Ed7
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 | 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 | 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. |