Kite's thoughts on pergens: Difference between revisions
Wikispaces>TallKite **Imported revision 626637515 - Original comment: ** |
Wikispaces>TallKite **Imported revision 626678573 - 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>2018-02-20 | : This revision was by author [[User:TallKite|TallKite]] and made on <tt>2018-02-20 17:10:47 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>626678573</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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P4/3: C - Dv - Eb^ - F | P4/3: C - Dv - Eb^ - F | ||
A4:/3 C - D - E - F# (the lack of ups and downs indicates that this interval was already split) | A4:/3 C - D - E - F# (the lack of ups and downs indicates that this interval was already split) | ||
m7/3: C - Eb^ - Gv - Bb | m7/3: C - Eb^ - Gv - Bb (also m7/6: C - Dv - Eb^ - F - Gv - Ab^ - Bb) | ||
M7/3: C - Ev - G^ - B | M7/3: C - Ev - G^ - B | ||
m10/3: C - F - Bb - Eb (also already split) (m10/9 also occurs) | m10/3: C - F - Bb - Eb (also already split) (m10/9 also occurs) | ||
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Given an edo, a period, and a generator, what is the pergen? There is usually more than one right answer. For 10edo with P = 5\10 and G = 2\10, it could be either (P8/2, P4/2) or (P8/2, P5/3). Every coprime period/generator pair results in a valid pergen. It isn't yet known if there are period/generator pairs that require a true double pergen, or if all such pairs can result from either a false double or single-split pergen. | Given an edo, a period, and a generator, what is the pergen? There is usually more than one right answer. For 10edo with P = 5\10 and G = 2\10, it could be either (P8/2, P4/2) or (P8/2, P5/3). Every coprime period/generator pair results in a valid pergen. It isn't yet known if there are period/generator pairs that require a true double pergen, or if all such pairs can result from either a false double or single-split pergen. | ||
This table lists all pergens up to quarter-splits, with all edos that support them. Partial support is indicated with an asterisk. The generator's keyspan depends on the multigen's keyspan, and thus on the 5th's keyspan. The latter is occasionally ambiguous, as in 13-edo and 18-edo. Since both of these edos are incompatible with heptatonic notation, 13edo's half-5th pergen is actually notated as a half-upfifth. 13b-edo and 18b-edo are listed as well. | This table lists all pergens up to quarter-splits, with all edos that support them. Partial support is indicated with an asterisk. The generator's keyspan depends on the multigen's keyspan, and thus on the 5th's keyspan. The latter is occasionally ambiguous, as in 13-edo and 18-edo. Since both of these edos are incompatible with heptatonic notation, 13edo's half-5th pergen is actually notated as a half-upfifth. 13b-edo and 18b-edo are listed as well. 11-edo and 23-edo. | ||
||||~ pergen ||~ supporting edos (12-31 only) || | ||||~ pergen ||~ supporting edos (12-31 only) || | ||
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P4/3: C - Dv - Eb^ - F<br /> | P4/3: C - Dv - Eb^ - F<br /> | ||
A4:/3 C - D - E - F# (the lack of ups and downs indicates that this interval was already split)<br /> | A4:/3 C - D - E - F# (the lack of ups and downs indicates that this interval was already split)<br /> | ||
m7/3: C - Eb^ - Gv - Bb | m7/3: C - Eb^ - Gv - Bb (also m7/6: C - Dv - Eb^ - F - Gv - Ab^ - Bb)<br /> | ||
M7/3: C - Ev - G^ - B<br /> | M7/3: C - Ev - G^ - B<br /> | ||
m10/3: C - F - Bb - Eb (also already split) (m10/9 also occurs)<br /> | m10/3: C - F - Bb - Eb (also already split) (m10/9 also occurs)<br /> | ||
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Given an edo, a period, and a generator, what is the pergen? There is usually more than one right answer. For 10edo with P = 5\10 and G = 2\10, it could be either (P8/2, P4/2) or (P8/2, P5/3). Every coprime period/generator pair results in a valid pergen. It isn't yet known if there are period/generator pairs that require a true double pergen, or if all such pairs can result from either a false double or single-split pergen.<br /> | Given an edo, a period, and a generator, what is the pergen? There is usually more than one right answer. For 10edo with P = 5\10 and G = 2\10, it could be either (P8/2, P4/2) or (P8/2, P5/3). Every coprime period/generator pair results in a valid pergen. It isn't yet known if there are period/generator pairs that require a true double pergen, or if all such pairs can result from either a false double or single-split pergen.<br /> | ||
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This table lists all pergens up to quarter-splits, with all edos that support them. Partial support is indicated with an asterisk. The generator's keyspan depends on the multigen's keyspan, and thus on the 5th's keyspan. The latter is occasionally ambiguous, as in 13-edo and 18-edo. Since both of these edos are incompatible with heptatonic notation, 13edo's half-5th pergen is actually notated as a half-upfifth. 13b-edo and 18b-edo are listed as well.<br /> | This table lists all pergens up to quarter-splits, with all edos that support them. Partial support is indicated with an asterisk. The generator's keyspan depends on the multigen's keyspan, and thus on the 5th's keyspan. The latter is occasionally ambiguous, as in 13-edo and 18-edo. Since both of these edos are incompatible with heptatonic notation, 13edo's half-5th pergen is actually notated as a half-upfifth. 13b-edo and 18b-edo are listed as well. 11-edo and 23-edo.<br /> | ||
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