Elf: Difference between revisions
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# For each interval of the temperament, keep only the least complex (in terms of [[Benedetti height]]) JI interpretation of that interval. | # For each interval of the temperament, keep only the least complex (in terms of [[Benedetti height]]) JI interpretation of that interval. | ||
# Order the remaining JI intervals by increasing temperamental complexity, breaking ties by increasing Benedetti complexity. | # Order the remaining JI intervals by increasing temperamental complexity, breaking ties by increasing Benedetti complexity. | ||
# Construct a detempering of n-edo as follows: For each integer value 1 | # Construct a detempering of n-edo as follows: For each integer value {{nowrap|1 ≤ ''i'' ≤ ''n''}}, set the ''i''th degree of the scale to be the least (according to the ordering in step 3) interval ''c'' in the listing such that {{nowrap|''V''(''c'') {{=}} ''i''}}; which is to say, the interval of least temperamental complexity with ties broken by Benedetti height. | ||
# Temper this detempering of n-edo using a [[tuning map]] for the temperament. | # Temper this detempering of n-edo using a [[tuning map]] for the temperament. | ||
The result is an elf. | The result is an elf. | ||
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== Rank two examples == | == Rank two examples == | ||
=== 13-limit leapday === | === 13-limit leapday === | ||
* [[ | * [[elfleapday7]] | ||
* [[ | * [[elfleapday8d]] | ||
* [[ | * [[elfleapday9]] | ||
* [[ | * [[elfleapday10]] | ||
* [[ | * [[elfleapday12f]] | ||
=== 11-limit magic === | === 11-limit magic === | ||
* [[ | * [[elfmagic7]] | ||
* [[ | * [[elfmagic8]] | ||
* [[ | * [[elfmagic8d]] | ||
* [[ | * [[elfmagic9]] | ||
* [[ | * [[elfmagic10]] | ||
* [[ | * [[elfmagic12]] | ||
=== 11-limit miracle === | === 11-limit miracle === | ||
* [[ | * [[elfmiracle7]] | ||
* [[ | * [[elfmiracle8d]] | ||
* [[ | * [[elfmiracle9]] | ||
* [[ | * [[elfmiracle10]] | ||
* [[ | * [[elfmiracle12]] | ||
=== 13-limit myna === | === 13-limit myna === | ||
* [[ | * [[elfmyna7]] | ||
* [[ | * [[elfmyna8d]] | ||
* [[ | * [[elfmyna9]] | ||
* [[ | * [[elfmyna10]] | ||
* [[ | * [[elfmyna12f]] | ||
=== 13-limit octacot === | === 13-limit octacot === | ||
* [[ | * [[elfoctacot7]] | ||
* [[ | * [[elfoctacot8d]] | ||
* [[ | * [[elfoctacot9]] | ||
* [[ | * [[elfoctacot10]] | ||
* [[ | * [[elfoctacot12f]] | ||
=== 13-limit qilin === | === 13-limit qilin === | ||
* [[ | * [[elfqilin7]] | ||
* [[ | * [[elfqilin8d]] | ||
* [[ | * [[elfqilin9]] | ||
* [[ | * [[elfqilin10]] | ||
* [[ | * [[elfqilin12f]] | ||
=== 13-limit sensus === | === 13-limit sensus === | ||
* [[ | * [[elfsensus7]] | ||
* [[ | * [[elfsensus8d]] | ||
* [[ | * [[elfsensus9]] | ||
* [[ | * [[elfsensus10]] | ||
* [[ | * [[elfsensus12]] | ||
* [[ | * [[elfsensus12f]] | ||
=== 11-limit valentine === | === 11-limit valentine === | ||
* [[ | * [[elfvalentine7]] | ||
* [[ | * [[elfvalentine8d]] | ||
* [[ | * [[elfvalentine9]] | ||
* [[ | * [[elfvalentine10]] | ||
* [[ | * [[elfvalentine12]] | ||
== Rank three examples == | == Rank three examples == | ||
=== 11-limit jove === | === 11-limit jove === | ||
* [[ | * [[elfjove7]] | ||
* [[ | * [[elfjove8d]] | ||
* [[ | * [[elfjove9]] | ||
* [[ | * [[elfjove10]] | ||
* [[ | * [[elfjove11c]] | ||
* [[ | * [[elfjove12]] | ||
=== 13-limit madagascar === | === 13-limit madagascar === | ||
* [[ | * [[elfmadagascar7]] | ||
* [[ | * [[elfmadagascar8d]] | ||
* [[ | * [[elfmadagascar9]] | ||
* [[ | * [[elfmadagascar10]] | ||
* [[ | * [[elfmadagascar12f]] | ||
* [[ | * [[elfmadagascar14c]] | ||
* [[ | * [[elfmadagascar15]] | ||
=== 11-limit portent === | === 11-limit portent === | ||
* [[ | * [[elfportent9]] | ||
* [[ | * [[elfportent10]] | ||
* [[ | * [[elfportent11c]] | ||
* [[ | * [[elfportent12]] | ||
* [[ | * [[elfportent15]] | ||
=== 11-limit thrush === | === 11-limit thrush === | ||
* [[ | * [[elfthrush7]] | ||
* [[ | * [[elfthrush8d]] | ||
* [[ | * [[elfthrush9]] | ||
* [[ | * [[elfthrush10]] | ||
* [[ | * [[elfthrush12]] | ||
=== 11-limit zeus === | === 11-limit zeus === | ||
* [[ | * [[zeus7tri]] | ||
* [[ | * [[elfzeus8]] | ||
* [[ | * [[elfzeus9]] | ||
* [[ | * [[elfzeus10]] | ||
* [[ | * [[elfzeus12]] | ||
== Rank four examples == | == Rank four examples == | ||
=== Keenanismic === | === Keenanismic === | ||
* [[ | * [[elfkeenanismic7]] | ||
* [[ | * [[elfkeenanismic8d]] | ||
* [[ | * [[elfkeenanismic9]] | ||
* [[ | * [[elfkeenanismic10]] | ||
* [[ | * [[elfkeenanismic11c]] | ||
* [[ | * [[elfkeenanismic12]] | ||
* [[ | * [[elfkeenanismic19]] | ||
=== Swetismic === | === Swetismic === | ||
* [[ | * [[elfswetismic8d]] | ||
* [[ | * [[elfswetismic9]] | ||
* [[ | * [[elfswetismic10]] | ||
* [[ | * [[elfswetismic12]] | ||
=== Valinorsmic === | === Valinorsmic === | ||
* [[ | * [[elfvalinorsmic7]] | ||
* [[ | * [[elfvalinorsmic8d]] | ||
* [[ | * [[elfvalinorsmic9]] | ||
* [[ | * [[elfvalinorsmic10]] | ||
* [[ | * [[elfvalinorsmic11c]] | ||
* [[ | * [[elfvalinorsmic12]] | ||
[[Category:Elves | [[Category:Elves]] <!-- main article --> | ||