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{{Infobox ET}}
{{Infobox ET}}
'''16EDT''' is [[EDT|equal division of the third harmonic]] into 16 parts of 118.872 cents each (corresponding to 10.0949 [[EDO]]).
{{ED intro}}


== 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.
As the double of [[8edt|8EDT]], this division of the tritave is harmonically fraternal to [[10edo|10EDO]]. Its unit step is ~1.128{{c}} 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.


== Harmonics ==
== Harmonics ==
Line 25: Line 25:
{| class="wikitable"
{| class="wikitable"
|-
|-
! rowspan="2"| Degree
! rowspan="2" | Degree
! colspan="2"| Size in  
! colspan="2" | Size in  
|-
|-
![[cent|Cents]]
! [[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
|}
|}
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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.
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)
=== [[Mirkwai clan #Subsedia|Subsedia]] (10 & 111) ===
'''7-limit'''<br>
==== 7-limit ====
Comma list: 16875/16807, 65536/64827<br>
Comma list: 16875/16807, 65536/64827
Mapping: [{{val|1 0 5 4}}, {{val|0 16 -27 -12}}]<br>
 
POTE generator: ~15/14 = 118.965<br>
Mapping: [{{val|1 0 5 4}}, {{val|0 16 -27 -12}}]
{{Optimal ET sequence|legend=1| 10, 101, 111, 121, 232d}}<br>
 
Badness: 0.157658<br><br>
POTE generator: ~15/14 = 118.965
'''11-limit'''<br>
 
Comma list: 540/539, 1375/1372, 65536/64827<br>
{{Optimal ET sequence|legend=1| 10, 101, 111, 121, 232d}}
Mapping: [{{val|1 0 5 4 -1}}, {{val|0 16 -27 -12 45}}]<br>
 
POTE generator: ~15/14 = 118.968<br>
Badness: 0.157658
{{Optimal ET sequence|legend=1| 10, 101, 111, 121, 232d}}<br>
 
Badness: 0.066838<br><br>
==== 11-limit ====
'''13-limit'''<br>
Comma list: 540/539, 1375/1372, 65536/64827
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>
Mapping: [{{val|1 0 5 4 -1}}, {{val|0 16 -27 -12 45}}]
POTE generator: ~15/14 = 118.968<br>
 
{{Optimal ET sequence|legend=1| 10, 101, 111, 121, 232d}}<br>
POTE generator: ~15/14 = 118.968
Badness: 0.031635<br><br>
 
'''17-limit'''<br>
{{Optimal ET sequence|legend=1| 10, 101, 111, 121, 232d}}
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>
Badness: 0.066838
POTE generator: ~15/14 = 118.968<br>
 
{{Optimal ET sequence|legend=1| 10, 101, 111, 121, 232dg}}<br>
==== 13-limit ====
Badness: 0.019707<br><br>
Comma list: 352/351, 540/539, 676/675, 1375/1372
 
Mapping: [{{val|1 0 5 4 -1 4}}, {{val|0 16 -27 -12 45 -3}}]
 
POTE generator: ~15/14 = 118.968
 
{{Optimal ET sequence|legend=1| 10, 101, 111, 121, 232d}}
 
Badness: 0.031635
 
==== 17-limit ====
Comma list: 256/255, 352/351, 442/441, 540/539, 715/714
 
Mapping: [{{val|1 0 5 4 -1 4 3}}, {{val|0 16 -27 -12 45 -3 11}}]
 
POTE generator: ~15/14 = 118.968
 
{{Optimal ET sequence|legend=1| 10, 101, 111, 121, 232dg}}
 
Badness: 0.019707


== 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]]


[[Category:Edt]]
[[Category:Macrotonal]]
[[Category:Macrotonal]]
{{todo|expand}}
Retrieved from "https://en.xen.wiki/w/16edt"