3ed4/3: Difference between revisions

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The Cube Root of the ~~[[Perfect_fourth|~~Perfect fourth]] (~~[[4~~/3~~|4:3]]~~) is a nonoctave scale which divides the just perfect fourth (frequency ratio 4:3) into three steps of approximately 166.015[[cent|¢]] each.

The '''Cube Root of the Perfect fourth''' (3ED4/3, CRP4) is a nonoctave scale which divides the just [[perfect fourth]] (frequency ratio [[4/3|4:3]]) into three steps of approximately 166.015[[cent|¢]] each.

~~==Intervals==~~

== Intervals ==

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[[~~Category:edonoi~~]]

[[Category:~~edp4~~]]

== Regular temperaments ==

[[Category:~~equal~~]]

CRP4 tuning is related to temperaments which temper out [[4000/3993]] (wizardharry temperament). The unit step of CRP4 is approximately a cent sharp of [[11/10]]. Tempering out 4000/3993 leads equating three 11/10s with 4/3, hence wizardharry temperaments split the fourth in three.

[[Category:~~nonoctave~~]]

[[Category:p4]]

Tempering out both [[55/54]] and [[100/99]] (equating 10/9 with 11/10 and 12/11) leads [[Subgroup temperaments #No-sevens subgroup|porkypine]] (2.3.5.11 subgroup) or [[Porcupine rank three family|sonic]] (full 11-limit). Sonic temperaments include [[porcupine]], [[hystrix]], [[porky]], [[coendou]], [[hedgehog]], [[nautilus]], [[ammonite]], [[ceratitid]], and [[opossum]].

Other wizardharry temperaments include [[octoid]], [[harry]], [[tritikleismic]], [[wizard]], [[Porwell temperaments #Septisuperfourth|septisuperfourth]], [[unthirds]], [[supers]], [[alphaquarter]], [[quincy]], [[Stearnsmic clan #Stearnscape|stearnscape]], [[pogo]], [[marvolo]], [[Breedsmic temperaments #Cotritone|cotritone]], [[echidna]], [[marvo]], [[mystery]], [[zarvo]], [[Escapade family #Escaped|escaped]], [[thuja]], and [[escapade]].

[[Category:Edonoi]]

[[Category:Equal-step tuning]]

[[Category:Nonoctave]]

[[Category:Perfect fourth]]

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-The Cube Root of the [[Perfect_fourth|Perfect fourth]] ([[4/3|4:3]]) is a nonoctave scale which divides the just perfect fourth (frequency ratio 4:3) into three steps of approximately 166.015[[cent|¢]] each.
+The '''Cube Root of the Perfect fourth''' (3ED4/3, CRP4) is a nonoctave scale which divides the just [[perfect fourth]] (frequency ratio [[4/3|4:3]]) into three steps of approximately 166.015[[cent|¢]] each.
-==Intervals==
+== Intervals ==
 {| class="wikitable"
 |-
@@ Line 105: / Line 104: @@
 | | 218.34
 |}
-[[Category:edonoi]]
-[[Category:edp4]]
+== Regular temperaments ==
-[[Category:equal]]
+CRP4 tuning is related to temperaments which temper out [[4000/3993]] (wizardharry temperament). The unit step of CRP4 is approximately a cent sharp of [[11/10]]. Tempering out 4000/3993 leads equating three 11/10s with 4/3, hence wizardharry temperaments split the fourth in three.
-[[Category:nonoctave]]
-[[Category:p4]]
+Tempering out both [[55/54]] and [[100/99]] (equating 10/9 with 11/10 and 12/11) leads [[Subgroup temperaments #No-sevens subgroup|porkypine]] (2.3.5.11 subgroup) or [[Porcupine rank three family|sonic]] (full 11-limit). Sonic temperaments include [[porcupine]], [[hystrix]], [[porky]], [[coendou]], [[hedgehog]], [[nautilus]], [[ammonite]], [[ceratitid]], and [[opossum]].
+Other wizardharry temperaments include [[octoid]], [[harry]], [[tritikleismic]], [[wizard]], [[Porwell temperaments #Septisuperfourth|septisuperfourth]], [[unthirds]], [[supers]], [[alphaquarter]], [[quincy]], [[Stearnsmic clan #Stearnscape|stearnscape]], [[pogo]], [[marvolo]], [[Breedsmic temperaments #Cotritone|cotritone]], [[echidna]], [[marvo]], [[mystery]], [[zarvo]], [[Escapade family #Escaped|escaped]], [[thuja]], and [[escapade]].
+[[Category:Edonoi]]
+[[Category:Equal-step tuning]]
+[[Category:Nonoctave]]
+[[Category:Perfect fourth]]