1619edo: Difference between revisions

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1619edo is excellent in the 13-limit, where it tempers out [[4225/4224]], [[4375/4374]], [[6656/6655]], 78125/78078, and 117649/117612. It also notably tempers out [[quartisma]] (117440512/117406179) and [[123201/123200]]. It supports [[vidar]], which has the comma basis 4225/4224, 4375/4374, and 6656/6655, and other unnamed expansions of the [[ragismic]] temperament such as the 270 & 441 & 1619, tempering out 4225/4224, 4375/4374, 655473/655360, or the 72 & 270 & 494 & 1619 temperament tempering out 6656/6655 and 2912000/2910897.

1619edo has 7/6 on 360th step, a highly divisible number, 27/25 on 180th, and 33/32 on 72nd as a consequence of tempering out the commas. This means that 72ed33/32 is virtually equivalent to 1619edo. When it comes to using 33/32 as the generator, 1619edo supports the ~~832 & 1619~~ temperament, which tempers out 196625/196608, 200000/199927, 2912000/2910897, and 3764768/3764475.

1619edo has 7/6 on 360th step, a highly divisible number, 27/25 on 180th, and 33/32 on 72nd as a consequence of tempering out the commas. This means that 72ed33/32 is virtually equivalent to 1619edo. When it comes to using 33/32 as the generator, 1619edo supports the [[ravine]] temperament, which tempers out 196625/196608, 200000/199927, 2912000/2910897, and 3764768/3764475.

1619edo is the 256th [[Prime edo]].

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|}

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

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

=== Rank-2 temperaments by generator ===

{| class="wikitable center-all left-5"

!Periods

per octave

!Generator

(reduced)

!Cents

(reduced)

!Associated

ratio

!Temperaments

|-

|1

|72\1619

|53.366

|33/32

|[[Ravine]]

|}

@@ Line 12: / Line 12: @@
 edo is excellent in the 13-limit, where it tempers out [[4225/4224]], [[4375/4374]], [[6656/6655]], 78125/78078, and 117649/117612. It also notably tempers out [[quartisma]] (117440512/117406179) and [[123201/123200]]. It supports [[vidar]], which has the comma basis 4225/4224, 4375/4374, and 6656/6655, and other unnamed expansions of the [[ragismic]] temperament such as the 270 & 441 & 1619, tempering out 4225/4224, 4375/4374, 655473/655360, or the 72 & 270 & 494 & 1619 temperament tempering out 6656/6655 and 2912000/2910897.
-edo has 7/6 on 360th step, a highly divisible number, 27/25 on 180th, and 33/32 on 72nd as a consequence of tempering out the commas. This means that 72ed33/32 is virtually equivalent to 1619edo. When it comes to using 33/32 as the generator, 1619edo supports the 832 & 1619 temperament, which tempers out 196625/196608, 200000/199927, 2912000/2910897, and 3764768/3764475.
+edo has 7/6 on 360th step, a highly divisible number, 27/25 on 180th, and 33/32 on 72nd as a consequence of tempering out the commas. This means that 72ed33/32 is virtually equivalent to 1619edo. When it comes to using 33/32 as the generator, 1619edo supports the [[ravine]] temperament, which tempers out 196625/196608, 200000/199927, 2912000/2910897, and 3764768/3764475.
 edo is the 256th [[Prime edo]].
@@ Line 66: / Line 66: @@
 |}
-[[Category:Equal divisions of the octave|####]] <!-- 4-digit number -->
+[[Category:Equal divisions of the octave|####]]
+=== Rank-2 temperaments by generator ===
+{| class="wikitable center-all left-5"
+!Periods
+per octave
+!Generator
+(reduced)
+!Cents
+(reduced)
+!Associated
+ratio
+!Temperaments
+|-
+|1
+|72\1619
+|53.366
+|33/32
+|[[Ravine]]
+|}<!-- 4-digit number -->