1051edo: Difference between revisions

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Created page with "{{Infobox ET}} {{EDO intro|1051}} == Theory == 1051et tempers out 2460375/2458624 in the 7-limit; 820125/819896, 2097152/2096325, 514714375/514434888, 180224/180075, 184549376..."
 
→Regular temperament properties: plz note 2.3.15 is equivalent to 2.3.5 and 2.3.15.35 is equivalent to 2.3.5.7. It doesn't seem to be supporting edson in any obvious way, either
Line 8: Line 8:
===Subsets and supersets===
===Subsets and supersets===
1051edo is the 177th [[prime edo]]. 2102edo, which doubles it, gives a good correction to the harmonic 5. 4212edo, which quadruples it, gives a good correction to the harmonic 7.
1051edo is the 177th [[prime edo]]. 2102edo, which doubles it, gives a good correction to the harmonic 5. 4212edo, which quadruples it, gives a good correction to the harmonic 7.
==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|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]] (¢)
![[TE simple badness|Relative]] (%)
! [[TE simple badness|Relative]] (%)
|-
|-
|2.3
| 2.3
|{{monzo|1666 -1051}}
| {{monzo| 1666 -1051 }}
|{{val|1051 1666}}
| {{val| 1051 1666 }}
| -0.0736
| -0.0736
| 0.0736
| 0.0736
| 6.45
| 6.45
|-
|-
|2.3.15
| 2.3.5
|{{monzo|-68 1 17}}, {{monzo|42 -61 14}}
| {{monzo| -68 18 17 }}, {{monzo| -26 -29 31 }}
|{{val|1051 1666 4106}}
| {{val| 1051 1666 2440 }} (1051)
| -0.0353
| +0.0077
| 0.0810
| 0.1298
| 7.09
| 11.4
|-
|-
|2.3.15.35
| 2.3.5
|2460375/2458624, 4096000/4084101, 299072265625/297538935552
| {{monzo| 40 7 -22 }}, {{monzo| 63 -50 7 }}
|{{val|1051 1666 4106 5391}}
| {{val| 1051 1666 2441 }} (1051c)
| -0.0333
| -0.1562
| 0.0702
| 0.1313
| 6.15
| 11.5
|-
|2.3.15.35.11
|6250/6237, 180224/180075, 2460375/2458624, 43923/43904
|{{val|1051 1666 4106 5391 3636}}
| -0.0357
| 0.0630
| 5.52
|-
|2.3.15.35.11.13
|1716/1715, 4096/4095, 6250/6237, 91125/91091, 6656/6655
|{{val|1051 1666 4106 5391 3636 3889}}
| -0.0214
| 0.0658
| 5.76
|-
|2.3.15.35.11.13.17
|1275/1274, 1716/1715, 2431/2430, 4096/4095, 6250/6237, 6656/6655
|{{val|1051 1666 4106 5391 3636 3889 4296}}
| -0.0214
| 0.0609
| 5.33
|-
|2.3.15.35.11.13.17.19
|1540/1539, 1275/1274, 1716/1715, 2431/2430, 4096/4095, 6250/6237, 41800/41769
|{{val|1051 1666 4106 5391 3636 3889 4296 4465}}
| -0.0331
| 0.0648
| 5.68
|}
|}
 
<!--
=== 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
|+Table of rank-2 temperaments by generator
! Periods<br>per 8ve
! Periods<br>per 8ve
! Generator<br>(reduced)
! Generator<br>(Reduced)
! Cents<br>(reduced)
! Cents<br>(Reduced)
! Associated<br>ratio
! Associated<br>Ratio
! Temperaments
! Temperaments
|-
|-
|1
|435\1051
|496.67
|5457/4096
|Edson
|}
|}
-->


==  Music ==
==  Music ==
*[https://www.youtube.com/watch?v=e1lARtnPl1E you have to run!] by [[User:Francium|Francium]]
*[https://www.youtube.com/watch?v=e1lARtnPl1E you have to run!] by [[User:Francium|Francium]]

Revision as of 08:19, 8 May 2023

← 1050edo 1051edo 1052edo →
Prime factorization 1051 (prime)
Step size 1.14177 ¢ 
Fifth 615\1051 (702.188 ¢)
Semitones (A1:m2) 101:78 (115.3 ¢ : 89.06 ¢)
Consistency limit 3
Distinct consistency limit 3

Template:EDO intro

Theory

1051et tempers out 2460375/2458624 in the 7-limit; 820125/819896, 2097152/2096325, 514714375/514434888, 180224/180075, 184549376/184528125, 43923/43904 and 20614528/20588575 in the 11-limit. From a regular temperament perspective, 1051edo only has a consistency limit of 3 and does poorly with approximating the harmonics 5 and 7. However, 1051edo has a good representation of the 2.3.11.13.15.17.19.35 subgroup.

Odd harmonics

Approximation of odd harmonics in 1051edo
Harmonic 3 5 7 9 11 13 15 17 19 21 23
Error Absolute (¢) +0.233 -0.396 +0.537 +0.467 +0.157 -0.185 -0.162 +0.087 +0.489 -0.372 -0.301
Relative (%) +20.4 -34.6 +47.0 +40.9 +13.7 -16.2 -14.2 +7.7 +42.8 -32.6 -26.4
Steps
(reduced) 		1666
(615) 		2440
(338) 		2951
(849) 		3332
(179) 		3636
(483) 		3889
(736) 		4106
(953) 		4296
(92) 		4465
(261) 		4616
(412) 		4754
(550)

Subsets and supersets

1051edo is the 177th prime edo. 2102edo, which doubles it, gives a good correction to the harmonic 5. 4212edo, which quadruples it, gives a good correction to the harmonic 7.

Regular temperament properties

Subgroup Comma List Mapping Optimal
8ve Stretch (¢) 		Tuning Error
Absolute (¢) Relative (%)
2.3 [1666 -1051⟩ ⟨1051 1666] -0.0736 0.0736 6.45
2.3.5 [-68 18 17⟩, [-26 -29 31⟩ ⟨1051 1666 2440] (1051) +0.0077 0.1298 11.4
2.3.5 [40 7 -22⟩, [63 -50 7⟩ ⟨1051 1666 2441] (1051c) -0.1562 0.1313 11.5

Music

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