Ed7: Difference between revisions

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'''Ed7''' means '''Division of the Seventh Harmonic ([[7/1]]) into n equal parts'''.
'''Equal divisions of the 7th harmonic''' ('''ed7''') are [[tuning]]s obtained by dividing the [[7/1|7th harmonic]] in a certain number of [[equal]] steps.  


== Properties ==
The seventh harmonic is particularly wide as far as equivalences go. There are (at absolute most) about 3.9 instances of the 7th harmonic in the human hearing range; imagine if that were the case with octaves. If one does indeed deal with equivalence of the 7th harmonic, this fact shapes one's musical approach dramatically.
The seventh harmonic is particularly wide as far as equivalences go. There are (at absolute most) ~3.9 heptataves within the human hearing range; imagine if that were the case with octaves. If one does indeed deal with heptatave equivalence, this fact shapes one's musical approach dramatically.


Incidentally, one way to treat 7/1 as an equivalence is to eliminate the primes 2, 3, and 5 and use the 7:11:13:(49) chord as the fundamental complete sonority in a very similar way to the 4:5:6:(8) chord in meantone Whereas in meantone it takes four [[3/2]] to get to [[5/4]], here it takes seven [[13/7]] to get to [[11/7]] (tempering out the comma 63412811/62748517 in the 7.11.13 subgroup). This temperament yields 10, 13, 16, 19, 22, 25, and 47 note MOS. If 7/1 is too wide to be used as an equivalence, the next best option would be [[Ed11/7|equal divisions of 11/7]].
Incidentally, one way to treat 7/1 as an equivalence is to eliminate the [[prime interval|primes]] [[2/1|2]], [[3/1|3]], and [[5/1|5]] and use the 7:11:13 chord as the fundamental complete sonority in a very similar way to the 4:5:6 chord in meantone. Whereas in meantone it takes four [[3/2]] to get to [[5/4]], here it takes seven [[13/7]]'s to get to [[11/7]] ([[tempering out]] the [[comma]] 63412811/62748517 in the 7.11.13 [[subgroup]]). This temperament yields 10-, 13-, 16-, 19-, 22-, 25-, and 47-note [[mos scale]]s. If 7/1 is too wide to be used as an equivalence, the next best option would be [[Ed11/7|equal divisions of 11/7]].  


== Table of similar ETs ==
== Individual pages for ed7's ==  
{| class="wikitable center-all"
|+ style=white-space:nowrap | 0…99
| [[0ed7|0]]
| [[1ed7|1]]
| [[2ed7|2]]
| [[3ed7|3]]
| [[4ed7|4]]
| [[5ed7|5]]
| [[6ed7|6]]
| [[7ed7|7]]
| [[8ed7|8]]
| [[9ed7|9]]
|-
| [[10ed7|10]]
| [[11ed7|11]]
| [[12ed7|12]]
| [[13ed7|13]]
| [[14ed7|14]]
| [[15ed7|15]]
| [[16ed7|16]]
| [[17ed7|17]]
| [[18ed7|18]]
| [[19ed7|19]]
|-
| [[20ed7|20]]
| [[21ed7|21]]
| [[22ed7|22]]
| [[23ed7|23]]
| [[24ed7|24]]
| [[25ed7|25]]
| [[26ed7|26]]
| [[27ed7|27]]
| [[28ed7|28]]
| [[29ed7|29]]
|-
| [[30ed7|30]]
| [[31ed7|31]]
| [[32ed7|32]]
| [[33ed7|33]]
| [[34ed7|34]]
| [[35ed7|35]]
| [[36ed7|36]]
| [[37ed7|37]]
| [[38ed7|38]]
| [[39ed7|39]]
|-
| [[40ed7|40]]
| [[41ed7|41]]
| [[42ed7|42]]
| [[43ed7|43]]
| [[44ed7|44]]
| [[45ed7|45]]
| [[46ed7|46]]
| [[47ed7|47]]
| [[48ed7|48]]
| [[49ed7|49]]
|-
| [[50ed7|50]]
| [[51ed7|51]]
| [[52ed7|52]]
| [[53ed7|53]]
| [[54ed7|54]]
| [[55ed7|55]]
| [[56ed7|56]]
| [[57ed7|57]]
| [[58ed7|58]]
| [[59ed7|59]]
|-
| [[60ed7|60]]
| [[61ed7|61]]
| [[62ed7|62]]
| [[63ed7|63]]
| [[64ed7|64]]
| [[65ed7|65]]
| [[66ed7|66]]
| [[67ed7|67]]
| [[68ed7|68]]
| [[69ed7|69]]
|-
| [[70ed7|70]]
| [[71ed7|71]]
| [[72ed7|72]]
| [[73ed7|73]]
| [[74ed7|74]]
| [[75ed7|75]]
| [[76ed7|76]]
| [[77ed7|77]]
| [[78ed7|78]]
| [[79ed7|79]]
|-
| [[80ed7|80]]
| [[81ed7|81]]
| [[82ed7|82]]
| [[83ed7|83]]
| [[84ed7|84]]
| [[85ed7|85]]
| [[86ed7|86]]
| [[87ed7|87]]
| [[88ed7|88]]
| [[89ed7|89]]
|-
| [[90ed7|90]]
| [[91ed7|91]]
| [[92ed7|92]]
| [[93ed7|93]]
| [[94ed7|94]]
| [[95ed7|95]]
| [[96ed7|96]]
| [[97ed7|97]]
| [[98ed7|98]]
| [[99ed7|99]]
|}
{| class="wikitable center-all mw-collapsible mw-collapsed"
|+ style=white-space:nowrap | 100…199
| [[100ed7|100]]
| [[101ed7|101]]
| [[102ed7|102]]
| [[103ed7|103]]
| [[104ed7|104]]
| [[105ed7|105]]
| [[106ed7|106]]
| [[107ed7|107]]
| [[108ed7|108]]
| [[109ed7|109]]
|-
| [[110ed7|110]]
| [[111ed7|111]]
| [[112ed7|112]]
| [[113ed7|113]]
| [[114ed7|114]]
| [[115ed7|115]]
| [[116ed7|116]]
| [[117ed7|117]]
| [[118ed7|118]]
| [[119ed7|119]]
|-
| [[120ed7|120]]
| [[121ed7|121]]
| [[122ed7|122]]
| [[123ed7|123]]
| [[124ed7|124]]
| [[125ed7|125]]
| [[126ed7|126]]
| [[127ed7|127]]
| [[128ed7|128]]
| [[129ed7|129]]
|-
| [[130ed7|130]]
| [[131ed7|131]]
| [[132ed7|132]]
| [[133ed7|133]]
| [[134ed7|134]]
| [[135ed7|135]]
| [[136ed7|136]]
| [[137ed7|137]]
| [[138ed7|138]]
| [[139ed7|139]]
|-
| [[140ed7|140]]
| [[141ed7|141]]
| [[142ed7|142]]
| [[143ed7|143]]
| [[144ed7|144]]
| [[145ed7|145]]
| [[146ed7|146]]
| [[147ed7|147]]
| [[148ed7|148]]
| [[149ed7|149]]
|-
| [[150ed7|150]]
| [[151ed7|151]]
| [[152ed7|152]]
| [[153ed7|153]]
| [[154ed7|154]]
| [[155ed7|155]]
| [[156ed7|156]]
| [[157ed7|157]]
| [[158ed7|158]]
| [[159ed7|159]]
|-
| [[160ed7|160]]
| [[161ed7|161]]
| [[162ed7|162]]
| [[163ed7|163]]
| [[164ed7|164]]
| [[165ed7|165]]
| [[166ed7|166]]
| [[167ed7|167]]
| [[168ed7|168]]
| [[169ed7|169]]
|-
| [[170ed7|170]]
| [[171ed7|171]]
| [[172ed7|172]]
| [[173ed7|173]]
| [[174ed7|174]]
| [[175ed7|175]]
| [[176ed7|176]]
| [[177ed7|177]]
| [[178ed7|178]]
| [[179ed7|179]]
|-
| [[180ed7|180]]
| [[181ed7|181]]
| [[182ed7|182]]
| [[183ed7|183]]
| [[184ed7|184]]
| [[185ed7|185]]
| [[186ed7|186]]
| [[187ed7|187]]
| [[188ed7|188]]
| [[189ed7|189]]
|-
| [[190ed7|190]]
| [[191ed7|191]]
| [[192ed7|192]]
| [[193ed7|193]]
| [[194ed7|194]]
| [[195ed7|195]]
| [[196ed7|196]]
| [[197ed7|197]]
| [[198ed7|198]]
| [[199ed7|199]]
|}


== Individual pages for ED7s ==
; 200 and above
* [[4ed7]]
* [[480ed7]]
* [[5ed7]]
* [[6ed7]]
* [[7ed7]] compare [[4edt]]
* [[8ed7]]
* [[9ed7]] compare [[5edt]]
* [[10ed7]]
* [[11ed7]] compare [[4edo]]
* [[12ed7]]
* [[13ed7]]
* [[14ed7]] compare [[5edo]]
* [[15ed7]]
* [[16ed7]] compare [[9edt]]
* [[17ed7]] compare [[6edo]]
* [[18ed7]] compare [[10edt]]
* [[19ed7]]
* [[20ed7]]
* [[21ed7]] compare [[12edt]]
* [[22ed7]]
* [[23ed7]] compare [[13edt]]
* [[24ed7]]
* [[25ed7]] compare [[9edo]]
* [[26ed7]]
* [[27ed7]]
* [[28ed7]] compare [[10edo]]
* [[29ed7]]
* [[30ed7]] compare [[17edt]]
* [[31ed7]] compare [[11edo]]
* [[32ed7]] compare [[18edt]]
* [[33ed7]]
* [[34ed7]] compare [[12edo]]
* [[35ed7]]
* [[36ed7]]
* [[37ed7]] compare [[21edt]]
* [[38ed7]]
* [[39ed7]] compare [[14edo]]
* [[40ed7]]
* [[41ed7]] compare [[23edt]]
* [[42ed7]] compare [[15edo]]
* [[43ed7]]
* [[44ed7]] compare [[25edt]]
* [[45ed7]] compare [[16edo]]
* [[46ed7]] compare [[26edt]]
* [[47ed7]]
* [[48ed7]] compare [[17edo]]
* [[49ed7]]
* [[50ed7]]
* [[51ed7]]
* [[52ed7]]
* [[53ed7]] compare [[30edt]]
* [[54ed7]]
* [[55ed7]] compare [[31edt]]
* [[56ed7]] compare [[20edo]]
* [[57ed7]] compare [[32edt]]
* [[58ed7]]
* [[59ed7]] compare [[21edo]]
* [[60ed7]] compare [[34edt]]
* [[61ed7]]
* [[62ed7]] compare [[22edo]]
* [[63ed7]]
* [[64ed7]] compare [[36edt]]
* [[65ed7]]
* [[66ed7]]
* [[67ed7]] compare [[38edt]]
* [[68ed7]]
* [[69ed7]] compare [[39edt]]
* [[70ed7]] compare [[25edo]]
* [[71ed7]] compare [[40edt]]
* [[72ed7]]
* [[73ed7]] compare [[26edo]]
* [[74ed7]]
* [[75ed7]]
* [[76ed7]] compare [[27edo]]
* [[77ed7]]
* [[78ed7]] compare [[44edt]]
* [[79ed7]]
* [[80ed7]] compare [[45edt]]
* [[81ed7]]
* [[82ed7]]
* [[83ed7]] compare [[47edt]]
* [[84ed7]] compare [[30edo]]
* [[85ed7]] compare [[48edt]]
* [[86ed7]]
* [[87ed7]] compare [[31edo]]
* [[88ed7]]
* [[89ed7]]
* [[90ed7]] compare [[32edo]]
* [[91ed7]]
* [[92ed7]] compare [[52edt]]
* [[93ed7]]
* [[94ed7]] compare [[53edt]]
* [[95ed7]]
* [[96ed7]] compare [[Carlos Gamma]]
* [[97ed7]]
* [[98ed7]] compare [[35edo]]
* [[99ed7]] compare [[56edt]]
* [[100ed7]]
* [[101ed7]]


[[Category:Ed7| ]] <!-- main article -->
== Table of similar equal tunings ==
[[Category:Equal-step tuning]]
{| class="wikitable"
! ED7 !! Similar EDO !! Similar EDT !! Similar EDF
|-
| [[7ed7]] ||  || [[4edt]] ||
|-
| [[9ed7]] ||  || [[5edt]] ||
|-
| [[11ed7]] || [[4edo]] ||  ||
|-
| [[14ed7]] || [[5edo]] ||  ||
|-
| [[16ed7]] ||  || [[9edt]] ||
|-
| [[17ed7]] || [[6edo]] ||  ||
|-
| [[18ed7]] ||  || [[10edt]] ||
|-
| [[21ed7]] ||  || [[12edt]] ||
|-
| [[23ed7]] ||  || [[13edt]] ||
|-
| [[25ed7]] || [[9edo]] ||  ||
|-
| [[28ed7]] || [[10edo]] ||  ||
|-
| [[30ed7]] ||  || [[17edt]] ||
|-
| [[31ed7]] || [[11edo]] ||  ||
|-
| [[32ed7]] ||  || [[18edt]] ||
|-
| [[34ed7]] || [[12edo]] ||  ||
|-
| [[37ed7]] ||  || [[21edt]] ||
|-
| [[39ed7]] || [[14edo]] ||  ||
|-
| [[41ed7]] ||  || [[23edt]] ||
|-
| [[42ed7]] || [[15edo]] ||  ||
|-
| [[44ed7]] ||  || [[25edt]] ||
|-
| [[45ed7]] || [[16edo]] ||  ||
|-
| [[46ed7]] ||  || [[26edt]] ||
|-
| [[48ed7]] || [[17edo]] ||  ||
|-
| [[53ed7]] ||  || [[30edt]] ||
|-
| [[55ed7]] ||  || [[31edt]] ||
|-
| [[56ed7]] || [[20edo]] ||  ||
|-
| [[57ed7]] ||  || [[32edt]] ||
|-
| [[59ed7]] || [[21edo]] ||  ||
|-
| [[60ed7]] ||  || [[34edt]] ||
|-
| [[62ed7]] || [[22edo]] ||  ||
|-
| [[64ed7]] ||  || [[36edt]] ||
|-
| [[67ed7]] ||  || [[38edt]] ||
|-
| [[69ed7]] ||  || [[39edt]] ||
|-
| [[70ed7]] || [[25edo]] ||  ||
|-
| [[71ed7]] ||  || [[40edt]] ||
|-
| [[73ed7]] || [[26edo]] ||  ||
|-
| [[76ed7]] || [[27edo]] ||  ||
|-
| [[78ed7]] ||  || [[44edt]] ||
|-
| [[80ed7]] ||  || [[45edt]] ||
|-
| [[83ed7]] ||  || [[47edt]] ||
|-
| [[84ed7]] || [[30edo]] ||  ||
|-
| [[85ed7]] ||  || [[48edt]] ||
|-
| [[87ed7]] || [[31edo]] ||  ||
|-
| [[90ed7]] || [[32edo]] ||  ||
|-
| [[92ed7]] ||  || [[52edt]] ||
|-
| [[94ed7]] ||  || [[53edt]] ||
|-
| [[96ed7]] ||  ||  || [[20edf]] (& [[Carlos Gamma]])
|-
| [[98ed7]] || [[35edo]] ||  ||
|-
| [[99ed7]] ||  || [[56edt]] ||
|}
 
{{Todo|inline=1|explain edonoi|text=Most people do not think 7/1 sounds like an equivalence, so there must be some other reason why people are dividing it — some property ''other than'' equivalence that makes people want to divide it. Please add to this page an explanation of what that reason is.}}
[[Category:Ed7's| ]] <!-- main article -->

Latest revision as of 09:05, 18 February 2026

Equal divisions of the 7th harmonic (ed7) are tunings obtained by dividing the 7th harmonic in a certain number of equal steps.

The seventh harmonic is particularly wide as far as equivalences go. There are (at absolute most) about 3.9 instances of the 7th harmonic in the human hearing range; imagine if that were the case with octaves. If one does indeed deal with equivalence of the 7th harmonic, this fact shapes one's musical approach dramatically.

Incidentally, one way to treat 7/1 as an equivalence is to eliminate the primes 2, 3, and 5 and use the 7:11:13 chord as the fundamental complete sonority in a very similar way to the 4:5:6 chord in meantone. Whereas in meantone it takes four 3/2 to get to 5/4, here it takes seven 13/7's to get to 11/7 (tempering out the comma 63412811/62748517 in the 7.11.13 subgroup). This temperament yields 10-, 13-, 16-, 19-, 22-, 25-, and 47-note mos scales. If 7/1 is too wide to be used as an equivalence, the next best option would be equal divisions of 11/7.

Individual pages for ed7's

0…99
0 1 2 3 4 5 6 7 8 9
10 11 12 13 14 15 16 17 18 19
20 21 22 23 24 25 26 27 28 29
30 31 32 33 34 35 36 37 38 39
40 41 42 43 44 45 46 47 48 49
50 51 52 53 54 55 56 57 58 59
60 61 62 63 64 65 66 67 68 69
70 71 72 73 74 75 76 77 78 79
80 81 82 83 84 85 86 87 88 89
90 91 92 93 94 95 96 97 98 99
100…199
100 101 102 103 104 105 106 107 108 109
110 111 112 113 114 115 116 117 118 119
120 121 122 123 124 125 126 127 128 129
130 131 132 133 134 135 136 137 138 139
140 141 142 143 144 145 146 147 148 149
150 151 152 153 154 155 156 157 158 159
160 161 162 163 164 165 166 167 168 169
170 171 172 173 174 175 176 177 178 179
180 181 182 183 184 185 186 187 188 189
190 191 192 193 194 195 196 197 198 199
200 and above

Table of similar equal tunings

ED7 Similar EDO Similar EDT Similar EDF
7ed7 4edt
9ed7 5edt
11ed7 4edo
14ed7 5edo
16ed7 9edt
17ed7 6edo
18ed7 10edt
21ed7 12edt
23ed7 13edt
25ed7 9edo
28ed7 10edo
30ed7 17edt
31ed7 11edo
32ed7 18edt
34ed7 12edo
37ed7 21edt
39ed7 14edo
41ed7 23edt
42ed7 15edo
44ed7 25edt
45ed7 16edo
46ed7 26edt
48ed7 17edo
53ed7 30edt
55ed7 31edt
56ed7 20edo
57ed7 32edt
59ed7 21edo
60ed7 34edt
62ed7 22edo
64ed7 36edt
67ed7 38edt
69ed7 39edt
70ed7 25edo
71ed7 40edt
73ed7 26edo
76ed7 27edo
78ed7 44edt
80ed7 45edt
83ed7 47edt
84ed7 30edo
85ed7 48edt
87ed7 31edo
90ed7 32edo
92ed7 52edt
94ed7 53edt
96ed7 20edf (& Carlos Gamma)
98ed7 35edo
99ed7 56edt
Todo: explain edonoi

Most people do not think 7/1 sounds like an equivalence, so there must be some other reason why people are dividing it — some property other than equivalence that makes people want to divide it. Please add to this page an explanation of what that reason is.

Retrieved from "https://en.xen.wiki/index.php?title=Ed7&oldid=224221"