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'''Ed6''' means '''Division of the Sixth Harmonic ([[6/1]]) into n equal parts'''.
=Division of the sixth harmonic into n equal parts=
=Division of the sixth harmonic into n equal parts=


The sixth harmonic is particularly wide as far as equivalences go.<span style=""> 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|44ed6]] and [[49ed6|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.
The sixth harmonic is particularly wide as far as equivalences go. 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, 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.
 
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|5edo]] and [[8edt|8edt]]
 
14ed6
 
15ed6
 
16ed6 [[Hemiwuerschmidt|hemiwuerschimdt]] generator (with octaves)
 
17ed6 [[Minortonic_family|Minortonic]] generator (with octaves)
 
18ed6 compare [[7edo|7edo]] and [[11edt|11edt]]
 
19ed6 [[Porcupine|Porcupine]] generator (with octaves)
 
20ed6
 
21ed6 [[Progression|progression]] generator (with octaves)
 
22ed6 compare 17ed4
 
23ed6 compare [[9edo|9edo]] and [[14edt|14edt]]
 
24ed6 [[Twothirdtonic|twothirdtonic]] generator (with octaves)
 
25ed6
 
26ed6 compare [[10edo|10edo]] and [[16edt|16edt]]
 
27ed6
 
28ed6
 
29ed6
 
30ed6
 
31ed6 compare [[12edo|12edo]] and [[19edt|19edt]]
 
32ed6
 
33ed6
 
34ed6
 
35ed6 [[Octacot|octacot]] generator (with octaves)
 
36ed6 compare [[14edo|14edo]] and [[22edt|22edt]]
 
37ed6
 
38ed6
 
39ed6 compare [[15edo|15edo]] and [[24edt|24edt]]
 
40ed6 [[Valentine|valentine]] generator (with octaves)
 
41ed6 compare [[16edo|16edo]] and [[25edt|25edt]]
 
42ed6
 
43ed6
 
[[44ed6|44ed6]] compare [[17edo|17edo]] and [[27edt|27edt]]
 
45ed6
 
46ed6
 
47ed6
 
48ed6 compare 56ed8
 
[[49ed6|49ed6]] compare [[19edo|19edo]] and [[30edt|30edt]]
 
50ed6
 
51ed6
 
52ed6 compare [[20edo|20edo]] and [[32edt|32edt]]
 
53ed6
 
54ed6 compare [[21edo|21edo]] and [[33edt|33edt]]
 
55ed6
 
56ed6
 
57ed6 compare [[22edo|22edo]] and [[35edt|35edt]]
 
58ed6
 
59ed6
 
60ed6
 
61ed6
 
62ed6 compare [[24edo|24edo]] and [[38edt|38edt]]
 
63ed6
 
64ed6
 
65ed6 (compare [[25edo|25edo]] and [[40edt|40edt]])
 
66ed6 compare 51ed4
 
67ed6 compare [[26edo|26edo]] and [[41edt|41edt]]
 
68ed6
 
69ed6
 
70ed6 compare [[27edo|27edo]] and [[43edt|43edt]]
 
71ed6 compare 55ed4
 
72ed6 compare [[28edo|28edo]] and [[44edt|44edt]]
 
73ed6


74ed6
*[[4ed6]] [[Squares|squares]] generator (with octaves)
*[[5ed6]] [[Tritonic|tritonic]] generator (with octaves)
*[[6ed6]]
*[[7ed6]] [[Sensi|sensi]] generator (with octaves)
*[[8ed6]] [[Würschmidt|würschmidt]] generator (with octaves)
*[[9ed6]]
*[[10ed6]] [[Myna|myna]] generator (with octaves)
*[[11ed6]]
*[[12ed6]]
*[[13ed6]] compare [[5edo]] and [[8edt]]
*[[14ed6]]
*[[15ed6]]
*[[16ed6]] [[Hemiwuerschmidt|hemiwürschimdt]] generator (with octaves)
*[[17ed6]] [[Minortonic_family|Minortonic]] generator (with octaves)
*[[18ed6]] compare [[7edo]] and [[11edt]]
*[[19ed6]] [[Porcupine|Porcupine]] generator (with octaves)
*[[20ed6]]
*[[21ed6]] [[Progression|progression]] generator (with octaves)
*[[22ed6]]
*[[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 [[19ED3|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]]
*[[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]]
*[[67ed6]] compare [[26edo]] and [[41edt]]
*[[68ed6]]
*[[69ed6]]
*[[70ed6]] compare [[27edo]] and [[43edt]]
*[[71ed6]]
*[[72ed6]] compare [[28edo]] and [[44edt]]
*[[73ed6]]
*[[74ed6]]
*[[75ed6]] compare [[29edo]] and [[46edt]]
*[[76ed6]]
*[[77ed6]]
*[[78ed6]]
*[[79ed6]]
*[[80ed6]] compare [[31edo]] and [[49edt]]
*[[81ed6]]
*[[82ed6]]
*[[83ed6]]
*[[84ed6]]
*[[85ed6]]
*[[86ed6]]
*[[87ed6]]
*[[88ed6]] compare [[34edo]] and [[54edt]]
*[[89ed6]]
*[[90ed6]]
*[[91ed6]]
*[[92ed6]]
*[[93ed6]] compare [[36edo]] and [[57edt]]
*[[94ed6]]
*[[95ed6]]
*[[96ed6]]
*[[97ed6]]
*[[98ed6]] compare [[38edo]] and [[60edt]]
*[[99ed6]]


75ed6 compare [[29edo|29edo]] and 46edt
[[Category:Ed6| ]]
[[Category:Edonoi]]

Revision as of 22:53, 20 January 2019

Ed6 means Division of the Sixth Harmonic (6/1) into n equal parts.

Division of the sixth harmonic into n equal parts

The sixth harmonic is particularly wide as far as equivalences go. 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, 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.

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