168edo: Difference between revisions

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'''168edo''' is the [[EDO|equal division of the octave]] into 168 parts of 7.1429 cents each. It is closely related to [[84edo]], but the patent vals differ on the mapping for 11 and 17. It is [[contorted]] in the 7-limit, tempering out 225/224, 1728/1715, and 78732/78125. Using the patent val, it tempers out 243/242, 2420/2401, 3025/3024, and 43923/43750 in the 11-limit; 351/350, 625/624, 640/637, 847/845, and 1573/1568 in the 13-limit; 375/374, 561/560, 715/714, 891/884, 936/935, and 1331/1326 in the 17-limit. Using the 168d val, it tempers out 3136/3125, 19683/19600, and 33075/32768 in the 7-limit; 243/242, 385/384, 3773/3750, and 9801/9800 in the 11-limit. Stacking alternating steps of 43 and 53 produces an optimal ~~Whitewood~~ [14] scale of 19 5 19 5 19 5 19 5 19 5 19 5 19 5 that spreads the overall flatness evenly between the major and minor thirds.

'''168edo''' is the [[EDO|equal division of the octave]] into 168 parts of 7.1429 cents each. It is closely related to [[84edo]], but the patent vals differ on the mapping for 11 and 17. It is [[contorted]] in the 7-limit, tempering out 225/224, 1728/1715, and 78732/78125. Using the patent val, it tempers out 243/242, 2420/2401, 3025/3024, and 43923/43750 in the 11-limit; 351/350, 625/624, 640/637, 847/845, and 1573/1568 in the 13-limit; 375/374, 561/560, 715/714, 891/884, 936/935, and 1331/1326 in the 17-limit. Using the 168d val, it tempers out 3136/3125, 19683/19600, and 33075/32768 in the 7-limit; 243/242, 385/384, 3773/3750, and 9801/9800 in the 11-limit.

Stacking alternating steps of 43 and 53 produces an optimal [[whitewood]] [14] scale of 19 5 19 5 19 5 19 5 19 5 19 5 19 5 that spreads the overall flatness evenly between the major and minor thirds. [[Substitute harmonic#Dotcom|dotcom]] is also supported.

=== Odd harmonics ===

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 {{Infobox ET}}
-'''168edo''' is the [[EDO|equal division of the octave]] into 168 parts of 7.1429 cents each. It is closely related to [[84edo]], but the patent vals differ on the mapping for 11 and 17. It is [[contorted]] in the 7-limit, tempering out 225/224, 1728/1715, and 78732/78125. Using the patent val, it tempers out 243/242, 2420/2401, 3025/3024, and 43923/43750 in the 11-limit; 351/350, 625/624, 640/637, 847/845, and 1573/1568 in the 13-limit; 375/374, 561/560, 715/714, 891/884, 936/935, and 1331/1326 in the 17-limit. Using the 168d val, it tempers out 3136/3125, 19683/19600, and 33075/32768 in the 7-limit; 243/242, 385/384, 3773/3750, and 9801/9800 in the 11-limit. Stacking alternating steps of 43 and 53 produces an optimal Whitewood [14] scale of 19 5 19 5 19 5 19 5 19 5 19 5 19 5 that spreads the overall flatness evenly between the major and minor thirds.
+'''168edo''' is the [[EDO|equal division of the octave]] into 168 parts of 7.1429 cents each. It is closely related to [[84edo]], but the patent vals differ on the mapping for 11 and 17. It is [[contorted]] in the 7-limit, tempering out 225/224, 1728/1715, and 78732/78125. Using the patent val, it tempers out 243/242, 2420/2401, 3025/3024, and 43923/43750 in the 11-limit; 351/350, 625/624, 640/637, 847/845, and 1573/1568 in the 13-limit; 375/374, 561/560, 715/714, 891/884, 936/935, and 1331/1326 in the 17-limit. Using the 168d val, it tempers out 3136/3125, 19683/19600, and 33075/32768 in the 7-limit; 243/242, 385/384, 3773/3750, and 9801/9800 in the 11-limit.
+Stacking alternating steps of 43 and 53 produces an optimal [[whitewood]] [14] scale of 19 5 19 5 19 5 19 5 19 5 19 5 19 5 that spreads the overall flatness evenly between the major and minor thirds. [[Substitute harmonic#Dotcom|dotcom]] is also supported.
 === Odd harmonics ===