30edo: Difference between revisions

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30edo's [[patent val]] is a doubled version of the patent val for [[15edo]] through the 11-limit, so 30 can be viewed as a [[contorted]] version of 15. In the 13-limit it supplies the optimal patent val for [[quindecic]] temperament. If 15edo's mappings are still considered acceptable despite their low relative accuracy in this tuning, it can be seen as supplying an improved mapping of the 13th harmonic to 15edo, much like how 24edo supplies an improved 11 and 13 to 12edo.

[[File:Plot30.png|alt=plot30.png|thumb|A plot of the Z function around 30.]]

However, 5\30 is 200{{c}}, which is a good (and familiar) approximation for 9/8, and hence 30edo can be viewed inconsistently, as having a 9/1 at 95\30 as well as 96\30.

However, 5\30 is 200[[{{c}}]], which is a good (and familiar) approximation for 9/8, and hence 30edo can be viewed inconsistently, as having a 9/1 at 95\30 as well as 96\30.

Instead of the 18\30 fifth of 720 cents, 30edo also makes available a 17\30 fifth of 680 cents. It is possible to interpret this fifth as [[mavila]] temperament using the 30bc [[val]], but the 360-cent [[5/4]] may be undesirable for some. When 30edo is used for pelogic, 5\30 can again be used inconsistently as a 9/8. An alternative option which uses the somewhat more accurate 400-cent [[5/4]] is [[shallowtone]] temperament using the 30b [[val]], although it is of very high [[badness]], being both high-[[error]] and high-[[complexity]]. [[Undecimation]] is also an option.

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|-

! Step

! ~~[[Cent]]s~~

! Cents

! colspan="3" | [[Ups and downs notation]]

! [[Armodue_theory|Armodue Notation]]

@@ Line 5: / Line 5: @@
 edo's [[patent val]] is a doubled version of the patent val for [[15edo]] through the 11-limit, so 30 can be viewed as a [[contorted]] version of 15. In the 13-limit it supplies the optimal patent val for [[quindecic]] temperament. If 15edo's mappings are still considered acceptable despite their low relative accuracy in this tuning, it can be seen as supplying an improved mapping of the 13th harmonic to 15edo, much like how 24edo supplies an improved 11 and 13 to 12edo.
 [[File:Plot30.png|alt=plot30.png|thumb|A plot of the Z function around 30.]]
-However, 5\30 is 200{{c}}, which is a good (and familiar) approximation for 9/8, and hence 30edo can be viewed inconsistently, as having a 9/1 at 95\30 as well as 96\30.
+However, 5\30 is 200[[{{c}}]], which is a good (and familiar) approximation for 9/8, and hence 30edo can be viewed inconsistently, as having a 9/1 at 95\30 as well as 96\30.
 Instead of the 18\30 fifth of 720 cents, 30edo also makes available a 17\30 fifth of 680 cents. It is possible to interpret this fifth as [[mavila]] temperament using the 30bc [[val]], but the 360-cent [[5/4]] may be undesirable for some. When 30edo is used for pelogic, 5\30 can again be used inconsistently as a 9/8. An alternative option which uses the somewhat more accurate 400-cent [[5/4]] is [[shallowtone]] temperament using the 30b [[val]], although it is of very high [[badness]], being both high-[[error]] and high-[[complexity]].  [[Undecimation]] is also an option.
@@ Line 21: / Line 21: @@
 |-
 ! Step
-! [[Cent]]s
+! Cents
 ! colspan="3" | [[Ups and downs notation]]
 ! [[Armodue_theory|Armodue Notation]]