1619edo: Difference between revisions
General cleanup |
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| Step size = 0.741198¢ | | Step size = 0.741198¢ | ||
| Fifth = 947\1619 (701.915¢) | | Fifth = 947\1619 (701.915¢) | ||
| Semitones = 153:122 (113.403¢ : 90.426¢) | | Semitones = 153:122 (113.403¢ : 90.426¢) | ||
| Consistency = 13 | | Consistency = 13 | ||
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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]]. | 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. | 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 | 1619edo supports the rank-5 temperament tempering out the jacobin comma, 6656/6655 and its fifth-order maximal evenness scale is represented by every 3rd step of the 72 & 270 & 494 & 1619 temperament{{clarify}}. | ||
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 | 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. | ||
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. It achieves this because 1620edo is contorted 270edo in the 11-limit, and its 13/8 is on the flat side coming from 324edo, and thus when it is octave stretched, steps sharpen enough to arrive at 1619edo's 13-limit excellence. | 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. It achieves this because 1620edo is contorted 270edo in the 11-limit, and its 13/8 is on the flat side coming from 324edo, and thus when it is octave stretched, steps sharpen enough to arrive at 1619edo's 13-limit excellence. | ||
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{{Harmonics in equal|1619|columns=10}} | {{Harmonics in equal|1619|columns=10}} | ||
== | === Miscellaneous properties === | ||
1619edo is the 256th [[prime edo]]. | |||
== Selected intervals == | |||
{| class="wikitable mw-collapsible mw-collapsed" | {| class="wikitable mw-collapsible mw-collapsed" | ||
|+Table of intervals in 1619edo | |+Table of intervals in 1619edo | ||
!Step | ! Step | ||
!Cents | ! Cents | ||
!Ratio | ! Ratio | ||
!Name | ! Name<nowiki>*</nowiki> | ||
|- | |- | ||
|0 | | 0 | ||
|0.000 | | 0.000 | ||
|1/1 | | 1/1 | ||
|prime, unison | | prime, unison | ||
|- | |- | ||
|6 | | 6 | ||
|4.447 | | 4.447 | ||
|385/384 | | 385/384 | ||
|keenanisma | | keenanisma | ||
|- | |- | ||
|72 | | 72 | ||
|53.366 | | 53.366 | ||
|33/32 | | 33/32 | ||
|al-Farabi quarter-tone | | al-Farabi quarter-tone | ||
|- | |- | ||
|360 | | 360 | ||
|266.831 | | 266.831 | ||
|7/6 | | 7/6 | ||
|septimal subminor third | | septimal subminor third | ||
|- | |- | ||
|1619 | | 1619 | ||
|1200.000 | | 1200.000 | ||
|2/1 | | 2/1 | ||
|perfect octave | | perfect octave | ||
|} | |} | ||
<nowiki>*</nowiki> named in accordance to their most just 13-limit counterpart using the names accepted on the wiki. | |||
== Regular temperament properties == | == Regular temperament properties == | ||
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|} | |} | ||
=== Rank-2 temperaments === | |||
=== Rank-2 temperaments | |||
{| class="wikitable center-all left-5" | {| class="wikitable center-all left-5" | ||
!Periods | ! Periods<br>per Octave | ||
per | ! Generator<br>(Reduced) | ||
!Generator | ! Cents<br>(Reduced) | ||
( | ! Associated<br>Ratio | ||
!Cents | ! Temperaments | ||
( | |||
!Associated | |||
!Temperaments | |||
|- | |- | ||
|1 | | 1 | ||
|6\1619 | | 6\1619 | ||
|4.447 | | 4.447 | ||
|385/384 | | 385/384 | ||
|[[ | | [[Keenanose]] | ||
|- | |- | ||
|1 | | 1 | ||
|72\1619 | | 72\1619 | ||
|53.366 | | 53.366 | ||
|33/32 | | 33/32 | ||
|[[Ravine]] | | [[Ravine]] | ||
|}<!-- 4-digit number --> | |} | ||
[[Category:Equal divisions of the octave|####]] <!-- 4-digit number --> | |||
[[Category:Quartismic]] | [[Category:Quartismic]] | ||
{{Todo| review }} | |||