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770edo: Difference between revisions

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Created page with "{{Infobox ET}} {{EDO intro|770}} ==Theory== 770edo tempers out 134217728/133984375, 703125/702464, 5250987/5242880 and 200120949/200000000 in the 7-limit; 56723625/5668995..."
 
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{{Infobox ET}}
{{Infobox ET}}
{{EDO intro|770}}
{{ED intro}}
==Theory==
 
770edo tempers out 134217728/133984375, [[703125/702464]], 5250987/5242880 and 200120949/200000000 in the 7-limit; 56723625/56689952, 161280/161051, 234375/234256, 2097152/2096325, 496125/495616, 151263/151250, 104857600/104825259, 172032/171875, 369140625/369098752, 825000/823543, 180224/180075, 160083/160000, 766656/765625, 43923/43904, 20614528/20588575 and 781258401/781250000 in the 11-limit.
== Theory ==
===Odd harmonics===
770edo is in[[consistent]] to the [[5-odd-limit]] and [[3/1|harmonic 3]] is about halfway between its steps. It has a reasonable approximation of the 2.9.5.7.11 [[subgroup]], where it notably [[tempering out|tempers out]] [[9801/9800]].  
 
=== Odd harmonics ===
{{Harmonics in equal|770}}
{{Harmonics in equal|770}}
===Subsets and supersets===
 
770 factors into 2 × 5 × 7 × 11 with subset edos {{EDOs| 2, 5, 7, 10, 11, 14, 22, 35, 55, 70, 77, 110, 154, and 385}}. [[1540edo]], which doubles it, gives a good correction to the harmonic 3.
=== Subsets and supersets ===
==Regular temperament properties==
Since 770 factors into {{factorization|770}}, 770edo has subset edos {{EDOs| 2, 5, 7, 10, 11, 14, 22, 35, 55, 70, 77, 110, 154, and 385}}. [[1540edo]], which doubles it, gives a good correction to the harmonic 3.
 
== 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]] (¢)
![[TE simple badness|Relative]] (%)
|-
|-
|2.9
! rowspan="2" | [[Subgroup]]
|{{monzo|2441 -770}}
! rowspan="2" | [[Comma list]]
|{{val|770 2441}}
! rowspan="2" | [[Mapping]]
| -0.0388
! rowspan="2" | Optimal<br />8ve stretch (¢)
! colspan="2" | Tuning error
|-
! [[TE error|Absolute]] (¢)
! [[TE simple badness|Relative]] (%)
|-
| 2.9
| {{monzo| 2441 -770 }}
| {{mapping| 770 2441 }}
| −0.0388
| 0.0388
| 0.0388
| 2.49
| 2.49
|-
|-
|2.9.5
| 2.9.5
|{{monzo|61 2 -29}}, {{monzo|40 -28 21}}
| {{monzo| 61 2 -29 }}, {{monzo| 40 -28 21 }}
|{{val|770 2441 1788}}
| {{mapping| 770 2441 1788 }}
| -0.0517
| −0.0517
| 0.0365
| 0.0365
| 2.34
| 2.34
|-
|-
|2.9.5.7
| 2.9.5.7
|43046721/43025920, 134217728/133984375, 1220703125/1219784832
| 43046721/43025920, 134217728/133984375, 1220703125/1219784832
|{{val|770 2441 1788 2162}}
| {{mapping| 770 2441 1788 2162 }}
| -0.0855
| −0.0855
| 0.0666
| 0.0666
| 4.27
| 4.27
|-
|-
|2.9.5.7.11
| 2.9.5.7.11
|9801/9800, 820125/819896, 1296000/1294139, 1362944/1361367
| 9801/9800, 820125/819896, 1296000/1294139, 1362944/1361367
|{{val|770 2441 1788 2162 2664}}
| {{mapping| 770 2441 1788 2162 2664 }}
| -0.0898
| −0.0898
| 0.0602
| 0.0602
| 3.86
| 3.86
|}
|}
==Scales==
 
== Scales ==
* [[Semidim8]]
* [[Semidim8]]
* [[Semidim13]]
* [[Semidim13]]
Retrieved from "https://en.xen.wiki/w/770edo"