Pergen names: Difference between revisions
Wikispaces>TallKite **Imported revision 622472781 - Original comment: ** |
Wikispaces>TallKite **Imported revision 622473225 - 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>2017-11-27 05: | : This revision was by author [[User:TallKite|TallKite]] and made on <tt>2017-11-27 05:28:10 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>622473225</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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27, 28*, 29, 30*, 31 || | 27, 28*, 29, 30*, 31 || | ||
||~ halves ||~ ||~ ||~ ||~ ||~ ||~ || | ||~ halves ||~ ||~ ||~ ||~ ||~ ||~ || | ||
||= {P8/2, P5} ||= ^^d2 ||= C^^ = B# ||= P8/2 = vA4 = ^d5 | ||= {P8/2, P5} ||= ^^d2, if 5th | ||
> 700¢ ||= C^^ = B# ||= P8/2 = vA4 = ^d5 ||= C - F#v=Gb^ - C ||= srutal | |||
^1 = 81/80 ||= 12, 14, 16, 18b, 20*, | ^1 = 81/80 ||= 12, 14, 16, 18b, 20*, | ||
22, 24*, 26, 28*, 30* || | 22, 24*, 26, 28*, 30* || | ||
||= " ||= vvd2 ||= C^^ = Db ||= P8/2 = ^A4 = vd5 | ||= " ||= vvd2, if 5th | ||
< 700¢) ||= C^^ = Db ||= P8/2 = ^A4 = vd5 ||= C - F#^=Gbv - C ||= large deep red | |||
^1 = 64/63 ||= " || | ^1 = 64/63 ||= " || | ||
||= " ||= vvM2 ||= C^^ = D ||= P8/2 = ^P4 = vP5 ||= C - F^=Gv - C ||= 128/121, | ||= " ||= vvM2 ||= C^^ = D ||= P8/2 = ^P4 = vP5 ||= C - F^=Gv - C ||= 128/121, | ||
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=Explanations= | =Explanations= | ||
Each enharmonic interval implies a different notation. If every pergen could use every enharmonic, there would be an overwhelming choice of notations! Fortunately, not all enharmonics work with all pergens. There are two logical restrictions on the enharmonic, one based on its degree and the other on its 3-exponent (implied edo). In addition, smaller degrees are always preferred. It should be either a unison or a 2nd, because equating two notes a 3rd or 4th apart is very disconcerting. | Each enharmonic interval implies a different notation. If every pergen could use every enharmonic, there would be an overwhelming choice of notations! Fortunately, not all enharmonics work with all pergens. There are two logical restrictions on the enharmonic, one based on its degree and the other on its 3-exponent (implied edo). In addition, smaller degrees are always preferred. It should be either a unison or a 2nd, because equating two notes a 3rd or 4th apart is very disconcerting. | ||
For {P8/M, multi-gen/N}, an octave = M periods ± some number of enharmonics, and a multi-gen = N generators ± some number of enharmonics. | For {P8/M, multi-gen/N}, an octave = M periods ± some number of enharmonics, and a multi-gen = N generators ± some number of enharmonics. | ||
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<td style="text-align: center;">{P8/2, P5}<br /> | <td style="text-align: center;">{P8/2, P5}<br /> | ||
</td> | </td> | ||
<td style="text-align: center;">^^d2<br /> | <td style="text-align: center;">^^d2, if 5th<br /> | ||
</td> | <ul class="quotelist"><li>700¢</li></ul></td> | ||
<td style="text-align: center;">C^^ = B#<br /> | <td style="text-align: center;">C^^ = B#<br /> | ||
</td> | </td> | ||
<td style="text-align: center;">P8/2 = vA4 = ^d5<br /> | <td style="text-align: center;">P8/2 = vA4 = ^d5<br /> | ||
</td> | </td> | ||
<td style="text-align: center;">C - F#v=Gb^ - C<br /> | <td style="text-align: center;">C - F#v=Gb^ - C<br /> | ||
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<td style="text-align: center;">&quot;<br /> | <td style="text-align: center;">&quot;<br /> | ||
</td> | </td> | ||
<td style="text-align: center;">vvd2<br /> | <td style="text-align: center;">vvd2, if 5th<br /> | ||
&lt; 700¢)<br /> | |||
</td> | </td> | ||
<td style="text-align: center;">C^^ = Db<br /> | <td style="text-align: center;">C^^ = Db<br /> | ||
</td> | </td> | ||
<td style="text-align: center;">P8/2 = ^A4 = vd5<br /> | <td style="text-align: center;">P8/2 = ^A4 = vd5<br /> | ||
</td> | </td> | ||
<td style="text-align: center;">C - F#^=Gbv - C<br /> | <td style="text-align: center;">C - F#^=Gbv - C<br /> | ||
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<!-- ws:start:WikiTextHeadingRule:25:&lt;h1&gt; --><h1 id="toc3"><a name="Explanations"></a><!-- ws:end:WikiTextHeadingRule:25 -->Explanations</h1> | <!-- ws:start:WikiTextHeadingRule:25:&lt;h1&gt; --><h1 id="toc3"><a name="Explanations"></a><!-- ws:end:WikiTextHeadingRule:25 -->Explanations</h1> | ||
<br /> | <br /> | ||
Each enharmonic interval implies a different notation. If every pergen could use every enharmonic, there would be an overwhelming choice of notations! Fortunately, not all enharmonics work with all pergens. There are two logical restrictions on the enharmonic, one based on its degree and the other on its 3-exponent (implied edo). In addition, smaller degrees are always preferred. It should be either a unison or a 2nd, because equating two notes a 3rd or 4th apart is very disconcerting. <br /> | Each enharmonic interval implies a different notation. If every pergen could use every enharmonic, there would be an overwhelming choice of notations! Fortunately, not all enharmonics work with all pergens. There are two logical restrictions on the enharmonic, one based on its degree and the other on its 3-exponent (implied edo). In addition, smaller degrees are always preferred. It should be either a unison or a 2nd, because equating two notes a 3rd or 4th apart is very disconcerting.<br /> | ||
<br /> | <br /> | ||
For {P8/M, multi-gen/N}, an octave = M periods ± some number of enharmonics, and a multi-gen = N generators ± some number of enharmonics.<br /> | For {P8/M, multi-gen/N}, an octave = M periods ± some number of enharmonics, and a multi-gen = N generators ± some number of enharmonics.<br /> | ||