1051edo: Difference between revisions

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== 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.

1051edo only has a [[consistency]] limit of 3 and does poorly with approximating the harmonic 5. However, it has a reasonable representation of the 2.3.7.11.17.19 subgroup.

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===

Assume the [[patent val]], 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.

=== Odd harmonics ===

===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.

=== Subsets and supersets ===

1051edo is the 177th [[prime edo]]. 2102edo, which doubles it, gives a good correction to the harmonic 5 and 7. 4212edo, which quadruples it, gives a good correction to the harmonic 3.

== Regular temperament properties ==

{| class="wikitable center-4 center-5 center-6"

|-

! rowspan="2" | [[Subgroup]]

! rowspan="2" | [[Comma list~~|Comma List~~]]

! rowspan="2" | [[Comma list]]

! rowspan="2" | [[Mapping]]

! rowspan="2" | Optimal 8ve ~~Stretch~~ (¢)

! rowspan="2" | Optimal 8ve stretch (¢)

! colspan="2" | Tuning ~~Error~~

! colspan="2" | Tuning error

|-

! [[TE error|Absolute]] (¢)

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| 2.3

| {{monzo| 1666 -1051 }}

| {{~~val~~| 1051 1666 }}

| {{mapping| 1051 1666 }}

| -0.0736

| −0.0736

| 0.0736

| 6.45

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| 2.3.5

| {{monzo| -68 18 17 }}, {{monzo| -26 -29 31 }}

| {{~~val~~| 1051 1666 2440 }} (1051)

| {{mapping| 1051 1666 2440 }} (1051)

| +0.0077

| 0.1298

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| 2.3.5

| {{monzo| 40 7 -22 }}, {{monzo| 63 -50 7 }}

| {{~~val~~| 1051 1666 2441 }} (1051c)

| {{mapping| 1051 1666 2441 }} (1051c)

| -0.1562

| −0.1562

| 0.1313

| 11.5

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=== Rank-2 temperaments ===

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

|+Table of rank-2 temperaments by generator

|+ style="font-size: 105%;" | Table of rank-2 temperaments by generator

! Periods per 8ve

|-

! Generator~~ (Reduced)~~

! Periods per 8ve

! Cents~~ (Reduced)~~

! Generator*

! Associated ~~Ratio~~

! Cents*

! Associated ratio*

! Temperaments

|-

|}

<nowiki />* [[Normal lists|Octave-reduced form]], reduced to the first half-octave, and [[Normal lists|minimal form]] in parentheses if distinct

-->

== Music ==

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

; [[Francium]]

* [https://www.youtube.com/watch?v=e1lARtnPl1E ''you have to run!''] (2023) – [[edson]] in 1051edo tuning

[[Category:Listen]]

@@ Line 1: / Line 1: @@
 {{Infobox ET}}
-{{EDO intro|1051}}
+{{ED intro}}
 == Theory ==
-et 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.
+edo only has a [[consistency]] limit of 3 and does poorly with approximating the harmonic 5. However, it has a reasonable representation of the 2.3.7.11.17.19 subgroup.
-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===
+Assume the [[patent val]], 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.
+=== Odd harmonics ===
 {{Harmonics in equal|1051}}
-===Subsets and supersets===
-edo 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.
+=== Subsets and supersets ===
+edo is the 177th [[prime edo]]. 2102edo, which doubles it, gives a good correction to the harmonic 5 and 7. 4212edo, which quadruples it, gives a good correction to the harmonic 3.
 == Regular temperament properties ==
 {| class="wikitable center-4 center-5 center-6"
+|-
 ! rowspan="2" | [[Subgroup]]
-! rowspan="2" | [[Comma list|Comma List]]
+! rowspan="2" | [[Comma list]]
 ! 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]] (¢)
@@ Line 21: / Line 27: @@
 | 2.3
 | {{monzo| 1666 -1051 }}
-| {{val| 1051 1666 }}
+| {{mapping| 1051 1666 }}
-| -0.0736
+| −0.0736
 | 0.0736
 | 6.45
@@ Line 28: / Line 34: @@
 | 2.3.5
 | {{monzo| -68 18 17 }}, {{monzo| -26 -29 31 }}
-| {{val| 1051 1666 2440 }} (1051)
+| {{mapping| 1051 1666 2440 }} (1051)
 | +0.0077
 | 0.1298
@@ Line 35: / Line 41: @@
 | 2.3.5
 | {{monzo| 40 7 -22 }}, {{monzo| 63 -50 7 }}
-| {{val| 1051 1666 2441 }} (1051c)
+| {{mapping| 1051 1666 2441 }} (1051c)
-| -0.1562
+| −0.1562
 | 0.1313
 | 11.5
@@ Line 43: / Line 49: @@
 === Rank-2 temperaments ===
 {| class="wikitable center-all left-5"
-|+Table of rank-2 temperaments by generator
+|+ style="font-size: 105%;" | Table of rank-2 temperaments by generator
-! Periods<br>per 8ve
+|-
-! Generator<br>(Reduced)
+! Periods<br />per 8ve
-! Cents<br>(Reduced)
+! Generator*
-! Associated<br>Ratio
+! Cents*
+! Associated<br />ratio*
 ! Temperaments
-|-
 |}
+<nowiki />* [[Normal lists|Octave-reduced form]], reduced to the first half-octave, and [[Normal lists|minimal form]] in parentheses if distinct
 -->
-==  Music ==
+== Music ==
-*[https://www.youtube.com/watch?v=e1lARtnPl1E you have to run!] by [[User:Francium|Francium]]
+; [[Francium]]
+* [https://www.youtube.com/watch?v=e1lARtnPl1E ''you have to run!''] (2023) – [[edson]] in 1051edo tuning
+[[Category:Listen]]