UDP: Difference between revisions
Wikispaces>genewardsmith **Imported revision 278343148 - Original comment: ** |
Wikispaces>mbattaglia1 **Imported revision 279063540 - 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: | : This revision was by author [[User:mbattaglia1|mbattaglia1]] and made on <tt>2011-11-25 15:46:17 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>279063540</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">=Modal UDP Notation= | <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">=Modal UDP Notation= | ||
Modal UDP notation is a way to uniquely specify a particular mode of any MOS. Its name is derived from up|down(period), or U|D(P) | Modal UDP notation is a way to uniquely specify a particular mode of any MOS. Its name is derived from up|down(period), or U|D(P). If accidentals are specified, it can also refer to the MODMOS's of those MOS's as well. | ||
UDP notation is | Any MOS has an ambiguous choice of generator: for example, the generator for meantone[7] can be viewed as either the perfect fourth or the perfect fifth. If the generator is chosen by picking the one which is the larger specific interval in its generic interval class, also called the //chroma-positive generator,// then the UDP notation for any mode is U|D(P) - where P is the number of periods per equivalence interval, U is the number of chroma-positive generators going up from the tonic times P, and D is the number of chroma-positive generators going down from the tonic times P. If P = 1, then it can be omitted, so that the UDP notation is simply U|D. | ||
This choice of generator means that the UDP notation simultaneously describes the following properties of the mode in question: | |||
# How many scale degrees are of the "larger" or "major" variant, vs the "smaller" or "minor" variant. | # How many scale degrees are of the "larger" or "major" variant, vs the "smaller" or "minor" variant. | ||
# How many generators up vs down from the tonic it requires to generate the mode. | # How many generators need to be stacked up vs down from the tonic it requires to generate the mode. | ||
Examples can be found below. | |||
=Mathematical Definition= | =Mathematical Definition= | ||
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=Examples= | =Examples= | ||
For example, the proper generator for meantone[7] is the perfect fifth, because it's larger than the other specific interval it shares a class with, the diminished fifth. Consequentially, meantone[7]'s Ionian mode is 5|1(1), which is 5|1 for short, and Aeolian is 2|4. We can add accidentals as well, so that meantone's harmonic minor is 2|4 #7. | |||
On the other hand, the chroma-positive generator for porcupine[7] is the larger 7th, which is about ~11/6; as a consequence, porcupine[7]'s Lssssss mode is 6|0, and sssLsss is 3|3. Likewise, mavila[7]'s ssLsssL anti-Ionian is 1|5, and Mavila[9]'s LLsLLLsLL "Olympian" mode is 4|4. | |||
It should be noted that the chroma-positive generator will vary from MOS to MOS even within the same temperament. For example, the chroma-positive generator for meantone[7] is the ~3/2, but is the ~4/3 for meantone[5]. | |||
**MOS's** | |||
* Meantone[7] Ionian, LLsLLLs: 5|1 | * Meantone[7] Ionian, LLsLLLs: 5|1 | ||
* Meantone[7] Aeolian, LsLLsLL: 2|4 | * Meantone[7] Aeolian, LsLLsLL: 2|4 | ||
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* Sensi[11] LLsLLLsLLLs: 8|2 | * Sensi[11] LLsLLLsLLLs: 8|2 | ||
* Pajara[10] Static Symmetrical Major, ssLssssLss: 4|4(2) | * Pajara[10] Static Symmetrical Major, ssLssssLss: 4|4(2) | ||
* Mavila/Mabila[9] Olympian, LLsLLLsLL 4|4 | * Mavila/Mabila[9] Olympian, LLsLLLsLL 4|4 | ||
**MODMOS's** | |||
* | |||
* Melodic minor is 5|1(1) b3, abbreviated 5|1 b3 for short, but could also be 3|3(1) #7, abbreviated 3|3 #7 for short. | * Melodic minor is 5|1(1) b3, abbreviated 5|1 b3 for short, but could also be 3|3(1) #7, abbreviated 3|3 #7 for short. | ||
* Paul Erlich's standard pentachordal major is 4|4(2) #8, or alternatively 6|2(2) b3. | * Paul Erlich's standard pentachordal major for Pajara[10] is 4|4(2) #8, or alternatively 6|2(2) b3. | ||
=Diagram= | =Diagram= | ||
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<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>Modal UDP Notation</title></head><body><!-- ws:start:WikiTextHeadingRule:0:&lt;h1&gt; --><h1 id="toc0"><a name="Modal UDP Notation"></a><!-- ws:end:WikiTextHeadingRule:0 -->Modal UDP Notation</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>Modal UDP Notation</title></head><body><!-- ws:start:WikiTextHeadingRule:0:&lt;h1&gt; --><h1 id="toc0"><a name="Modal UDP Notation"></a><!-- ws:end:WikiTextHeadingRule:0 -->Modal UDP Notation</h1> | ||
Modal UDP notation is a way to uniquely specify a particular mode of any MOS. Its name is derived from up|down(period), or U|D(P) | Modal UDP notation is a way to uniquely specify a particular mode of any MOS. Its name is derived from up|down(period), or U|D(P). If accidentals are specified, it can also refer to the MODMOS's of those MOS's as well.<br /> | ||
<br /> | <br /> | ||
Any MOS has an ambiguous choice of generator: for example, the generator for meantone[7] can be viewed as either the perfect fourth or the perfect fifth. If the generator is chosen by picking the one which is the larger specific interval in its generic interval class, also called the <em>chroma-positive generator,</em> then the UDP notation for any mode is U|D(P) - where P is the number of periods per equivalence interval, U is the number of chroma-positive generators going up from the tonic times P, and D is the number of chroma-positive generators going down from the tonic times P. If P = 1, then it can be omitted, so that the UDP notation is simply U|D.<br /> | |||
<br /> | <br /> | ||
This choice of generator means that the UDP notation simultaneously describes the following properties of the mode in question:<br /> | |||
< | <ol><li>How many scale degrees are of the &quot;larger&quot; or &quot;major&quot; variant, vs the &quot;smaller&quot; or &quot;minor&quot; variant.</li><li>How many generators need to be stacked up vs down from the tonic it requires to generate the mode.</li></ol><br /> | ||
Examples can be found below.<br /> | |||
<br /> | <br /> | ||
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< | <br /> | ||
For example, the proper generator for meantone[7] is the perfect fifth, because it's larger than the other specific interval it shares a class with, the diminished fifth. Consequentially, meantone[7]'s Ionian mode is 5|1(1), which is 5|1 for short, and Aeolian is 2|4. We can add accidentals as well, so that meantone's harmonic minor is 2|4 #7.<br /> | |||
<br /> | |||
On the other hand, the chroma-positive generator for porcupine[7] is the larger 7th, which is about ~11/6; as a consequence, porcupine[7]'s Lssssss mode is 6|0, and sssLsss is 3|3. Likewise, mavila[7]'s ssLsssL anti-Ionian is 1|5, and Mavila[9]'s LLsLLLsLL &quot;Olympian&quot; mode is 4|4.<br /> | |||
<br /> | <br /> | ||
It should be noted that the chroma-positive generator will vary from MOS to MOS even within the same temperament. For example, the chroma-positive generator for meantone[7] is the ~3/2, but is the ~4/3 for meantone[5].<br /> | |||
<br /> | <br /> | ||
</li><li>Meantone[7]'s | <strong>MOS's</strong><br /> | ||
<ul><li>Meantone[7] Ionian, LLsLLLs: 5|1</li><li>Meantone[7] Aeolian, LsLLsLL: 2|4</li><li>Mavila[7] Anti-Ionian, ssLsssL: 1|5</li><li>Mavila[7] Anti-Aeolian, Herman Miller's sLssLss mode: 4|2</li><li>Porcupine[7] Lssssss: 6|0</li><li>Porcupine[7] Lssssss mode, but altered with 7/4 instead of 11/6: 6|0 b7</li><li>Porcupine[7] sssLsss: 3|3</li><li>Diminished[8] sLsLsLsL 0|4(4)</li><li>Diminished[8] LsLsLsLs 4|0(4)</li><li>Triforce[9] LLsLLsLLs: 6|0(3)</li><li>Meantone[5] minor pentatonic, LssLs: 3|1</li><li>Meantone[5] major pentatonic, ssLsL: 0|4</li><li>Sensi[11] LLsLLLsLLLs: 8|2</li><li>Pajara[10] Static Symmetrical Major, ssLssssLss: 4|4(2)</li><li>Mavila/Mabila[9] Olympian, LLsLLLsLL 4|4</li></ul><br /> | |||
<strong>MODMOS's</strong><br /> | |||
<ul><li>Melodic minor is 5|1(1) b3, abbreviated 5|1 b3 for short, but could also be 3|3(1) #7, abbreviated 3|3 #7 for short.</li><li>Paul Erlich's standard pentachordal major for Pajara[10] is 4|4(2) #8, or alternatively 6|2(2) b3.</li></ul><br /> | |||
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