1277edo: Difference between revisions

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== Theory ==

1277edo is [[consistent]] to the [[11-odd-limit]]. ~~The~~ equal temperament [[tempering out|tempers out]] [[4375/4374]], 52734375/52706752, 645700815/645657712 ([[starscape comma]]) and {{monzo| 51 -13 -1 -10 }} ([[technologisma]]) in the 7-limit; 151263/151250, 759375/758912, and 2097152/2096325 in the 11-limit. It [[support]]s [[monzismic]], [[supermajor]], [[revopent]], as well as the rank-3 temperament [[bragi]].

1277edo is [[consistent]] to the [[11-odd-limit]]. As an equal temperament, it [[tempering out|tempers out]] [[4375/4374]], 52734375/52706752, 645700815/645657712 ([[starscape comma]]) and {{monzo| 51 -13 -1 -10 }} ([[technologisma]]) in the 7-limit; 151263/151250, 759375/758912, and 2097152/2096325 in the 11-limit. It [[support]]s [[monzismic]], [[supermajor (temperament)|supermajor]], [[revopent]], as well as the rank-3 temperament [[bragi]].

=== Prime harmonics ===

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== 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~~| 2024 -1277 }}

| {{Monzo| 2024 -1277 }}

| {{~~mapping~~| 1277 2024 }}

| {{Mapping| 1277 2024 }}

| -0.0009

| −0.0009

| 0.0009

| 0.10

|-

| 2.3.5

| {{~~monzo~~| 54 -37 2 }}, {{monzo| -67 -9 35 }}

| {{Monzo| 54 -37 2 }}, {{monzo| -67 -9 35 }}

| {{~~mapping~~| 1277 2024 2965 }}

| {{Mapping| 1277 2024 2965 }}

| +0.0132

| 0.0199

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| 2.3.5.7

| 4375/4374, 52734375/52706752, {{monzo| 51 -13 -1 -10 }}

| {{~~mapping~~| 1277 2024 2965 3585 }}

| {{Mapping| 1277 2024 2965 3585 }}

| +0.0093

| 0.0186

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| 2.3.5.7.11

| 4375/4374, 151263/151250, 759375/758912, 2097152/2096325

| {{~~mapping~~| 1277 2024 2965 3585 4418 }}

| {{Mapping| 1277 2024 2965 3585 4418 }}

| -0.0092

| −0.0092

| 0.0405

| 4.31

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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*

! Cents*

! Associated ~~Ratio~~*

! Associated ratio*

! Temperaments

|-

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| 265\1277

| 249.021

| {{~~monzo~~| -27 11 3 1 }}

| {{Monzo| -27 11 3 1 }}

| [[Monzismic]]

|-

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| 435.082

| 9/7

| [[Supermajor]]

| [[Supermajor (temperament)|Supermajor]]

|}

<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]]

* "mututhery" from ''albumwithoutspaces'' (2024) – [https://open.spotify.com/track/6EUbC14BVFJ20b1C4cCOFe Spotify] | [https://francium223.bandcamp.com/track/mututhery Bandcamp] | [https://www.youtube.com/watch?v=0j7yaypCOts YouTube] – ~~monzismic~~[19] in 1277edo tuning

* "mututhery" from ''albumwithoutspaces'' (2024) – [https://open.spotify.com/track/6EUbC14BVFJ20b1C4cCOFe Spotify] | [https://francium223.bandcamp.com/track/mututhery Bandcamp] | [https://www.youtube.com/watch?v=0j7yaypCOts YouTube] – in Monzismic[19], 1277edo tuning

* "Makeup Is Soothing." from ''Random Sentences'' (2025) – [https://open.spotify.com/track/6SJHf64ENaPnzQKlnO315x Spotify] | [https://francium223.bandcamp.com/track/makeup-is-soothing Bandcamp] | [https://www.youtube.com/watch?v=zw1oavPPnqU YouTube] – in aunusic, 1277edo tuning

[[Category:Listen]]

@@ Line 1: / Line 1: @@
 {{Infobox ET}}
-{{EDO intro|1277}}
+{{ED intro}}
 == Theory ==
-edo is [[consistent]] to the [[11-odd-limit]]. The equal temperament [[tempering out|tempers out]] [[4375/4374]], 52734375/52706752, 645700815/645657712 ([[starscape comma]]) and {{monzo| 51 -13 -1 -10 }} ([[technologisma]]) in the 7-limit; 151263/151250, 759375/758912, and 2097152/2096325 in the 11-limit. It [[support]]s [[monzismic]], [[supermajor]], [[revopent]], as well as the rank-3 temperament [[bragi]].
+edo is [[consistent]] to the [[11-odd-limit]]. As an equal temperament, it [[tempering out|tempers out]] [[4375/4374]], 52734375/52706752, 645700815/645657712 ([[starscape comma]]) and {{monzo| 51 -13 -1 -10 }} ([[technologisma]]) in the 7-limit; 151263/151250, 759375/758912, and 2097152/2096325 in the 11-limit. It [[support]]s [[monzismic]], [[supermajor (temperament)|supermajor]], [[revopent]], as well as the rank-3 temperament [[bragi]].
 === Prime harmonics ===
@@ Line 13: / Line 13: @@
 == 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| 2024 -1277 }}
+| {{Monzo| 2024 -1277 }}
-| {{mapping| 1277 2024 }}
+| {{Mapping| 1277 2024 }}
-| -0.0009
+| −0.0009
 | 0.0009
 | 0.10
 |-
 | 2.3.5
-| {{monzo| 54 -37 2 }}, {{monzo| -67 -9 35 }}
+| {{Monzo| 54 -37 2 }}, {{monzo| -67 -9 35 }}
-| {{mapping| 1277 2024 2965 }}
+| {{Mapping| 1277 2024 2965 }}
 | +0.0132
 | 0.0199
@@ Line 38: / Line 39: @@
 | 2.3.5.7
 | 4375/4374, 52734375/52706752, {{monzo| 51 -13 -1 -10 }}
-| {{mapping| 1277 2024 2965 3585 }}
+| {{Mapping| 1277 2024 2965 3585 }}
 | +0.0093
 | 0.0186
@@ Line 45: / Line 46: @@
 | 2.3.5.7.11
 | 4375/4374, 151263/151250, 759375/758912, 2097152/2096325
-| {{mapping| 1277 2024 2965 3585 4418 }}
+| {{Mapping| 1277 2024 2965 3585 4418 }}
-| -0.0092
+| −0.0092
 | 0.0405
 | 4.31
@@ Line 53: / Line 54: @@
 === 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 63: / Line 65: @@
 | 265\1277
 | 249.021
-| {{monzo| -27 11 3 1 }}
+| {{Monzo| -27 11 3 1 }}
 | [[Monzismic]]
 |-
@@ Line 76: / Line 78: @@
 | 435.082
 | 9/7
-| [[Supermajor]]
+| [[Supermajor (temperament)|Supermajor]]
 |}
-<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]]
-* "mututhery" from ''albumwithoutspaces'' (2024) – [https://open.spotify.com/track/6EUbC14BVFJ20b1C4cCOFe Spotify] | [https://francium223.bandcamp.com/track/mututhery Bandcamp] | [https://www.youtube.com/watch?v=0j7yaypCOts YouTube] – monzismic[19] in 1277edo tuning
+* "mututhery" from ''albumwithoutspaces'' (2024) – [https://open.spotify.com/track/6EUbC14BVFJ20b1C4cCOFe Spotify] | [https://francium223.bandcamp.com/track/mututhery Bandcamp] | [https://www.youtube.com/watch?v=0j7yaypCOts YouTube] – in Monzismic[19], 1277edo tuning
+* "Makeup Is Soothing." from ''Random Sentences'' (2025) – [https://open.spotify.com/track/6SJHf64ENaPnzQKlnO315x Spotify] | [https://francium223.bandcamp.com/track/makeup-is-soothing Bandcamp] | [https://www.youtube.com/watch?v=zw1oavPPnqU YouTube] – in aunusic, 1277edo tuning
+[[Category:Listen]]