1019edo: Difference between revisions

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Created page with "{{Infobox ET}} {{EDO intro|1019}} == Theory == 1019edo is consistent to the 17-odd-limit, tempering out 1275/1274, 3025/3024, 1716/1715, ..."
 
It's best to present nullity-1 temps in terms of commas. Sorting comma lists.
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== Theory ==
== Theory ==
1019edo is [[consistent]] to the [[17-odd-limit]], [[temper out|tempering out]] [[1275/1274]], [[3025/3024]], [[1716/1715]], [[4096/4095]], [[2500/2499]] and 3536379/3536000. Using the 2.3.5.11.17.29.43 [[subgroup]], it tempers out [[17545/17544]]. It [[support]]s [[tritomere]].
1019edo is [[consistent]] to the [[17-odd-limit]]. As an equal temperament, it [[tempering out|tempers out]] [[3025/3024]] and [[1771561/1771470]] in the 11-limit; [[1716/1715]] and [[4096/4095]] in the 13-limit; and [[1275/1274]], [[2500/2499]] and 3536379/3536000 in the 17-limit. Using the 2.3.5.11.17.29.43 [[subgroup]], it tempers out [[17545/17544]].  


=== Prime harmonics ===
=== Prime harmonics ===
Line 9: Line 9:


=== Subsets and supersets ===
=== Subsets and supersets ===
1019edo is the 171st [[prime EDO]].
1019edo is the 171st [[prime edo]].


== 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|-1615 1019}}
| {{monzo| -1615 1019 }}
| {{mapping|1019 1615}}
| {{mapping| 1019 1615 }}
| +0.0285
| +0.0285
| 0.0285
| 0.0285
Line 30: Line 30:
|-
|-
| 2.3.5
| 2.3.5
| {{monzo|-31 43 -16}}, {{monzo|-68 18 17}}
| {{monzo| -31 43 -16 }}, {{monzo| -68 18 17 }}
| {{mapping|1019 1615 2366}}
| {{mapping| 1019 1615 2366 }}
| +0.0266
| +0.0266
| 0.0235
| 0.0235
Line 38: Line 38:
| 2.3.5.7
| 2.3.5.7
| 703125/702464, 14348907/14336000, 283115520/282475249
| 703125/702464, 14348907/14336000, 283115520/282475249
| {{mapping|1019 1615 2366 2861}}
| {{mapping| 1019 1615 2366 2861 }}
| -0.0121
| -0.0121
| 0.0700
| 0.0700
Line 44: Line 44:
|-
|-
| 2.3.5.7.11
| 2.3.5.7.11
| 3025/3024, 759375/758912, 180224/180075, 14348907/14336000
| 3025/3024, 180224/180075, 759375/758912, 14348907/14336000
| {{mapping|1019 1615 2366 2861 3525}}
| {{mapping| 1019 1615 2366 2861 3525 }}
| +0.0013
| +0.0013
| 0.0681
| 0.0681
Line 51: Line 51:
|-
|-
| 2.3.5.7.11.13
| 2.3.5.7.11.13
| 3025/3024, 1716/1715, 4096/4095, 540000/539539, 216513/216320
| 1716/1715, 3025/3024, 4096/4095, 216513/216320, 540000/539539
| {{mapping|1019 1615 2366 2861 3525 3771}}
| {{mapping| 1019 1615 2366 2861 3525 3771 }}
| -0.0123
| -0.0123
| 0.0692
| 0.0692
Line 58: Line 58:
|-
|-
| 2.3.5.7.11.13.17
| 2.3.5.7.11.13.17
| 1275/1274, 3025/3024, 1716/1715, 4096/4095, 2500/2499, 3536379/3536000
| 1275/1274, 1716/1715, 2500/2499, 3025/3024, 4096/4095, 3536379/3536000
| {{mapping|1019 1615 2366 2861 3525 3771 4165}}
| {{mapping| 1019 1615 2366 2861 3525 3771 4165 }}
| -0.0054
| -0.0054
| 0.0662
| 0.0662
| 5.62
| 5.62
|}
|}

Revision as of 14:42, 14 November 2024

← 1018edo 1019edo 1020edo →
Prime factorization 1019 (prime)
Step size 1.17763 ¢ 
Fifth 596\1019 (701.865 ¢)
Semitones (A1:m2) 96:77 (113.1 ¢ : 90.68 ¢)
Consistency limit 17
Distinct consistency limit 17

Template:EDO intro

Theory

1019edo is consistent to the 17-odd-limit. As an equal temperament, it tempers out 3025/3024 and 1771561/1771470 in the 11-limit; 1716/1715 and 4096/4095 in the 13-limit; and 1275/1274, 2500/2499 and 3536379/3536000 in the 17-limit. Using the 2.3.5.11.17.29.43 subgroup, it tempers out 17545/17544.

Prime harmonics

Approximation of prime harmonics in 1019edo
Harmonic 2 3 5 7 11 13 17 19 23 29 31
Error Absolute (¢) +0.000 -0.090 -0.053 +0.360 -0.189 +0.297 -0.147 +0.426 +0.577 -0.333 -0.384
Relative (%) +0.0 -7.7 -4.5 +30.5 -16.1 +25.2 -12.5 +36.2 +49.0 -28.3 -32.6
Steps
(reduced) 		1019
(0) 		1615
(596) 		2366
(328) 		2861
(823) 		3525
(468) 		3771
(714) 		4165
(89) 		4329
(253) 		4610
(534) 		4950
(874) 		5048
(972)

Subsets and supersets

1019edo is the 171st prime edo.

Regular temperament properties

Subgroup Comma List Mapping Optimal
8ve Stretch (¢) 		Tuning Error
Absolute (¢) Relative (%)
2.3 [-1615 1019⟩ [⟨1019 1615]] +0.0285 0.0285 2.42
2.3.5 [-31 43 -16⟩, [-68 18 17⟩ [⟨1019 1615 2366]] +0.0266 0.0235 2.00
2.3.5.7 703125/702464, 14348907/14336000, 283115520/282475249 [⟨1019 1615 2366 2861]] -0.0121 0.0700 5.94
2.3.5.7.11 3025/3024, 180224/180075, 759375/758912, 14348907/14336000 [⟨1019 1615 2366 2861 3525]] +0.0013 0.0681 5.78
2.3.5.7.11.13 1716/1715, 3025/3024, 4096/4095, 216513/216320, 540000/539539 [⟨1019 1615 2366 2861 3525 3771]] -0.0123 0.0692 5.88
2.3.5.7.11.13.17 1275/1274, 1716/1715, 2500/2499, 3025/3024, 4096/4095, 3536379/3536000 [⟨1019 1615 2366 2861 3525 3771 4165]] -0.0054 0.0662 5.62
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