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1553edo: Difference between revisions

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{{Infobox ET}}
{{Infobox ET}}
{{EDO intro|1553}}
{{ED intro}}
 
== Theory ==
== Theory ==
1553edo is only [[consistent]] to the 5-odd-limit and harmonic 3 is about halfway between its steps. Assume the [[patent val]], 1553et tempers out 200120949/200000000 in the 7-limit; 102487/102400, 759375/758912, 2359296/2358125, and 369140625/369098752 in the 11-limit; 1716/1715, 40656/40625, 59535/59488, 105644/105625, 196625/196608, 200000/199927, 823875/823543, 8859375/8859136, 34034175/34027136, and 75000000/74942413, in the 13-limit.
1553edo is only [[consistent]] to the [[5-odd-limit]] and [[3/1|harmonic 3]] is about halfway between its steps. It has a reasonable approximation of the 2.9.5.7.13 [[subgroup]], where it notably tempers out [[4096/4095]] and 140625/140608.  


=== Odd harmonics ===
=== Odd harmonics ===
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1553edo is the 245th [[prime edo]]. 3106edo, which doubles it, provides a good correction to the harmonic 3.
1553edo is the 245th [[prime edo]]. 3106edo, which doubles it, provides a good correction to the harmonic 3.


==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" |[[Comma list|Comma List]]
! rowspan="2" |[[Mapping]]
! rowspan="2" |Optimal<br>8ve Stretch (¢)
! colspan="2" |Tuning Error
|-
|-
![[TE error|Absolute]] (¢)
! rowspan="2" | [[Subgroup]]
![[TE simple badness|Relative]] (%)
! rowspan="2" | [[Comma list]]
! rowspan="2" | [[Mapping]]
! rowspan="2" | Optimal<br />8ve stretch (¢)
! colspan="2" | Tuning error
|-
|-
|2.3
! [[TE error|Absolute]] (¢)
|{{monzo|-2461 1553}}
! [[TE simple badness|Relative]] (%)
|{{val|1553 2461}}
| 0.1089
| 0.1089
| 14.09
|-
|-
|2.3.5
| 2.9
|1224440064/1220703125, {{monzo|-201 99 19}}
| {{monzo| 4923 -1553 }}
|{{val|1553 2461 3606}}
| {{mapping| 1553 4923 }}
| 0.0675
| −0.0130
| 0.1064
| 0.0130
| 13.77
| 1.68
|-
|-
|2.3.5.7
| 2.9.5
|200120949/200000000, 2579890176/2573571875, 23066015625/23018340352
| {{monzo| 93 -33 5 }}, {{monzo| -36 -26 51 }}
|{{val|1553 2461 3606 4360}}
| {{mapping| 1553 4923 3606 }}
| 0.0384
| −0.0137
| 0.1051
| 0.0106
| 13.60
| 1.38
|-
|-
|2.3.5.7.11
| 2.9.5.7
|24057/24010, 759375/758912, 2359296/2358125, 992436543/991232000
| {{monzo| -5 5 5 -8 }}, {{monzo| 2 -10 14 -1 }}, {{monzo| 37 1 -4 -11 }}
|{{val|1553 2461 3606 4360 5372}}
| {{mapping| 1553 4923 3606 4360 }}
| 0.0529
| −0.0225
| 0.0984
| 0.0178
| 12.73
| 2.31
|-
|-
|2.3.5.7.11.13
| 2.9.5.7.13
|729/728, 1716/1715, 40656/40625, 196625/196608, 14085981/14080000
| 4096/4095, 140625/140608, 28829034/28824005, {{monzo| 4 10 -9 0 -4 }}
|{{val|1553 2461 3606 4360 5372 5747}}
| {{mapping| 1553 4923 3606 4360 5372 }}
| 0.0366
| −0.0271
| 0.0970
| 0.0184
| 12.55
| 2.38
|-
|2.3.5.7.11.13.17
|729/728, 1716/1715, 1089/1088, 14400/14399, 27648/27625, 14085981/14080000
|{{val|1553 2461 3606 4360 5372 5747 6348}}
| 0.0267
| 0.0930
| 12.04
|-
|2.3.5.7.11.13.17.19
|729/728, 1716/1715, 1089/1088, 5985/5984, 4200/4199, 21888/21875, 287469/287375
|{{val|1553 2461 3606 4360 5372 5747 6348 6597}}
| 0.0241
| 0.0872
| 11.29
|}
|}
== Music ==
; [[Francium]]
* [https://www.youtube.com/watch?v=gdxwRJSLyvw ''Stumbling Over Mystery''] (2023)
[[Category:Listen]]
Retrieved from "https://en.xen.wiki/w/1553edo"