# Ed5

**Ed5** means **Division of the Fifth Harmonic (5/1) into n equal parts**.

## Contents

# Division of the fifth harmonic into n equal parts

The fifth harmonic is particularly wide as far as equivalences go. There are (at absolute most) ~4.8 pentaves within the human hearing range; imagine if that were the case with octaves. If one does indeed deal with pentave equivalence, this fact shapes one's musical approach dramatically. Following this, the quintessential example of a pentave based tuning is hyperpyth (see 17ed5). However, perhaps the more common reason to use these scales is in approximation with lower harmonic factors than 5. This approach is highlighted by Hieronymus (20ed5) which itself is a zeta peak tuning (not "no-fives", full on zeta). Other reasons for taking the nth root of 5 include finding temperaments like orwell, meantone, and thuja. This approach can of course be used indiscriminately.

Below is a large list of ED5s; additionally, some equal divisions of the pentave are known by alternate names or have special interest:

- 3ed5 orwell generator (with octaves)
- 4ed5 meantone generator (with octaves)
- 5ed5 thuja generator (with octaves)
- 6ed5 uncle generator (with octaves)
- Hyperpyth tuning (e.g. 17ed5)
- Hieronymus Tuning
- 25ed5 (Stockhausen, McLaren)

# Individual pages for ED5s

- 3ed5
- 4ed5
- 5ed5
- 6ed5
- 7ed5
- 8ed5
- 9ed5
- 10ed5
- 11ed5
- 12ed5
- 13ed5
- 14ed5
- 15ed5
- 16ed5
- 17ed5
- 18ed5
- 19ed5
- 20ed5
- 21ed5
- 22ed5
- 23ed5
- 24ed5
- 25ed5
- 26ed5
- 27ed5
- 28ed5
- 29ed5
- 30ed5
- 31ed5
- 32ed5
- 33ed5
- 34ed5
- 35ed5
- 36ed5
- 37ed5
- 38ed5
- 39ed5
- 40ed5
- 41ed5
- 42ed5
- 43ed5
- 44ed5
- 45ed5
- 46ed5
- 47ed5
- 48ed5
- 49ed5
- 50ed5
- 51ed5
- 52ed5
- 53ed5
- 54ed5
- 55ed5
- 56ed5
- 57ed5
- 58ed5
- 59ed5
- 60ed5
- 61ed5
- 62ed5
- 63ed5
- 64ed5
- 65ed5
- 66ed5
- 67ed5
- 68ed5
- 69ed5
- 70ed5
- 71ed5
- 72ed5
- 73ed5
- 74ed5
- 75ed5
- 76ed5
- 77ed5
- 78ed5
- 79ed5
- 80ed5
- 81ed5
- 82ed5
- 83ed5
- 84ed5
- 85ed5
- 86ed5
- 87ed5
- 88ed5
- 89ed5
- 90ed5
- 91ed5
- 92ed5
- 93ed5
- 94ed5
- 95ed5
- 96ed5
- 97ed5
- 98ed5
- 99ed5
- 100ed5
- 101ed5

- 102ed5
- 103ed5
- 104ed5
- 105ed5
- 106ed5
- 107ed5
- 108ed5
- 109ed5
- 110ed5
- 111ed5
- 112ed5
- 113ed5
- 114ed5
- 115ed5
- 116ed5
- 117ed5
- 118ed5
- 119ed5
- 120ed5
- 121ed5
- 122ed5
- 123ed5
- 124ed5
- 125ed5
- 126ed5
- 127ed5
- 128ed5
- 129ed5
- 130ed5
- 131ed5
- 132ed5
- 133ed5
- 134ed5
- 135ed5
- 136ed5
- 137ed5
- 138ed5
- 139ed5
- 140ed5
- 141ed5
- 142ed5
- 143ed5
- 144ed5
- 145ed5
- 146ed5
- 147ed5
- 148ed5
- 149ed5
- 150ed5
- 151ed5
- 152ed5
- 153ed5
- 154ed5
- 155ed5
- 156ed5
- 157ed5
- 158ed5
- 159ed5
- 160ed5
- 161ed5
- 162ed5
- 163ed5
- 164ed5
- 165ed5
- 166ed5
- 167ed5
- 168ed5
- 169ed5
- 170ed5
- 171ed5
- 172ed5
- 173ed5
- 174ed5
- 175ed5
- 176ed5
- 177ed5
- 178ed5
- 179ed5
- 180ed5
- 181ed5
- 182ed5
- 183ed5
- 184ed5
- 185ed5
- 186ed5
- 187ed5
- 188ed5
- 189ed5
- 190ed5
- 191ed5
- 192ed5
- 193ed5
- 194ed5
- 195ed5
- 196ed5
- 197ed5
- 198ed5
- 199ed5
- 200ed5

- 201ed5
- 202ed5
- 203ed5
- 204ed5
- 205ed5
- 206ed5
- 207ed5
- 208ed5
- 209ed5
- 210ed5
- 211ed5
- 212ed5
- 213ed5
- 214ed5
- 215ed5
- 216ed5
- 217ed5
- 218ed5
- 219ed5
- 220ed5
- 221ed5
- 222ed5
- 223ed5
- 224ed5
- 225ed5
- 226ed5
- 227ed5
- 228ed5
- 229ed5
- 230ed5
- 231ed5
- 232ed5
- 233ed5
- 234ed5
- 235ed5
- 236ed5
- 237ed5
- 238ed5
- 239ed5
- 240ed5
- 241ed5
- 242ed5
- 243ed5
- 244ed5
- 245ed5
- 246ed5
- 247ed5
- 248ed5
- 249ed5
- 250ed5
- 251ed5
- 252ed5
- 253ed5
- 254ed5
- 255ed5
- 256ed5
- 257ed5
- 258ed5
- 259ed5
- 260ed5
- 261ed5
- 262ed5
- 263ed5
- 264ed5
- 265ed5
- 266ed5
- 267ed5
- 268ed5
- 269ed5
- 270ed5
- 271ed5
- 272ed5
- 273ed5
- 274ed5
- 275ed5
- 276ed5
- 277ed5
- 278ed5
- 279ed5
- 280ed5
- 281ed5
- 282ed5
- 283ed5
- 284ed5
- 285ed5
- 286ed5
- 287ed5
- 288ed5
- 289ed5
- 290ed5
- 291ed5
- 292ed5
- 293ed5
- 294ed5
- 295ed5
- 296ed5
- 297ed5
- 298ed5
- 299ed5

# ED5-EDO correspondence

ED5 | EDO | Comments |
---|---|---|

7ed5 | 3edo | 7ed5 is 3edo with ~5.9 cent compressed octaves. Equivalently, 3edo is 7ed5 with pentaves stretched by ~13.7 cents. Patent vals match through the 67-limit. |

8ed5 | Mohajira generator without octaves | |

9ed5 | 4edo | Very rough correspondence, but patent vals agree through the 7-limit. |

10ed5 | Every tenth note of 43edo, getting ~.44 cent flatter as it ascends the scale | |

11ed5 | Every fourth note of 19edo, getting ~.67 cent sharper as it ascends the scale | |

12ed5 | 5edo | Very rough correspondence, but patent 2s also agree |

13ed5 | Every fifth note of 28edo, getting ~.05 cent sharper as it ascends the scale | |

14ed5 | 6edo | Same 5.9 cent octave compression as 7ed5~3edo. Patent vals agree through the 17-limit. |

15ed5 | Every other note of 13edo, getting ~1.1 cents sharper as it ascends the scale | |

16ed5 | 7edo | Only rough correspondence. Patent vals differ in the 7-limit. |

17ed5 | This Hyperpyth tuning is every third note of 22edo, getting ~.26 cent sharper as it ascends the scale | |

18ed5 | Every fourth note of 31edo, getting ~.04 cent flatter as it ascends the scale | |

19ed5 | 8edo | Very rough correspondence, but patent vals agree through the 5-limit. |

20ed5 | Hieronymus Tuning is every fifth note of 43edo, getting ~.22 cent flatter as it ascends the scale | |

21ed5 | 9edo | Same 5.9 cent octave compression as 7ed5~3edo. Patent vals agree through the 59-limit. |

22ed5 | Every other note of 19edo, getting ~.335 cent sharper as it ascends the scale | |

23ed5 | 10edo | 23ed5 is 10edo with ~11 cent stretched octaves. Patent vals match through the 23-limit, with the exception of 11 and 17. |

24ed5 | Every third note of 31edo, getting ~.03 cent flatter as it ascends the scale | |

25ed5 | Every fourth note of 43edo, getting ~.18 cent flatter as it ascends the scale | |

26ed5 | 11edo | Very rough correspondence, but patent vals agree through the 7-limit with the exception of 3 (which neither represents well). |

27ed5 | Every third note of 35edo, getting ~.03 cent sharper as it ascends the scale | |

28ed5 | 12edo | Same 5.9 cent octave compression as 7ed5~3edo. Patent vals match through the 19-limit, with the exception of 13 (as expected). |

29ed5 | Every other note of 25edo, getting ~.08 cent sharper as it ascends the scale | |

30ed5 | 13edo | 30ed5 is 13edo with ~7.4 cent stretched octaves. Patent vals match through the 19-limit, with the exception of 3 (which neither represents well). |

31ed5 | Every third note of 40edo, getting ~.12 cent flatter as it ascends the scale | |

32ed5 | Every fourth note of 55edo, getting ~.2 cent flatter as it ascends the scale | |

33ed5 | Every fifth note of 71edo, getting ~.07 cent flatter as it ascends the scale | |

34ed5 | Every third note of 44edo, getting ~.13 cent sharper as it ascends the scale | |

35ed5 | 15edo | Same 5.9 cent octave compression as 7ed5~3edo. Patent vals agree through the 13-limit. |

36ed5 | Every other note of 31edo, getting ~.02 cent flatter as it ascends the scale | |

37ed5 | 16edo | 37ed5 is 16edo with ~4.9 cent stretched octaves. Patent vals match through the 23-limit. |

38ed5 | Every third note of 49edo, getting ~.145 cent flatter as it ascends the scale | |

39ed5 | Every fifth note of 84edo, getting ~.015 cent sharper as it ascends the scale | |

40ed5 | Every fourth note of 69edo, getting ~.09 cent sharper as it ascends the scale | |

41ed5 | Every third note of 53edo, getting ~.03 cent flatter as it ascends the scale | |

42ed5 | 18edo | Same 5.9 cent octave compression as 7ed5~3edo. Patent vals match through the 17-limit, with the exception of 11. |

43ed5 | Every other note of 37edo, getting ~.07 cent flatter as it ascends the scale | |

44ed5 | 19edo | 44ed5 is 19edo with ~3.2 cent stretched octaves. Patent vals match through the 13-limit. |

45ed5 | Every fifth note of 97edo, getting ~.09 cent sharper as it ascends the scale | |

46ed5 | 20edo | Same ~11 cent octave stretch as 23ed5~10edo. Patent vals match through the 23-limit, with the exception of 13 and 17. |

47ed5 | Every fourth note of 81edo, getting ~.02 cent sharper as it ascends the scale | |

48ed5 | Every third note of 62edo, getting ~.02 cent flatter as it ascends the scale | |

49ed5 | 21edo | Same 5.9 cent octave compression as 7ed5~3edo. Patent vals agree through the 17-limit. |

50ed5 | Every other note of 43edo, getting ~.09 cent flatter as it ascends the scale | |

51ed5 | 22edo | 51ed5 is 22edo with ~1.9 cent stretched octaves. Patent vals match through the 19-limit. |

52ed5 | Every fifth note of 112edo, getting ~.01 cent sharper as it ascends the scale | |

53ed5 | 23edo | 58ed5 is 23edo with ~9.1 cent stretched octaves. Patent vals match through the 5-limit. |

54ed5 | Every fourth note of 93edo, getting ~.015 cent flatter as it ascends the scale | |

55ed5 | Every third note of 71edo, getting ~.04 cent flatter as it ascends the scale | |

56ed5 | 24edo | This is a rough correspondence, as the (7n)ed5 ~ (3n)edo sequence begins to break down. Patent vals match through the 13-limit, with the exception of 7. |

57ed5 | Every other note of 49edo, getting ~.1 cent flatter as it ascends the scale | |

58ed5 | 25edo | 58ed5 is 25edo with ~1.0 cent stretched octaves. Patent vals match through the 73-limit, with the exception of 13. |

59ed5 | Every other note of 51edo, getting ~.17 cent sharper as it ascends the scale | |

60ed5 | 26edo | Same ~7.4 cent octave stretch as 30ed5~13edo. Patent vals match through the 29-limit. |

61ed5 | Every fourth note of 105edo, getting ~.04 cent flatter as it ascends the scale | |

62ed5 | Every third note of 80edo, getting ~.06 cent flatter as it ascends the scale | |

63ed5 | 27edo | This is a rough correspondence, as the (7n)ed5 ~ (3n)edo sequence is momentarily fixed. Patent vals match through the 13-limit. |

64ed5 | Every other note of 55edo, getting ~.1 cent flatter as it ascends the scale | |

65ed5 | 28edo | 65ed5 is 28edo with ~0.26 cent stretched octaves. Patent vals match through the 43-limit. |

66ed5 | Every fifth note of 142edo, getting ~.04 cent flatter as it ascends the scale | |

67ed5 | Every fifth note of 144edo, getting ~.08 cent flatter as it ascends the scale | |

68ed5 | Every third note of 88edo, getting ~.07 cent sharper as it ascends the scale | |

69ed5 | Same ~11 cent octave stretch as 23ed5~10edo. Matches Mavila tuned in 30edo. | |

70ed5 | 30edo | This is a rough correspondence, as the (7n)ed5 ~ (3n)edo sequence begins to break down again. Patent vals match through the 11-limit, with the exception of 7. |

71ed5 | Every other note of 61edo, getting ~.1 cent flatter as it ascends the scale | |

72ed5 | 31edo | 72ed5 is 31edo with ~0.34 cent compressed octaves. Patent vals match through the 31-limit. |

73ed5 | Every other note of 63edo, getting ~.07 cent sharper as it ascends the scale | |

74ed5 | 32edo | Same ~4.9 cent octave stretch as 37ed5~16edo. Patent vals match through the 13-limit with the exception of 7 and 11. |

75ed5 | Every third note of 97edo, getting ~.04 cent sharper as it ascends the scale | |

76ed5 | Every third note of 98edo, getting ~.07 cent flatter as it ascends the scale | |

77ed5 | 33edo | This is a rough correspondence, as the (7n)ed5 ~ (3n)edo sequence continues to break down. Patent vals match through the 7-limit. |

78ed5 | Every other note of 67edo, getting ~.1 cent flatter as it ascends the scale | |

79ed5 | 34edo | 79ed5 is 34edo with ~0.83 cent compressed octaves. Patent vals match through the 17-limit, with the exception of 7 (which neither represents well). |

80ed5 | Every other note of 69edo, getting ~.05 cent sharper as it ascends the scale | |

81ed5 | 35edo | 81ed5 is 35edo with ~4.0 cent stretched octaves. Patent vals match through the 11-limit. |

82ed5 | Every third note of 106edo, getting ~.02 cent sharper as it ascends the scale | |

83ed5 | Every fourth note of 143edo, getting ~.04 cent sharper as it ascends the scale | |

84ed5 | 36edo | This is a rough correspondence, as the (7n)ed5 ~ (3n)edo sequence is momentarily fixed again. Patent vals match through the 11-limit, with the exception of 7. |

85ed5 | Every other note of 73edo, getting ~.1 cent flatter as it ascends the scale | |

86ed5 | 37edo | 86ed5 is 37edo with ~1.2 cent compressed octaves. Patent vals match through the 19-limit. |

87ed5 | Every other note of 75edo, getting ~.03 cent sharper as it ascends the scale | |

88ed5 | 38edo | Same 3.2 cent octave stretch as 44ed5~19edo. Patent vals differ in the 7-limit. |

89ed5 | Every third note of 115edo, getting ~.0025 cent sharper as it ascends the scale | |

90ed5 | Same ~7.4 cent octave stretch as 30ed5~13edo, but really matches the tuning with generator 4\155 of an octave. | |

91ed5 | 39edo | This is a rough correspondence, as the (7n)ed5 ~ (3n)edo sequence begins to break down again. Patent vals match through the 7-limit. |

92ed5 | Every fifth note of 198edo, getting ~.02 cent flatter as it ascends the scale | |

93ed5 | 40edo | 93ed5 is 40edo with ~1.6 cent compressed octaves. Patent vals match through the 7-limit. |

94ed5 | Every other note of 81edo, getting ~.01 cent sharper as it ascends the scale | |

95ed5 | 41edo | 95ed5 is 41edo with ~2.5 cent stretched octaves. Patent vals match through the 11-limit. |

96ed5 | Every third note of 124edo, getting ~.01 cent flatter as it ascends the scale | |

97ed5 | Every fourth note of 167edo, getting ~.02 cent flatter as it ascends the scale | |

98ed5 | 42edo | This is a rough correspondence, as the (7n)ed5 ~ (3n)edo sequence momentarily stops breaking down further. |

99ed5 | Every third note of 128edo, getting ~.02 cent sharper as it ascends the scale | |

100ed5 | 43edo | 100ed5 is 43edo with ~1.9 cent compressed octaves. Patent vals match through the 37-limit. |

101ed5 | Every other note of 87edo, getting ~.001 cent sharper as it ascends the scale | |

102ed5 | 44edo | Same 1.9 cent octave stretch as 51ed5~22edo. Patent vals match through the 23-limit, with the exception of 7. |

103ed5 | Every other note of 89edo, getting ~.009 cent sharper as it ascends the scale | |

104ed5 | 45edo | 104ed5 is 45edo with ~5.6 cent stretched octaves. Patent vals match through the 7-limit. |

105ed5 | This is a rough correspondence, as the (7n)ed5 ~ (3n)edo sequence begins to break down again. Patent vals match through the 5-limit, with the exception of 3. | |

106ed5 | Every third note of 137edo, getting ~.009 cent sharper as it ascends the scale | |

107ed5 | 46edo | 107ed5 is 46edo with ~2.1 cent compressed octaves. Patent vals match through the 11-limit. |

108ed5 | Every other note of 93edo, getting ~.007 cent flatter as it ascends the scale | |

109ed5 | 47edo | 109ed5 is 47edo with ~1.4 cent stretched octaves. Patent vals match through the 17-limit, with the exception of 11. |

110ed5 | Every other note of 95edo, getting ~.67 cent sharper as it ascends the scale | |

111ed5 | 48edo | Same ~4.9 cent octave stretch as 37ed5~16edo. Patent vals match through the 5-limit. |

112ed5 | This is a rough correspondence, as the (7n)ed5 ~ (3n)edo sequence is momentarily fixed again. Patent vals match through the 7-limit, with the exception of 5. | |

113ed5 | Every third note of 146edo, getting ~.0001 cent sharper as it ascends the scale | |

114ed5 | 49edo | 114ed5 is 49edo with ~2.4 cent compressed octaves. Patent vals match through the 11-limit. |

115ed5 | Every other note of 99edo, getting ~.001 cent flatter as it ascends the scale | |

116ed5 | 50edo | Same 1.0 cent octave stretch as 58ed5~25edo. Patent vals agree through the 43-limit. |

117ed5 | Every other note of 101edo, getting ~.05 cent sharper as it ascends the scale | |

118ed5 | 51edo | 118ed5 is 51edo with ~4.25 cent stretched octaves. Patent vals match through the 17-limit with the exception of 13. |

119ed5 | This is a rough correspondence, as the (7n)ed5 ~ (3n)edo sequence has finally broken down more or less altogether. Patent vals match through the 3-limit. | |

120ed5 | Same 7.4 cent octave stretch as 30ed5~13edo, but really matches the tuning with generator 3\155 of an octave. | |

121ed5 | 52edo | 121ed5 is 52edo with ~2.6 cent compressed octaves, but the correspondence is rough. Patent vals match through the 11-limit, with the exception of 3 (which neither represents well). |

122ed5 | Every other note of 105edo, getting ~.002 cent flatter as it ascends the scale | |

123ed5 | 53edo | 123ed5 is 53edo with ~0.61 cent stretched octaves. Patent vals match through the 29-limit. |

124ed5 | Every other note of 107edo, getting ~.04 cent sharper as it ascends the scale | |

125ed5 | 54edo | 125ed5 is 54edo with ~3.7 cent stretched octaves, but the correspondence is rough. Patent vals match through the 5-limit, with the exception of 3 (which neither represents well). |

126ed5 | Same rough correspondence as 119ed5~51edo | |

127ed5 | Every third note of 164edo, getting ~.01 cent flatter as it ascends the scale | |

128ed5 | 55edo | 128ed5 is 55edo with ~2.8 cent compressed octaves, but the correspondence is rough. Patent vals differ in the 7-limit. |

129ed5 | Every other note of 111edo, getting ~.02 cent flatter as it ascends the scale | |

130ed5 | 56edo | Same 0.26 cent octave stretch as 65ed5~28edo. Patent vals agree through the 103-limit. |

131ed5 | Every other note of 113edo, getting ~.03 cent sharper as it ascends the scale | |

132ed5 | 57edo | Same 3.2 cent octave stretch as 44ed5~19edo. Patent vals differ in the 11-limit. |

133ed5 | This is a rough correspondence, as the (7n)ed5 ~ (3n)edo sequence has finally broken down more or less altogether. Patent vals match through the 2-limit. | |

134ed5 | Every third note of 173edo, getting ~.02 cent flatter as it ascends the scale | |

135ed5 | 58edo | 135ed5 is 58edo with ~2.9 cent compressed octaves. Patent vals match through the 13-limit. |

136ed5 | Every other note of 117edo, getting ~.025 cent flatter as it ascends the scale | |

137ed5 | 59edo | 137ed5 is 59edo with ~0.05 cent compressed octaves. Patent vals match through the 179-limit. |

138ed5 | Every other note of 119edo, getting ~.02 cent sharper as it ascends the scale | |

139ed5 | 60edo | 139ed5 is 60edo with ~2.7 cent stretched octaves. Pantent vals match through the 31-limit with the exception of 11. |

140ed5 | Same rough correspondence as 133ed5~57edo | |

141ed5 | Every third note of 182edo, getting ~.02 cent flatter as it ascends the scale | |

142ed5 | 61edo | 142ed5 is 61edo with ~3.1 cent compressd octaves. Patent vals match through the 13-limit, with the exception of 7 and 11. |

143ed5 | Every other note of 123edo, getting ~.03 cent flatter as it ascends the scale | |

144ed5 | 62edo | Same 0.34 cent octave compression as 72ed5~31edo. Patent vals match through the 19-limit, with the exception of 11. |

145ed5 | Every other note of 125edo, getting ~.02 cent sharper as it ascends the scale | |

146ed5 | 63edo | 146ed5 is 63edo with ~2.3 cent stretched octaves. Patent vals match through the 13-limit. |

147ed5 | Same rough correspondence as 133ed5~57edo | |

148ed5 | Same ~4.9 cent octave stretch as 37ed5~16edo, but really matches the tuning with generator 4\255 of an octave. | |

149ed5 | 64edo | 149ed5 is 64edo with ~3.2 cent compressed octaves. Patent vals match through the 7-limit, with the exception of 3 |

150ed5 | Every other note of 129edo, getting ~.02 cent sharper as it ascends the scale | |

151ed5 | 65edo | 151ed5 is 65edo with ~0.59 cent compressed octaves. Patent vals match through the 53-limit, with the exception of 7 (as expected). |

152ed5 | Every other note of 131edo, getting ~.001 cent sharper as it ascends the scale | |

153ed5 | 66edo | Same 1.9 cent octave stretch as 51ed5~22edo. Patent vals match through the 13-limit, with the exception of 3. |

154ed5 | Same rough correspondence as 133ed5~57edo | |

155ed5 | Every fourth note of 267edo, getting ~.001 cent flatter as it ascends the scale | |

156ed5 | 67edo | 156ed5 is 67edo with ~3.3 cent compressed octaves. Patent vals match through the 11-limit, with the exception of 7 |

157ed5 | Every other note of 135edo, getting ~.03 cent flatter as it ascends the scale | |

158ed5 | 68edo | Same 0.83 cent octave compression as 79ed5~34edo. Patent vals agree through the 23-limit. |

159ed5 | Every other note of 137edo, getting ~.006 cent sharper as it ascends the scale | |

160ed5 | 69edo | 160ed5 is 69edo with ~1.6 cent stretched octaves. Patent vals differ in the 7-limit. |

161ed5 | Same 11 cent octave stretch as 23ed5~10edo, but really matches the tuning with generator 3\208 of an octave. | |

162ed5 | Every third note of 209edo, getting ~.025 cent flatter as it ascends the scale | |

163ed5 | 70edo | 163ed5 is 70edo with ~3.4 cent compressed octaves. Patent vals match through the 7-limit. |

164ed5 | Every other note of 141edo, getting ~.03 cent flatter as it ascends the scale | |

165ed5 | 71edo | 165ed5 is 71edo with ~1.0 cent compressed octaves. Patent vals match through the 37-limit. |

166ed5 | Every other note of 143edo, getting ~.02 cent sharper as it ascends the scale | |

167ed5 | 72edo | 167ed5 is 72edo with ~1.3 cent stretched octaves. Patent vals agree through the 19-limit. |

168ed5 | Same rough correspondence as 133ed5~57edo | |

169ed5 | Every third note of 218edo, getting ~.03 cent flatter as it ascends the scale | |

170ed5 | 73edo | 170ed5 is 73edo with ~3.5 cent compressed octaves, but the correspondence is rough. Patent vals match through the 7-limit. |

171ed5 | Every other note of 147edo, getting ~.03 cent flatter as it ascends the scale | |

172ed5 | 74edo | Same 1.2 cent octave compression as 86ed5~37edo. Patent vals agree through the 13-limit. |

173ed5 | Every other note of 149edo, getting ~.0015 cent flatter as it ascends the scale | |

174ed5 | 75edo | Same 1.0 cent octave stretch as 58ed5~25edo. Patent vals differ in the 7-limit. |

175ed5 | Every other note of 151edo, getting ~.03 cent flatter as it ascends the scale | |

176ed5 | 76edo | Same 3.2 cent octave stretch as 44ed5~19edo. Patent vals differ in the 11-limit. |

177ed5 | Every fourth note of 305edo, getting ~.004 cent sharper as it ascends the scale | |

178ed5 | Every third note of 230edo, getting ~.001 cent sharper as it ascends the scale | |

179ed5 | 77edo | 179ed5 is 77edo with ~1.4 cent compressed octaves. Patent vals match through the 19-limit, with the exception of 11. |

180ed5 | Same 7.4 cent octave stretch as 30ed5~13edo, but really matches the tuning with generator 2\155 of an octave. | |

181ed5 | 78edo | 181ed5 is 78edo with ~0.73 cent stretched octaves. Patent vals match through the 59-limit, with the exception of 13. |

182ed5 | Same 5.9 cent octave compression as 91ed5~39edo, but really matches the tuning with generator 5\392 of an octave. | |

183ed5 | 79edo | 183ed5 is 79edo with ~2.8 cent compressed octaves. Patent vals match through the 11-limit, with the exception of 7 |

184ed5 | Same 11 cent octave stretch as 23ed5~10edo, but really matches the tuning with generator 4\317 of an octave. | |

185ed5 | Same 4.9 cent octave stretch as 37ed5~16edo, but really matches the tuning with generator 3\239 of an octave. | |

186ed5 | 80edo | Same 1.6 cent octave compression as 93ed5~40edo. Patent vals agree through the 29-limit. |

187ed5 | Every other note of 161edo, getting ~.007 cent flatter as it ascends the scale | |

188ed5 | 81edo | 188ed5 is 81edo with ~0.49 cent stretched octaves. Patent vals match through the 41-limit. |

189ed5 | Every other note of 163edo, getting ~.002 cent sharper as it ascends the scale | |

190ed5 | 82edo | Same 2.5 cent octave stretch as 95ed5~41edo. Patent vals match through the 11-limit, with the exception of 13 and 17 |

191ed5 | Every fourth note of 329edo, getting ~.002 cent flatter as it ascends the scale | |

192ed5 | Every third note of 248edo, getting ~.01 cent flatter as it ascends the scale | |

193ed5 | 83edo | 193ed5 is 83edo with ~1.7 cent compressed octaves. Patent vals match through the 7-limit. |

194ed5 | Every other note of 167edo, getting ~.009 cent flatter as it ascends the scale | |

195ed5 | 84edo | Same 0.26 cent octave stretch as 65ed5~28edo. Patent vals agree through the 31-limit. |

196ed5 | Every other note of 169edo, getting ~.015 cent sharper as it ascends the scale | |

197ed5 | 85edo | 197ed5 is 85edo with ~2.2 cent stretched octaves.Patent vals match alternate primes through the 17-limit. |

198ed5 | Every fourth note of 341edo, getting ~.004 cent flatter as it ascends the scale | |

199ed5 | Every third note of 257edo, getting ~.007 cent flatter as it ascends the scale | |

200ed5 | 86edo | Same 1.9 cent octeave compression as 100ed5~43edo. Patent vals match alternate primes through the 17-limit. |

201ed5 | Every other note of 173edo, getting ~.001 cent flatter as it ascends the scale | |

202ed5 | 87edo | 202ed5 is 87edo with ~0.05 cent stretched octaves. Patent vals match through the 71-limit. |

203ed5 | Every other note of 175edo, getting ~.002 cent sharper as it ascends the scale | |

204ed5 | 88edo | Same 1.9 cent octave stretch as 51ed5~22edo. Patent vals match through the 7-limit. |

205ed5 | Every fourth note of 353edo, getting ~.006 cent flatter as it ascends the scale | |

206ed5 | Every third note of 266edo, getting ~.008 cent flatter as it ascends the scale | |

207ed5 | 89edo | 207ed5 is 89edo with ~2 cent compressed octaves. Patent vals match through the 23, with the exception of 13 and19. |

208ed5 | Every other note of 179edo, getting ~.01 cent flatter as it ascends the scale | |

209ed5 | 90edo | 209ed5 is 90edo with ~0.15 cent compressed octaves. Patent vals match through the 53-limit. |

210ed5 | Every other note of 181edo, getting ~.0085 cent sharper as it ascends the scale | |

211ed5 | 91edo | 211ed5 is 91edo with ~1.7 cent stretched octaves. Patent vals match through the 7-limit. |

212ed5 | Every third note of 274edo, getting ~.004 cent sharper as it ascends the scale | |

213ed5 | Every fourth note of 367edo, getting ~.002 cent sharper as it ascends the scale | |

214ed5 | 92edo | Same 2.1 cent octave compression as 107ed5~46edo, but the correspondence is rough. Patent vals match through the 5-limit. |

215ed5 | Every other note of 185edo, getting ~.13 cent flatter as it ascends the scale | |

216ed5 | 93edo | Same 0.34 cent octave compression as 72ed5~31edo. Patent vals agree through the 31-limit. |

217ed5 | Every other note of 187edo, getting ~.006 cent sharper as it ascends the scale | |

218ed5 | 94edo | Same 1.4 cent octave stretch as 109ed5~47edo. Patent vals match through the 23-limit, with the exception of 13. |

219ed5 | Every third note of 286edo, getting ~.135 cent sharper as it ascends the scale | |

220ed5 | Same 3.2 cent octave stretch as 44ed5~19edo, but really matches the tuning with generator 3\379 of an octave.. | |

221ed5 | 95edo | 221ed5 is 95edo with ~2.3 cent compressed octaves. Patent vals match through the 29-limit with the exception of 13 and 23 |

222edo | Every other note of 191edo, getting ~.01 cent flatter as it ascends the scale | |

223ed5 | 96edo | 223ed5 is 96edo with ~0.51 cent compressed octaves. Patent vals match through the 13-limit. |

224ed5 | Every other note of 193edo, getting ~.004 cent sharper as it ascends the scale | |

225ed5 | 97edo | 225ed5 is 97edo with ~1.2 cent stretched octaves. Patent vals match through the 19-limit, with the exception of 11. |

226edo | Every third note of 292edo, getting ~.000055 cent sharper as it ascends the scale | |

227ed5 | Every fourth note of 391edo, getting ~.002 cent flatter as it ascends the scale | |

228ed5 | 98edo | Same 2.4 octave compression as 114ed5~49edo, but the correspondence is rough. Patent vals match through the 5-limit with the exception of 3. |

229ed5 | Every other note of 197edo, getting ~.015 cent flatter as it ascends the scale | |

230ed5 | 99edo | 230ed5 is 99edo with ~0.67 cent compressed octaves. Patent vals match through the 7-limit. |

231ed5 | Every other note of 199edo, getting ~.002 cent sharper as it ascends the scale | |

232ed5 | 100edo | Same 1.0 cent octave stretch as 58ed5~25edo. Patent vals match through the 13-limit. |

233ed5 | Every third note of 301edo, getting ~.0002 cent flatter as it ascends the scale | |

234edo | Every fourth note of 403edo, getting ~.003 cent flatter as it ascends the scale | |

235ed5 | 101edo | 235ed5 is 101edo with ~2.5 cent compressed octaves. Patent vals match through the 19-limit, with the exception of 13 and 17. |

236ed5 | Same 4.25 cent octave compression as 118ed5~51edo, but really matches the tuning with generator 2\203 of an octave | |

237ed5 | 102edo | Same 0.83 cent octave compression as 79ed5~34edo. Patent vals differ in the 7-limit. |

238ed5 | Every other note of 205edo, getting ~.0001 cent flatter as it ascends the scale | |

239ed5 | 103edo | 239ed5 is 103edo with ~0.80 cent stretched octaves. Patent vals match through the 17-limit. |

240ed5 | Every other note of 207edo, getting ~.015 cent sharper as it ascends the scale | |

241ed5 | 104edo | 241ed5 is 104edo with ~2.4 cent stretched octaves. Patent vals match through the 17-limit, with the exception of 7 through 13 |

242ed5 | Same 2.6 cent octave compression as 121ed5~52edo, but really matches the tuning with generator 4\417 of an octave | |

243ed5 | Every third note of 314edo, getting ~.001 cent sharper as it ascends the scale | |

244ed5 | 105edo | 244ed5 is 105edo with ~0.97 cent compressed octaves. Patent vals disagree in the 5-limit and higher prime limit. |

245ed6 | Every other note of 211edo, getting ~.002 cent flatter as it ascends the scale | |

246ed5 | 106edo | Same 0.61 cent octave stretch as 123ed5~53edo. Patent vals match through the 43-limit, with the exception of 7. |

247ed5 | Every other note of 213edo, getting ~.01 cent sharper as it ascends the scale | |

248ed5 | 107edo | 248ed5 is 107edo with ~2.2 cent stretched octaves. Patent vals match through the 17-limit with the exception of 11 and 13. |

249ed5 | Every fourth note of 429edo, getting ~.001 cent sharper as it ascends the scale | |

250ed5 | Same 3.7 cent octave stretch as 125ed5~54edo, but really matches the tuning with generator 3/323 of an octave | |

251ed5 | 108edo | 251ed5 is 108edo with ~1.1 cent compressed octaves. Patent vals match through the 13-limit. |

252ed5 | Every other note of 217edo, getting ~.003 cent flatter as it ascends the scale | |

253ed5 | 109edo | 253ed5 is 109edo with ~0.43 cent stretched octaves. Patent vals match through the 13-limit. |

254ed5 | Every other note of 219edo, getting ~.01 cent sharper as it ascends the scale | |

255ed5 | 110edo | Same 1.9 cent octave stretch as 51ed5~22edo. Patent vals match through the 5-limit. |

256ed5 | Same 2.8 cent octave compression as 128ed5~55edo, but actually matches the tuning with generator 4/441 of an octave | |

257ed5 | Every third note of 332edo, getting ~.002 cent flatter as it ascends the scale | |

258ed5 | 111edo | Same 1.2 cent octave compression as 86ed5~37edo. Patent vals agree through the 19-limit. |

259ed5 | Every other note of 223edo, getting ~.004 cent flatter as it ascends the scale | |

260ed5 | 112edo | Same 0.26 cent octave stretch as 65ed5~28edo. Patent vals match through the 47-limit, with the exception of 3. |

261ed5 | Every other note of 225edo, getting ~.009 cent sharpter as it ascends the scale | |

262ed5 | 113edo | 262ed5 is 113edo with ~1.7 cent stretched octaves. Patent vals match through the 13-limit with the exception of 11. |

263ed5 | Every fourth note of 453edo, getting ~.002 cent flatter as it ascends the scale | |

264ed5 | Same 3.2 cent octave stretch as 44ed5~19edo, but actually matches the tuning with generator 3/341 of an octave. | |

265ed5 | 114edo | 265edo is 114edo with ~2.2 cent compressed octaves. Patent vals match through the 43-limit, with the exception of 11, 19 and 37. |

266ed5 | Every other note of 229edo, getting ~.0055 cent flatter as it ascends the scale | |

267ed5 | 115edo | 267ed5 is 115edo with ~0.10 cent stretched octaves. Patent vals match through the 17-limit. |

268ed5 | Every other note of 231edo, getting ~.008 cent sharper as it ascends the scale | |

269ed5 | 116edo | 269ed5 is 116edo with ~1.5 cent stretched octaves. Patent vals match through the 17-limit with the exception of 7. |

270ed5 | Same 2.9 cent octave compression as 135ed5~58edo, but really matches the tuning with generator 4/465 of an octave | |

271ed5 | Every third note of 350edo, getting ~.004 cent flatter as it ascends the scale | |

272ed5 | 117edo | 272ed5 is 117edo with ~1.5 cent stretched octaves. Patent vals match through the 11-limit with the exception of 7. |

273ed5 | Every other note of 235edo, getting ~.0065 cent flatter as it ascends the scale | |

274ed5 | 118edo | Same 0.05 cent octave compression as 137ed5~59edo. Patent vals agree through the 103-limit. |

275ed5 | Every other note of 237edo, getting ~.0055 cent sharper as it ascends the scale | |

276ed5 | 119edo | 276ed5 is 119edo with ~1.35 cent stretched octaves. Patent vals agree through the 23-limit with the exception of 13 and 19. |

277ed5 | Every fourth note of 477edo, getting ~.004 cent flatter as it ascends the scale | |

278ed5 | Every third note of 359edo, getting ~.005 cent flatter as it ascends the scale | |

279ed5 | 120edo | 279ed5 is 120edo with ~1.6 cent compressed octaves. Patent vals match through the 19-limit with the exception of 11 through 17. |

280ed5 | Every other note of 241edo, getting ~.007 cent flatter as it ascends the scale | |

281ed5 | 121edo | 281ed5 is 121edo with ~0.20 cent compressed octaves. Patent vals match through the 29-limit. |

282ed5 | Every other note of 243edo, getting ~.004 cent sharper as it ascends the scale | |

283ed5 | 122edo | 283ed5 is 122edo with ~1.2 cent stretched octaves. Patent vals match through the 13-limit. |

284ed5 | Every third note of 367edo, getting ~.002 cent sharper as it ascends the scale | |

285ed5 | Same 2.5 cent octave stretch as 95ed5~41edo, but really matches the tuning with generator 4/491 of an octave. | |

286ed5 | 123edo | 286edo is 123edo with ~1.7 cent compressed octaves. Patent vals match through the 17-limit, with the exception of 7 and 13. |

287ed5 | Every other note of 247edo, getting ~.008 cent flatter as it ascends the scale | |

288ed5 | 124edo | Same 0.34 cent octave compression as 72ed5~31edo. Patent vals agree through the 23-limit. |

289ed5 | Every other note of 249edo, getting ~.003 cent sharper as it ascends the scale | |

290ed5 | 125edo | Same 1 cent octave stretch as 58ed5~25edo. Patent vals match through the 37-limit, with the exception of 13. |

291ed5 | Every third note of 376edo, getting ~.0004 cent sharper as it ascends the scale | |

292ed5 | Same 2.3 cent octave stretch as 146ed5~63edo, but really matches the tuning with generator 4/503 of an octave | |

293ed5 | 126edo | 293ed5 is 126edo with ~2.2 cent compressed octaves. Patent vals match through the 7-limit. |

294ed5 | Every other note of 253edo, getting ~.009 cent flatter as it ascends the scale | |

295ed5 | 127edo | 295ed5 is 127edo with ~0.47 cent compressed octaves. Patent vals match through the 17-limit, with the exception of 11. |

296ed5 | Every other note of 255edo, getting ~.0055 cent sharper as it ascends the scale | |

297ed5 | 128edo | 297ed5 is 128edo with ~0.84 cent stretched octaves. Patent vals match through the 7-limit. |

298ed5 | Same 3.2 cent octave compression as 149ed5~64edo, but really matches the tuning with generator 3/385 of an octave | |

299ed5 | Every fourth note of 515edo, getting ~.002 cent flatter as it ascends the scale | |

300ed5 | 129edo | Same 1.9 cent octeave compression as 100ed5~43edo. Patent vals match alternate primes through the 5-limit. |

301ed5 | Every other note of 259edo, getting ~.01 cent flatter as it ascends the scale | |

302ed5 | 130edo | Same .59 cent octave compression as 151ed5~65edo. Patent vals match through the 41-limit with the exception of 11, 19 and 23. |

303ed5 | Every other note of 261edo, getting ~.002 cent sharper as it ascends the scale | |

304ed5 | 131edo | 304ed5 is 131edo with ~.68 cent stretched octaves. Patent vals match through the 41-limit with the exception of 13 and 23. |

305ed5 | Every other note of 263edo, getting ~.01 cent sharper as it ascends the scale | |

306ed5 | 132edo | Same 1.9 cent octave stretch as 51ed5~22edo. Patent vals match through the 13-limit with the exception of 7 and 11. |

307ed5 | Every fourth note of 529edo, getting ~.002 cent sharper as it ascends the scale | |

308ed5 | Every third note of 398edo, getting ~.001 cent sharper as it ascends the scale | |

309ed5 | 133edo | 309ed5 is 133edo with ~.73 cent compressed octaves. Patent vals match through the 71-limit with the exception of 7 and 59. |

310ed5 | Every other note of 267edo, getting ~.0006 cent flatter as it ascends the scale | |

311ed5 | 134edo | 311ed5 is 134edo with ~.53 cent stretched octaves. Patent vals match through the 59-limit with the exception of 11, 19 and 53 |

312ed5 | Same 3.3 cent octave compression as 156ed5~67edo, but really matches the tuning with generator 2/269 of an octave | |

313ed5 | 135edo | 313ed5 is 135edo with ~1.8 cent stretched octaves. Patent vals match through the 5-limit. |

314ed5 | Every fourth note of 541edo, getting ~.001 cent sharper as it ascends the scale | |

315ed5 | Every third note of 407edo, getting ~.002 cent sharper as it ascends the scale | |

316ed5 | 136edo | Same 0.83 cent octave compression as 79ed5~34edo. Patent vals match through the 41-limit with the exception of 13 and 23. |

317ed5 | Every other note of 273edo, getting ~.002 cent flatter as it ascends the scale | |

318ed5 | 137edo | 318ed5 is 137edo with ~.39 cent stretched octaves. Patent vals match through the 71-limit with the exception of 29. 61 and 71. |

319ed5 | Every other note of 275edo, getting ~.007 cent sharper as it ascends the scale | |

320ed5 | 138edo | Same 1.6 cent octave compression as 160ed5~69edo. Patent vals match through the 5-limit with the exception of t3. |

321ed5 | Same 2.1 cent octave compression as 107ed5~46edo, but really matches the tuning with generator 4\553 of an octave. | |

322ed5 | Every third note of 416edo, getting ~.0007 cent flatter as it ascends the scale | |

323ed5 | 139edo | 323ed5 is 139edo with ~.94 cent compressed compressed octaves. Patent vals match alternating primes through the 11-limit |

324ed5 | Every other note of 279edo, getting ~.002 cent flatter as it ascends the scale | |

325ed5 | 140edo | Same 0.26 cent octave stretch as 65ed5~28edo. Patent vals match through the 73-limit, with the exception of 31 and 67. |

326ed5 | Same ~3.4 cent octave compression 163ed5~70edo, but really matches the tuning with generator 2\281 of an octave. | |

327ed5 | 141edo | Same 1.4 cent octave stretch as 109ed5~47edo. Patent vals match through the 5-limit, with the exception of 3. |

328ed5 | Every fourth note of 565edo, getting ~.0007 cent flatter as it ascends the scale | |

329ed5 | Every third note of 425edo, getting ~.0015 cent flatter as it ascends the scale | |

330ed5 | 142edo | Same ~1 cent octave compression as 165ed5~71edo. Patent vals match through the 13-limit with the exceotion of 11. |

331ed5 | Every other note of 285edo, getting ~.003 cent flatter as it ascends the scale | |

332ed5 | 143edo | 332ed5 is 143edo with ~.13 cent stretched octaves. Patent vals match through the 29-limit with the exception of 7, 17 and19 |

333ed5 | Every other note of 287edo, getting ~.005 cent sharper as it ascends the scale | |

334ed5 | 144edo | Same 1.3 cent octave stretch as 167ed5~72edo. Patent vals match through the 5-limit. |

335ed5 | Every fourth note of 577edo, getting ~.0015 cent flatter as it ascends the scale | |

336ed5 | Every third note of 434edo, getting ~.002 cent flatter as it ascends the scale | |

337ed5 | 145edo | 337edo is 145edo with ~1.1 cent compressed octaves. Patent vals match through the 17-limit with the exception of 7. |

338ed5 | Every other note of 291edo, getting ~.004 cent flatter as it ascends the scale | |

339ed5 | 146edo | 339ed5 is practically identical to 146edo, with a slight octave stretch (~0.0053 cents). Patent vals match through the 827-limit. |