10edt: Difference between revisions

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'''10EDT''' is the [[Edt|equal division of the third harmonic (tritave)]] into ten parts of 190.1955 [[cent|cents]] each, corresponding to 6.3093 [[edo]]. It is related to the pocus temperament, which tempers out 169/168, 225/224, and 245/243 in the 2.3.5.7.13 subgroup.

== Theory ==

10edt has very accurate 5-limit harmony for such a small number of steps per tritave, most notably the [[5/4]] inherited from 5edt. 10edt introduces some new harmonic properties though — such as the 571 cent tritone, which can function as [[7/5]]. We can use this to readily construct chords such as 4:5:7:12, although the [[7/4]], being 18 cents flat, does considerable damage to the consonance of this chord.

10edt also splits the major third in half, categorizing this tuning as a fringe variety of "meantone" temperament.

One step of 10edt can serve as the generator for [[pocus]] temperament, a [[Temperament merging|merge]] of [[sensamagic]] and 2.3.5.7.13 [[catakleismic]], which tempers out [[169/168]], [[225/224]], and [[245/243]] in the 2.3.5.7.13 subgroup.

=== Harmonics ===

=== Interval table ===

{| class="wikitable"

|-

| | Degrees

| | ~~Cents~~

| | [[Cent]]s

~~!Hekts~~

| | [[Hekt]]s

| | Approximate Ratios

|-

Line 63:

Line 75:

|}

~~== Prime harmonics ==~~

[[Category:Edt]]

~~{{Harmonics in equal|10|3|1|intervals=prime}}~~

[[Category:Macrotonal]]

10edt, like [[5edt]], has very accurate 5-limit harmony for such a small number of steps per tritave. 10edt introduces some new harmonic properties though; notably the 571 cent tritone which can function as 7/5. It also splits the major third in half, categorizing this tuning as a fringe variety of "meantone" temperament.

[[Category:~~edt~~]]

[[~~category~~:~~macrotonal~~]]

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 {{Infobox ET}}
-'''10EDT''' is the [[Edt|equal division of the third harmonic (tritave)]] into ten parts of 190.1955 [[cent|cents]] each, corresponding to 6.3093 [[edo]]. It is related to the pocus temperament, which tempers out 169/168, 225/224, and 245/243 in the 2.3.5.7.13 subgroup.
+{{EDO intro}}
+== Theory ==
+edt has very accurate 5-limit harmony for such a small number of steps per tritave, most notably the [[5/4]] inherited from 5edt. 10edt introduces some new harmonic properties though — such as the 571 cent tritone, which can function as [[7/5]]. We can use this to readily construct chords such as 4:5:7:12, although the [[7/4]], being 18 cents flat, does considerable damage to the consonance of this chord.
+edt also splits the major third in half, categorizing this tuning as a fringe variety of "meantone" temperament.
+One step of 10edt can serve as the generator for [[pocus]] temperament, a [[Temperament merging|merge]] of [[sensamagic]] and 2.3.5.7.13 [[catakleismic]], which tempers out [[169/168]], [[225/224]], and [[245/243]] in the 2.3.5.7.13 subgroup.
+=== Harmonics ===
+{{Harmonics in equal|10|3|1}}
+{{Harmonics in equal|10|3|1|intervals=prime}}
+=== Interval table ===
 {| class="wikitable"
 |-
 | | Degrees
-| | Cents
+| | [[Cent]]s
-!Hekts
+| | [[Hekt]]s
 | | Approximate Ratios
 |-
@@ Line 63: / Line 75: @@
 |}
-== Prime harmonics ==
+[[Category:Edt]]
-{{Harmonics in equal|10|3|1|intervals=prime}}
+[[Category:Macrotonal]]
-edt, like [[5edt]], has very accurate 5-limit harmony for such a small number of steps per tritave. 10edt introduces some new harmonic properties though; notably the 571 cent tritone which can function as 7/5. It also splits the major third in half, categorizing this tuning as a fringe variety of "meantone" temperament.
-[[Category:edt]]
-[[category:macrotonal]]