ===__Why not always choose the chroma-positive generator?__=== | ||
| Line 186: | Line 186: | ||
Admins: Please delete the blank page at http://xenharmonic.wikispaces.com/Modal+Notation+by+Genchain+Position</pre></div> | Admins: Please delete the blank page at http://xenharmonic.wikispaces.com/Modal+Notation+by+Genchain+Position</pre></div> | ||
<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>Mode numbers | <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><strong>Mode numbers</strong> provide a way to name MOS, MODMOS and even non-MOS rank-2 scales and modes systematically. Like <a class="wiki_link" href="http://xenharmonic.wikispaces.com/Modal%20UDP%20notation">Modal UDP notation</a>, it starts with the convention of using <em>some-temperament-name</em>[<em>some-number</em>] to create a generator-chain, and adds a way to number each mode uniquely. For example, here are all the modes of Meantone[7], using ~3/2 as the generator:<br /> | ||
| Line 289: | Line 289: | ||
<br /> | <br /> | ||
These <a class="wiki_link" href="/MOSScales">MOS scales</a> are formed from a segment of the <a class="wiki_link" href="/periods%20and%20generators">generator-chain</a>, or genchain. The first note in the genchain is the tonic of mode #1, the 2nd note is the tonic of mode #2, etc., somewhat analogous to harmonica positions. 4th Meantone[7] is spoken as &quot;fourth meantone heptatonic&quot;. If in D, as above, it would be &quot;D fourth meantone heptatonic&quot;.<br /> | These <a class="wiki_link" href="/MOSScales">MOS scales</a> are formed from a segment of the <a class="wiki_link" href="/periods%20and%20generators">generator-chain</a>, or genchain. The first note in the genchain is the tonic of mode #1, the 2nd note is the tonic of mode #2, etc., somewhat analogous to harmonica positions. 4th Meantone[7] is spoken as &quot;fourth meantone heptatonic&quot; or possibly &quot;fourth meantone seven&quot;. If in D, as above, it would be &quot;D fourth meantone heptatonic&quot;.<br /> | ||
<br /> | <br /> | ||
The same seven modes, all with C as the tonic, to illustrate the difference between modes. Similar modes are grouped together. The modes proceed from sharper (Lydian) to flatter (Locrian).<br /> | The same seven modes, all with C as the tonic, to illustrate the difference between modes. Similar modes are grouped together. The modes proceed from sharper (Lydian) to flatter (Locrian).<br /> | ||
| Line 939: | Line 939: | ||
<br /> | <br /> | ||
There are only two Blackwood[10] modes. The period is a fifth-octave = 240¢. The generator is 5/4 = 386¢. L = 146¢ and s = 94¢. There are five short genchains. Ups and downs are used to distinguish between 5/4 and 2\5, in order to avoid duplicate note names.<br /> | There are only two Blackwood[10] modes. The period is a fifth-octave = 240¢. The generator is a just 5/4 = 386¢. L = 146¢ and s = 94¢. There are five short genchains. Ups and downs are used to distinguish between 5/4 and 2\5, in order to avoid duplicate note names.<br /> | ||
| Line 1,013: | Line 1,013: | ||
<br /> | <br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule:6:&lt;h2&gt; --><h2 id="toc3"><a name="x-Explanation / Rationale"></a><!-- ws:end:WikiTextHeadingRule:6 --><u>Explanation / Rationale</u></h2> | <!-- ws:start:WikiTextHeadingRule:6:&lt;h2&gt; --><h2 id="toc3"><a name="x-Explanation / Rationale"></a><!-- ws:end:WikiTextHeadingRule:6 --><!-- ws:start:WikiTextAnchorRule:21:&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:21 --><u>Explanation / Rationale</u></h2> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule:8:&lt;h3&gt; --><h3 id="toc4"><a name="x-Explanation / Rationale-Why not number the modes in the order they occur in the scale?"></a><!-- ws:end:WikiTextHeadingRule:8 --><strong><u>Why not number the modes in the order they occur in the scale?</u></strong></h3> | <!-- ws:start:WikiTextHeadingRule:8:&lt;h3&gt; --><h3 id="toc4"><a name="x-Explanation / Rationale-Why not number the modes in the order they occur in the scale?"></a><!-- ws:end:WikiTextHeadingRule:8 --><strong><u>Why not number the modes in the order they occur in the scale?</u></strong></h3> | ||
| Line 1,025: | Line 1,025: | ||
&quot;The syntonic temperament is a system of musical tuning in which the frequency ratio of each musical interval is a product of powers of an octave and a tempered perfect <u><strong>fifth</strong></u>.&quot; -- <a class="wiki_link_ext" href="https://en.wikipedia.org/wiki/Syntonic_temperament" rel="nofollow">en.wikipedia.org/wiki/Syntonic_temperament</a><br /> | &quot;The syntonic temperament is a system of musical tuning in which the frequency ratio of each musical interval is a product of powers of an octave and a tempered perfect <u><strong>fifth</strong></u>.&quot; -- <a class="wiki_link_ext" href="https://en.wikipedia.org/wiki/Syntonic_temperament" rel="nofollow">en.wikipedia.org/wiki/Syntonic_temperament</a><br /> | ||
<br /> | <br /> | ||
&quot;Meantone is constructed the same way as Pythagorean tuning, as a stack of perfect <u><strong>fifths</strong></u>&quot; --<br /> | &quot;Meantone is constructed the same way as Pythagorean tuning, as a stack of perfect <u><strong>fifths</strong></u>.&quot; --<br /> | ||
<a class="wiki_link_ext" href="https://en.wikipedia.org/wiki/Meantone_temperament" rel="nofollow">en.wikipedia.org/wiki/Meantone_temperament</a><br /> | <a class="wiki_link_ext" href="https://en.wikipedia.org/wiki/Meantone_temperament" rel="nofollow">en.wikipedia.org/wiki/Meantone_temperament</a><br /> | ||
<br /> | <br /> | ||
| Line 1,033: | Line 1,033: | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule:12:&lt;h3&gt; --><h3 id="toc6"><a name="x-Explanation / Rationale-Then why not always choose the larger of the two generators?"></a><!-- ws:end:WikiTextHeadingRule:12 --><u><strong>Then why not always choose the larger of the two generators?</strong></u></h3> | <!-- ws:start:WikiTextHeadingRule:12:&lt;h3&gt; --><h3 id="toc6"><a name="x-Explanation / Rationale-Then why not always choose the larger of the two generators?"></a><!-- ws:end:WikiTextHeadingRule:12 --><u><strong>Then why not always choose the larger of the two generators?</strong></u></h3> | ||
Because the interval arithmetic is easier with smaller intervals. It's easier to | Because the interval arithmetic is easier with smaller intervals. It's easier to add up stacked 2nds than stacked 7ths. Also, when the generator is a 2nd, the genchain is often identical to the scale, simplifying mode numbering. (See Porcupine[7] above.)<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule:14:&lt;h3&gt; --><h3 id="toc7"><a name="x-Explanation / Rationale-Why not always choose the chroma-positive generator?"></a><!-- ws:end:WikiTextHeadingRule:14 --><u>Why not always choose the chroma-positive generator?</u></h3> | <!-- ws:start:WikiTextHeadingRule:14:&lt;h3&gt; --><h3 id="toc7"><a name="x-Explanation / Rationale-Why not always choose the chroma-positive generator?"></a><!-- ws:end:WikiTextHeadingRule:14 --><u>Why not always choose the chroma-positive generator?</u></h3> | ||
| Line 1,224: | Line 1,224: | ||
<br /> | <br /> | ||
<br /> | <br /> | ||
Admins: Please delete the blank page at <!-- ws:start:WikiTextUrlRule: | Admins: Please delete the blank page at <!-- ws:start:WikiTextUrlRule:1397: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:1397 --></body></html></pre></div> | ||