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1000edo is notable mostly because it is the equal division corresponding to millioctaves.
1000edo is notable mostly because it is the equal division corresponding to millioctaves.
== Theory ==
== Theory ==
1000edo is related to 200edo, but the [[patent val]]s differ on the mapping for 5 and 7. In the [[5-limit]], it tempers out luna comma, 274877906944/274658203125 and senior comma, {{Monzo| -17 62 -35 }}. In the [[7-limit]], it tempers out 4375/4374, 201768035/201326592, and 165288374272/164794921875, leading to the [[lunatic temperament]] and [[seniority temperament]]. It also tempers out 3025/3024, 9801/9800, and 391314/390625 in the [[11-limit]]; 1001/1000, 4225/4224, 4459/4455, and 10648/10647 in the [[13-limit]], leading to the [[deca temperament]] and [[donar temperament]].  
1000edo is related to 200edo, but the [[patent val]]s differ on the mapping for 5 and 7. In the [[5-limit]], it tempers out luna comma, 274877906944/274658203125 and senior comma, {{monzo| -17 62 -35 }}. In the [[7-limit]], it tempers out [[4375/4374]], 201768035/201326592, and 165288374272/164794921875, leading to the [[lunatic]] temperament and [[seniority]] temperament. It also tempers out [[3025/3024]], [[9801/9800]], and 391314/390625 in the [[11-limit]]; [[1001/1000]], [[4225/4224]], 4459/4455, and [[10648/10647]] in the [[13-limit]], leading to the [[deca]] temperament and [[donar]] temperament.  
 
=== Prime harmonics ===
=== Prime harmonics ===
{{harmonics in equal|1000}}
{{Harmonics in equal|1000}}
 
=== Subsets and supersets ===
=== Subsets and supersets ===
1000edo carries the interval size measure ''millioctave'' and has subset edos {{EDOs|1, 2, 4, 5, 8, 10, 20, 25, 40, 50, 100, 125, 200, 250, 500}}.
1000edo carries the interval size measure ''millioctave'' and has subset edos {{EDOs| 1, 2, 4, 5, 8, 10, 20, 25, 40, 50, 100, 125, 200, 250, 500 }}.


[[2000edo]], which doubles 1000edo, is consistent in the 29-odd-limit and thus provides good corrections for the 2.7.11.13.17.23 subgroup.
[[2000edo]], which doubles 1000edo, is consistent in the 29-odd-limit and thus provides good corrections for the 2.7.11.13.17.23 subgroup.
==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|317 -200}}
| {{monzo| 317 -200 }}
|{{val|1000 1585}}
| {{mapping| 1000 1585 }}
| -0.0142
| -0.0142
| 0.0142
| 0.0142
| 1.18
| 1.18
|-
|-
|2.3.5
| 2.3.5
|{{monzo|38 -2 -15}}, {{monzo|55 -64 20}}
| {{monzo| 38 -2 -15 }}, {{monzo| 55 -64 20 }}
|{{val|1000 1585 2322}}
| {{mapping| 1000 1585 2322 }}
| -0.0219
| -0.0219
| 0.0159
| 0.0159
| 1.33
| 1.33
|-
|-
|2.3.5.7
| 2.3.5.7
|4375/4374, 4202539929/4194304000, 578509309952/576650390625
| 4375/4374, 4202539929/4194304000, 578509309952/576650390625
|{{val|1000 1585 2322 2807}}
| {{mapping| 1000 1585 2322 2807 }}
| +0.0215
| +0.0215
| 0.0764
| 0.0764
| 6.37
| 6.37
|-
|-
|2.3.5.7.11
| 2.3.5.7.11
|3025/3024, 4375/4374, 422576/421875, 5907360375/5905580032
| 3025/3024, 4375/4374, 422576/421875, 5907360375/5905580032
|{{val|1000 1585 2322 2807 3459}}
| {{mapping| 1000 1585 2322 2807 3459 }}
| +0.0472
| +0.0472
| 0.0854
| 0.0854
| 7.12
| 7.12
|-
|-
|2.3.5.7.11.13
| 2.3.5.7.11.13
|1001/1000, 3025/3024, 4459/4455, 43904/43875, 708883245/708837376
| 1001/1000, 3025/3024, 4459/4455, 43904/43875, 708883245/708837376
|{{val|1000 1585 2322 2807 3459 3700}}
| {{mapping| 1000 1585 2322 2807 3459 3700 }}
| +0.0631
| +0.0631
| 0.0857
| 0.0857
Line 59: Line 63:


== Music ==
== Music ==
* [https://www.youtube.com/watch?v=EWuVnLOcaRg Moongazing] by Xotla
; [[Xotla]]
 
* "Moongazing" from ''Lessor Groove'' (2020) [https://xotla.bandcamp.com/track/moongazing-luna-25 Bandcamp] | [https://www.youtube.com/watch?v=EWuVnLOcaRg YouTube] – atmospheric-electro, luna[25] in 1000edo
[[Category:Equal divisions of the octave|####]] <!-- 4-digit number -->

Revision as of 07:40, 5 September 2023

← 999edo 1000edo 1001edo →
Prime factorization 23 × 53
Step size 1.2 ¢ 
Fifth 585\1000 (702 ¢) (→ 117\200)
Semitones (A1:m2) 95:75 (114 ¢ : 90 ¢)
Consistency limit 9
Distinct consistency limit 9

Template:EDO intro

1000edo is notable mostly because it is the equal division corresponding to millioctaves.

Theory

1000edo is related to 200edo, but the patent vals differ on the mapping for 5 and 7. In the 5-limit, it tempers out luna comma, 274877906944/274658203125 and senior comma, [-17 62 -35⟩. In the 7-limit, it tempers out 4375/4374, 201768035/201326592, and 165288374272/164794921875, leading to the lunatic temperament and seniority temperament. It also tempers out 3025/3024, 9801/9800, and 391314/390625 in the 11-limit; 1001/1000, 4225/4224, 4459/4455, and 10648/10647 in the 13-limit, leading to the deca temperament and donar temperament.

Prime harmonics

Approximation of prime harmonics in 1000edo
Harmonic 2 3 5 7 11 13 17 19 23 29 31
Error Absolute (¢) +0.000 +0.045 +0.086 -0.426 -0.518 -0.528 -0.555 +0.087 +0.526 +0.023 -0.236
Relative (%) +0.0 +3.7 +7.2 -35.5 -43.2 -44.0 -46.3 +7.2 +43.8 +1.9 -19.6
Steps
(reduced) 		1000
(0) 		1585
(585) 		2322
(322) 		2807
(807) 		3459
(459) 		3700
(700) 		4087
(87) 		4248
(248) 		4524
(524) 		4858
(858) 		4954
(954)

Subsets and supersets

1000edo carries the interval size measure millioctave and has subset edos 1, 2, 4, 5, 8, 10, 20, 25, 40, 50, 100, 125, 200, 250, 500.

2000edo, which doubles 1000edo, is consistent in the 29-odd-limit and thus provides good corrections for the 2.7.11.13.17.23 subgroup.

Regular temperament properties

Subgroup Comma List Mapping Optimal
8ve Stretch (¢) 		Tuning Error
Absolute (¢) Relative (%)
2.3 [317 -200⟩ [⟨1000 1585]] -0.0142 0.0142 1.18
2.3.5 [38 -2 -15⟩, [55 -64 20⟩ [⟨1000 1585 2322]] -0.0219 0.0159 1.33
2.3.5.7 4375/4374, 4202539929/4194304000, 578509309952/576650390625 [⟨1000 1585 2322 2807]] +0.0215 0.0764 6.37
2.3.5.7.11 3025/3024, 4375/4374, 422576/421875, 5907360375/5905580032 [⟨1000 1585 2322 2807 3459]] +0.0472 0.0854 7.12
2.3.5.7.11.13 1001/1000, 3025/3024, 4459/4455, 43904/43875, 708883245/708837376 [⟨1000 1585 2322 2807 3459 3700]] +0.0631 0.0857 7.14

Music

Xotla
  • "Moongazing" from Lessor Groove (2020) Bandcamp | YouTube – atmospheric-electro, luna[25] in 1000edo
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