Ploidacot/Omega-pentacot: Difference between revisions

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In quintilischis, the generator is 18/17, three ~~generators~~ make [[19/16]], five make 4/3, and 40 make [[10/1|10th harmonic]] in the 2.3.5.17.19 subgroup, so [[4624/4617]], [[6144/6137]], and [[6885/6859]] are tempered out. This temperament is a weak extension of [[schismic]], splitting the fourth in five~~, and supported by {{Optimal ET sequence| 12, 253, 265, 277, 289, 301, 313, and 325 }} edos~~.

In quintilischis, the generator is 18/17, three of which make [[19/16]], five make 4/3, and 40 make [[10/1|10th harmonic]] in the 2.3.5.17.19 subgroup, so [[4624/4617]], [[6144/6137]], and [[6885/6859]] are tempered out. This temperament is a weak extension of [[schismic]], splitting the fourth in five. In the 2.3.5.7.17.19 subgroup, tempering out [[400/399]] (equating 20/19 and 21/20) leads to [[quintilipyth]] (12 & 253), and tempering out [[476/475]] (equating 19/17 with 28/25) leads to [[quintaschis]] (12 & 289).

In the 2.3.5.7.17.19 subgroup, tempering out [[400/399]] (equating 20/19 and 21/20) leads to [[quintilipyth]] (12 & 253), and tempering out [[476/475]] (equating 19/17 with 28/25) leads to [[quintaschis]] (12 & 289).

=== Quindromeda ===

In [[quindromeda]], the generator is 18/17, three ~~generators~~ make 19/16, five make 4/3, and 28 make [[5/1|5th harmonic]] in the 2.3.5.17.19 subgroup, so [[1216/1215]], [[1445/1444]], and [[6144/6137]] are tempered out. ~~This temperament is supported by {{Optimal ET sequence| 12, 169, 181, 193, 205, 217, 229, and 241 }} edos.~~

In [[quindromeda]], the generator is 18/17, three of which make 19/16, five make 4/3, and 28 make [[5/1|5th harmonic]] in the 2.3.5.17.19 subgroup, so [[1216/1215]], [[1445/1444]], and [[6144/6137]] are tempered out. Equating 225/224 with 256/255 leads to [[quintakwai]] (12 & 193), which tempers out 400/399 (also equating 20/19 and 21/20) in the 2.3.5.7.17.19 subgroup, and 361/360 with 400/399 leads to [[quintagar]] (12 & 217), which tempers out 476/475 (also equating 19/17 with 28/25) in the 2.3.5.7.17.19 subgroup.

Equating 225/224 with 256/255 leads to [[quintakwai]] (12 & 193), which tempers out 400/399 (also equating 20/19 and 21/20) in the 2.3.5.7.17.19 subgroup, and 361/360 with 400/399 leads to [[quintagar]] (12 & 217), which tempers out 476/475 (also equating 19/17 with 28/25) in the 2.3.5.7.17.19 subgroup.

=== Quintaleap ===

In [[quintaleap]], the generator is 18/17, three ~~generators~~ make 19/16, five make 4/3, and 16 make [[5/2]] in the 2.3.5.17.19 subgroup, so [[256/255]], [[361/360]], and [[4624/4617]] are tempered out. ~~This temperament is supported by {{Optimal ET sequence| 12, 109, 121, 133, 145, and 157 }} edos.~~

In [[quintaleap]], the generator is 18/17, three of which make 19/16, five make 4/3, and 16 make [[5/2]] in the 2.3.5.17.19 subgroup, so [[256/255]], [[361/360]], and [[4624/4617]] are tempered out. In the 2.3.5.7.17.19 subgroup, tempering out 400/399 leads to [[quintupole]] (12 & 121), and tempering out 476/475 leads to [[quinticosiennic]] (12 & 145).

In the 2.3.5.7.17.19 subgroup, tempering out 400/399 leads to [[quintupole]] (12 & 121), and tempering out 476/475 leads to [[quinticosiennic]] (12 & 145).

=== Passion ===

In [[passion]], the generator is [[16/15]], four ~~generators~~ make [[5/4]], and five make 4/3. It is best tuned with a slightly flat generator of about 98.7{{c}}, and follows that both 3 and 5 should be tuned sharp. The canonical mapping of 7 places [[7/4]] at 10 generators, and follows that the generator should be tuned flatter (about 98.1{{c}}).

In [[passion]], the generator is [[16/15]], four of which make [[5/4]], and five make 4/3. It is best tuned with a slightly flat generator of about 98.7{{c}}, and follows that both 3 and 5 should be tuned sharp. The canonical mapping of 7 places [[7/4]] at 10 generators, and follows that the generator should be tuned flatter (about 98.1{{c}}).

=== Ripple ===

In [[ripple]], the generator is [[27/25]], five of which make 4/3, and eight make [[8/5]]. It is best tuned with a sharp generator of about 101–102{{c}}, giving the [[11L 1s]] MOS structure (rather than 1L 11s), and follows that 3 should be tuned flat.

[[Category:Ploidacots]]

[[Category:Ploidacots|Omega-pentacot]]

@@ Line 330: / Line 330: @@
 {{See also| Schismatic family }}
-In quintilischis, the generator is 18/17, three generators make [[19/16]], five make 4/3, and 40 make [[10/1|10th harmonic]] in the 2.3.5.17.19 subgroup, so [[4624/4617]], [[6144/6137]], and [[6885/6859]] are tempered out. This temperament is a weak extension of [[schismic]], splitting the fourth in five, and supported by {{Optimal ET sequence| 12, 253, 265, 277, 289, 301, 313, and 325 }} edos.
+In quintilischis, the generator is 18/17, three of which make [[19/16]], five make 4/3, and 40 make [[10/1|10th harmonic]] in the 2.3.5.17.19 subgroup, so [[4624/4617]], [[6144/6137]], and [[6885/6859]] are tempered out. This temperament is a weak extension of [[schismic]], splitting the fourth in five. In the 2.3.5.7.17.19 subgroup, tempering out [[400/399]] (equating 20/19 and 21/20) leads to [[quintilipyth]] (12 &amp; 253), and tempering out [[476/475]] (equating 19/17 with 28/25) leads to [[quintaschis]] (12 &amp; 289).
-In the 2.3.5.7.17.19 subgroup, tempering out [[400/399]] (equating 20/19 and 21/20) leads to [[quintilipyth]] (12 &amp; 253), and tempering out [[476/475]] (equating 19/17 with 28/25) leads to [[quintaschis]] (12 &amp; 289).
 === Quindromeda ===
 {{Main| Quindromeda family }}
-In [[quindromeda]], the generator is 18/17, three generators make 19/16, five make 4/3, and 28 make [[5/1|5th harmonic]] in the 2.3.5.17.19 subgroup, so [[1216/1215]], [[1445/1444]], and [[6144/6137]] are tempered out. This temperament is supported by {{Optimal ET sequence| 12, 169, 181, 193, 205, 217, 229, and 241 }} edos.
+In [[quindromeda]], the generator is 18/17, three of which make 19/16, five make 4/3, and 28 make [[5/1|5th harmonic]] in the 2.3.5.17.19 subgroup, so [[1216/1215]], [[1445/1444]], and [[6144/6137]] are tempered out. Equating 225/224 with 256/255 leads to [[quintakwai]] (12 &amp; 193), which tempers out 400/399 (also equating 20/19 and 21/20) in the 2.3.5.7.17.19 subgroup, and 361/360 with 400/399 leads to [[quintagar]] (12 &amp; 217), which tempers out 476/475 (also equating 19/17 with 28/25) in the 2.3.5.7.17.19 subgroup.
-Equating 225/224 with 256/255 leads to [[quintakwai]] (12 &amp; 193), which tempers out 400/399 (also equating 20/19 and 21/20) in the 2.3.5.7.17.19 subgroup, and 361/360 with 400/399 leads to [[quintagar]] (12 &amp; 217), which tempers out 476/475 (also equating 19/17 with 28/25) in the 2.3.5.7.17.19 subgroup.
 === Quintaleap ===
 {{Main| Quintaleap family }}
-In [[quintaleap]], the generator is 18/17, three generators make 19/16, five make 4/3, and 16 make [[5/2]] in the 2.3.5.17.19 subgroup, so [[256/255]], [[361/360]], and [[4624/4617]] are tempered out. This temperament is supported by {{Optimal ET sequence| 12, 109, 121, 133, 145, and 157 }} edos.
+In [[quintaleap]], the generator is 18/17, three of which make 19/16, five make 4/3, and 16 make [[5/2]] in the 2.3.5.17.19 subgroup, so [[256/255]], [[361/360]], and [[4624/4617]] are tempered out. In the 2.3.5.7.17.19 subgroup, tempering out 400/399 leads to [[quintupole]] (12 &amp; 121), and tempering out 476/475 leads to [[quinticosiennic]] (12 &amp; 145).
-In the 2.3.5.7.17.19 subgroup, tempering out 400/399 leads to [[quintupole]] (12 &amp; 121), and tempering out 476/475 leads to [[quinticosiennic]] (12 &amp; 145).
 === Passion ===
 {{Main| Passion family }}
-In [[passion]], the generator is [[16/15]], four generators make [[5/4]], and five make 4/3. It is best tuned with a slightly flat generator of about 98.7{{c}}, and follows that both 3 and 5 should be tuned sharp. The canonical mapping of 7 places [[7/4]] at 10 generators, and follows that the generator should be tuned flatter (about 98.1{{c}}).
+In [[passion]], the generator is [[16/15]], four of which make [[5/4]], and five make 4/3. It is best tuned with a slightly flat generator of about 98.7{{c}}, and follows that both 3 and 5 should be tuned sharp. The canonical mapping of 7 places [[7/4]] at 10 generators, and follows that the generator should be tuned flatter (about 98.1{{c}}).
+=== Ripple ===
+{{Main| Ripple family }}
+In [[ripple]], the generator is [[27/25]], five of which make 4/3, and eight make [[8/5]]. It is best tuned with a sharp generator of about 101–102{{c}}, giving the [[11L 1s]] MOS structure (rather than 1L 11s), and follows that 3 should be tuned flat.
-[[Category:Ploidacots]]
+[[Category:Ploidacots|Omega-pentacot]]