Kite's thoughts on pergens: Difference between revisions
Wikispaces>TallKite **Imported revision 628136231 - Original comment: ** |
Wikispaces>TallKite **Imported revision 628165867 - 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>2018-03- | : This revision was by author [[User:TallKite|TallKite]] and made on <tt>2018-03-31 06:27:07 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>628165867</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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The **genchain** (chain of generators) in the table is only a short section of the full genchain. | The **genchain** (chain of generators) in the table is only a short section of the full genchain. | ||
<span style="display: block; text-align: center;">C - G implies ...Eb Bb F C G D A E B F# C#...</span><span style="display: block; text-align: center;">C - Eb^=Ev - G implies ...F -- Ab^=Av -- C -- Eb^=Ev -- G -- Bb^=Bv -- D...</span> | <span style="display: block; text-align: center;">C - G implies ...Eb Bb F C G D A E B F# C#...</span><span style="display: block; text-align: center;">C - Eb^=Ev - G implies ...F -- Ab^=Av -- C -- Eb^=Ev -- G -- Bb^=Bv -- D...</span> | ||
If the octave is split, the table has a **perchain** ("peer-chain", chain of periods) that shows the octave: C -- F#v=Gb^ -- C | If the octave is split, the table has a **perchain** ("peer-chain", chain of periods) that shows the octave: C -- F#v=Gb^ -- C. Genchains have a theoretically infinite length, but perchains have a finite length. The full rank-2 lattice has genchains running horizontally and perchains running vertically. | ||
||~ ||~ pergen ||~ enharmonic | ||~ ||~ pergen ||~ enharmonic | ||
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||= (P8, P4/2) ||= half-4th ||= m2/2, M6/2, m7/4, A8/2, m10/6, A11/4, P12/2 || | ||= (P8, P4/2) ||= half-4th ||= m2/2, M6/2, m7/4, A8/2, m10/6, A11/4, P12/2 || | ||
||= (P8, P5/2) ||= half-5th ||= A1/2, m3/2, M7/2, m9/2, P11/2 || | ||= (P8, P5/2) ||= half-5th ||= A1/2, m3/2, M7/2, m9/2, P11/2 || | ||
||= (P8/2, P4/2) ||= half-everything ||= every 3-limit interval is split twice as | ||= (P8/2, P4/2) ||= half-everything ||= every 3-limit interval is split twice as much as before || | ||
||||~ third-splits ||~ || | ||||~ third-splits ||~ || | ||
||= (P8/3, P5) ||= third-8ve ||= m3/3, M6/3, d5/6, A11/3, d12/3 || | ||= (P8/3, P5) ||= third-8ve ||= m3/3, M6/3, d5/6, A11/3, d12/3 || | ||
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The <strong>genchain</strong> (chain of generators) in the table is only a short section of the full genchain.<br /> | The <strong>genchain</strong> (chain of generators) in the table is only a short section of the full genchain.<br /> | ||
<span style="display: block; text-align: center;">C - G implies ...Eb Bb F C G D A E B F# C#...</span><span style="display: block; text-align: center;">C - Eb^=Ev - G implies ...F -- Ab^=Av -- C -- Eb^=Ev -- G -- Bb^=Bv -- D...</span><br /> | <span style="display: block; text-align: center;">C - G implies ...Eb Bb F C G D A E B F# C#...</span><span style="display: block; text-align: center;">C - Eb^=Ev - G implies ...F -- Ab^=Av -- C -- Eb^=Ev -- G -- Bb^=Bv -- D...</span><br /> | ||
If the octave is split, the table has a <strong>perchain</strong> (&quot;peer-chain&quot;, chain of periods) that shows the octave: C -- F#v=Gb^ -- C<br /> | If the octave is split, the table has a <strong>perchain</strong> (&quot;peer-chain&quot;, chain of periods) that shows the octave: C -- F#v=Gb^ -- C. Genchains have a theoretically infinite length, but perchains have a finite length. The full rank-2 lattice has genchains running horizontally and perchains running vertically.<br /> | ||
<br /> | <br /> | ||
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<td style="text-align: center;">half-everything<br /> | <td style="text-align: center;">half-everything<br /> | ||
</td> | </td> | ||
<td style="text-align: center;">every 3-limit interval is split twice as | <td style="text-align: center;">every 3-limit interval is split twice as much as before<br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||