1000edo: Difference between revisions

Line 3:

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

== 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 ===

=== 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.

==Regular temperament properties==

== Regular temperament properties ==

{| 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

| 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

| 0.0159

| 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

| 0.0764

| 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

| 0.0854

| 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

| 0.0857

Line 59:

Line 63:

== 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|####]~~] ~~~~

@@ Line 3: / Line 3: @@
 edo is notable mostly because it is the equal division corresponding to millioctaves.
 == Theory ==
-edo 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]].
+edo 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 ===
-{{harmonics in equal|1000}}
+{{Harmonics in equal|1000}}
 === Subsets and supersets ===
-edo 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}}.
+edo 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.
-==Regular temperament properties==
+== Regular temperament properties ==
 {| 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
 | 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
 | 0.0159
 | 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
 | 0.0764
 | 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
 | 0.0854
 | 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
 | 0.0857
@@ Line 59: / Line 63: @@
 == 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 -->