Pergen names: Difference between revisions

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<h2>IMPORTED REVISION FROM WIKISPACES</h2>

This is an imported revision from Wikispaces. The revision metadata is included below for reference:

: This revision was by author [[User:TallKite|TallKite]] and made on <tt>2017-11-20 23:52:08 UTC</tt>.

: This revision was by author [[User:TallKite|TallKite]] and made on <tt>2017-11-20 23:54:11 UTC</tt>.

: The original revision id was <tt>~~622073733~~</tt>.

: The original revision id was <tt>622073789</tt>.

: The revision comment was: <tt></tt>

The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.

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Not all possible combinations of periods and generators are unique pergens. {P8/2, P5/2} is actually {P8/2, P4/2}. There is no {P8, M2/2}, and {P8/2, M2/2} is actually {P8/2, P5}. The following table lists all the rank-2 pergens that contain primes 2 and 3, grouped by the size of the larger splitting factor.

The enharmonic interval can be added to or subtracted from any note or interval, and it will be renamed, but unchanged. It's analogous to the dim 2nd in 12-edo, which equates A1 with m2, A4 with d5, etc. In a single-comma temperament, the comma maps to the enharmonic interval.

The enharmonic interval can be added to or subtracted from any note or interval, and it will be renamed, but the pitch of the note (or width of the interval) will be unchanged. It's analogous to the dim 2nd in 12-edo, which equates C# with Db, A1 with m2, A4 with d5, etc. In a single-comma temperament, the comma maps to the enharmonic interval.

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.

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Not all possible combinations of periods and generators are unique pergens. {P8/2, P5/2} is actually {P8/2, P4/2}. There is no {P8, M2/2}, and {P8/2, M2/2} is actually {P8/2, P5}. The following table lists all the rank-2 pergens that contain primes 2 and 3, grouped by the size of the larger splitting factor.

The enharmonic interval can be added to or subtracted from any note or interval, and it will be renamed, but unchanged. It's analogous to the dim 2nd in 12-edo, which equates A1 with m2, A4 with d5, etc. In a single-comma temperament, the comma maps to the enharmonic interval.

The enharmonic interval can be added to or subtracted from any note or interval, and it will be renamed, but the pitch of the note (or width of the interval) will be unchanged. It's analogous to the dim 2nd in 12-edo, which equates C# with Db, A1 with m2, A4 with d5, etc. In a single-comma temperament, the comma maps to the enharmonic interval.

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.

@@ Line 1: / Line 1: @@
 <h2>IMPORTED REVISION FROM WIKISPACES</h2>
 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 23:52:08 UTC</tt>.<br>
+: This revision was by author [[User:TallKite|TallKite]] and made on <tt>2017-11-20 23:54:11 UTC</tt>.<br>
-: The original revision id was <tt>622073733</tt>.<br>
+: The original revision id was <tt>622073789</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>
@@ Line 107: / Line 107: @@
 Not all possible combinations of periods and generators are unique pergens. {P8/2, P5/2} is actually {P8/2, P4/2}. There is no {P8, M2/2}, and {P8/2, M2/2} is actually {P8/2, P5}. The following table lists all the rank-2 pergens that contain primes 2 and 3, grouped by the size of the larger splitting factor.
-The enharmonic interval can be added to or subtracted from any note or interval, and it will be renamed, but unchanged. It's analogous to the dim 2nd in 12-edo, which equates A1 with m2, A4 with d5, etc. In a single-comma temperament, the comma maps to the enharmonic interval.
+The enharmonic interval can be added to or subtracted from any note or interval, and it will be renamed, but the pitch of the note (or width of the interval) will be unchanged. It's analogous to the dim 2nd in 12-edo, which equates C# with Db, A1 with m2, A4 with d5, etc. In a single-comma temperament, the comma maps to the enharmonic interval.
 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.
@@ Line 729: / Line 729: @@
 Not all possible combinations of periods and generators are unique pergens. {P8/2, P5/2} is actually {P8/2, P4/2}. There is no {P8, M2/2}, and {P8/2, M2/2} is actually {P8/2, P5}. The following table lists all the rank-2 pergens that contain primes 2 and 3, grouped by the size of the larger splitting factor.&lt;br /&gt;
 &lt;br /&gt;
-The enharmonic interval can be added to or subtracted from any note or interval, and it will be renamed, but unchanged. It's analogous to the dim 2nd in 12-edo, which equates A1 with m2, A4 with d5, etc. In a single-comma temperament, the comma maps to the enharmonic interval.&lt;br /&gt;
+The enharmonic interval can be added to or subtracted from any note or interval, and it will be renamed, but the pitch of the note (or width of the interval) will be unchanged. It's analogous to the dim 2nd in 12-edo, which equates C# with Db, A1 with m2, A4 with d5, etc. In a single-comma temperament, the comma maps to the enharmonic interval.&lt;br /&gt;
 &lt;br /&gt;
 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.&lt;br /&gt;