Xenharmonic Wiki

16edt: Difference between revisions

← Older editNewer edit →
VisualWikitext
No edit summary
Xenllium (talk | contribs)
autopatrolled, emailconfirmed
5,030 edits
No edit summary
Line 1: Line 1:
=Properties=
'''16EDT''' is [[EDT|equal division of the third harmonic]] into 16 parts of 118.872 cents each (corresponding to 10.0949 [[EDO]]).
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=
== 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.
 
== Intervals ==


{| class="wikitable"
{| class="wikitable"
Line 11: Line 12:
|-
|-
![[cent|Cents]]
![[cent|Cents]]
!Hekts
! 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
| 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
| 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
| 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
| 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
| 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
| 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
| 568.75
|-
|-
| style="text-align:center;" | 8
| style="text-align:center;" | 8
| style="text-align:right;" | 950.9775
| style="text-align:right;" | 950.9775
|650
| 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
| 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
| 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
| 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
| 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
| 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
| 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
| 1218.75
|-
|-
| style="text-align:center;" | 16
| style="text-align:center;" | 16
| style="text-align:right;" | 1901.955
| style="text-align:right;" | 1901.955
|1300
| 1300
|}
|}


=Music=
== Related temperament ==
16EDT is also be thought of as a generator of the ''subsedia'' temperament, which is a [[cluster temperament]] with 10 clusters of notes in an octave.
 
; [[Mirkwai clan #Subsedia|Subsedia]] (10 & 111)
'''7-limit'''<br>
Comma list: 16875/16807, 65536/64827<br>
Mapping: [{{val|1 0 5 4}}, {{val|0 16 -27 -12}}]<br>
POTE generator: ~15/14 = 118.965<br>
Vals: 10, 101, 111, 121, 232d<br>
Badness: 0.157658<br><br>
'''11-limit'''<br>
Comma list: 540/539, 1375/1372, 65536/64827<br>
Mapping: [{{val|1 0 5 4 -1}}, {{val|0 16 -27 -12 45}}]<br>
POTE generator: ~15/14 = 118.968<br>
Vals: 10, 101, 111, 121, 232d<br>
Badness: 0.066838<br><br>
'''13-limit'''<br>
Comma list: 352/351, 540/539, 676/675, 1375/1372<br>
Mapping: [{{val|1 0 5 4 -1 4}}, {{val|0 16 -27 -12 45 -3}}]<br>
POTE generator: ~15/14 = 118.968<br>
Vals: 10, 101, 111, 121, 232d<br>
Badness: 0.031635<br><br>
'''17-limit'''<br>
Comma list: 256/255, 352/351, 442/441, 540/539, 715/714<br>
Mapping: [{{val|1 0 5 4 -1 4 3}}, {{val|0 16 -27 -12 45 -3 11}}]<br>
POTE generator: ~15/14 = 118.968<br>
Vals: 10, 101, 111, 121, 232dg<br>
Badness: 0.019707<br><br>
 
== 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]]
[[Category:Edt]]
[[Category:Macrotonal]]
Retrieved from "https://en.xen.wiki/w/16edt"