251edo: Difference between revisions

(7 intermediate revisions by 2 users not shown)

Line 1:

== Theory ==

251et [[tempering out|tempers out]] 1600000/1594323 ([[amity comma]]) and {{monzo| 49 -6 -17 }} ([[maquila comma]]) in the 5-limit; [[4375/4374]], [[5120/5103]], and 40500000/40353607 in the 7-limit, [[support]]ing [[amity]], [[supermajor]], and [[acrokleismic]].

251et [[tempering out|tempers out]] 1600000/1594323 ([[amity comma]]) and {{monzo| 49 -6 -17 }} ([[maquila comma]]) in the 5-limit; [[4375/4374]], [[5120/5103]], and 40500000/40353607 in the 7-limit, [[support]]ing [[amity]], [[supermajor (temperament)|supermajor]], and [[acrokleismic]].

Using the [[patent val]] {{val| 251 398 583 705 '''868''' }}, it tempers out 1331/1323, 1375/1372, 16896/16807, and 24057/24010 in the 11-limit; [[352/351]], [[676/675]], [[847/845]], and [[1573/1568]] in the 13-limit.

Line 17:

== 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]] (¢)

! [[TE simple badness|Relative]] (%)

|-

| 2.3

| {{~~monzo~~| 398 -251 }}

| {{Monzo| 398 -251 }}

| {{~~mapping~~| 251 398 }}

| {{Mapping| 251 398 }}

| -0.2630

| −0.2630

| 0.2630

| 5.50

|-

| 2.3.5

| {{~~monzo~~| 9 -13 5 }}, {{monzo| 49 -6 -17 }}

| {{Monzo| 9 -13 5 }}, {{monzo| 49 -6 -17 }}

| {{~~mapping~~| 251 398 583 }}

| {{Mapping| 251 398 583 }}

| -0.3099

| −0.3099

| 0.2247

| 4.70

Line 42:

Line 43:

| 2.3.5.7

| 4375/4374, 5120/5103, 40500000/40353607

| {{~~mapping~~| 251 398 583 705 }}

| {{Mapping| 251 398 583 705 }}

| -0.3830

| −0.3830

| 0.2322

| 4.86

Line 50:

Line 51:

=== 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*

! Cents*

! Associated ~~Ratio~~*

! Associated ratio*

! Temperaments

|-

Line 73:

Line 75:

| 435.06

| 9/7

| [[Supermajor]]

| [[Supermajor (temperament)|Supermajor]]

|-

| 1

Line 87:

Line 89:

| [[Maquila]]

|}

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

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

== Music ==

; [[Francium]]

* "hope in dark times" from ''hope in dark times'' (2024) – [https://open.spotify.com/track/1zSiYXz46ugWAmqySaEN2A Spotify] | [https://francium223.bandcamp.com/track/hope-in-dark-times Bandcamp] | [https://www.youtube.com/watch?v=yHl3oku_NmY YouTube]

* "The Living Space" from ''Check Us Out'' (2026) – [https://open.spotify.com/track/66H2fQ5ogT1j33ludkD0ug Spotify] | [https://francium223.bandcamp.com/track/the-living-space Bandcamp] | [https://www.youtube.com/watch?v=Q4O5l0SnZMI YouTube]

[[Category:Listen]]

@@ Line 1: / Line 1: @@
 {{Infobox ET}}
-{{EDO intro|251}}
+{{ED intro}}
 == Theory ==
-et [[tempering out|tempers out]] 1600000/1594323 ([[amity comma]]) and {{monzo| 49 -6 -17 }} ([[maquila comma]]) in the 5-limit; [[4375/4374]], [[5120/5103]], and 40500000/40353607 in the 7-limit, [[support]]ing [[amity]], [[supermajor]], and [[acrokleismic]].
+et [[tempering out|tempers out]] 1600000/1594323 ([[amity comma]]) and {{monzo| 49 -6 -17 }} ([[maquila comma]]) in the 5-limit; [[4375/4374]], [[5120/5103]], and 40500000/40353607 in the 7-limit, [[support]]ing [[amity]], [[supermajor (temperament)|supermajor]], and [[acrokleismic]].
 Using the [[patent val]] {{val| 251 398 583 705 '''868''' }}, it tempers out 1331/1323, 1375/1372, 16896/16807, and 24057/24010 in the 11-limit; [[352/351]], [[676/675]], [[847/845]], and [[1573/1568]] in the 13-limit.
@@ Line 17: / Line 17: @@
 == 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]] (¢)
 ! [[TE simple badness|Relative]] (%)
 |-
 | 2.3
-| {{monzo| 398 -251 }}
+| {{Monzo| 398 -251 }}
-| {{mapping| 251 398 }}
+| {{Mapping| 251 398 }}
-| -0.2630
+| −0.2630
 | 0.2630
 | 5.50
 |-
 | 2.3.5
-| {{monzo| 9 -13 5 }}, {{monzo| 49 -6 -17 }}
+| {{Monzo| 9 -13 5 }}, {{monzo| 49 -6 -17 }}
-| {{mapping| 251 398 583 }}
+| {{Mapping| 251 398 583 }}
-| -0.3099
+| −0.3099
 | 0.2247
 | 4.70
@@ Line 42: / Line 43: @@
 | 2.3.5.7
 | 4375/4374, 5120/5103, 40500000/40353607
-| {{mapping| 251 398 583 705 }}
+| {{Mapping| 251 398 583 705 }}
-| -0.3830
+| −0.3830
 | 0.2322
 | 4.86
@@ Line 50: / Line 51: @@
 === 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*
 ! Cents*
-! Associated<br>Ratio*
+! Associated<br>ratio*
 ! Temperaments
 |-
@@ Line 73: / Line 75: @@
 | 435.06
 | 9/7
-| [[Supermajor]]
+| [[Supermajor (temperament)|Supermajor]]
 |-
 | 1
@@ Line 87: / Line 89: @@
 | [[Maquila]]
 |}
-<nowiki>*</nowiki> [[Normal lists|octave-reduced form]], reduced to the first half-octave, and [[Normal lists|minimal form]] in parentheses if it is distinct
+<nowiki/>* [[Normal forms #Equave-reduced-generator form|Octave-reduced form]], reduced to the first half-octave, and [[Normal forms|minimal form]] in parentheses if distinct
 == Music ==
 ; [[Francium]]
 * "hope in dark times" from ''hope in dark times'' (2024) – [https://open.spotify.com/track/1zSiYXz46ugWAmqySaEN2A Spotify] | [https://francium223.bandcamp.com/track/hope-in-dark-times Bandcamp] | [https://www.youtube.com/watch?v=yHl3oku_NmY YouTube]
+* "The Living Space" from ''Check Us Out'' (2026) – [https://open.spotify.com/track/66H2fQ5ogT1j33ludkD0ug Spotify] | [https://francium223.bandcamp.com/track/the-living-space Bandcamp] | [https://www.youtube.com/watch?v=Q4O5l0SnZMI YouTube]
 [[Category:Listen]]