Ed6
IMPORTED REVISION FROM WIKISPACES
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- This revision was by author JosephRuhf and made on 2016-10-24 20:59:20 UTC.
- The original revision id was 596767008.
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Original Wikitext content:
=Division of the sixth harmonic into n equal parts= The sixth harmonic is particularly wide as far as equivalences go.<span class="commentBody"> There are (at absolute most) ~4.3 hexataves within the human hearing range; imagine if that were the case with octaves. If one does indeed deal with hexatave equivalence, </span>this fact shapes one's musical approach dramatically. Even so, the hexatave is one of the three particularly interesting composite harmonics whereof there are enough within the human hearing range to fill three periods of keyboard (the 10th, and to a lesser extent, the 12th share this property). Following this, the quintessential reason for using a hexatave based tuning is that it will split the difference between octave and tritave based tunings, which is a potentially very desirable thing for a tuning to do given the importance of these harmonics in the musics of much of the world (see [[44ed6]] and [[49ed6]]). However, this is not to say of ed6s not supporting this important 13&18 temperament that they can be dismissed out of hand as entirely worthless, for to do that would shut off all non-patent musical approaches to this equivalence. In fact, taking the nth root of 6 is itself an approach to finding temperaments like squares, tritonic, and sensi. This approach can of course be used indiscriminately. 4ed6 [[Squares|squares]] generator (with octaves) 5ed6 [[Tritonic|tritonic]] generator (with octaves) 6ed6 compare 7ed8 7ed6 [[Sensi|sensi]] generator (with octaves) 8ed6 [[Würschmidt|würschmidt]] generator (with octaves) 9ed6 compare 7ed4 10ed6 [[Myna|myna]] generator (with octaves) 11ed6 compare 17ed16 12ed6 compare 14ed8 13ed6 compare [[5edo]] and [[8edt]] 14ed6 15ed6 16ed6 [[Hemiwuerschmidt|hemiwuerschimdt]] generator (with octaves) 17ed6 [[Minortonic family|Minortonic]] generator (with octaves) 18ed6 compare [[7edo]] and [[11edt]] 19ed6 [[Porcupine]] generator (with octaves) 20ed6 21ed6 [[Progression|progression]] generator (with octaves) 22ed6 compare 17ed4 23ed6 compare [[9edo]] and [[14edt]] 24ed6 [[Twothirdtonic|twothirdtonic]] generator (with octaves) 25ed6 26ed6 compare [[10edo]] and [[16edt]] 27ed6 28ed6 29ed6 30ed6 31ed6 compare [[12edo]] and [[19edt]] 32ed6 33ed6 34ed6 35ed6 [[Octacot|octacot]] generator (with octaves) 36ed6 compare [[14edo]] and [[22edt]] 37ed6 38ed6 39ed6 compare [[15edo]] and [[24edt]] 40ed6 [[Valentine|valentine]] generator (with octaves) 41ed6 compare [[16edo]] and [[25edt]] 42ed6 43ed6 [[44ed6]] compare [[17edo]] and [[27edt]] 45ed6 46ed6 47ed6 48ed6 compare 56ed8 [[49ed6]] compare [[19edo]] and [[30edt]] 50ed6 51ed6 52ed6 compare [[20edo]] and [[32edt]] 53ed6 54ed6 compare [[21edo]] and [[33edt]] 55ed6 56ed6 57ed6 compare [[22edo]] and [[35edt]] 58ed6 59ed6 60ed6 61ed6 62ed6 compare [[24edo]] and [[38edt]] 63ed6 64ed6 65ed6 (compare [[25edo]] and [[40edt]]) 66ed6 compare 51ed4 67ed6 compare [[26edo]] and [[41edt]] 68ed6 69ed6 70ed6 compare [[27edo]] and [[43edt]] 71ed6 compare 55ed4 72ed6 compare [[28edo]] and [[44edt]] 73ed6 74ed6 75ed6 compare [[29edo]] and [[46edo]]
Original HTML content:
<html><head><title>ed6</title></head><body><!-- ws:start:WikiTextHeadingRule:0:<h1> --><h1 id="toc0"><a name="Division of the sixth harmonic into n equal parts"></a><!-- ws:end:WikiTextHeadingRule:0 -->Division of the sixth harmonic into n equal parts</h1> <br /> The sixth harmonic is particularly wide as far as equivalences go.<span class="commentBody"> There are (at absolute most) ~4.3 hexataves within the human hearing range; imagine if that were the case with octaves. If one does indeed deal with hexatave equivalence, </span>this fact shapes one's musical approach dramatically. Even so, the hexatave is one of the three particularly interesting composite harmonics whereof there are enough within the human hearing range to fill three periods of keyboard (the 10th, and to a lesser extent, the 12th share this property). Following this, the quintessential reason for using a hexatave based tuning is that it will split the difference between octave and tritave based tunings, which is a potentially very desirable thing for a tuning to do given the importance of these harmonics in the musics of much of the world (see <a class="wiki_link" href="/44ed6">44ed6</a> and <a class="wiki_link" href="/49ed6">49ed6</a>). However, this is not to say of ed6s not supporting this important 13&18 temperament that they can be dismissed out of hand as entirely worthless, for to do that would shut off all non-patent musical approaches to this equivalence. In fact, taking the nth root of 6 is itself an approach to finding temperaments like squares, tritonic, and sensi. This approach can of course be used indiscriminately.<br /> <br /> 4ed6 <a class="wiki_link" href="/Squares">squares</a> generator (with octaves)<br /> 5ed6 <a class="wiki_link" href="/Tritonic">tritonic</a> generator (with octaves)<br /> 6ed6 compare 7ed8<br /> 7ed6 <a class="wiki_link" href="/Sensi">sensi</a> generator (with octaves)<br /> 8ed6 <a class="wiki_link" href="/W%C3%BCrschmidt">würschmidt</a> generator (with octaves)<br /> 9ed6 compare 7ed4<br /> 10ed6 <a class="wiki_link" href="/Myna">myna</a> generator (with octaves)<br /> 11ed6 compare 17ed16<br /> 12ed6 compare 14ed8<br /> 13ed6 compare <a class="wiki_link" href="/5edo">5edo</a> and <a class="wiki_link" href="/8edt">8edt</a><br /> 14ed6<br /> 15ed6<br /> 16ed6 <a class="wiki_link" href="/Hemiwuerschmidt">hemiwuerschimdt</a> generator (with octaves)<br /> 17ed6 <a class="wiki_link" href="/Minortonic%20family">Minortonic</a> generator (with octaves)<br /> 18ed6 compare <a class="wiki_link" href="/7edo">7edo</a> and <a class="wiki_link" href="/11edt">11edt</a><br /> 19ed6 <a class="wiki_link" href="/Porcupine">Porcupine</a> generator (with octaves)<br /> 20ed6<br /> 21ed6 <a class="wiki_link" href="/Progression">progression</a> generator (with octaves)<br /> 22ed6 compare 17ed4<br /> 23ed6 compare <a class="wiki_link" href="/9edo">9edo</a> and <a class="wiki_link" href="/14edt">14edt</a><br /> 24ed6 <a class="wiki_link" href="/Twothirdtonic">twothirdtonic</a> generator (with octaves)<br /> 25ed6<br /> 26ed6 compare <a class="wiki_link" href="/10edo">10edo</a> and <a class="wiki_link" href="/16edt">16edt</a><br /> 27ed6<br /> 28ed6<br /> 29ed6<br /> 30ed6<br /> 31ed6 compare <a class="wiki_link" href="/12edo">12edo</a> and <a class="wiki_link" href="/19edt">19edt</a><br /> 32ed6<br /> 33ed6<br /> 34ed6<br /> 35ed6 <a class="wiki_link" href="/Octacot">octacot</a> generator (with octaves)<br /> 36ed6 compare <a class="wiki_link" href="/14edo">14edo</a> and <a class="wiki_link" href="/22edt">22edt</a><br /> 37ed6<br /> 38ed6<br /> 39ed6 compare <a class="wiki_link" href="/15edo">15edo</a> and <a class="wiki_link" href="/24edt">24edt</a><br /> 40ed6 <a class="wiki_link" href="/Valentine">valentine</a> generator (with octaves)<br /> 41ed6 compare <a class="wiki_link" href="/16edo">16edo</a> and <a class="wiki_link" href="/25edt">25edt</a><br /> 42ed6<br /> 43ed6<br /> <a class="wiki_link" href="/44ed6">44ed6</a> compare <a class="wiki_link" href="/17edo">17edo</a> and <a class="wiki_link" href="/27edt">27edt</a><br /> 45ed6<br /> 46ed6<br /> 47ed6<br /> 48ed6 compare 56ed8<br /> <a class="wiki_link" href="/49ed6">49ed6</a> compare <a class="wiki_link" href="/19edo">19edo</a> and <a class="wiki_link" href="/30edt">30edt</a><br /> 50ed6<br /> 51ed6<br /> 52ed6 compare <a class="wiki_link" href="/20edo">20edo</a> and <a class="wiki_link" href="/32edt">32edt</a><br /> 53ed6<br /> 54ed6 compare <a class="wiki_link" href="/21edo">21edo</a> and <a class="wiki_link" href="/33edt">33edt</a><br /> 55ed6<br /> 56ed6<br /> 57ed6 compare <a class="wiki_link" href="/22edo">22edo</a> and <a class="wiki_link" href="/35edt">35edt</a><br /> 58ed6<br /> 59ed6<br /> 60ed6<br /> 61ed6<br /> 62ed6 compare <a class="wiki_link" href="/24edo">24edo</a> and <a class="wiki_link" href="/38edt">38edt</a><br /> 63ed6<br /> 64ed6<br /> 65ed6 (compare <a class="wiki_link" href="/25edo">25edo</a> and <a class="wiki_link" href="/40edt">40edt</a>)<br /> 66ed6 compare 51ed4<br /> 67ed6 compare <a class="wiki_link" href="/26edo">26edo</a> and <a class="wiki_link" href="/41edt">41edt</a><br /> 68ed6<br /> 69ed6<br /> 70ed6 compare <a class="wiki_link" href="/27edo">27edo</a> and <a class="wiki_link" href="/43edt">43edt</a><br /> 71ed6 compare 55ed4<br /> 72ed6 compare <a class="wiki_link" href="/28edo">28edo</a> and <a class="wiki_link" href="/44edt">44edt</a><br /> 73ed6<br /> 74ed6<br /> 75ed6 compare <a class="wiki_link" href="/29edo">29edo</a> and <a class="wiki_link" href="/46edo">46edo</a></body></html>