Kite's thoughts on pergens: 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>2018-02-19 20:02:11 UTC</tt>.

: This revision was by author [[User:TallKite|TallKite]] and made on <tt>2018-02-20 01:55:22 UTC</tt>.

: The original revision id was <tt>~~626631169~~</tt>.

: The original revision id was <tt>626637515</tt>.

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

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For a pergen (P8/m, M/n), let x be any number that divides m, R be any 3-limit ratio, and z be any integer. The interval z·P8 ± x·R splits into x parts. Let y be any number that divides n, the interval z·M ± y·R splits into y parts. If x divides both m and n, the interval z·P8 + z'·M ± x·R splits into x parts (z' is any integer).

A double-split perhgen like (P8/3. P4/2) contains all the secondary splits of both (P8/3, P5) and (P8, P4/2), plus others. The following table shows the secondary splits for all pergens up to the third-splits. ~~The~~ split ~~intervals~~ range from d5 to A5 on the genchain of 5ths. For convenience, naturally occuring splits are listed too, under "all pergens".

A double-split perhgen like (P8/3. P4/2) contains all the secondary splits of both (P8/3, P5) and (P8, P4/2), plus others. The following table shows the secondary splits for all pergens up to the third-splits. A split interval is only included if it falls in the range from d5 to A5 on the genchain of 5ths, others are too remote. For convenience, naturally occuring splits are listed too, under "all pergens".

||~ block ||||~ pergen ||~ secondary splits <= 12th ||

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For a pergen (P8/m, M/n), let x be any number that divides m, R be any 3-limit ratio, and z be any integer. The interval z·P8 ± x·R splits into x parts. Let y be any number that divides n, the interval z·M ± y·R splits into y parts. If x divides both m and n, the interval z·P8 + z'·M ± x·R splits into x parts (z' is any integer).

A double-split perhgen like (P8/3. P4/2) contains all the secondary splits of both (P8/3, P5) and (P8, P4/2), plus others. The following table shows the secondary splits for all pergens up to the third-splits. ~~The~~ split ~~intervals~~ range from d5 to A5 on the genchain of 5ths. For convenience, naturally occuring splits are listed too, under &quot;all pergens&quot;.

A double-split perhgen like (P8/3. P4/2) contains all the secondary splits of both (P8/3, P5) and (P8, P4/2), plus others. The following table shows the secondary splits for all pergens up to the third-splits. A split interval is only included if it falls in the range from d5 to A5 on the genchain of 5ths, others are too remote. For convenience, naturally occuring splits are listed too, under &quot;all pergens&quot;.

@@ 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>2018-02-19 20:02:11 UTC</tt>.<br>
+: This revision was by author [[User:TallKite|TallKite]] and made on <tt>2018-02-20 01:55:22 UTC</tt>.<br>
-: The original revision id was <tt>626631169</tt>.<br>
+: The original revision id was <tt>626637515</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 337: / Line 337: @@
 For a pergen (P8/m, M/n), let x be any number that divides m, R be any 3-limit ratio, and z be any integer. The interval z·P8 ± x·R splits into x parts. Let y be any number that divides n, the interval z·M ± y·R splits into y parts. If x divides both m and n, the interval z·P8 + z'·M ± x·R splits into x parts (z' is any integer).
-A double-split perhgen like (P8/3. P4/2) contains all the secondary splits of both (P8/3, P5) and (P8, P4/2), plus others. The following table shows the secondary splits for all pergens up to the third-splits. The split intervals range from d5 to A5 on the genchain of 5ths. For convenience, naturally occuring splits are listed too, under "all pergens".
+A double-split perhgen like (P8/3. P4/2) contains all the secondary splits of both (P8/3, P5) and (P8, P4/2), plus others. The following table shows the secondary splits for all pergens up to the third-splits. A split interval is only included if it falls in the range from d5 to A5 on the genchain of 5ths, others are too remote. For convenience, naturally occuring splits are listed too, under "all pergens".
 ||~ block ||||~ pergen ||~ secondary splits &lt;= 12th ||
@@ Line 2,527: / Line 2,527: @@
 For a pergen (P8/m, M/n), let x be any number that divides m, R be any 3-limit ratio, and z be any integer. The interval z·P8 ± x·R splits into x parts. Let y be any number that divides n, the interval z·M ± y·R splits into y parts. If x divides both m and n, the interval z·P8 + z'·M ± x·R splits into x parts (z' is any integer).&lt;br /&gt;
 &lt;br /&gt;
-A double-split perhgen like (P8/3. P4/2) contains all the secondary splits of both (P8/3, P5) and (P8, P4/2), plus others. The following table shows the secondary splits for all pergens up to the third-splits. The split intervals range from d5 to A5 on the genchain of 5ths. For convenience, naturally occuring splits are listed too, under &amp;quot;all pergens&amp;quot;.&lt;br /&gt;
+A double-split perhgen like (P8/3. P4/2) contains all the secondary splits of both (P8/3, P5) and (P8, P4/2), plus others. The following table shows the secondary splits for all pergens up to the third-splits. A split interval is only included if it falls in the range from d5 to A5 on the genchain of 5ths, others are too remote. For convenience, naturally occuring splits are listed too, under &amp;quot;all pergens&amp;quot;.&lt;br /&gt;
 &lt;br /&gt;