Ed6: Difference between revisions

<div style="width:100%; max-height:400pt; overflow:auto; background-color:#f8f9fa; border: 1px solid #eaecf0; padding:0em"><pre style="margin:0px;border:none;background:none;word-wrap:break-word;white-space: pre-wrap ! important" class="old-revision-html">=Division of the sixth harmonic into n equal parts=  

The sixth harmonic is particularly wide as far as equivalences go.&lt;span class="commentBody"&gt; 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, &lt;/span&gt;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&amp;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.

13ed6 compare [[5edo]] and [[8edt]]

17ed6 [[Minortonic family|Minortonic]] generator (with octaves)

18ed6 compare [[7edo]] and [[11edt]]

19ed6 [[Porcupine]] generator (with octaves)

23ed6 compare [[9edo]] and [[14edt]]

26ed6 compare [[10edo]] and [[16edt]]

31ed6 compare [[12edo]] and [[19edt]]

36ed6 compare [[14edo]] and [[22edt]]

39ed6 compare [[15edo]] and [[24edt]]

41ed6 compare [[16edo]] and [[25edt]]

[[44ed6]] compare [[17edo]] and [[27edt]]

[[49ed6]] compare [[19edo]] and [[30edt]]

52ed6 compare [[20edo]] and [[32edt]]

54ed6 compare [[21edo]] and [[33edt]]

57ed6 compare [[22edo]] and [[35edt]]

62ed6 compare [[24edo]] and [[38edt]]

65ed6 (compare [[25edo]] and [[40edt]])

67ed6 compare [[26edo]] and [[41edt]]

70ed6 compare [[27edo]] and [[43edt]]

72ed6 compare [[28edo]] and [[44edt]]

75ed6 compare [[29edo]] and 46edt</pre></div>