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{{Infobox ET}}
{{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.
{{ED intro}}


== 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 ===
{{Harmonics in equal|10|3|1}}
{{Harmonics in equal|10|3|1|intervals=prime}}
=== Interval table ===
{| class="wikitable"
{| class="wikitable"
|-
|-
| | Degrees
! Degrees
| | Cents
! [[Cent]]s
!Hekts
! [[Hekt]]s
| | Approximate Ratios
! Approximate Ratios
|-
|-
! colspan="3" | 0
| colspan="3" | 0
| | <span style="color: #660000;">[[1/1]]</span>
| <span style="color: #660000;">[[1/1]]</span>
|-
|-
| | 1
| 1
| | 190.196
| 190.196
|130
| 130
| | [[10/9]], [[28/25]]
| [[10/9]], [[28/25]]
|-
|-
| | 2
| 2
| | 380.391
| 380.391
|260
| 260
| | <span style="color: #660000;">[[5/4]]</span>
| <span style="color: #660000;">[[5/4]]</span>
|-
|-
| | 3
| 3
| | 570.587
| 570.587
|390
| 390
| | [[7/5]]
| [[7/5]]
|-
|-
| | 4
| 4
| | 760.782
| 760.782
|520
| 520
| | <span style="color: #660000;">[[14/9]]</span>
| <span style="color: #660000;">[[14/9]]</span>
|-
|-
| | 5
| 5
| | 950.978
| 950.978
|650
| 650
| | 45/26, [[26/15]]
| 45/26, [[26/15]]
|-
|-
| | 6
| 6
| | 1141.173
| 1141.173
|780
| 780
| | <span style="color: #660000;">[[27/14]]</span>
| <span style="color: #660000;">[[27/14]]</span>
|-
|-
| | 7
| 7
| | 1331.369
| 1331.369
|910
| 910
| | [[15/7]] ([[15/14]] plus an octave)
| [[15/7]] ([[15/14]] plus an octave)
|-
|-
| | 8
| 8
| | 1521.564
| 1521.564
|1040
| 1040
| | [[12/5]] (<span style="color: #660000;">[[6/5]]</span> plus an octave)
| [[12/5]] (<span style="color: #660000;">[[6/5]]</span> plus an octave)
|-
|-
| | 9
| 9
| | 1711.760
| 1711.760
|1170
| 1170
| | [[27/20|27/10]]
| [[27/20|27/10]]
|-
|-
| | 10
| 10
| | 1901.955
| 1901.955
|1300
| 1300
| | [[3/1]]
| [[3/1]]
|}
|}


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:Macrotonal]]
[[Category:edt]]
[[category:macrotonal]]
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