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=Properties= | =Properties= | ||
As the double of [[8edt|8edt]], this division of the tritave is harmonically fraternal to [[10edo|10edo]]. Its unit step is ~1.128 cents flat of 1\10edo. Unlike 10edo, it does not really have a 7 or 13 because it is not using its approximation of 2 as equivalent though the accumulated flatness of a stack of its unit step leads to an excellent [[21/13|13:21]] and a decent [[13/7|7:13]]. When twos are admitted, it turns into a tritave-repeating version of Blackwood temperament.[[category:macrotonal]] | As the double of [[8edt|8edt]], this division of the tritave is harmonically fraternal to [[10edo|10edo]]. Its unit step is ~1.128 cents flat of 1\10edo. Unlike 10edo, it does not really have a 7 or 13 because it is not using its approximation of 2 as equivalent though the accumulated flatness of a stack of its unit step leads to an excellent [[21/13|13:21]] and a decent [[13/7|7:13]]. When twos are admitted, it turns into a tritave-repeating version of Blackwood temperament. | ||
[[category:macrotonal]] | |||
=Intervals= | =Intervals= | ||
| Line 6: | Line 7: | ||
{| class="wikitable" | {| class="wikitable" | ||
|- | |- | ||
! | Degree | ! rowspan="2"| Degree | ||
! | Size in [[cent|Cents]] | ! colspan="2"| Size in | ||
|- | |||
![[cent|Cents]] | |||
!Hekts | |||
|- | |- | ||
| style="text-align:center;" | 1 | | style="text-align:center;" | 1 | ||
| style="text-align:right;" | 118.87219 | | style="text-align:right;" | 118.87219 | ||
|81.25 | |||
|- | |- | ||
| style="text-align:center;" | 2 | | style="text-align:center;" | 2 | ||
| style="text-align:right;" | 237.74438 | | style="text-align:right;" | 237.74438 | ||
|162.5 | |||
|- | |- | ||
| style="text-align:center;" | 3 | | style="text-align:center;" | 3 | ||
| style="text-align:right;" | 356.61656 | | style="text-align:right;" | 356.61656 | ||
|243.75 | |||
|- | |- | ||
| style="text-align:center;" | 4 | | style="text-align:center;" | 4 | ||
| style="text-align:right;" | 475.48875 | | style="text-align:right;" | 475.48875 | ||
|325 | |||
|- | |- | ||
| style="text-align:center;" | 5 | | style="text-align:center;" | 5 | ||
| style="text-align:right;" | 594.36094 | | style="text-align:right;" | 594.36094 | ||
|406.25 | |||
|- | |- | ||
| style="text-align:center;" | 6 | | style="text-align:center;" | 6 | ||
| style="text-align:right;" | 713.23312 | | style="text-align:right;" | 713.23312 | ||
|487.5 | |||
|- | |- | ||
| style="text-align:center;" | 7 | | style="text-align:center;" | 7 | ||
| style="text-align:right;" | 832.10531 | | style="text-align:right;" | 832.10531 | ||
|568.75 | |||
|- | |- | ||
| style="text-align:center;" | 8 | | style="text-align:center;" | 8 | ||
| style="text-align:right;" | 950. | | style="text-align:right;" | 950.9775 | ||
|650 | |||
|- | |- | ||
| style="text-align:center;" | 9 | | style="text-align:center;" | 9 | ||
| style="text-align:right;" | 1069.84969 | | style="text-align:right;" | 1069.84969 | ||
|731.25 | |||
|- | |- | ||
| style="text-align:center;" | 10 | | style="text-align:center;" | 10 | ||
| style="text-align:right;" | 1188.72188 | | style="text-align:right;" | 1188.72188 | ||
|812.5 | |||
|- | |- | ||
| style="text-align:center;" | 11 | | style="text-align:center;" | 11 | ||
| style="text-align:right;" | 1307.59406 | | style="text-align:right;" | 1307.59406 | ||
|893.75 | |||
|- | |- | ||
| style="text-align:center;" | 12 | | style="text-align:center;" | 12 | ||
| style="text-align:right;" | 1426.46625 | | style="text-align:right;" | 1426.46625 | ||
|975 | |||
|- | |- | ||
| style="text-align:center;" | 13 | | style="text-align:center;" | 13 | ||
| style="text-align:right;" | 1545.33844 | | style="text-align:right;" | 1545.33844 | ||
|1056.25 | |||
|- | |- | ||
| style="text-align:center;" | 14 | | style="text-align:center;" | 14 | ||
| style="text-align:right;" | 1664.21063 | | style="text-align:right;" | 1664.21063 | ||
|1137.5 | |||
|- | |- | ||
| style="text-align:center;" | 15 | | style="text-align:center;" | 15 | ||
| style="text-align:right;" | 1783.08281 | | style="text-align:right;" | 1783.08281 | ||
|1218.75 | |||
|- | |- | ||
| style="text-align:center;" | 16 | | style="text-align:center;" | 16 | ||
| style="text-align:right;" | 1901. | | style="text-align:right;" | 1901.955 | ||
|1300 | |||
|} | |} | ||
=Music= | =Music= | ||
[http://soonlabel.com/xenharmonic/wp-content/uploads/2011/11/16-edt.mp3 A Short Tune in 16EDT] by [[Peter_'Rush'_Kosmorsky|Peter 'Rush' Kosmorsky]] | [http://soonlabel.com/xenharmonic/wp-content/uploads/2011/11/16-edt.mp3 A Short Tune in 16EDT] by [[Peter_'Rush'_Kosmorsky|Peter 'Rush' Kosmorsky]] | ||
Revision as of 17:41, 13 April 2019
Properties
As the double of 8edt, this division of the tritave is harmonically fraternal to 10edo. Its unit step is ~1.128 cents flat of 1\10edo. Unlike 10edo, it does not really have a 7 or 13 because it is not using its approximation of 2 as equivalent though the accumulated flatness of a stack of its unit step leads to an excellent 13:21 and a decent 7:13. When twos are admitted, it turns into a tritave-repeating version of Blackwood temperament.
Intervals
| Degree | Size in | |
|---|---|---|
| Cents | Hekts | |
| 1 | 118.87219 | 81.25 |
| 2 | 237.74438 | 162.5 |
| 3 | 356.61656 | 243.75 |
| 4 | 475.48875 | 325 |
| 5 | 594.36094 | 406.25 |
| 6 | 713.23312 | 487.5 |
| 7 | 832.10531 | 568.75 |
| 8 | 950.9775 | 650 |
| 9 | 1069.84969 | 731.25 |
| 10 | 1188.72188 | 812.5 |
| 11 | 1307.59406 | 893.75 |
| 12 | 1426.46625 | 975 |
| 13 | 1545.33844 | 1056.25 |
| 14 | 1664.21063 | 1137.5 |
| 15 | 1783.08281 | 1218.75 |
| 16 | 1901.955 | 1300 |