11edt: Difference between revisions

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== Theory ==

From a no-~~two~~ point of view, 11edt has a [[5/3]] major sixth that is 19.8 cents flat. However, 11edt has an extremely inaccurate seventh harmonic [[7/1]], which is off by almost half a step (or about a semitone), which causes it to temper out [[49/45]] in the 7-limit. 11edt is at the extreme end of [[arcturus]] temperament, defined by tempering out [[15625/15309]] in the 3.5.7 subgroup. It gives an equalized interpretation for the [[9L 2s (3/1-equivalent)|sub-arcturus]] [[~~MOS~~]] ~~scale~~.

11edt can be seen as a very [[stretched and compressed tuning|stretched]] version of [[7edo]], with octaves sharpened by 10.3 cents. The octave stretching makes the [[3/2]] perfect fifth in better tune, while preserving a just [[3/1]] tritave.

From a no-2 point of view, 11edt has a [[5/3]] major sixth that is 19.8 cents flat. However, 11edt has an extremely inaccurate seventh harmonic [[7/1]], which is off by almost half a step (or about a semitone), which causes it to temper out [[49/45]] in the 7-limit. 11edt is at the extreme end of [[arcturus]] temperament, defined by tempering out [[15625/15309]] in the 3.5.7 subgroup. It gives an equalized interpretation for the [[9L 2s (3/1-equivalent)|sub-arcturus]] [[mos scale]].

The 11th harmonic, [[11/1]], only 1.6 cents flat, is very close to just. By exploiting the badly tuned seventh harmonic, 11edt tempers out [[35/33]] and [[77/75]] in the 11-limit. In the 3.5.11 subgroup, it tempers out [[125/121]].

=== ~~Relation to edos~~ ===

=== Harmonics ===

~~11edt can be seen as a very stretched version of [[7edo]], with octaves sharpened by 10.~~3 ~~cents. The octave stretching makes the [[3/2]] perfect fifth~~ in ~~better tune, while preserving a just [[~~3/1~~]] tritave.~~

{{Harmonics in equal|11|3|1|intervals=integer|columns=12|start=12|collapsed=true|title=Approximation of harmonics in 11edt (continued)}}

==~~= Prime harmonics ===~~

== Intervals ==

~~{{Harmonics in equal|11|3|1}}~~

{| class="wikitable center-1 right-2 right-3"

~~{{Harmonics in equal|11|3|1|intervals=prime}}~~

~~=== Interval table =~~==

{| class="wikitable center-~~all~~"

|-

! #

Line 23:

Line 22:

! [[Arcturus]] nonatonic notation (J = 1/1)

|-

| ~~colspan = "3"~~ | 0

| 0

| 0.0

| [[1/1]]

| J

Line 82:

Line 83:

|-

| 10

| 1729

| 1729.0

| 1181

| 1181.0

|

| R

|-

| 11

| 1902

| 1902.0

| 1300

| 1300.0

|

| J

|}

== ~~Pieces~~ ==

== Music ==

Mozart's [http://micro.soonlabel.com/6th-comma-meantone/K331-period/k331-walter-piano-11edt.mp3 ~~sonata #~~11 in A ~~Major K331 in 11 EDT~~] (using a 11 ~~=>~~ 12 key mapping so octaves become tritaves)

=== Modern renderings ===

; {{W|Wolfgang Amadeus Mozart}}

[http://micro.soonlabel.com/tritave_in_11/11of_tritave_improv.mp3 Frozen Time Occupies Wall Street] by [http://www.chrisvaisvil.com Chris Vaisvil] =>[http://chrisvaisvil.com/?p=1392 information about the piece]

* [https://web.archive.org/web/20201127012444/http://micro.soonlabel.com/6th-comma-meantone/K331-period/k331-walter-piano-11edt.mp3 ''Piano Sonata No. 11'' in A major, K. 331] – using a 11 → 12 key mapping so octaves become tritaves

[http://micro.soonlabel.com/~~11edt~~/~~daily20111118-3-11of-edt-mollys-playground~~.mp3 Molly's Playground~~] by~~ [~~http~~://www.chrisvaisvil.com ~~Chris Vaisvil~~] ~~=>~~ [http://~~chrisvaisvil~~.com/~~?p=1716 information about the piece]~~

=== 21st century ===

~~[[category:macrotonal]~~]

; [[Chris Vaisvil]]

* ''Frozen Time Occupies Wall Street'' (2011) – [https://www.chrisvaisvil.com/frozen-time-occupies-wall-street/ blog] | [https://web.archive.org/web/20220911143825/http://micro.soonlabel.com/tritave_in_11/11of_tritave_improv.mp3 play]

* ''Molly's Playground'' (2011) – [https://www.chrisvaisvil.com/mollys-playground/ blog] | [https://web.archive.org/web/20201127013949/http://micro.soonlabel.com/11edt/daily20111118-3-11of-edt-mollys-playground.mp3 play]

@@ Line 3: / Line 3: @@
 == Theory ==
-From a no-two point of view, 11edt has a [[5/3]] major sixth that is 19.8 cents flat. However, 11edt has an extremely inaccurate seventh harmonic [[7/1]], which is off by almost half a step (or about a semitone), which causes it to temper out [[49/45]] in the 7-limit. 11edt is at the extreme end of [[arcturus]] temperament, defined by tempering out [[15625/15309]] in the 3.5.7 subgroup. It gives an equalized interpretation for the [[9L 2s (3/1-equivalent)|sub-arcturus]] [[MOS]] scale.
+edt can be seen as a very [[stretched and compressed tuning|stretched]] version of [[7edo]], with octaves sharpened by 10.3 cents. The octave stretching makes the [[3/2]] perfect fifth in better tune, while preserving a just [[3/1]] tritave.
+From a no-2 point of view, 11edt has a [[5/3]] major sixth that is 19.8 cents flat. However, 11edt has an extremely inaccurate seventh harmonic [[7/1]], which is off by almost half a step (or about a semitone), which causes it to temper out [[49/45]] in the 7-limit. 11edt is at the extreme end of [[arcturus]] temperament, defined by tempering out [[15625/15309]] in the 3.5.7 subgroup. It gives an equalized interpretation for the [[9L 2s (3/1-equivalent)|sub-arcturus]] [[mos scale]].
 The 11th harmonic, [[11/1]], only 1.6 cents flat, is very close to just. By exploiting the badly tuned seventh harmonic, 11edt tempers out [[35/33]] and [[77/75]] in the 11-limit. In the 3.5.11 subgroup, it tempers out [[125/121]].
-=== Relation to edos ===
+=== Harmonics ===
-edt can be seen as a very stretched version of [[7edo]], with octaves sharpened by 10.3 cents. The octave stretching makes the [[3/2]] perfect fifth in better tune, while preserving a just [[3/1]] tritave.
+{{Harmonics in equal|11|3|1|intervals=integer|columns=11}}
+{{Harmonics in equal|11|3|1|intervals=integer|columns=12|start=12|collapsed=true|title=Approximation of harmonics in 11edt (continued)}}
-=== Prime harmonics ===
+== Intervals ==
-{{Harmonics in equal|11|3|1}}
+{| class="wikitable center-1 right-2 right-3"
-{{Harmonics in equal|11|3|1|intervals=prime}}
-=== Interval table ===
-{| class="wikitable center-all"
 |-
 ! #
@@ Line 23: / Line 22: @@
 ! [[Arcturus]] nonatonic notation (J = 1/1)
 |-
-| colspan = "3" | 0
+| 0
+| 0.0
+| 0.0
 | [[1/1]]
 | J
@@ Line 82: / Line 83: @@
 |-
 | 10
-| 1729
+| 1729.0
-| 1181
+| 1181.0
 |
 | R
 |-
 | 11
-| 1902
+| 1902.0
-| 1300
+| 1300.0
 |
 | J
 |}
-== Pieces ==
+== Music ==
-Mozart's [http://micro.soonlabel.com/6th-comma-meantone/K331-period/k331-walter-piano-11edt.mp3 sonata #11 in A Major K331 in 11 EDT] (using a 11 =&gt; 12 key mapping so octaves become tritaves)
+=== Modern renderings ===
+; {{W|Wolfgang Amadeus Mozart}}
-[http://micro.soonlabel.com/tritave_in_11/11of_tritave_improv.mp3 Frozen Time Occupies Wall Street] by [http://www.chrisvaisvil.com Chris Vaisvil] =&gt;[http://chrisvaisvil.com/?p=1392  information about the piece]
+* [https://web.archive.org/web/20201127012444/http://micro.soonlabel.com/6th-comma-meantone/K331-period/k331-walter-piano-11edt.mp3 ''Piano Sonata No. 11'' in A major, K. 331] – using a 11 → 12 key mapping so octaves become tritaves
-[http://micro.soonlabel.com/11edt/daily20111118-3-11of-edt-mollys-playground.mp3 Molly's Playground] by [http://www.chrisvaisvil.com Chris Vaisvil] =&gt; [http://chrisvaisvil.com/?p=1716  information about the piece]
+=== 21st century ===
-[[category:macrotonal]]
+; [[Chris Vaisvil]]
+* ''Frozen Time Occupies Wall Street'' (2011) – [https://www.chrisvaisvil.com/frozen-time-occupies-wall-street/ blog] | [https://web.archive.org/web/20220911143825/http://micro.soonlabel.com/tritave_in_11/11of_tritave_improv.mp3 play]
+* ''Molly's Playground'' (2011) – [https://www.chrisvaisvil.com/mollys-playground/ blog] | [https://web.archive.org/web/20201127013949/http://micro.soonlabel.com/11edt/daily20111118-3-11of-edt-mollys-playground.mp3 play]