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 [[generator]]s 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. [[POTE tuning|POTE generator]]: 63.779 Map: [<1 1 2|, <0 11 6|] EDOs: [[18edo|18]], [[19edo|19]], [[56edo|56]], [[75edo|75]], [[94edo|94]], 207, 508 ==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 by 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. Commas: 686/675, 875/864 [[POTE tuning|POTE generator]]: 63.995 Map: [<1 1 2 2|, <0 11 6 15|] EDOs: 18, 19, 56, 75 11-limit Commas: 100/99, 385/384, 686/675 [[POTE tuning|POTE generator]]: 64.268 Map: [<1 1 2 2 4|, <0 11 6 15 -10|] EDOs: 18, 19, [[37edo|37]], 56 ===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 ...||. Commas: 225/224, 1071875/1062882 [[POTE tuning|POTE generator]]: 63.701 Map: [<1 1 2 1|, <0 11 6 34|] EDOs: 19, 75, 94, 113, 433 11-limit Commas: 225/224, 385/384, 218750/216513 [[POTE tuning|POTE generator]]: 63.776 Map: [<1 1 2 1 5|, <0 11 6 34 -29|] EDOs: 19, 75, 94, 207
Original HTML content:
<html><head><title>Sycamore family</title></head><body>The head of the sycamore family is <a class="wiki_link" href="/5-limit">5-limit</a> sycamore, which tempers out (25/24)^6/(5/4) = |-16 -6 11> = 48828125/47775744. The dual of the <a class="wiki_link" href="/monzo">monzo</a> is the <a class="wiki_link" href="/wedgie">wedgie</a>, <<11 6 -16||, which tells us that six chromatic semitone <a class="wiki_link" href="/generator">generator</a>s 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. <a class="wiki_link" href="/MOS">MOS</a> 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 /> <a class="wiki_link" href="/POTE%20tuning">POTE generator</a>: 63.779<br /> <br /> Map: [<1 1 2|, <0 11 6|]<br /> EDOs: <a class="wiki_link" href="/18edo">18</a>, <a class="wiki_link" href="/19edo">19</a>, <a class="wiki_link" href="/56edo">56</a>, <a class="wiki_link" href="/75edo">75</a>, <a class="wiki_link" href="/94edo">94</a>, 207, 508<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 by 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 /> Commas: 686/675, 875/864<br /> <br /> <a class="wiki_link" href="/POTE%20tuning">POTE generator</a>: 63.995<br /> <br /> Map: [<1 1 2 2|, <0 11 6 15|]<br /> EDOs: 18, 19, 56, 75<br /> <br /> <br /> 11-limit<br /> Commas: 100/99, 385/384, 686/675<br /> <br /> <a class="wiki_link" href="/POTE%20tuning">POTE generator</a>: 64.268<br /> <br /> Map: [<1 1 2 2 4|, <0 11 6 15 -10|]<br /> EDOs: 18, 19, <a class="wiki_link" href="/37edo">37</a>, 56<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 ...||.<br /> <br /> Commas: 225/224, 1071875/1062882<br /> <br /> <a class="wiki_link" href="/POTE%20tuning">POTE generator</a>: 63.701<br /> <br /> Map: [<1 1 2 1|, <0 11 6 34|]<br /> EDOs: 19, 75, 94, 113, 433<br /> <br /> 11-limit<br /> Commas: 225/224, 385/384, 218750/216513<br /> <br /> <a class="wiki_link" href="/POTE%20tuning">POTE generator</a>: 63.776<br /> <br /> Map: [<1 1 2 1 5|, <0 11 6 34 -29|]<br /> EDOs: 19, 75, 94, 207</body></html>