1619edo: Difference between revisions

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== Theory ==

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 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]].

1619edo is the 256th [[Prime edo]]. It can be seen as a prime counterpart to [[270edo]] in its excellent ability to act as a very fine closed 13-limit system, and it has an advantage over 270edo in being prime, since every generator produces a unique MOS.

=== Temperaments ===

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 supports the rank 5 temperament tempering out the jacobin comma, 6656/6655 and its fifth-order maximal evenness scale, 24 & 72 & 270 & 494 & 1619, is represented by every 3rd step of the 72 & 270 & 494 & 1619 temperament.

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 tunes [[keenanisma]] very finely, to 6 steps, and can use it as a microchroma. In addition, it can use the keenanisma as a generator in the keenanose temperament, 270 & 1619, in which it highlights the relationship between 270 keenanismas and the octave. It also achieves this since 270 * 6 = 1620, and 1619 is 1 short of that and also excellent in the 13-limit. 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~~]].

Since 33/32 is close to 1\45, 7\6 is close to 1\9, and 385/384 is close to 1\270, 1619edo can be thought of as [[1620edo]] where one step was extracted and all others were moved into a more harmonically just position.

=== Prime harmonics ===

== Table of intervals ==

Intervals named in accordance to their most just 13-limit counterpart using the names accepted on the wiki.

{| class="wikitable mw-collapsible mw-collapsed"

|+Table of intervals in 1619edo

!Step

!Cents

!Ratio

!Name

|-

|0

|0.000

|1/1

|prime, unison

|-

|6

|4.447

|385/384

|keenanisma

|-

|72

|53.366

|33/32

|al-Farabi quarter-tone

|-

|360

|266.831

|7/6

|septimal subminor third

|-

|1619

|1200.000

|2/1

|perfect octave

|}

== Regular temperament properties ==

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|[[Ravine]]

|}

[[Category:Quartismic]]

@@ Line 10: / Line 10: @@
 == Theory ==
-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 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]].
+edo is the 256th [[Prime edo]]. It can be seen as a prime counterpart to [[270edo]] in its excellent ability to act as a very fine closed 13-limit system, and it has an advantage over 270edo in being prime, since every generator produces a unique MOS.
+=== Temperaments ===
+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 supports the rank 5 temperament tempering out the jacobin comma, 6656/6655 and its fifth-order maximal evenness scale, 24 & 72 & 270 & 494 & 1619, is represented by every 3rd step of the 72 & 270 & 494 & 1619 temperament.
-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 tunes [[keenanisma]] very finely, to 6 steps, and can use it as a microchroma. In addition, it can use the keenanisma as a generator in the keenanose temperament, 270 & 1619, in which it highlights the relationship between 270 keenanismas and the octave. It also achieves this since 270 * 6 = 1620, and 1619 is 1 short of that and also excellent in the 13-limit. 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.
-edo is the 256th [[Prime edo]].
+Since 33/32 is close to 1\45, 7\6 is close to 1\9, and 385/384 is close to 1\270, 1619edo can be thought of as [[1620edo]] where one step was extracted and all others were moved into a more harmonically just position.
 === Prime harmonics ===
 {{Harmonics in equal|1619|columns=10}}
+== Table of intervals ==
+Intervals named in accordance to their most just 13-limit counterpart using the names accepted on the wiki.
+{| class="wikitable mw-collapsible mw-collapsed"
+|+Table of intervals in 1619edo
+!Step
+!Cents
+!Ratio
+!Name
+|-
+|0
+|0.000
+|1/1
+|prime, unison
+|-
+|6
+|4.447
+|385/384
+|keenanisma
+|-
+|72
+|53.366
+|33/32
+|al-Farabi quarter-tone
+|-
+|360
+|266.831
+|7/6
+|septimal subminor third
+|-
+|1619
+|1200.000
+|2/1
+|perfect octave
+|}
 == Regular temperament properties ==
@@ Line 94: / Line 134: @@
 |[[Ravine]]
 |}<!-- 4-digit number -->
+[[Category:Quartismic]]