1ed33/32: Difference between revisions

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~~The~~ '''equal multiplication of [[33/32]]~~''',~~ the Alpharabian quarter-tone, results in ~~an interesting~~ nonoctave tuning, equivalent to 22.5255 EDO.

'''1 equal division of 33/32''' ('''1ed33/32'''), also known as '''ambitonal sequence of 33/32''' ('''AS33/32''') or '''33/32 equal-step tuning''', is an equal multiplication of [[33/32]] (the Alpharabian quarter-tone), and results in a nonoctave tuning equivalent to 22.5255 EDO.

Lookalikes: 5ed7/6, 45ed4

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== Theory ==

In this tuning, 2 steps correspond to the parapotome [[1089/1024]],

In this tuning, 2 steps by definition correspond to the parapotome [[1089/1024]].

Intervals with excellent approximation in this tuning are: 7/6 (5), 20/13 (14), 18/11 (16). Other intervals with good approximation are: 6/5, 7/5, 9/5, 13/7, 13/9, 11/10, 19/12, 17/16, 17/15, 16/15.

In the 5-limit, 33/32 ~~equal step tuning~~ tempers out the syntonic comma 81/80.

In the 5-limit, 1ed33/32 tempers out the syntonic comma 81/80, making it meantone.

== Regular temperament ~~comma lists~~ ==

In the 7-limit, as a consequence of representing 6/5 and 7/6 well, it's great at representing the 5:6:7 otonal tetrad. This means that 385/384 is tempered out.

== Regular temperament properties ==

"Normal" subgroups calculated using the 23edo val that matches 33/32 equal step tuning patent val.

{| class="wikitable"

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-The '''equal multiplication of [[33/32]]''', the Alpharabian quarter-tone, results in an interesting nonoctave tuning, equivalent to 22.5255 EDO.
+{{todo|merge articles|inline=1|text=Merge into [[33/32]]?}}
+{{Infobox ET|1ed33/32}}
+'''1 equal division of 33/32''' ('''1ed33/32'''), also known as '''ambitonal sequence of 33/32''' ('''AS33/32''') or '''33/32 equal-step tuning''', is an equal multiplication of [[33/32]] (the Alpharabian quarter-tone), and results in a nonoctave tuning equivalent to 22.5255 EDO.
 Lookalikes: 5ed7/6, 45ed4
@@ Line 5: / Line 7: @@
 == Theory ==
 {{Harmonics in equal|1|33|32|columns=11|intervals=prime}}
-In this tuning, 2 steps correspond to the parapotome [[1089/1024]],
+In this tuning, 2 steps by definition correspond to the parapotome [[1089/1024]].
 Intervals with excellent approximation in this tuning are: 7/6 (5), 20/13 (14), 18/11 (16). Other intervals with good approximation  are: 6/5, 7/5, 9/5, 13/7, 13/9, 11/10, 19/12, 17/16, 17/15, 16/15.
-In the 5-limit, 33/32 equal step tuning tempers out the syntonic comma 81/80.
+In the 5-limit, 1ed33/32 tempers out the syntonic comma 81/80, making it meantone.
-== Regular temperament comma lists ==
+In the 7-limit, as a consequence of representing 6/5 and 7/6 well, it's great at representing the 5:6:7 otonal tetrad. This means that 385/384 is tempered out.
+== Regular temperament properties ==
 "Normal" subgroups calculated using the 23edo val that matches 33/32 equal step tuning patent val.
 {| class="wikitable"