Sycamore family
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The head of the sycamore family is 5-limit sycamore, which tempers out (25/24)^6/(5/4) = |-16 -6 11> = 48828125/47775744. The dual of the monzo is the wedgie, <<11 6 -16||, which tells us that six chromatic semitone generators give 5/4 (and hence five 6/5) and eleven give 3/2. [[94edo]] supports sycamore, and 5/94 is reommendable as a generator. It can be described as the 19&94 temperament, and uses a decidedly flat version of the chromatic semitone as a generator. MOS of 18 or 19 notes to the octave give enough room for sycamore's triads, but 37 notes can be tried by the adventurous. Another possible tuning uses a generator which is a pure 3/2 divided into 11 parts, and this makes the generator chain of sycamore exactly the same as [[Carlos Beta]]. In fact, Carlos Beta is characterized by Carlos as taking five steps to reach 6/5 and six to reach 5/4, which means it tempers out the sycamore comma. It can be described as the generator chain of sycamore, or sycamore can be called Carlos Beta with octaves. ==Seven limit children== ===Septimal sycamore=== The second element of the [[Normal lists|normal comma list]] for septimal sycamore is 875/864, the keema, and it also tempers out 686/675, the senga, and 3136/3125, hemimean. It has <<11 6 15 -16 -7 18|| for a wedgie, and may also be called the 19&56 temperament. This may also be used as the name for the temperament obtained hy adding 100/99 to sycamore's commas, giving unidecimal sycamore, where 10 generator steps reaches 16/11, 11 reach 3/2, and 15 give 7/4, adding a considerable dose of 11-limit harmonies to the 19-note MOS. [[75edo]] is an excellent tuning for 7-limit sycamore, and [[56edo]] for the 11-limit version. ===Betic=== Septimal sycamore sharpens the fifth from where it stands in the 5-limit, and lowers accuracy in order to reach 7-limit harmonies. If we retain tunings approximately (eg 94et) or exactly those of Carlos Beta, we get the 19&94 temperament, betic, for the 7-limit. This adds 225/224 to the sycamore comma, and has <<11 6 34 -16 23 62|| as a wedgie. The Carlos Beta tuning, with pure fifths, is a good tuning choice, but 94 or 113 equal are as well. Betic extends to the 11-limit upon addition of 385/384 or 540/539 to the list of commas, which means it supports both 7 and 11-limit marvel. The wedgie starts <<11 6 34 -29 ...||.
Original HTML content:
<html><head><title>Sycamore family</title></head><body>The head of the sycamore family is 5-limit sycamore, which tempers out (25/24)^6/(5/4) = |-16 -6 11> = 48828125/47775744. The dual of the monzo is the wedgie, <<11 6 -16||, which tells us that six chromatic semitone generators give 5/4 (and hence five 6/5) and eleven give 3/2. <a class="wiki_link" href="/94edo">94edo</a> supports sycamore, and 5/94 is reommendable as a generator. It can be described as the 19&94 temperament, and uses a decidedly flat version of the chromatic semitone as a generator. MOS of 18 or 19 notes to the octave give enough room for sycamore's triads, but 37 notes can be tried by the adventurous.<br /> <br /> Another possible tuning uses a generator which is a pure 3/2 divided into 11 parts, and this makes the generator chain of sycamore exactly the same as <a class="wiki_link" href="/Carlos%20Beta">Carlos Beta</a>. In fact, Carlos Beta is characterized by Carlos as taking five steps to reach 6/5 and six to reach 5/4, which means it tempers out the sycamore comma. It can be described as the generator chain of sycamore, or sycamore can be called Carlos Beta with octaves.<br /> <br /> <!-- ws:start:WikiTextHeadingRule:0:<h2> --><h2 id="toc0"><a name="x-Seven limit children"></a><!-- ws:end:WikiTextHeadingRule:0 -->Seven limit children</h2> <br /> <!-- ws:start:WikiTextHeadingRule:2:<h3> --><h3 id="toc1"><a name="x-Seven limit children-Septimal sycamore"></a><!-- ws:end:WikiTextHeadingRule:2 -->Septimal sycamore</h3> The second element of the <a class="wiki_link" href="/Normal%20lists">normal comma list</a> for septimal sycamore is 875/864, the keema, and it also tempers out 686/675, the senga, and 3136/3125, hemimean. It has <<11 6 15 -16 -7 18|| for a wedgie, and may also be called the 19&56 temperament. This may also be used as the name for the temperament obtained hy adding 100/99 to sycamore's commas, giving unidecimal sycamore, where 10 generator steps reaches 16/11, 11 reach 3/2, and 15 give 7/4, adding a considerable dose of 11-limit harmonies to the 19-note MOS. <a class="wiki_link" href="/75edo">75edo</a> is an excellent tuning for 7-limit sycamore, and <a class="wiki_link" href="/56edo">56edo</a> for the 11-limit version.<br /> <br /> <!-- ws:start:WikiTextHeadingRule:4:<h3> --><h3 id="toc2"><a name="x-Seven limit children-Betic"></a><!-- ws:end:WikiTextHeadingRule:4 -->Betic</h3> Septimal sycamore sharpens the fifth from where it stands in the 5-limit, and lowers accuracy in order to reach 7-limit harmonies. If we retain tunings approximately (eg 94et) or exactly those of Carlos Beta, we get the 19&94 temperament, betic, for the 7-limit. This adds 225/224 to the sycamore comma, and has <<11 6 34 -16 23 62|| as a wedgie. The Carlos Beta tuning, with pure fifths, is a good tuning choice, but 94 or 113 equal are as well. Betic extends to the 11-limit upon addition of 385/384 or 540/539 to the list of commas, which means it supports both 7 and 11-limit marvel. The wedgie starts <<11 6 34 -29 ...||.</body></html>