Ed12: Difference between revisions
BudjarnLambeth moved page Ed12 to User:BudjarnLambeth/Ed12 Tag: New redirect |
m Removing from Category:Edonoi using Cat-a-lot |
||
| (11 intermediate revisions by 3 users not shown) | |||
| Line 1: | Line 1: | ||
'''Equal divisions of the 12th harmonic''' ('''ed12''') are [[tuning system|tunings]] obtained by dividing the [[12/1|12th harmonic]] in a certain number of [[equal]] steps. | |||
The twelfth harmonic, duodecuple, or dodecatave, is particularly wide as far as [[equivalence]]s go, as there are at absolute most about 3.1 instances of the 12th harmonic within the [[human hearing range]]. This width means that the listener probably will not hear the interval as an equivalence, but instead will hear the [[pseudo-octave]] or pseudo-tritave or similar as one – this disconnect between period versus equivalence could be used by a composer to surprise their listener, in a similar way that [[13edo]] can be used to make melodies that sound like [[12edo]], until they suddenly do not. | |||
However, using ed12's does not necessarily imply using the 12th harmonic as an interval of equivalence. The quintessential reason for using a 12th-harmonic based tuning is that it is a compromise between [[2/1|octave]] and [[3/1|twelfth]] based tunings, like an [[ed6]] – but ed12 leans more towards octaves than ed6 does. In fact, ed12's optimize for the 1:2:3:4:6:12 chord, with equal magnitudes and opposite signs of [[error]] on 3 and 4 and on 2 and 6. | |||
As such, an ed12 sometimes gives you the right amount of [[stretched and compressed tuning|stretch]] for equal temperaments whose 3 is more inaccurate than its higher [[prime interval|primes]]. Here for example, you can choose how much you wish to stretch [[31edo]] depending on your harmonic style: [[80ed6]] vs [[111ed12]]. | |||
== Individual pages for ed12's == | |||
{| class="wikitable center-all" | |||
|+ style=white-space:nowrap | 0…99 | |||
| [[0ed12|0]] | |||
| [[1ed12|1]] | |||
| [[2ed12|2]] | |||
| [[3ed12|3]] | |||
| [[4ed12|4]] | |||
| [[5ed12|5]] | |||
| [[6ed12|6]] | |||
| [[7ed12|7]] | |||
| [[8ed12|8]] | |||
| [[9ed12|9]] | |||
|- | |||
| [[10ed12|10]] | |||
| [[11ed12|11]] | |||
| [[12ed12|12]] | |||
| [[13ed12|13]] | |||
| [[14ed12|14]] | |||
| [[15ed12|15]] | |||
| [[16ed12|16]] | |||
| [[17ed12|17]] | |||
| [[18ed12|18]] | |||
| [[19ed12|19]] | |||
|- | |||
| [[20ed12|20]] | |||
| [[21ed12|21]] | |||
| [[22ed12|22]] | |||
| [[23ed12|23]] | |||
| [[24ed12|24]] | |||
| [[25ed12|25]] | |||
| [[26ed12|26]] | |||
| [[27ed12|27]] | |||
| [[28ed12|28]] | |||
| [[29ed12|29]] | |||
|- | |||
| [[30ed12|30]] | |||
| [[31ed12|31]] | |||
| [[32ed12|32]] | |||
| [[33ed12|33]] | |||
| [[34ed12|34]] | |||
| [[35ed12|35]] | |||
| [[36ed12|36]] | |||
| [[37ed12|37]] | |||
| [[38ed12|38]] | |||
| [[39ed12|39]] | |||
|- | |||
| [[40ed12|40]] | |||
| [[41ed12|41]] | |||
| [[42ed12|42]] | |||
| [[43ed12|43]] | |||
| [[44ed12|44]] | |||
| [[45ed12|45]] | |||
| [[46ed12|46]] | |||
| [[47ed12|47]] | |||
| [[48ed12|48]] | |||
| [[49ed12|49]] | |||
|- | |||
| [[50ed12|50]] | |||
| [[51ed12|51]] | |||
| [[52ed12|52]] | |||
| [[53ed12|53]] | |||
| [[54ed12|54]] | |||
| [[55ed12|55]] | |||
| [[56ed12|56]] | |||
| [[57ed12|57]] | |||
| [[58ed12|58]] | |||
| [[59ed12|59]] | |||
|- | |||
| [[60ed12|60]] | |||
| [[61ed12|61]] | |||
| [[62ed12|62]] | |||
| [[63ed12|63]] | |||
| [[64ed12|64]] | |||
| [[65ed12|65]] | |||
| [[66ed12|66]] | |||
| [[67ed12|67]] | |||
| [[68ed12|68]] | |||
| [[69ed12|69]] | |||
|- | |||
| [[70ed12|70]] | |||
| [[71ed12|71]] | |||
| [[72ed12|72]] | |||
| [[73ed12|73]] | |||
| [[74ed12|74]] | |||
| [[75ed12|75]] | |||
| [[76ed12|76]] | |||
| [[77ed12|77]] | |||
| [[78ed12|78]] | |||
| [[79ed12|79]] | |||
|- | |||
| [[80ed12|80]] | |||
| [[81ed12|81]] | |||
| [[82ed12|82]] | |||
| [[83ed12|83]] | |||
| [[84ed12|84]] | |||
| [[85ed12|85]] | |||
| [[86ed12|86]] | |||
| [[87ed12|87]] | |||
| [[88ed12|88]] | |||
| [[89ed12|89]] | |||
|- | |||
| [[90ed12|90]] | |||
| [[91ed12|91]] | |||
| [[92ed12|92]] | |||
| [[93ed12|93]] | |||
| [[94ed12|94]] | |||
| [[95ed12|95]] | |||
| [[96ed12|96]] | |||
| [[97ed12|97]] | |||
| [[98ed12|98]] | |||
| [[99ed12|99]] | |||
|} | |||
{| class="wikitable center-all mw-collapsible mw-collapsed" | |||
|+ style=white-space:nowrap | 100…199 | |||
| [[100ed12|100]] | |||
| [[101ed12|101]] | |||
| [[102ed12|102]] | |||
| [[103ed12|103]] | |||
| [[104ed12|104]] | |||
| [[105ed12|105]] | |||
| [[106ed12|106]] | |||
| [[107ed12|107]] | |||
| [[108ed12|108]] | |||
| [[109ed12|109]] | |||
|- | |||
| [[110ed12|110]] | |||
| [[111ed12|111]] | |||
| [[112ed12|112]] | |||
| [[113ed12|113]] | |||
| [[114ed12|114]] | |||
| [[115ed12|115]] | |||
| [[116ed12|116]] | |||
| [[117ed12|117]] | |||
| [[118ed12|118]] | |||
| [[119ed12|119]] | |||
|- | |||
| [[120ed12|120]] | |||
| [[121ed12|121]] | |||
| [[122ed12|122]] | |||
| [[123ed12|123]] | |||
| [[124ed12|124]] | |||
| [[125ed12|125]] | |||
| [[126ed12|126]] | |||
| [[127ed12|127]] | |||
| [[128ed12|128]] | |||
| [[129ed12|129]] | |||
|- | |||
| [[130ed12|130]] | |||
| [[131ed12|131]] | |||
| [[132ed12|132]] | |||
| [[133ed12|133]] | |||
| [[134ed12|134]] | |||
| [[135ed12|135]] | |||
| [[136ed12|136]] | |||
| [[137ed12|137]] | |||
| [[138ed12|138]] | |||
| [[139ed12|139]] | |||
|- | |||
| [[140ed12|140]] | |||
| [[141ed12|141]] | |||
| [[142ed12|142]] | |||
| [[143ed12|143]] | |||
| [[144ed12|144]] | |||
| [[145ed12|145]] | |||
| [[146ed12|146]] | |||
| [[147ed12|147]] | |||
| [[148ed12|148]] | |||
| [[149ed12|149]] | |||
|- | |||
| [[150ed12|150]] | |||
| [[151ed12|151]] | |||
| [[152ed12|152]] | |||
| [[153ed12|153]] | |||
| [[154ed12|154]] | |||
| [[155ed12|155]] | |||
| [[156ed12|156]] | |||
| [[157ed12|157]] | |||
| [[158ed12|158]] | |||
| [[159ed12|159]] | |||
|- | |||
| [[160ed12|160]] | |||
| [[161ed12|161]] | |||
| [[162ed12|162]] | |||
| [[163ed12|163]] | |||
| [[164ed12|164]] | |||
| [[165ed12|165]] | |||
| [[166ed12|166]] | |||
| [[167ed12|167]] | |||
| [[168ed12|168]] | |||
| [[169ed12|169]] | |||
|- | |||
| [[170ed12|170]] | |||
| [[171ed12|171]] | |||
| [[172ed12|172]] | |||
| [[173ed12|173]] | |||
| [[174ed12|174]] | |||
| [[175ed12|175]] | |||
| [[176ed12|176]] | |||
| [[177ed12|177]] | |||
| [[178ed12|178]] | |||
| [[179ed12|179]] | |||
|- | |||
| [[180ed12|180]] | |||
| [[181ed12|181]] | |||
| [[182ed12|182]] | |||
| [[183ed12|183]] | |||
| [[184ed12|184]] | |||
| [[185ed12|185]] | |||
| [[186ed12|186]] | |||
| [[187ed12|187]] | |||
| [[188ed12|188]] | |||
| [[189ed12|189]] | |||
|- | |||
| [[190ed12|190]] | |||
| [[191ed12|191]] | |||
| [[192ed12|192]] | |||
| [[193ed12|193]] | |||
| [[194ed12|194]] | |||
| [[195ed12|195]] | |||
| [[196ed12|196]] | |||
| [[197ed12|197]] | |||
| [[198ed12|198]] | |||
| [[199ed12|199]] | |||
|} | |||
; 200 and beyond | |||
* [[258ed12|258]] | |||
<!-- Uncomment this when there are more pages | |||
{| class="wikitable center-all mw-collapsible mw-collapsed" | |||
|+ style=white-space:nowrap | 200…299 | |||
| [[200ed12|200]] | |||
| [[201ed12|201]] | |||
| [[202ed12|202]] | |||
| [[203ed12|203]] | |||
| [[204ed12|204]] | |||
| [[205ed12|205]] | |||
| [[206ed12|206]] | |||
| [[207ed12|207]] | |||
| [[208ed12|208]] | |||
| [[209ed12|209]] | |||
|- | |||
| [[210ed12|210]] | |||
| [[211ed12|211]] | |||
| [[212ed12|212]] | |||
| [[213ed12|213]] | |||
| [[214ed12|214]] | |||
| [[215ed12|215]] | |||
| [[216ed12|216]] | |||
| [[217ed12|217]] | |||
| [[218ed12|218]] | |||
| [[219ed12|219]] | |||
|- | |||
| [[220ed12|220]] | |||
| [[221ed12|221]] | |||
| [[222ed12|222]] | |||
| [[223ed12|223]] | |||
| [[224ed12|224]] | |||
| [[225ed12|225]] | |||
| [[226ed12|226]] | |||
| [[227ed12|227]] | |||
| [[228ed12|228]] | |||
| [[229ed12|229]] | |||
|- | |||
| [[230ed12|230]] | |||
| [[231ed12|231]] | |||
| [[232ed12|232]] | |||
| [[233ed12|233]] | |||
| [[234ed12|234]] | |||
| [[235ed12|235]] | |||
| [[236ed12|236]] | |||
| [[237ed12|237]] | |||
| [[238ed12|238]] | |||
| [[239ed12|239]] | |||
|- | |||
| [[240ed12|240]] | |||
| [[241ed12|241]] | |||
| [[242ed12|242]] | |||
| [[243ed12|243]] | |||
| [[244ed12|244]] | |||
| [[245ed12|245]] | |||
| [[246ed12|246]] | |||
| [[247ed12|247]] | |||
| [[248ed12|248]] | |||
| [[249ed12|249]] | |||
|- | |||
| [[250ed12|250]] | |||
| [[251ed12|251]] | |||
| [[252ed12|252]] | |||
| [[253ed12|253]] | |||
| [[254ed12|254]] | |||
| [[255ed12|255]] | |||
| [[256ed12|256]] | |||
| [[257ed12|257]] | |||
| [[258ed12|258]] | |||
| [[259ed12|259]] | |||
|- | |||
| [[260ed12|260]] | |||
| [[261ed12|261]] | |||
| [[262ed12|262]] | |||
| [[263ed12|263]] | |||
| [[264ed12|264]] | |||
| [[265ed12|265]] | |||
| [[266ed12|266]] | |||
| [[267ed12|267]] | |||
| [[268ed12|268]] | |||
| [[269ed12|269]] | |||
|- | |||
| [[270ed12|270]] | |||
| [[271ed12|271]] | |||
| [[272ed12|272]] | |||
| [[273ed12|273]] | |||
| [[274ed12|274]] | |||
| [[275ed12|275]] | |||
| [[276ed12|276]] | |||
| [[277ed12|277]] | |||
| [[278ed12|278]] | |||
| [[279ed12|279]] | |||
|- | |||
| [[280ed12|280]] | |||
| [[281ed12|281]] | |||
| [[282ed12|282]] | |||
| [[283ed12|283]] | |||
| [[284ed12|284]] | |||
| [[285ed12|285]] | |||
| [[286ed12|286]] | |||
| [[287ed12|287]] | |||
| [[288ed12|288]] | |||
| [[289ed12|289]] | |||
|- | |||
| [[290ed12|290]] | |||
| [[291ed12|291]] | |||
| [[292ed12|292]] | |||
| [[293ed12|293]] | |||
| [[294ed12|294]] | |||
| [[295ed12|295]] | |||
| [[296ed12|296]] | |||
| [[297ed12|297]] | |||
| [[298ed12|298]] | |||
| [[299ed12|299]] | |||
|} | |||
--> | |||
[[Category:Ed12's| ]] | |||
<!-- main article --> | |||
[[Category:List of scales]] | |||