Ed5

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

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:

Individual pages for ED5s


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.

See also