227edo: Difference between revisions

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~~<h2>IMPORTED REVISION FROM WIKISPACES</h2>~~

~~This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>~~

~~: This revision was by author~~ [[~~User:genewardsmith~~|~~genewardsmith~~]] and ~~made on <tt>2011~~-07-~~06 03:19:50 UTC</tt>.<br>~~

~~: The original revision id was <tt>240161321</tt>.<br>~~

== Theory ==

~~: The revision comment was: <tt></tt><br>~~

227et [[tempering out|tempers out]] 15625/15552 ([[15625/15552|kleisma]]) and {{monzo| 61 -37 -1 }} in the [[5-limit]]; [[5120/5103]], [[65625/65536]], and 117649/116640 in the [[7-limit]], so that it [[support]]s [[countercata]]. In the [[11-limit]], it tempers out [[385/384]], [[2200/2187]], [[3388/3375]], and [[12005/11979]], so that it provides the [[optimal patent val]] for 11-limit countercata. In the [[13-limit]], it tempers out [[325/324]], [[352/351]], [[625/624]], [[676/675]], and [[847/845]], and again supplies a good tuning for 13-limit countercata, although [[140edo]] tunes it better in this case.

~~The revision contents are below, presented both~~ in the ~~original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.<br>~~

~~<h4>Original Wikitext content:</h4>~~

227edo is accurate for the [[13/1|13th harmonic]], as the denominator of a convergent to log<sub>2</sub>13, after [[10edo|10]] and before [[5231edo|5231]].

~~<div style="width:100%; max~~-~~height:400pt~~; overflow:auto; background-color:#f8f9fa; border: 1px solid #eaecf0; padding:0em"><pre style="margin:0px;border:none;background:none;word-wrap:break-word;white-space: pre-wrap ! important" class="old-revision-html">The /~~/227 equal temperament// divides the octave into 227 equal parts of 5.286 cents each. It tempers out the kleisma~~, ~~15625~~/~~15552~~, ~~in the 5-limit~~ and ~~5120~~/~~5103~~ in the 7-limit, so that it ~~supports~~ [[~~Kleismic family#Countercata|~~countercata ~~temperament~~]]~~, and it also tempers out 117649/116640~~. In the 11-limit it tempers out 385/384 and it provides the [[optimal patent val]] for 11-limit countercata.</~~pre><~~/~~div>~~

<h4>~~Original HTML content:~~</h4>

=== Prime harmonics ===

~~<div style~~="~~width:100%; max~~-~~height:400pt; overflow:auto; background~~-~~color:#f8f9fa; border: 1px solid #eaecf0; padding:0em~~">~~<pre style~~="~~margin:0px;border:none;background:none;word~~-~~wrap:break~~-~~word;width:200%;white~~-~~space: pre~~-~~wrap ! important" class="old~~-~~revision~~-~~html"><html><head><title>227edo<~~/~~title><~~/~~head><body>The <em>~~227 ~~equal temperament<~~/~~em> divides the octave into~~ 227 ~~equal parts of~~ 5.~~286 cents each~~. ~~It tempers out the kleisma~~, ~~15625~~/~~15552~~, ~~in the~~ 5~~-limit and 5120~~/~~5103 in the~~ 7-~~limit, so that it supports <a~~ class="~~wiki_link~~" ~~href~~="/~~Kleismic%20family#~~Countercata~~">countercata temperament<~~/~~a>~~, and ~~it also tempers out 117649~~/~~116640~~. ~~In the 11~~-~~limit it tempers out 385~~/~~384 and it provides the <a class~~="~~wiki_link~~" ~~href~~="/~~optimal%20patent%20val~~"~~>optimal patent val<~~/~~a> for 11-limit countercata~~.~~<~~/~~body><~~/~~html><~~/~~pre><~~/~~div>~~

=== Subsets and supersets ===

227edo is the 49th [[prime edo]].

== Intervals ==

== Regular temperament properties ==

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

|-

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

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

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

! rowspan="2" | Optimal<br />8ve stretch (¢)

! colspan="2" | Tuning error

|-

! [[TE error|Absolute]] (¢)

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

|-

| 2.3

| {{monzo| 360 -227 }}

| {{mapping| 227 360 }}

| −0.3561

| 0.3560

| 6.73

|-

| 2.3.5

| 15625/15552, {{monzo| 61 -37 -1 }}

| {{mapping| 227 360 527 }}

| −0.1785

| 0.3842

| 7.27

|-

| 2.3.5.7

| 5120/5103, 15625/15552, 117649/116640

| {{mapping| 227 360 527 637 }}

| −0.0071

| 0.4461

| 8.44

|-

| 2.3.5.7.11

| 385/384, 2200/2187, 3388/3375, 12005/11979

| {{mapping| 227 360 527 637 785 }}

| +0.0832

| 0.4380

| 8.29

|-

| 2.3.5.7.11.13

| 325/324, 352/351, 385/384, 625/624, 12005/11979

| {{mapping| 227 360 527 637 785 840 }}

| +0.0693

| 0.4010

| 7.59

|-

| 2.3.5.7.11.13.17

| 325/324, 352/351, 385/384, 595/594, 625/624, 3185/3179

| {{mapping| 227 360 527 637 785 840 928 }}

| +0.0324

| 0.3821

| 7.23

|}

=== Rank-2 temperaments ===

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

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

|-

! Periods<br />per 8ve

! Generator*

! Cents*

! Associated<br />ratio*

! Temperaments

|-

| 1

| 25\227

| 132.16

| 121/112

| [[Kastro]]

|-

| 1

| 60\227

| 317.18

| 6/5

| [[Countercata]]

|-

| 1

| 94\227

| 496.92

| 4/3

| [[Undecental]]

|}

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

== Music ==

; [[Francium]]

* "little hope" from ''hope in dark times'' (2024) – [https://open.spotify.com/track/1J6VKSGTkTRFs75WlEb6GP Spotify] | [https://francium223.bandcamp.com/track/little-hope Bandcamp] | [https://www.youtube.com/watch?v=juMfOpUu25I YouTube]

* "Cuckoo Cucumber" from ''Cursed Cuckoo Creations'' (2024) – [https://open.spotify.com/track/4WSc7cTf1ctWIiOXjTSAmc Spotify] | [https://francium223.bandcamp.com/track/cuckoo-cucumber Bandcamp] | [https://www.youtube.com/watch?v=po7hrgzSeb8 YouTube]

* "Did You Put Resistors In My Brain?" from ''Questions'' (2024) – [https://open.spotify.com/track/3QS6mj3GAMSmfJuQSsOE7Y Spotify] | [https://francium223.bandcamp.com/track/did-you-put-resistors-in-my-brain Bandcamp] | [https://www.youtube.com/watch?v=-FzOGzpxPv4 YouTube]

* "Too Bad Homeboy" from ''Abbreviations Gone Wrong'' (2024) – [https://open.spotify.com/track/6VPup7pwSC10c0VzsBU4PG Spotify] | [https://francium223.bandcamp.com/track/too-bad-homeboy Bandcamp] | [https://www.youtube.com/watch?v=Y246sdIRbwQ YouTube]

[[Category:Countercata]]

[[Category:Listen]]

@@ Line 1: / Line 1: @@
-<h2>IMPORTED REVISION FROM WIKISPACES</h2>
+{{Infobox ET}}
-This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>
+{{ED intro}}
-: This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2011-07-06 03:19:50 UTC</tt>.<br>
-: The original revision id was <tt>240161321</tt>.<br>
+== Theory ==
-: The revision comment was: <tt></tt><br>
+et [[tempering out|tempers out]] 15625/15552 ([[15625/15552|kleisma]]) and {{monzo| 61 -37 -1 }} in the [[5-limit]]; [[5120/5103]], [[65625/65536]], and 117649/116640 in the [[7-limit]], so that it [[support]]s [[countercata]]. In the [[11-limit]], it tempers out [[385/384]], [[2200/2187]], [[3388/3375]], and [[12005/11979]], so that it provides the [[optimal patent val]] for 11-limit countercata. In the [[13-limit]], it tempers out [[325/324]], [[352/351]], [[625/624]], [[676/675]], and [[847/845]], and again supplies a good tuning for 13-limit countercata, although [[140edo]] tunes it better in this case.
-The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.<br>
-<h4>Original Wikitext content:</h4>
+edo is accurate for the [[13/1|13th harmonic]], as the denominator of a convergent to log<sub>2</sub>13, after [[10edo|10]] and before [[5231edo|5231]].
-<div style="width:100%; max-height:400pt; overflow:auto; background-color:#f8f9fa; border: 1px solid #eaecf0; padding:0em"><pre style="margin:0px;border:none;background:none;word-wrap:break-word;white-space: pre-wrap ! important" class="old-revision-html">The //227 equal temperament// divides the octave into 227 equal parts of 5.286 cents each. It tempers out the kleisma, 15625/15552, in the 5-limit and 5120/5103 in the 7-limit, so that it supports [[Kleismic family#Countercata|countercata temperament]], and it also tempers out 117649/116640. In the 11-limit it tempers out 385/384 and it provides the [[optimal patent val]] for 11-limit countercata.</pre></div>
-<h4>Original HTML content:</h4>
+=== Prime harmonics ===
-<div style="width:100%; max-height:400pt; overflow:auto; background-color:#f8f9fa; border: 1px solid #eaecf0; padding:0em"><pre style="margin:0px;border:none;background:none;word-wrap:break-word;width:200%;white-space: pre-wrap ! important" class="old-revision-html">&lt;html&gt;&lt;head&gt;&lt;title&gt;227edo&lt;/title&gt;&lt;/head&gt;&lt;body&gt;The &lt;em&gt;227 equal temperament&lt;/em&gt; divides the octave into 227 equal parts of 5.286 cents each. It tempers out the kleisma, 15625/15552, in the 5-limit and 5120/5103 in the 7-limit, so that it supports &lt;a class="wiki_link" href="/Kleismic%20family#Countercata"&gt;countercata temperament&lt;/a&gt;, and it also tempers out 117649/116640. In the 11-limit it tempers out 385/384 and it provides the &lt;a class="wiki_link" href="/optimal%20patent%20val"&gt;optimal patent val&lt;/a&gt; for 11-limit countercata.&lt;/body&gt;&lt;/html&gt;</pre></div>
+{{Harmonics in equal|227}}
+=== Subsets and supersets ===
+edo is the 49th [[prime edo]].
+== Intervals ==
+{{Main|Table of 227edo intervals}}
+== Regular temperament properties ==
+{| class="wikitable center-4 center-5 center-6"
+|-
+! rowspan="2" | [[Subgroup]]
+! rowspan="2" | [[Comma list]]
+! rowspan="2" | [[Mapping]]
+! rowspan="2" | Optimal<br />8ve stretch (¢)
+! colspan="2" | Tuning error
+|-
+! [[TE error|Absolute]] (¢)
+! [[TE simple badness|Relative]] (%)
+|-
+| 2.3
+| {{monzo| 360 -227 }}
+| {{mapping| 227 360 }}
+| −0.3561
+| 0.3560
+| 6.73
+|-
+| 2.3.5
+| 15625/15552, {{monzo| 61 -37 -1 }}
+| {{mapping| 227 360 527 }}
+| −0.1785
+| 0.3842
+| 7.27
+|-
+| 2.3.5.7
+| 5120/5103, 15625/15552, 117649/116640
+| {{mapping| 227 360 527 637 }}
+| −0.0071
+| 0.4461
+| 8.44
+|-
+| 2.3.5.7.11
+| 385/384, 2200/2187, 3388/3375, 12005/11979
+| {{mapping| 227 360 527 637 785 }}
+| +0.0832
+| 0.4380
+| 8.29
+|-
+| 2.3.5.7.11.13
+| 325/324, 352/351, 385/384, 625/624, 12005/11979
+| {{mapping| 227 360 527 637 785 840 }}
+| +0.0693
+| 0.4010
+| 7.59
+|-
+| 2.3.5.7.11.13.17
+| 325/324, 352/351, 385/384, 595/594, 625/624, 3185/3179
+| {{mapping| 227 360 527 637 785 840 928 }}
+| +0.0324
+| 0.3821
+| 7.23
+|}
+=== Rank-2 temperaments ===
+{| class="wikitable center-all left-5"
+|+ style="font-size: 105%;" | Table of rank-2 temperaments by generator
+|-
+! Periods<br />per 8ve
+! Generator*
+! Cents*
+! Associated<br />ratio*
+! Temperaments
+|-
+| 1
+| 25\227
+| 132.16
+| 121/112
+| [[Kastro]]
+|-
+| 1
+| 60\227
+| 317.18
+| 6/5
+| [[Countercata]]
+|-
+| 1
+| 94\227
+| 496.92
+| 4/3
+| [[Undecental]]
+|}
+<nowiki />* [[Normal lists|Octave-reduced form]], reduced to the first half-octave, and [[Normal lists|minimal form]] in parentheses if distinct
+== Music ==
+; [[Francium]]
+* "little hope" from ''hope in dark times'' (2024) – [https://open.spotify.com/track/1J6VKSGTkTRFs75WlEb6GP Spotify] | [https://francium223.bandcamp.com/track/little-hope Bandcamp] | [https://www.youtube.com/watch?v=juMfOpUu25I YouTube]
+* "Cuckoo Cucumber" from ''Cursed Cuckoo Creations'' (2024) – [https://open.spotify.com/track/4WSc7cTf1ctWIiOXjTSAmc Spotify] | [https://francium223.bandcamp.com/track/cuckoo-cucumber Bandcamp] | [https://www.youtube.com/watch?v=po7hrgzSeb8 YouTube]
+* "Did You Put Resistors In My Brain?" from ''Questions'' (2024) – [https://open.spotify.com/track/3QS6mj3GAMSmfJuQSsOE7Y Spotify] | [https://francium223.bandcamp.com/track/did-you-put-resistors-in-my-brain Bandcamp] | [https://www.youtube.com/watch?v=-FzOGzpxPv4 YouTube]
+* "Too Bad Homeboy" from ''Abbreviations Gone Wrong'' (2024) – [https://open.spotify.com/track/6VPup7pwSC10c0VzsBU4PG Spotify] | [https://francium223.bandcamp.com/track/too-bad-homeboy Bandcamp] | [https://www.youtube.com/watch?v=Y246sdIRbwQ YouTube]
+[[Category:Countercata]]
+[[Category:Listen]]