Augmented family
IMPORTED REVISION FROM WIKISPACES
This is an imported revision from Wikispaces. The revision metadata is included below for reference:
- This revision was by author genewardsmith and made on 2011-01-12 00:35:04 UTC.
- The original revision id was 192637528.
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Original Wikitext content:
The 5-limit parent comma for the augmented family is 128/125, the diesis. Its [[monzo]] is |7 0 -3>, and flipping that yields <<3 0 -7|| for the [[wedgie]]. Hence the period is 1/3 octave, and this is what is used for a major third. The [[generator]] can be taken as a fifth or a semitone, and [[12edo]], with its excellent fifth, is an obvious tuning for 5-limit augmented, though a sharper fifth might be preferred to go with the sharp third. ==Seven limit children== The second comma of the [[Normal lists|normal comma list]] defines which 7-limit family member we are looking at. August adds 36/35, augene 64/63, hexe 256/245, and hemiaug 245/243. Hexe splits the period to 1/6 octave, and hemiaug the generator, giving quarter-tones instead of semitones. ==August== Commas: 36/35, 128/125 [[POTE tuning|POTE generator]]: 696.011 Map: [<3 0 7 -1|, <0 1 0 2|] Wedgie: <<3 0 6 -7 1 14|| EDOs: [[9edo|9]], [[12edo|12]], [[69edo|69]], [[81edo|81]] Badness: 0.0265 ==Augene== Commas: 64/63, 126/125 [[POTE tuning|POTE generator]]: 709.257 Map: [<3 0 7 18|, <0 1 0 -2|] Wedgie: <<3 0 -6 -7 -18 -14|| EDOs: [[12edo|12]], [[27edo|27]], [[66edo|66]] Badness: 0.0248
Original HTML content:
<html><head><title>Augmented family</title></head><body>The 5-limit parent comma for the augmented family is 128/125, the diesis. Its <a class="wiki_link" href="/monzo">monzo</a> is |7 0 -3>, and flipping that yields <<3 0 -7|| for the <a class="wiki_link" href="/wedgie">wedgie</a>. Hence the period is 1/3 octave, and this is what is used for a major third. The <a class="wiki_link" href="/generator">generator</a> can be taken as a fifth or a semitone, and <a class="wiki_link" href="/12edo">12edo</a>, with its excellent fifth, is an obvious tuning for 5-limit augmented, though a sharper fifth might be preferred to go with the sharp third. <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> The second comma of the <a class="wiki_link" href="/Normal%20lists">normal comma list</a> defines which 7-limit family member we are looking at. August adds 36/35, augene 64/63, hexe 256/245, and hemiaug 245/243. Hexe splits the period to 1/6 octave, and hemiaug the generator, giving quarter-tones instead of semitones.<br /> <br /> <!-- ws:start:WikiTextHeadingRule:2:<h2> --><h2 id="toc1"><a name="x-August"></a><!-- ws:end:WikiTextHeadingRule:2 -->August</h2> Commas: 36/35, 128/125<br /> <br /> <a class="wiki_link" href="/POTE%20tuning">POTE generator</a>: 696.011<br /> <br /> Map: [<3 0 7 -1|, <0 1 0 2|]<br /> Wedgie: <<3 0 6 -7 1 14||<br /> EDOs: <a class="wiki_link" href="/9edo">9</a>, <a class="wiki_link" href="/12edo">12</a>, <a class="wiki_link" href="/69edo">69</a>, <a class="wiki_link" href="/81edo">81</a><br /> Badness: 0.0265<br /> <br /> <!-- ws:start:WikiTextHeadingRule:4:<h2> --><h2 id="toc2"><a name="x-Augene"></a><!-- ws:end:WikiTextHeadingRule:4 -->Augene</h2> Commas: 64/63, 126/125<br /> <br /> <a class="wiki_link" href="/POTE%20tuning">POTE generator</a>: 709.257<br /> <br /> Map: [<3 0 7 18|, <0 1 0 -2|]<br /> Wedgie: <<3 0 -6 -7 -18 -14||<br /> EDOs: <a class="wiki_link" href="/12edo">12</a>, <a class="wiki_link" href="/27edo">27</a>, <a class="wiki_link" href="/66edo">66</a><br /> Badness: 0.0248</body></html>