1000edo: Difference between revisions

Line 5:

== 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 {{monzo| 38 -2 -15 }} (luna comma) and {{monzo| -17 62 -35 }} (senior comma). 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 ===

Line 41:

|-

| 2.3.5.7

| 4375/4374, ~~4202539929~~/~~4194304000~~, ~~578509309952/576650390625~~

| 4375/4374, 201768035/201326592, {{monzo| 12 -3 -14 9 }}

| {{mapping| 1000 1585 2322 2807 }}

| +0.0215

Line 48:

|-

| 2.3.5.7.11

| 3025/3024, 4375/4374, ~~422576~~/~~421875~~, ~~5907360375/5905580032~~

| 3025/3024, 4375/4374, 391314/390625, {{monzo| -32 13 1 2 1 }}

| {{mapping| 1000 1585 2322 2807 3459 }}

| +0.0472

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|-

| 2.3.5.7.11.13

| 1001/1000, 3025/3024, ~~4459~~/~~4455~~, ~~43904~~/~~43875~~, 708883245/708837376

| 1001/1000, 3025/3024, 4225/4224, 4375/4374, 708883245/708837376

| {{mapping| 1000 1585 2322 2807 3459 3700 }}

| +0.0631

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| 7.14

|}

=== Rank-2 temperaments ===

{| class="wikitable center-all left-5"

|+Table of rank-2 temperaments by generator

! Periods per 8ve

! Generator (~~reduced~~)

! Generator (Reduced)

! Cents (~~reduced~~)

! Cents (Reduced)

! Associated ~~ratio~~

! Associated Ratio

! Temperaments

|-

|1

| 1

|161\1000

| 161\1000

|193.200

| 193.200

|262144/234375

| 262144/234375

|[[~~Luna~~]]

| [[Lunatic]] (7-limit)

|-

|1

| 1

|269\1000

| 269\1000

|322.800

| 322.800

|~~{{monzo|-6 23 -13}}~~

| 3087/2560

|[[~~Senior]] / [[seniority~~]]

| [[Seniority]]

|-

|4

| 4

|317\1000 (67\1000)

| 317\1000 (67\1000)

|380.400 (80.400)

| 380.400 (80.400)

|5103/4096 (22/21)

| 5103/4096 (22/21)

|[[Quasithird]]

| [[Quasithird]]

|-

|10

| 10

|263\1000 (37\1000)

| 263\1000 (37\1000)

|315.600 (44.400)

| 315.600 (44.400)

|6/5 (15/14)

| 6/5 (15/14)

|[[Deca]]

| [[Deca]]

|}

@@ Line 5: / Line 5: @@
 == 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 {{monzo| 38 -2 -15 }} (luna comma) and {{monzo| -17 62 -35 }} (senior comma). 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 ===
@@ Line 41: / Line 41: @@
 |-
 | 2.3.5.7
-| 4375/4374, 4202539929/4194304000, 578509309952/576650390625
+| 4375/4374, 201768035/201326592, {{monzo| 12 -3 -14 9 }}
 | {{mapping| 1000 1585 2322 2807 }}
 | +0.0215
@@ Line 48: / Line 48: @@
 |-
 | 2.3.5.7.11
-| 3025/3024, 4375/4374, 422576/421875, 5907360375/5905580032
+| 3025/3024, 4375/4374, 391314/390625, {{monzo| -32 13 1 2 1 }}
 | {{mapping| 1000 1585 2322 2807 3459 }}
 | +0.0472
@@ Line 55: / Line 55: @@
 |-
 | 2.3.5.7.11.13
-| 1001/1000, 3025/3024, 4459/4455, 43904/43875, 708883245/708837376
+| 1001/1000, 3025/3024, 4225/4224, 4375/4374, 708883245/708837376
 | {{mapping| 1000 1585 2322 2807 3459 3700 }}
 | +0.0631
@@ Line 61: / Line 61: @@
 | 7.14
 |}
 === Rank-2 temperaments ===
 {| class="wikitable center-all left-5"
 |+Table of rank-2 temperaments by generator
 ! Periods<br>per 8ve
-! Generator<br>(reduced)
+! Generator<br>(Reduced)
-! Cents<br>(reduced)
+! Cents<br>(Reduced)
-! Associated<br>ratio
+! Associated<br>Ratio
 ! Temperaments
 |-
-|1
+| 1
-|161\1000
+| 161\1000
-|193.200
+| 193.200
-|262144/234375
+| 262144/234375
-|[[Luna]]
+| [[Lunatic]] (7-limit)
 |-
-|1
+| 1
-|269\1000
+| 269\1000
-|322.800
+| 322.800
-|{{monzo|-6 23 -13}}
+| 3087/2560
-|[[Senior]] / [[seniority]]
+| [[Seniority]]
 |-
-|4
+| 4
-|317\1000<br>(67\1000)
+| 317\1000<br>(67\1000)
-|380.400<br>(80.400)
+| 380.400<br>(80.400)
-|5103/4096<br>(22/21)
+| 5103/4096<br>(22/21)
-|[[Quasithird]]
+| [[Quasithird]]
 |-
-|10
+| 10
-|263\1000<br>(37\1000)
+| 263\1000<br>(37\1000)
-|315.600<br>(44.400)
+| 315.600<br>(44.400)
-|6/5<br>(15/14)
+| 6/5<br>(15/14)
-|[[Deca]]
+| [[Deca]]
 |}