ED5: Difference between revisions
| Line 493: | Line 493: | ||
|[[48ed5]] | |[[48ed5]] | ||
| | | | ||
| | |Every third note of [[62edo]], getting ~.02 cent flatter as it ascends the scale | ||
|- | |- | ||
| | [[49ed5]] | | | [[49ed5]] | ||
| Line 509: | Line 509: | ||
|[[52ed5]] | |[[52ed5]] | ||
| | | | ||
| | |Every fifth note of [[112edo]], getting ~.01 cent sharper as it ascends the scale | ||
|- | |- | ||
|[[53ed5]] | |[[53ed5]] | ||
| Line 517: | Line 517: | ||
|[[54ed5]] | |[[54ed5]] | ||
| | | | ||
| | |Every fourth note of [[93edo]], getting ~.015 cent flatter as it ascends the scale | ||
|- | |- | ||
|[[55ed5]] | |[[55ed5]] | ||
| Line 549: | Line 549: | ||
|[[62ed5]] | |[[62ed5]] | ||
| | | | ||
| | |Every third note of [[80edo]], getting ~.06 cent flatter as it ascends the scale | ||
|- | |- | ||
|[[63ed5]] | |[[63ed5]] | ||
| Line 565: | Line 565: | ||
|[[66ed5]] | |[[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]] | | | [[72ed5]] | ||
| | [[31edo]] | | | [[31edo]] | ||
| | 72ed5 is 31edo with ~0.34 cent compressed octaves. Patent vals match through the 31-limit. | | | 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]] | | | [[79ed5]] | ||
| | [[34edo]] | | | [[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). | | | 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]] | | | [[81ed5]] | ||
| | [[35edo]] | | | [[35edo]] | ||
| | 81ed5 is 35edo with ~4.0 cent stretched octaves. Patent vals match through the 11-limit. | | | 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]] | | | [[86ed5]] | ||
| | [[37edo]] | | | [[37edo]] | ||
| | 86ed5 is 37edo with ~1.2 cent compressed octaves. Patent vals match through the 19-limit. | | | 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]] | | | [[88ed5]] | ||
| | [[38edo]] | | | [[38edo]] | ||
| | Same 3.2 cent octave stretch as 44ed5~19edo. Patent vals differ in the 7-limit. | | | 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]] | | | [[93ed5]] | ||
| | [[40edo]] | | | [[40edo]] | ||
| | 93ed5 is 40edo with ~1.6 cent compressed octaves. Patent vals match through the 7-limit. | | | 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]] | | | [[95ed5]] | ||
| | [[41edo]] | | | [[41edo]] | ||
| | 95ed5 is 41edo with ~2.5 cent stretched octaves. Patent vals match through the 11-limit. | | | 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]] | | | [[100ed5]] | ||
| | [[43edo]] | | | [[43edo]] | ||
| | 100ed5 is 43edo with ~1.9 cent compressed octaves. Patent vals match through the 37-limit. | | | 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]] | | | [[102ed5]] | ||
| | [[44edo]] | | | [[44edo]] | ||
| | Same 1.9 cent octave stretch as 51ed5~22edo. Patent vals match through the 23-limit, with the exception of 7. | | | 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]] | | | [[107ed5]] | ||
| | [[46edo]] | | | [[46edo]] | ||
| | 107ed5 is 46edo with ~2.1 cent compressed octaves. Patent vals match through the 11-limit. | | | 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]] | | | [[109ed5]] | ||
| | [[47edo]] | | | [[47edo]] | ||
| | 109ed5 is 47edo with ~1.4 cent stretched octaves. Patent vals match through the 17-limit, with the exception of 11. | | | 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]] | | | [[114ed5]] | ||
| | [[49edo]] | | | [[49edo]] | ||
| | 114ed5 is 49edo with ~2.4 cent compressed octaves. Patent vals match through the 11-limit. | | | 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]] | | | [[116ed5]] | ||
| | [[50edo]] | | | [[50edo]] | ||
| | Same 1.0 cent octave stretch as 58ed5~25edo. Patent vals agree through the 43-limit. | | | 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]] | | | [[121ed5]] | ||
| | [[52edo]] | | | [[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). | | | 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]] | | | [[123ed5]] | ||
| | [[53edo]] | | | [[53edo]] | ||
| | 123ed5 is 53edo with ~0.61 cent stretched octaves. Patent vals match through the 29-limit. | | | 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]] | | | [[128ed5]] | ||
| | [[55edo]] | | | [[55edo]] | ||
| | 128ed5 is 55edo with ~2.8 cent compressed octaves, but the correspondence is rough. Patent vals differ in the 7-limit. | | | 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]] | | | [[130ed5]] | ||
| | [[56edo]] | | | [[56edo]] | ||
| | Same 0.26 cent octave stretch as 65ed5~28edo. Patent vals agree through the 103-limit. | | | 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]] | | | [[137ed5]] | ||
| | [[59edo]] | | | [[59edo]] | ||
| | 137ed5 is 59edo with ~0.05 cent compressed octaves. Patent vals match through the 179-limit. | | | 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]] | | | [[144ed5]] | ||
| | [[62edo]] | | | [[62edo]] | ||
| | Same 0.34 cent octave compression as 72ed5~31edo. Patent vals match through the 19-limit, with the exception of 11. | | | 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]] | | | [[146ed5]] | ||
| | [[63edo]] | | | [[63edo]] | ||
| | 146ed5 is 63edo with ~2.3 cent stretched octaves. Patent vals match through the 13-limit. | | | 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]] | | | [[151ed5]] | ||
| | [[65edo]] | | | [[65edo]] | ||
| | 151ed5 is 65edo with ~0.59 cent compressed octaves. Patent vals match through the 53-limit, with the exception of 7 (as expected). | | | 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]] | | | [[153ed5]] | ||
| | [[66edo]] | | | [[66edo]] | ||
| | Same 1.9 cent octave stretch as 51ed5~22edo. Patent vals match through the 13-limit, with the exception of 3. | | | 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]] | | | [[158ed5]] | ||
| | [[68edo]] | | | [[68edo]] | ||
| | Same 0.83 cent octave compression as 79ed5~34edo. Patent vals agree through the 23-limit. | | | 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]] | | | [[160ed5]] | ||
| | [[69edo]] | | | [[69edo]] | ||
| | 160ed5 is 69edo with ~1.6 cent stretched octaves. Patent vals differ in the 7-limit. | | | 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]] | | | [[165ed5]] | ||
| | [[71edo]] | | | [[71edo]] | ||
| | 165ed5 is 71edo with ~1.0 cent compressed octaves. Patent vals match through the 37-limit. | | | 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]] | | | [[167ed5]] | ||
| | [[72edo]] | | | [[72edo]] | ||
| | 167ed5 is 72edo with ~1.3 cent stretched octaves. Patent vals agree through the 19-limit. | | | 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]] | | | [[172ed5]] | ||
| | [[74edo]] | | | [[74edo]] | ||
| | Same 1.2 cent octave compression as 86ed5~37edo. Patent vals agree through the 13-limit. | | | 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]] | | | [[174ed5]] | ||
| | [[75edo]] | | | [[75edo]] | ||
| | Same 1.0 cent octave stretch as 58ed5~25edo. Patent vals differ in the 7-limit. | | | 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]] | | | [[179ed5]] | ||
| | [[77edo]] | | | [[77edo]] | ||
| | 179ed5 is 77edo with ~1.4 cent compressed octaves. Patent vals match through the 19-limit, with the exception of 11. | | | 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]] | | | [[181ed5]] | ||
| | [[78edo]] | | | [[78edo]] | ||
| | 181ed5 is 78edo with ~0.73 cent stretched octaves. Patent vals match through the 59-limit, with the exception of 13. | | | 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]] | | | [[186ed5]] | ||
| | [[80edo]] | | | [[80edo]] | ||
| | Same 1.6 cent octave compression as 93ed5~40edo. Patent vals agree through the 29-limit. | | | 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]] | | | [[188ed5]] | ||
| | [[81edo]] | | | [[81edo]] | ||
| | 188ed5 is 81edo with ~0.49 cent stretched octaves. Patent vals match through the 41-limit. | | | 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]] | | | [[193ed5]] | ||
| | [[83edo]] | | | [[83edo]] | ||
| | 193ed5 is 83edo with ~1.7 cent compressed octaves. Patent vals match through the 7-limit. | | | 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]] | | | [[195ed5]] | ||
| | [[84edo]] | | | [[84edo]] | ||
| | Same 0.26 cent octave stretch as 65ed5~28edo. Patent vals agree through the 31-limit. | | | 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]] | | | [[202ed5]] | ||
| | [[87edo]] | | | [[87edo]] | ||
| | 202ed5 is 87edo with ~0.05 cent stretched octaves. Patent vals match through the 71-limit. | | | 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]] | | | [[209ed5]] | ||
| | [[90edo]] | | | [[90edo]] | ||
| | 209ed5 is 90edo with ~0.15 cent compressed octaves. Patent vals match through the 53-limit. | | | 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]] | | | [[211ed5]] | ||
| | [[91edo]] | | | [[91edo]] | ||
| | 211ed5 is 91edo with ~1.7 cent stretched octaves. Patent vals match through the 7-limit. | | | 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]] | | | [[216ed5]] | ||
| | [[93edo]] | | | [[93edo]] | ||
| | Same 0.34 cent octave compression as 72ed5~31edo. Patent vals agree through the 31-limit. | | | 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]] | | | [[218ed5]] | ||
| | [[94edo]] | | | [[94edo]] | ||
| | Same 1.4 cent octave stretch as 109ed5~47edo. Patent vals match through the 23-limit, with the exception of 13. | | | 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]] | | | [[223ed5]] | ||
| | [[96edo]] | | | [[96edo]] | ||
| | 223ed5 is 96edo with ~0.51 cent compressed octaves. Patent vals match through the 13-limit. | | | 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]] | | | [[225ed5]] | ||
| | [[97edo]] | | | [[97edo]] | ||
| | 225ed5 is 97edo with ~1.2 cent stretched octaves. Patent vals match through the 19-limit, with the exception of 11. | | | 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]] | | | [[230ed5]] | ||
| | [[99edo]] | | | [[99edo]] | ||
| | 230ed5 is 99edo with ~0.67 cent compressed octaves. Patent vals match through the 7-limit. | | | 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]] | | | [[232ed5]] | ||
| | [[100edo]] | | | [[100edo]] | ||
| | Same 1.0 cent octave stretch as 58ed5~25edo. Patent vals match through the 13-limit. | | | 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]] | | | [[237ed5]] | ||
| | [[102edo]] | | | [[102edo]] | ||
| | Same 0.83 cent octave compression as 79ed5~34edo. Patent vals differ in the 7-limit. | | | 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]] | | | [[239ed5]] | ||
| Line 811: | Line 1,323: | ||
*[[Pentave_Reduced_Harmonics|Pentave Reduced Harmonics]] | *[[Pentave_Reduced_Harmonics|Pentave Reduced Harmonics]] | ||
*[[Pentave_Reduced_Subharmonics|Pentave Reduced Subharmonics]] | *[[Pentave_Reduced_Subharmonics|Pentave Reduced Subharmonics]] | ||
*http://www.nonoctave.com/tuning/fifth_harmonic.html | *http://www.nonoctave.com/tuning/fifth_harmonic.html [[Category:Ed5| ]] <!-- main article --> | ||
[[Category:Equal-step tuning]] | [[Category:Equal-step tuning]] | ||
[[Category:Overview]] | [[Category:Overview]] | ||
[[Category:todo:add_sound_examples]] | [[Category:todo:add_sound_examples]] | ||