Kite's thoughts on pergens: Difference between revisions
Wikispaces>TallKite **Imported revision 626876991 - Original comment: ** |
Wikispaces>TallKite **Imported revision 626878565 - 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:TallKite|TallKite]] and made on <tt>2018-02-25 | : This revision was by author [[User:TallKite|TallKite]] and made on <tt>2018-02-25 20:30:28 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>626878565</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> | ||
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unsplit ||= none ||= none ||= none ||= C - G ||= pythagorean, meantone, dominant, | unsplit ||= none ||= none ||= none ||= C - G ||= pythagorean, meantone, dominant, | ||
schismic, mavila, archy, etc. || | schismic, mavila, archy, etc. || | ||
||~ ||~ | ||~ ||~ half-splits ||~ ||~ ||~ ||~ ||~ || | ||
||= 2 ||= (P8/2, P5) | ||= 2 ||= (P8/2, P5) | ||
half-8ve ||= ^^d2 (if 5th | half-8ve ||= ^^d2 (if 5th | ||
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^1 = 81/80 | ^1 = 81/80 | ||
/1 = 33/32 || | /1 = 33/32 || | ||
||~ ||~ | ||~ ||~ third-splits ||~ ||~ ||~ ||~ ||~ || | ||
||= 6 ||= (P8/3, P5) | ||= 6 ||= (P8/3, P5) | ||
third-8ve ||= ^<span style="vertical-align: super;">3</span>d2 ||= C^<span style="vertical-align: super;">3 </span> ``=`` B# ||= P8/3 = vM3 = ^^d4 ||= C - Ev - Ab^ - C ||= augmented | third-8ve ||= ^<span style="vertical-align: super;">3</span>d2 ||= C^<span style="vertical-align: super;">3 </span> ``=`` B# ||= P8/3 = vM3 = ^^d4 ||= C - Ev - Ab^ - C ||= augmented | ||
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\\A1 ||= C^<span style="vertical-align: super;">3</span> ``=`` B# | \\A1 ||= C^<span style="vertical-align: super;">3</span> ``=`` B# | ||
C``//`` = C# ||= P8/3 = vM3 = ^^d4 | C``//`` = C# ||= P8/3 = vM3 = ^^d4 | ||
P5/2 = /m3 = \M3 ||= C - Ev - Ab | P5/2 = /m3 = \M3 ||= C - Ev - Ab^ - C | ||
C - Eb/=E\ - G ||= small sixfold blue || | C - Eb/=E\ - G ||= small sixfold blue | ||
^1 = 49/48, /1 = 343/324 || | |||
||= 12 ||= (P8/2, P4/3) | ||= 12 ||= (P8/2, P4/3) | ||
half-8ve, third-4th ||= ^^d2 | half-8ve, third-4th ||= ^^d2 | ||
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C``///`` = Db ||= P8/2 = vA4 = ^d5 | C``///`` = Db ||= P8/2 = vA4 = ^d5 | ||
P5/3 = /M2 = \\m3 ||= C - F#v=Gb^ - C | P5/3 = /M2 = \\m3 ||= C - F#v=Gb^ - C | ||
C - /D - \F - G ||= lemba (50/49 & 1029/1024) || | C - /D - \F - G ||= lemba (50/49 & 1029/1024) | ||
^1 = (,-6,1,-1), /1 = 64/63 || | |||
||= 14 ||= (P8/2, P11/3) | ||= 14 ||= (P8/2, P11/3) | ||
half-8ve, third-11th ||= v<span style="vertical-align: super;">6</span>M2 ||= C^<span style="vertical-align: super;">6</span> ``=`` D ||= P8/2 = ^<span style="vertical-align: super;">3</span>4 = v<span style="vertical-align: super;">3</span>5 | half-8ve, third-11th ||= v<span style="vertical-align: super;">6</span>M2 ||= C^<span style="vertical-align: super;">6</span> ``=`` D ||= P8/2 = ^<span style="vertical-align: super;">3</span>4 = v<span style="vertical-align: super;">3</span>5 | ||
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^1 = 81/80 | ^1 = 81/80 | ||
/1 = 64/63 || | /1 = 64/63 || | ||
||~ ||~ | ||~ ||~ quarter-splits ||~ ||~ ||~ ||~ ||~ || | ||
||= 16 ||= (P8/4, P5) ||= ^<span style="vertical-align: super;">4</span>d2 ||= C^<span style="vertical-align: super;">4</span> ``=`` B# ||= P8/4 = vm3 = ^<span style="vertical-align: super;">3</span>A2 ||= C Ebv Gbvv=F#^^ A^ C ||= diminished || | ||= 16 ||= (P8/4, P5) ||= ^<span style="vertical-align: super;">4</span>d2 ||= C^<span style="vertical-align: super;">4</span> ``=`` B# ||= P8/4 = vm3 = ^<span style="vertical-align: super;">3</span>A2 ||= C Ebv Gbvv=F#^^ A^ C ||= diminished || | ||
||= 17 ||= (P8, P4/4) ||= ^<span style="vertical-align: super;">4</span>dd2 ||= C^<span style="vertical-align: super;">4</span> ``=`` B## ||= P4/4 = ^m2 = v<span style="vertical-align: super;">3</span>AA1 ||= C Db^ Ebb^^=D#vv Ev F ||= negri || | ||= 17 ||= (P8, P4/4) ||= ^<span style="vertical-align: super;">4</span>dd2 ||= C^<span style="vertical-align: super;">4</span> ``=`` B## ||= P4/4 = ^m2 = v<span style="vertical-align: super;">3</span>AA1 ||= C Db^ Ebb^^=D#vv Ev F ||= negri || | ||
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<th><br /> | <th><br /> | ||
</th> | </th> | ||
<th> | <th>half-splits<br /> | ||
</th> | </th> | ||
<th><br /> | <th><br /> | ||
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<th><br /> | <th><br /> | ||
</th> | </th> | ||
<th> | <th>third-splits<br /> | ||
</th> | </th> | ||
<th><br /> | <th><br /> | ||
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P5/2 = /m3 = \M3<br /> | P5/2 = /m3 = \M3<br /> | ||
</td> | </td> | ||
<td style="text-align: center;">C - Ev - Ab | <td style="text-align: center;">C - Ev - Ab^ - C<br /> | ||
C - Eb/=E\ - G<br /> | C - Eb/=E\ - G<br /> | ||
</td> | </td> | ||
<td style="text-align: center;">small sixfold blue<br /> | <td style="text-align: center;">small sixfold blue<br /> | ||
^1 = 49/48, /1 = 343/324<br /> | |||
</td> | </td> | ||
</tr> | </tr> | ||
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</td> | </td> | ||
<td style="text-align: center;">lemba (50/49 &amp; 1029/1024)<br /> | <td style="text-align: center;">lemba (50/49 &amp; 1029/1024)<br /> | ||
^1 = (,-6,1,-1), /1 = 64/63<br /> | |||
</td> | </td> | ||
</tr> | </tr> | ||
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<th><br /> | <th><br /> | ||
</th> | </th> | ||
<th> | <th>quarter-splits<br /> | ||
</th> | </th> | ||
<th><br /> | <th><br /> | ||
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finish proofs<br /> | finish proofs<br /> | ||
link from: ups and downs page, Kite Giedraitis page, MOS scale names page,<br /> | link from: ups and downs page, Kite Giedraitis page, MOS scale names page,<br /> | ||
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<!-- ws:start:WikiTextHeadingRule:101:&lt;h3&gt; --><h3 id="toc22"><a name="Further Discussion-Supplemental materials*-Notaion guide PDF"></a><!-- ws:end:WikiTextHeadingRule:101 -->Notaion guide PDF</h3> | <!-- ws:start:WikiTextHeadingRule:101:&lt;h3&gt; --><h3 id="toc22"><a name="Further Discussion-Supplemental materials*-Notaion guide PDF"></a><!-- ws:end:WikiTextHeadingRule:101 -->Notaion guide PDF</h3> | ||
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This PDF is a rank-2 notation guide that shows the full lattice for the first 15 pergens, up through the third-splits block. It includes alternate enharmonics for many pergens.<br /> | This PDF is a rank-2 notation guide that shows the full lattice for the first 15 pergens, up through the third-splits block. It includes alternate enharmonics for many pergens.<br /> | ||
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(screenshot)<br /> | (screenshot)<br /> | ||
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Alt-pergenLister lists out thousands of pergens, and suggests periods, generators and enharmonics for each one. Alternate enharmonics are not listed, but single-pair notation for false-double pergens is. It can also list only those pergens supported by a specific edo. Written in Jesusonic, runs inside Reaper.<br /> | Alt-pergenLister lists out thousands of pergens, and suggests periods, generators and enharmonics for each one. Alternate enharmonics are not listed, but single-pair notation for false-double pergens is. It can also list only those pergens supported by a specific edo. Written in Jesusonic, runs inside Reaper.<br /> | ||
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Screenshot of the first 38 pergens:<br /> | Screenshot of the first 38 pergens:<br /> | ||