78edt: Difference between revisions

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'''78EDT''' is the [[Edt|equal division of the third harmonic]] into 78 parts of 24.3840 [[cent|cents]] each, corresponding to 49.2125 [[edo]]. It has a distinct flat tendency, in the sense that if 3 is pure, 2 (octave), 5, 7, 11, 13, 17, and 19 are all flat. It is consistent to the no-twos 19-limit, tempering out 245/243 and 3125/3087 in the 7-limit; 1331/1323, 6655/6561, and 9375/9317 in the 11-limit; 275/273, 847/845, 1575/1573, and 2197/2187 in the 13-limit; 875/867 and 2025/2023 in the 17-limit; 325/323, 363/361, 665/663, 935/931, and 1547/1539 in the 19-limit (no-twos subgroup).

'''78EDT''' is the [[Edt|equal division of the third harmonic]] into 78 parts of 24.3840 [[cent|cents]] each, corresponding to 49.2125 [[edo]]. It is contorted in the [[3.5.7 subgroup]], sharing [[13edt]]'s structure. It has a distinct flat tendency, in the sense that if 3 is pure, 2 (octave), 5, 7, 11, 13, 17, and 19 are all flat. It is consistent to the no-twos 19-limit, tempering out 245/243 and 3125/3087 in the 7-limit; 1331/1323, 6655/6561, and 9375/9317 in the 11-limit; 275/273, 847/845, 1575/1573, and 2197/2187 in the 13-limit; 875/867 and 2025/2023 in the 17-limit; 325/323, 363/361, 665/663, 935/931, and 1547/1539 in the 19-limit (no-twos subgroup).

78EDT is related to [[49edo|49 edo]], but with octave compression of 5.1821 cents. ~~Patent~~ vals match through the 11-limit, tempering out 64/63, 100/99, 245/243, and 1331/1323. 78EDT tempers out 144/143, 196/195, 275/273, 325/324, 364/363, and 572/567 in the 13-limit; 120/119, 136/135, 154/153, 170/169, and 224/221 in the 17-limit; 96/95, 190/189, and 210/209 in the 19-limit (full integer limit).

78EDT is related to [[49edo|49 edo]], but with octave compression of 5.1821 cents. Their patent vals match only through the 11-limit.

~~[[Category:Edt]]~~

== Intervals ==

~~[[Category:Edonoi]]~~

== Harmonics ==

{{Harmonics in equal

| steps = 78

| num = 3

| denom = 1

| intervals = prime

}}

{{Harmonics in equal

| steps = 78

| num = 3

| denom = 1

| start = 12

| collapsed = 1

| intervals = prime

}}

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-'''78EDT''' is the [[Edt|equal division of the third harmonic]] into 78 parts of 24.3840 [[cent|cents]] each, corresponding to 49.2125 [[edo]]. It has a distinct flat tendency, in the sense that if 3 is pure, 2 (octave), 5, 7, 11, 13, 17, and 19 are all flat. It is consistent to the no-twos 19-limit, tempering out 245/243 and 3125/3087 in the 7-limit; 1331/1323, 6655/6561, and 9375/9317 in the 11-limit; 275/273, 847/845, 1575/1573, and 2197/2187 in the 13-limit; 875/867 and 2025/2023 in the 17-limit; 325/323, 363/361, 665/663, 935/931, and 1547/1539 in the 19-limit (no-twos subgroup).
+{{Infobox ET}}
+'''78EDT''' is the [[Edt|equal division of the third harmonic]] into 78 parts of 24.3840 [[cent|cents]] each, corresponding to 49.2125 [[edo]]. It is contorted in the [[3.5.7 subgroup]], sharing [[13edt]]'s structure. It has a distinct flat tendency, in the sense that if 3 is pure, 2 (octave), 5, 7, 11, 13, 17, and 19 are all flat. It is consistent to the no-twos 19-limit, tempering out 245/243 and 3125/3087 in the 7-limit; 1331/1323, 6655/6561, and 9375/9317 in the 11-limit; 275/273, 847/845, 1575/1573, and 2197/2187 in the 13-limit; 875/867 and 2025/2023 in the 17-limit; 325/323, 363/361, 665/663, 935/931, and 1547/1539 in the 19-limit (no-twos subgroup).
-EDT is related to [[49edo|49 edo]], but with octave compression of 5.1821 cents. Patent vals match through the 11-limit, tempering out 64/63, 100/99, 245/243, and 1331/1323. 78EDT tempers out 144/143, 196/195, 275/273, 325/324, 364/363, and 572/567 in the 13-limit; 120/119, 136/135, 154/153, 170/169, and 224/221 in the 17-limit; 96/95, 190/189, and 210/209 in the 19-limit (full integer limit).
+EDT is related to [[49edo|49 edo]], but with octave compression of 5.1821 cents. Their patent vals match only through the 11-limit.
-[[Category:Edt]]
+== Intervals ==
-[[Category:Edonoi]]
+{{Interval table}}
+== Harmonics ==
+{{Harmonics in equal
+| steps = 78
+| num = 3
+| denom = 1
+| intervals = prime
+}}
+{{Harmonics in equal
+| steps = 78
+| num = 3
+| denom = 1
+| start = 12
+| collapsed = 1
+| intervals = prime
+}}