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98304edo: Difference between revisions

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{{Infobox ET}}
{{Infobox ET}}
{{EDO intro|98304}}
{{ED intro}}


== Theory ==
== Theory ==
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=== As a tuning standard ===
=== As a tuning standard ===
A step of 98304edo is known as a '''tridecamu''' (thirteenth MIDI-resolution unit, 13mu, 2<sup>13</sup> = 8192 equal divisions of the [[12edo]] semitone). The internal data structure of the 13mu requires two bytes, with the first bits of each byte reserved as flags to indicate the byte's status as data, and one bit in the first byte to indicate the sign (+ or &minus;) showing the direction of the pitch-bend up or down; all bits are used. The first data byte transmitted is the Least Significant Byte (LSB), equivalent to a fine-tuning. The second data byte transmitted is the Most Significant Byte (MSB), equivalent to a coarse-tuning.
A step of 98304edo is known as a '''tridecamu''' (thirteenth MIDI-resolution unit, 13mu, 2<sup>13</sup> = 8192 equal divisions of the [[12edo]] semitone). The internal data structure of the 13mu requires two bytes, with the first bits of each byte reserved as flags to indicate the byte's status as data, and one bit in the first byte to indicate the sign (+ or −) showing the direction of the pitch-bend up or down; all bits are used. The first data byte transmitted is the Least Significant Byte (LSB), equivalent to a fine-tuning. The second data byte transmitted is the Most Significant Byte (MSB), equivalent to a coarse-tuning.


=== Prime harmonics ===
=== Prime harmonics ===
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{| class="wikitable right-1 right-2 center-3 right-4 right-5"
{| class="wikitable right-1 right-2 center-3 right-4 right-5"
|-
|-
! rowspan="2"| #
! rowspan="2" | #
! rowspan="2"| Cents
! rowspan="2" | Cents
! colspan="2"| JI Interval
! colspan="2" | JI interval
! rowspan="2"| Error<br>(Cents)
! rowspan="2" | Error<br>(cents)
|-
|-
! Ratio
! Ratio
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| [[1/1]]
| [[1/1]]
| 0.0000
| 0.0000
| &plusmn;0.00000
| ±0.00000
|-
|-
| 3995
| 3995
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| [[36/35]]
| [[36/35]]
| 48.7704
| 48.7704
| &minus;0.00329
| −0.00329
|-
|-
| 4111
| 4111
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| 35/34
| 35/34
| 50.1842
| 50.1842
| &minus;0.00111
| −0.00111
|-
|-
| 4234
| 4234
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| [[33/32]]
| [[33/32]]
| 53.2729
| 53.2729
| &minus;0.00146
| −0.00146
|-
|-
| 5158
| 5158
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| [[27/26]]
| [[27/26]]
| 65.3373
| 65.3373
| &minus;0.00531
| −0.00531
|-
|-
| 5562
| 5562
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| [[26/25]]
| [[26/25]]
| 67.9002
| 67.9002
| &minus;0.00473
| −0.00473
|-
|-
| 6598
| 6598
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| [[18/17]]
| [[18/17]]
| 98.9546
| 98.9546
| &minus;0.00440
| −0.00440
|-
|-
| 8598
| 8598
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| [[16/15]]
| [[16/15]]
| 111.7313
| 111.7313
| &minus;0.00033
| −0.00033
|-
|-
| 9785
| 9785
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| [[14/13]]
| [[14/13]]
| 128.2982
| 128.2982
| &minus;0.00235
| −0.00235
|-
|-
| 11352
| 11352
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| [[12/11]]
| [[12/11]]
| 150.6371
| 150.6371
| &minus;0.00229
| −0.00229
|-
|-
| 13517
| 13517
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| [[11/10]]
| [[11/10]]
| 165.0042
| 165.0042
| &minus;0.00179
| −0.00179
|-
|-
| 14943
| 14943
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| [[19/17]]
| [[19/17]]
| 192.5576
| 192.5576
| &minus;0.00390
| −0.00390
|-
|-
| 16704
| 16704
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| [[9/8]]
| [[9/8]]
| 203.9100
| 203.9100
| &minus;0.00375
| −0.00375
|-
|-
| 17751
| 17751
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| [[7/6]]
| [[7/6]]
| 266.8709
| 266.8709
| &minus;0.00079
| −0.00079
|-
|-
| 23049
| 23049
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| [[13/11]]
| [[13/11]]
| 289.2097
| 289.2097
| &minus;0.00074
| −0.00074
|-
|-
| 24372
| 24372
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| [[19/16]]
| [[19/16]]
| 297.5130
| 297.5130
| &minus;0.00325
| −0.00325
|-
|-
| 25857
| 25857
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| [[6/5]]
| [[6/5]]
| 315.6413
| 315.6413
| &minus;0.00408
| −0.00408
|-
|-
| 27536
| 27536
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| [[19/15]]
| [[19/15]]
| 409.2443
| 409.2443
| &minus;0.00358
| −0.00358
|-
|-
| 34202
| 34202
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| [[14/11]]
| [[14/11]]
| 417.5080
| 417.5080
| &minus;0.00308
| −0.00308
|-
|-
| 35642
| 35642
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| [[9/7]]
| [[9/7]]
| 435.0841
| 435.0841
| &minus;0.00109
| −0.00109
|-
|-
| 36566
| 36566
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| [[22/17]]
| [[22/17]]
| 446.3625
| 446.3625
| &minus;0.00023
| −0.00023
|-
|-
| 37209
| 37209
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| [[13/10]]
| [[13/10]]
| 454.2139
| 454.2139
| &minus;0.00252
| −0.00252
|-
|-
| 38046
| 38046
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| [[21/16]]
| [[21/16]]
| 470.7809
| 470.7809
| &minus;0.00454
| −0.00454
|-
|-
| 40800
| 40800
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| [[19/14]]
| [[19/14]]
| 528.6871
| 528.6871
| &minus;0.00059
| −0.00059
|-
|-
| 43987
| 43987
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| [[15/11]]
| [[15/11]]
| 536.9508
| 536.9508
| &minus;0.00009
| −0.00009
|-
|-
| 44484
| 44484
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| [[18/13]]
| [[18/13]]
| 563.3823
| 563.3823
| &minus;0.00343
| −0.00343
|-
|-
| 47719
| 47719
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| [[7/5]]
| [[7/5]]
| 582.5122
| 582.5122
| &minus;0.00487
| −0.00487
|-
|-
| 48906
| 48906
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| [[24/17]]
| [[24/17]]
| 596.9996
| 596.9996
| &minus;0.00252
| −0.00252
|-
|-
| 49398
| 49398
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| [[3/2]]
| [[3/2]]
| 701.9550
| 701.9550
| &minus;0.00188
| −0.00188
|-
|-
| 62662
| 62662
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| [[8/5]]
| [[8/5]]
| 813.6863
| 813.6863
| &minus;0.00220
| −0.00220
|-
|-
| 72447
| 72447
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| [[7/4]]
| [[7/4]]
| 968.8259
| 968.8259
| &minus;0.00266
| −0.00266
|-
|-
| 98304
| 98304
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| [[Octave|2/1]]
| [[Octave|2/1]]
| 1200.0000
| 1200.0000
| &plusmn;0.00000
| ±0.00000
|}
|}


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