168edo: Difference between revisions

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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.

168edo is closely related to [[84edo]], but the [[patent val]]s differ on the mapping for [[11/1|11]] and [[17/1|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.

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 ===

~~[[Category:Equal divisions of the octave|###]] ~~

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 {{EDO intro}}
-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.
+edo is closely related to [[84edo]], but the [[patent val]]s differ on the mapping for [[11/1|11]] and [[17/1|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.
+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 ===
 {{Harmonics in equal|168}}
-[[Category:Equal divisions of the octave|###]] <!-- 3-digit number -->