Pergen names: Difference between revisions
Wikispaces>TallKite **Imported revision 621993889 - Original comment: ** |
Wikispaces>TallKite **Imported revision 621994241 - 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>2017-11-20 02: | : This revision was by author [[User:TallKite|TallKite]] and made on <tt>2017-11-20 02:42:36 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>621994241</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 shown is a short section of the full genchain. C - G implies ...Eb Bb F C G D A E B F# C#... And C - Eb^=Ev - G implies ...F - Ab^=Av - C - Eb^=Ev - G - Bb^=Bv - D - F^=F#v - A - C^=C#v - E... If the octave is split, the genchain shows the octave: In C - F#v=Gb^ - C, the last C is an octave above the first one. | The genchain shown is a short section of the full genchain. C - G implies ...Eb Bb F C G D A E B F# C#... And C - Eb^=Ev - G implies ...F - Ab^=Av - C - Eb^=Ev - G - Bb^=Bv - D - F^=F#v - A - C^=C#v - E... If the octave is split, the genchain shows the octave: In C - F#v=Gb^ - C, the last C is an octave above the first one. | ||
An edo is incompatible with a pergen if the split is impossible. For example, all odd-numbered edos are incompatible with half-octave pergens. An edo is somewhat incompatible with a pergen if the period and generator can only generate a subset of the edo. For example, 15-edo is somewhat incompatible with {P8, P5}, because any chain-of-5ths scale would translate to a 5-edo subset. Such edos are marked with asterisks. | An edo is incompatible with a pergen if the split is impossible. For example, all odd-numbered edos are incompatible with half-octave pergens. An edo is somewhat incompatible with a pergen if the period and generator can only generate a subset of the edo. For example, 15-edo is somewhat incompatible with {P8, P5}, because any chain-of-5ths scale would translate to a 5-edo subset. Such edos are marked with asterisks. 13b is incompatible with {P8, P5/2}, but 13 isn't. However, 13 is incompatible with heptatonic notation. | ||
(table is under construction) | (table is under construction) | ||
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25*, 26, 30*, 31 || | 25*, 26, 30*, 31 || | ||
||= {P8, P11/3} ||= ||= ||= ||= ||= ||= same as {P8, P4/3} || | ||= {P8, P11/3} ||= ||= ||= ||= ||= ||= same as {P8, P4/3} || | ||
||= {P8/3, P4/2} ||= ||= ||= ||= ||= ||= 15, 18b*, 24, 30 | ||= {P8/3, P4/2} ||= ||= ||= ||= ||= ||= 15, 18b*, 24, 30 || | ||
||= {P8/3, P5/2} ||= ||= ||= ||= ||= ||= 18b, 24, 30 || | ||= {P8/3, P5/2} ||= ||= ||= ||= ||= ||= 18b, 24, 30 || | ||
||= {P8/2, P4/3} ||= ||= ||= ||= ||= ||= 14, 22, 28*, 30* || | ||= {P8/2, P4/3} ||= ||= ||= ||= ||= ||= 14, 22, 28*, 30* || | ||
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||= {P8/3, P4/3} ||= ||= ||= ||= ||= ||= 15, 21, 30* || | ||= {P8/3, P4/3} ||= ||= ||= ||= ||= ||= 15, 21, 30* || | ||
||~ quarters ||~ ||~ ||~ ||~ ||~ ||~ || | ||~ quarters ||~ ||~ ||~ ||~ ||~ ||~ || | ||
||= {P8/4, P5} ||= ||= ||= ||= ||= ||= | ||= {P8/4, P5} ||= ||= ||= ||= ||= ||= 12, 16, 20, 24*, 28 || | ||
||= {P8, P4/4} ||= ||= ||= ||= ||= ||= || | ||= {P8, P4/4} ||= ||= ||= ||= ||= ||= || | ||
||= {P8, P5/4} ||= ||= ||= ||= ||= ||= || | ||= {P8, P5/4} ||= ||= ||= ||= ||= ||= || | ||
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||= {P8/2, P5/4} ||= ||= ||= ||= ||= ||= || | ||= {P8/2, P5/4} ||= ||= ||= ||= ||= ||= || | ||
||= ||= ||= ||= ||= ||= ||= || | ||= ||= ||= ||= ||= ||= ||= || | ||
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The genchain shown is a short section of the full genchain. C - G implies ...Eb Bb F C G D A E B F# C#... And C - Eb^=Ev - G implies ...F - Ab^=Av - C - Eb^=Ev - G - Bb^=Bv - D - F^=F#v - A - C^=C#v - E... If the octave is split, the genchain shows the octave: In C - F#v=Gb^ - C, the last C is an octave above the first one.<br /> | The genchain shown is a short section of the full genchain. C - G implies ...Eb Bb F C G D A E B F# C#... And C - Eb^=Ev - G implies ...F - Ab^=Av - C - Eb^=Ev - G - Bb^=Bv - D - F^=F#v - A - C^=C#v - E... If the octave is split, the genchain shows the octave: In C - F#v=Gb^ - C, the last C is an octave above the first one.<br /> | ||
<br /> | <br /> | ||
An edo is incompatible with a pergen if the split is impossible. For example, all odd-numbered edos are incompatible with half-octave pergens. An edo is somewhat incompatible with a pergen if the period and generator can only generate a subset of the edo. For example, 15-edo is somewhat incompatible with {P8, P5}, because any chain-of-5ths scale would translate to a 5-edo subset. Such edos are marked with asterisks.<br /> | An edo is incompatible with a pergen if the split is impossible. For example, all odd-numbered edos are incompatible with half-octave pergens. An edo is somewhat incompatible with a pergen if the period and generator can only generate a subset of the edo. For example, 15-edo is somewhat incompatible with {P8, P5}, because any chain-of-5ths scale would translate to a 5-edo subset. Such edos are marked with asterisks. 13b is incompatible with {P8, P5/2}, but 13 isn't. However, 13 is incompatible with heptatonic notation.<br /> | ||
<br /> | <br /> | ||
(table is under construction)<br /> | (table is under construction)<br /> | ||
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<td style="text-align: center;"><br /> | <td style="text-align: center;"><br /> | ||
</td> | </td> | ||
<td style="text-align: center;">15, 18b*, 24, 30 | <td style="text-align: center;">15, 18b*, 24, 30<br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
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<td style="text-align: center;"><br /> | <td style="text-align: center;"><br /> | ||
</td> | </td> | ||
<td style="text-align: center;"><br /> | <td style="text-align: center;">12, 16, 20, 24*, 28<br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
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