Xenharmonic Wiki

494edo: Difference between revisions

← Older edit
VisualWikitext
Cleanup; clarify the title row of the rank-2 temp table; -redundant categories
m Text replacement - "Octave-reduced form, reduced to the first half-octave, and minimal form in parentheses if distinct" to "Octave-reduced form, reduced to the first half-octave, and minimal form in parentheses if distinct"
 
(7 intermediate revisions by 2 users not shown)
Line 1: Line 1:
{{Infobox ET}}
{{Infobox ET}}
{{EDO intro|494}}
{{ED intro}}


== Theory ==
== Theory ==
494 is a very strong [[13-limit|13]]- and [[17-limit]] equal temperament. 494edo is a [[zeta edo|zeta peak and zeta peak integer edo]] and [[consistency|distinctly consistent]] through the [[17-odd-limit]]. It [[tempering out|tempers out]] the [[enneadeca]], {{monzo| -14 -19 19 }}, the [[tricot comma]], {{monzo| 39 -29 3 }}, and the [[kwazy comma]], {{monzo| -53 10 16 }} in the [[5-limit]]. In the [[7-limit]], it tempers out [[4375/4374]] and [[703125/702464]]; in the [[11-limit]] [[3025/3024]] and [[9801/9800]]; in the [[13-limit]] [[1716/1715]], [[2080/2079]], [[4096/4095]], [[4225/4224]] and [[6656/6655]]; and in the 17-limit, [[1156/1155]], 1275/1274, 2431/2430, and 2500/2499.  
494 is a very strong [[13-limit|13]]- and [[17-limit]] equal temperament. 494edo is a [[zeta edo|zeta peak and zeta peak integer edo]] and [[consistency|distinctly consistent]] through the [[17-odd-limit]]. It [[tempering out|tempers out]] the [[enneadeca]], {{monzo| -14 -19 19 }}, the [[alphatricot comma]], {{monzo| 39 -29 3 }}, and the [[kwazy comma]], {{monzo| -53 10 16 }} in the [[5-limit]]. In the [[7-limit]], it tempers out [[4375/4374]] and [[703125/702464]]; in the [[11-limit]] [[3025/3024]] and [[9801/9800]]; in the [[13-limit]] [[1716/1715]], [[2080/2079]], [[4096/4095]], [[4225/4224]] and [[6656/6655]]; and in the 17-limit, [[1156/1155]], 1275/1274, 2431/2430, and 2500/2499.  


Since the step size is close to [[729/728]], the squbema, the accepted name for 494edo's step is ''squb''.
Since the step size is close to [[729/728]], the squbema, the accepted name for 494edo's step is ''squb''.
Line 17: Line 17:
== Intervals ==
== Intervals ==
{{Main| Table of 494edo intervals }}
{{Main| Table of 494edo intervals }}
{{Q-odd-limit intervals|494}}


== Regular temperament properties ==
== Regular temperament properties ==
{| class="wikitable center-4 center-5 center-6"
{| class="wikitable center-4 center-5 center-6"
|-
! rowspan="2" | [[Subgroup]]
! rowspan="2" | [[Subgroup]]
! rowspan="2" | [[Comma list|Comma List]]
! rowspan="2" | [[Comma list]]
! rowspan="2" | [[Mapping]]
! rowspan="2" | [[Mapping]]
! rowspan="2" | Optimal<br>8ve Stretch (¢)
! rowspan="2" | Optimal<br>8ve stretch (¢)
! colspan="2" | Tuning Error
! colspan="2" | Tuning error
|-
|-
! [[TE error|Absolute]] (¢)
! [[TE error|Absolute]] (¢)
Line 30: Line 32:
|-
|-
| 2.3
| 2.3
| {{monzo| 783 -494 }}
| {{Monzo| 783 -494 }}
| {{mapping| 494 783 }}
| {{Mapping| 494 783 }}
| -0.0219
| −0.0219
| 0.0219
| 0.0219
| 0.90
| 0.90
|-
|-
| 2.3.5
| 2.3.5
| {{monzo| -14 -19 19 }}, {{monzo| 39 -23 3 }}
| {{Monzo| -14 -19 19 }}, {{monzo| 39 -23 3 }}
| {{mapping| 494 783 1147 }}
| {{Mapping| 494 783 1147 }}
| -0.0032
| −0.0032
| 0.0318
| 0.0318
| 1.31
| 1.31
Line 45: Line 47:
| 2.3.5.7
| 2.3.5.7
| 4375/4374, 703125/702464, {{monzo| 21 3 1 -10 }}
| 4375/4374, 703125/702464, {{monzo| 21 3 1 -10 }}
| {{mapping| 494 783 1147 1387 }}
| {{Mapping| 494 783 1147 1387 }}
| -0.0385
| −0.0385
| 0.0670
| 0.0670
| 2.76
| 2.76
Line 52: Line 54:
| 2.3.5.7.11
| 2.3.5.7.11
| 3025/3024, 4375/4374, 131072/130977, 234375/234256
| 3025/3024, 4375/4374, 131072/130977, 234375/234256
| {{mapping| 494 783 1147 1387 1709 }}
| {{Mapping| 494 783 1147 1387 1709 }}
| -0.0365
| −0.0365
| 0.0600
| 0.0600
| 2.47
| 2.47
Line 59: Line 61:
| 2.3.5.7.11.13
| 2.3.5.7.11.13
| 1716/1715, 2080/2079, 3025/3024, 4096/4095, 31250/31213
| 1716/1715, 2080/2079, 3025/3024, 4096/4095, 31250/31213
| {{mapping| 494 783 1147 1387 1709 1828 }}
| {{Mapping| 494 783 1147 1387 1709 1828 }}
| -0.0286
| −0.0286
| 0.0576
| 0.0576
| 2.37
| 2.37
Line 66: Line 68:
| 2.3.5.7.11.13.17
| 2.3.5.7.11.13.17
| 1156/1155, 1275/1274, 1716/1715, 2080/2079, 2431/2430, 4096/4095
| 1156/1155, 1275/1274, 1716/1715, 2080/2079, 2431/2430, 4096/4095
| {{mapping| 494 783 1147 1387 1709 1828 2019 }}
| {{Mapping| 494 783 1147 1387 1709 1828 2019 }}
| -0.0069
| −0.0069
| 0.0752
| 0.0752
| 3.09
| 3.09
Line 75: Line 77:
=== Rank-2 temperaments ===
=== Rank-2 temperaments ===
{| class="wikitable center-all left-5"
{| class="wikitable center-all left-5"
|+Table of rank-2 temperaments by generator
|+ style="font-size: 105%;" | Table of rank-2 temperaments by generator
|-
! Periods<br>per 8ve
! Periods<br>per 8ve
! Generator*
! Generator*
! Cents*
! Cents*
! Associated<br>Ratio*
! Associated<br>ratio*
! Temperaments
! Temperaments
|-
|-
Line 98: Line 101:
| 565.99
| 565.99
| 104/75
| 104/75
| [[Tricot]] / [[trillium]]
| [[Alphatrillium]]
|-
|-
| 2
| 2
Line 104: Line 107:
| 162.75
| 162.75
| 1125/1024
| 1125/1024
| [[Kwazy]]
| [[Crazy]]
|-
|-
| 2
| 2
Line 114: Line 117:
| 13
| 13
| 205\494<br>(15\494)
| 205\494<br>(15\494)
| 497.98<br>(36.43)
| 497.98<br/>(36.43)
| 4/3<br>(?)
| 4/3<br>(?)
| [[Aluminium]]
| [[Aluminium]]
Line 136: Line 139:
| [[Semihemienneadecal]]
| [[Semihemienneadecal]]
|}
|}
<nowiki>*</nowiki> [[Normal lists|octave-reduced form]], reduced to the first half-octave, and [[Normal lists|minimal form]] in parentheses if it is distinct
<nowiki/>* [[Normal forms #Equave-reduced-generator form|Octave-reduced form]], reduced to the first half-octave, and [[normal forms #Minimal-generator form|minimal form]] in parentheses if distinct


== Music ==
== Music ==
Line 144: Line 147:
[[Category:Enneadecal]]
[[Category:Enneadecal]]
[[Category:Kwazy]]
[[Category:Kwazy]]
[[Category:Tricot]]
[[Category:Listen]]
[[Category:Listen]]
[[Category:Alphatricot]]
Retrieved from "https://en.xen.wiki/w/494edo"