Pergen names: Difference between revisions
Wikispaces>TallKite **Imported revision 624380271 - Original comment: ** |
Wikispaces>TallKite **Imported revision 624380857 - 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>2018-01-03 | : This revision was by author [[User:TallKite|TallKite]] and made on <tt>2018-01-03 03:25:39 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>624380857</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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||= (P8, P5) ||= unsplit ||= 81/80 ||= meantone ||= green ||= gT || | ||= (P8, P5) ||= unsplit ||= 81/80 ||= meantone ||= green ||= gT || | ||
||= " ||= " ||= 64/63 ||= archy ||= red ||= rT || | ||= " ||= " ||= 64/63 ||= archy ||= red ||= rT || | ||
||= " ||= " ||= (-14,8 | ||= " ||= " ||= (-14,8,1) ||= schismic ||= large yellow ||= LyT || | ||
||= (P8/2, P5) ||= half-octave ||= (11, -4, -2) ||= srutal ||= small deep green ||= sggT || | ||= (P8/2, P5) ||= half-octave ||= (11, -4, -2) ||= srutal ||= small deep green ||= sggT || | ||
||= " ||= " ||= 81/80, 50/49 ||= injera ||= deep reddish and green ||= rryy&gT || | ||= " ||= " ||= 81/80, 50/49 ||= injera ||= deep reddish and green ||= rryy&gT || | ||
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==Alternate enharmonics== | ==Alternate enharmonics== | ||
Sometimes the enharmonic found by rounding off the gedra can be greatly improved by rounding off differently. For example, (P8/3, P4/4) unreduces to (P8/3, WWM6/12), a false double. The bare alternate generator is WWM6/12 = [33,19]/12 = [3,2] = m3. The bare enharmonic is [33,19] - 12*[3,2] = [-3,-5] = a quintuple-diminished 6th! This would make for a very confusing notation. However, [33,19]/12 can be rounded | Sometimes the enharmonic found by rounding off the gedra can be greatly improved by rounding off differently. For example, (P8/3, P4/4) unreduces to (P8/3, WWM6/12), a false double. The bare alternate generator is WWM6/12 = [33,19]/12 = [3,2] = m3. The bare enharmonic is [33,19] - 12*[3,2] = [-3,-5] = a quintuple-diminished 6th! This would make for a very confusing notation. However, [33,19]/12 can be rounded way up to [4,2] = M3. The enharmonic becomes [33,19] - 12*[4,2] = [-15,-5] = -5*[3,1] = -5 * v<span style="vertical-align: super;">12</span>A2, which is an improvement but still awkward. The period is ^<span style="vertical-align: super;">4</span>m3 and the generator is v<span style="vertical-align: super;">3</span>M2. | ||
<span style="display: block; text-align: center;"> | <span style="display: block; text-align: center;"> P1 -- ^<span style="vertical-align: super;">4</span>m3 -- v<span style="vertical-align: super;">4</span>M6 -- C | ||
P1 -- ^<span style="vertical-align: super;">4</span>m3 -- v<span style="vertical-align: super;">4</span>M6 -- C | |||
C -- Eb^<span style="vertical-align: super;">4</span> -- Av<span style="vertical-align: super;">4</span> -- C | C -- Eb^<span style="vertical-align: super;">4</span> -- Av<span style="vertical-align: super;">4</span> -- C | ||
P1 -- v<span style="vertical-align: super;">3</span>M2 -- v<span style="vertical-align: super;">6</span>M3=^<span style="vertical-align: super;">6</span>m2 -- ^<span style="vertical-align: super;">3</span>m3 -- P4 | P1 -- v<span style="vertical-align: super;">3</span>M2 -- v<span style="vertical-align: super;">6</span>M3=^<span style="vertical-align: super;">6</span>m2 -- ^<span style="vertical-align: super;">3</span>m3 -- P4 | ||
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</span><span style="display: block; text-align: center;">C -- Ev -- Ab^ -- C | </span><span style="display: block; text-align: center;">C -- Ev -- Ab^ -- C | ||
</span><span style="display: block; text-align: center;">P1 -- /m2 -- ``//``d3=\\A2 -- \M3 -- P4 | </span><span style="display: block; text-align: center;">P1 -- /m2 -- ``//``d3=\\A2 -- \M3 -- P4 | ||
</span><span style="display: block; text-align: center;">C -- Db/ -- Ebb``//``=D#\\ -- E\ -- F</span | </span><span style="display: block; text-align: center;">C -- Db/ -- Ebb``//``=D#\\ -- E\ -- F</span> | ||
Sometimes the temperament being notated implies a certain enharmonic. Specifically, the comma tempered out should map to the enharmonic, or some multiple of it. | |||
The comma equals xE and/or yE'. | The comma equals xE and/or yE'. | ||
If M' = [a,b], then G' = [round(a/n'), round(b/n')] makes the smallest zE", but not always the smallest E" | If M' = [a,b], then G' = [round(a/n'), round(b/n')] makes the smallest zE", but not always the smallest E" | ||
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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;">(-14,8 | <td style="text-align: center;">(-14,8,1)<br /> | ||
</td> | </td> | ||
<td style="text-align: center;">schismic<br /> | <td style="text-align: center;">schismic<br /> | ||
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</td> | </td> | ||
<td style="text-align: center;">LyT<br /> | <td style="text-align: center;">LyT<br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
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<!-- ws:start:WikiTextHeadingRule:49:&lt;h2&gt; --><h2 id="toc9"><a name="Further Discussion-Alternate enharmonics"></a><!-- ws:end:WikiTextHeadingRule:49 -->Alternate enharmonics</h2> | <!-- ws:start:WikiTextHeadingRule:49:&lt;h2&gt; --><h2 id="toc9"><a name="Further Discussion-Alternate enharmonics"></a><!-- ws:end:WikiTextHeadingRule:49 -->Alternate enharmonics</h2> | ||
<br /> | <br /> | ||
Sometimes the enharmonic found by rounding off the gedra can be greatly improved by rounding off differently. For example, (P8/3, P4/4) unreduces to (P8/3, WWM6/12), a false double. The bare alternate generator is WWM6/12 = [33,19]/12 = [3,2] = m3. The bare enharmonic is [33,19] - 12*[3,2] = [-3,-5] = a quintuple-diminished 6th! This would make for a very confusing notation. However, [33,19]/12 can be rounded | Sometimes the enharmonic found by rounding off the gedra can be greatly improved by rounding off differently. For example, (P8/3, P4/4) unreduces to (P8/3, WWM6/12), a false double. The bare alternate generator is WWM6/12 = [33,19]/12 = [3,2] = m3. The bare enharmonic is [33,19] - 12*[3,2] = [-3,-5] = a quintuple-diminished 6th! This would make for a very confusing notation. However, [33,19]/12 can be rounded way up to [4,2] = M3. The enharmonic becomes [33,19] - 12*[4,2] = [-15,-5] = -5*[3,1] = -5 * v<span style="vertical-align: super;">12</span>A2, which is an improvement but still awkward. The period is ^<span style="vertical-align: super;">4</span>m3 and the generator is v<span style="vertical-align: super;">3</span>M2.<br /> | ||
<span style="display: block; text-align: center;"> | <span style="display: block; text-align: center;"> P1 -- ^<span style="vertical-align: super;">4</span>m3 -- v<span style="vertical-align: super;">4</span>M6 -- C<br /> | ||
P1 -- ^<span style="vertical-align: super;">4</span>m3 -- v<span style="vertical-align: super;">4</span>M6 -- C<br /> | |||
C -- Eb^<span style="vertical-align: super;">4</span> -- Av<span style="vertical-align: super;">4</span> -- C<br /> | C -- Eb^<span style="vertical-align: super;">4</span> -- Av<span style="vertical-align: super;">4</span> -- C<br /> | ||
P1 -- v<span style="vertical-align: super;">3</span>M2 -- v<span style="vertical-align: super;">6</span>M3=^<span style="vertical-align: super;">6</span>m2 -- ^<span style="vertical-align: super;">3</span>m3 -- P4<br /> | P1 -- v<span style="vertical-align: super;">3</span>M2 -- v<span style="vertical-align: super;">6</span>M3=^<span style="vertical-align: super;">6</span>m2 -- ^<span style="vertical-align: super;">3</span>m3 -- P4<br /> | ||
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</span><span style="display: block; text-align: center;">C -- Ev -- Ab^ -- C<br /> | </span><span style="display: block; text-align: center;">C -- Ev -- Ab^ -- C<br /> | ||
</span><span style="display: block; text-align: center;">P1 -- /m2 -- <!-- ws:start:WikiTextRawRule:029:``//`` -->//<!-- ws:end:WikiTextRawRule:029 -->d3=\\A2 -- \M3 -- P4<br /> | </span><span style="display: block; text-align: center;">P1 -- /m2 -- <!-- ws:start:WikiTextRawRule:029:``//`` -->//<!-- ws:end:WikiTextRawRule:029 -->d3=\\A2 -- \M3 -- P4<br /> | ||
</span><span style="display: block; text-align: center;">C -- Db/ -- Ebb<!-- ws:start:WikiTextRawRule:030:``//`` -->//<!-- ws:end:WikiTextRawRule:030 -->=D#\\ -- E\ -- F</span>< | </span><span style="display: block; text-align: center;">C -- Db/ -- Ebb<!-- ws:start:WikiTextRawRule:030:``//`` -->//<!-- ws:end:WikiTextRawRule:030 -->=D#\\ -- E\ -- F</span><br /> | ||
</ | Sometimes the temperament being notated implies a certain enharmonic. Specifically, the comma tempered out should map to the enharmonic, or some multiple of it.<br /> | ||
<br /> | |||
<br /> | |||
The comma equals xE and/or yE'.<br /> | The comma equals xE and/or yE'.<br /> | ||
If M' = [a,b], then G' = [round(a/n'), round(b/n')] makes the smallest zE&quot;, but not always the smallest E&quot;<br /> | If M' = [a,b], then G' = [round(a/n'), round(b/n')] makes the smallest zE&quot;, but not always the smallest E&quot;<br /> | ||