Xenharmonic Wiki

196608edo: Difference between revisions

← Older edit
VisualWikitext
m →External links: Misc. edits
Tristanbay (talk | contribs)
autopatrolled
844 edits
Added software tuning message
 
(One intermediate revision by one other user not shown)
Line 1: Line 1:
{{Software tuning}}
{{Infobox ET}}
{{Infobox ET}}
{{EDO intro|196608}}
{{ED intro}}


== Theory ==
== Theory ==
Line 8: Line 9:
[[File:Tetradecamu Approximation Quality.png|thumb|Approximation quality of smaller edos in tetradecamu, maximum relative error against edo from 1 to 16808. ]]
[[File:Tetradecamu Approximation Quality.png|thumb|Approximation quality of smaller edos in tetradecamu, maximum relative error against edo from 1 to 16808. ]]


A step of 196608edo is known as a '''MIDI Tuning Standard unit''' ('''MTSU''') or a '''tetradecamu''' (fourteenth MIDI-resolution unit, 14mu, 2<sup>14</sup> = 16384 equal divisions of the [[12edo]] semitone). The 14mu is specified in the [[MIDI]] spec (1983) as the smallest increment available for the pitch-bend controller, and as the frequency data format for MTS (1999). The 14mu is the smallest unit of tuning resolution which has ever been put into common musical use, and provides extremely accurate tuning in microtonal electronic music.
A step of 196608edo is known as a '''MIDI Tuning Standard unit''' ('''MTSU''') or a '''tetradecamu''' (fourteenth MIDI-resolution unit, 14mu, {{nowrap|2<sup>14</sup> {{=}} 16384}} equal divisions of the [[12edo]] semitone). The 14mu is specified in the [[MIDI]] spec (1983) as the smallest increment available for the pitch-bend controller, and as the frequency data format for MTS (1999). The 14mu is the smallest unit of tuning resolution which has ever been put into common musical use, and provides extremely accurate tuning in microtonal electronic music.


The main application of 196608edo is thus not as a compositional device, but as a technical tuning standard. If we adopt direct approximation, some JI intervals are indeed improved, which makes sense since we are only quantizing JI to the grid of this edo.  
The main application of 196608edo is thus not as a compositional device, but as a technical tuning standard. If we adopt direct approximation, some JI intervals are indeed improved, which makes sense since we are only quantizing JI to the grid of this edo.  
Line 19: Line 20:
== Selected intervals ==
== Selected intervals ==
Below is a list for just intervals.
Below is a list for just intervals.
{| class="wikitable right-1 right-2 center-3 right-4 right-5"
{| class="wikitable right-1 right-2 center-3 right-4 right-5"
|-
|-
Line 34: Line 36:
| [[1/1]]
| [[1/1]]
| 0.000000000000
| 0.000000000000
| &plusmn;0.000000
| ±0.000000
| &plusmn;0.000000000000
| ±0.000000000000
|-
|-
| 18306
| 18306
Line 41: Line 43:
| [[16/15]]
| [[16/15]]
| 111.731285269778
| 111.731285269778
| &minus;0.053779
| −0.053779
| &minus;0.000328238528
| −0.000328238528
|-
|-
| 19570
| 19570
Line 55: Line 57:
| [[14/13]]
| [[14/13]]
| 128.298244699814
| 128.298244699814
| &minus;0.384412
| −0.384412
| &minus;0.002346262314
| −0.002346262314
|-
|-
| 22704
| 22704
Line 69: Line 71:
| [[12/11]]
| [[12/11]]
| 150.637058500631
| 150.637058500631
| &minus;0.375665
| −0.375665
| &minus;0.002292875631
| −0.002292875631
|-
|-
| 27034
| 27034
Line 76: Line 78:
| [[11/10]]
| [[11/10]]
| 165.004228499922
| 165.004228499922
| &minus;0.292797
| −0.292797
| &minus;0.001787093672
| −0.001787093672
|-
|-
| 29885
| 29885
Line 83: Line 85:
| [[10/9]]
| [[10/9]]
| 182.403712134060
| 182.403712134060
| &minus;0.024196
| −0.024196
| &minus;0.000147680935
| −0.000147680935
|-
|-
| 33409
| 33409
Line 111: Line 113:
| [[7/6]]
| [[7/6]]
| 266.870905603738
| 266.870905603738
| &minus;0.129174
| −0.129174
| &minus;0.000788416238
| −0.000788416238
|-
|-
| 47384
| 47384
Line 118: Line 120:
| [[13/11]]
| [[13/11]]
| 289.209719404554
| 289.209719404554
| &minus;0.120427
| −0.120427
| &minus;0.000735029554
| −0.000735029554
|-
|-
| 51715
| 51715
Line 132: Line 134:
| [[11/9]]
| [[11/9]]
| 347.407940633982
| 347.407940633982
| &minus;0.316993
| −0.316993
| &minus;0.001934774607
| −0.001934774607
|-
|-
| 58896
| 58896
Line 160: Line 162:
| [[9/7]]
| [[9/7]]
| 435.084095261650
| 435.084095261650
| &minus;0.178168
| −0.178168
| &minus;0.001087449150
| −0.001087449150
|-
|-
| 74418
| 74418
Line 167: Line 169:
| [[13/10]]
| [[13/10]]
| 454.213947904476
| 454.213947904476
| &minus;0.413225
| −0.413225
| &minus;0.002522123226
| −0.002522123226
|-
|-
| 81600
| 81600
Line 181: Line 183:
| [[15/11]]
| [[15/11]]
| 536.950772365466
| 536.950772365466
| &minus;0.014544
| −0.014544
| &minus;0.000088771716
| −0.000088771716
|-
|-
| 90328
| 90328
Line 209: Line 211:
| [[10/7]]
| [[10/7]]
| 617.487807395710
| 617.487807395710
| &minus;0.202364
| −0.202364
| &minus;0.001235130085
| −0.001235130085
|-
|-
| 106280
| 106280
Line 216: Line 218:
| [[16/11]]
| [[16/11]]
| 648.682057635243
| 648.682057635243
| &minus;0.068323
| −0.068323
| &minus;0.000417010243
| −0.000417010243
|-
|-
| 115008
| 115008
Line 223: Line 225:
| [[3/2]]
| [[3/2]]
| 701.955000865387
| 701.955000865387
| &minus;0.307342
| −0.307342
| &minus;0.001875865387
| −0.001875865387
|-
|-
| 125324
| 125324
Line 237: Line 239:
| [[11/7]]
| [[11/7]]
| 782.492035895632
| 782.492035895632
| &minus;0.495161
| −0.495161
| &minus;0.003022223757
| −0.003022223757
|-
|-
| 133314
| 133314
Line 244: Line 246:
| [[8/5]]
| [[8/5]]
| 813.686286135165
| 813.686286135165
| &minus;0.361120
| −0.361120
| &minus;0.002204103915
| −0.002204103915
|-
|-
| 139689
| 139689
Line 258: Line 260:
| [[5/3]]
| [[5/3]]
| 884.358712999447
| 884.358712999447
| &minus;0.331538
| −0.331538
| &minus;0.002023546322
| −0.002023546322
|-
|-
| 152884
| 152884
Line 272: Line 274:
| [[7/4]]
| [[7/4]]
| 968.825906469125
| 968.825906469125
| &minus;0.436516
| −0.436516
| &minus;0.002664281625
| −0.002664281625
|-
|-
| 163199
| 163199
Line 279: Line 281:
| [[16/9]]
| [[16/9]]
| 996.089998269225
| 996.089998269225
| &minus;0.385316
| −0.385316
| &minus;0.002351784850
| −0.002351784850
|-
|-
| 166723
| 166723
Line 307: Line 309:
| [[Octave|2/1]]
| [[Octave|2/1]]
| 1200.000000000000
| 1200.000000000000
| &plusmn;0.000000
| ±0.000000
| &plusmn;0.000000000000
| ±0.000000000000
|}
|}


Retrieved from "https://en.xen.wiki/w/196608edo"