3072edo: Difference between revisions

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== Theory ==

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=== As a tuning standard ===

3072edo~~'s step~~ is known as '''octamu''' (eighth MIDI-resolution unit, 8mu, 2<sup>8</sup> = 256 equal divisions of the [[12edo]] semitone). The internal data structure of the 8mu 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, and 5 other bits which are not 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 3072edo is known as an '''octamu''' (eighth MIDI-resolution unit, 8mu, 2<sup>8</sup> = 256 equal divisions of the [[12edo]] semitone). The internal data structure of the 8mu 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, and 5 other bits which are not 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 ===

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== Regular temperament properties ==

{| class="wikitable center-4 center-5 center-6"

|-

! rowspan="2" | [[Subgroup]]

! rowspan="2" | [[Comma list]]

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| {{monzo| 37 25 -33 }}, {{monzo| 161 -84 -12 }}

| {{mapping| 3072 4869 7133 }}

| -0.002

| −0.002

| 0.003

|

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| 250047/250000, {{monzo| -2 -25 1 14 }}, {{monzo| -53 -1 9 12 }}

| {{mapping| 3072 4869 7133 8624 }}

| 0.006

| +0.006

| 0.013

|

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| 9801/9800, 151263/151250, 184549376/184528125, 73525096183/73466403840

| {{mapping| 3072 4869 7133 8624 10627 }}

| 0.013

| +0.013

| 0.019

|

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| 9801/9800, 140625/140608, 151263/151250, 196625/196608, 3327500/3326427

| {{mapping| 3072 4869 7133 8624 10627 11638 }}

| 0.006

| +0.006

| 0.022

|

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== External links ==

* [http://tonalsoft.com/enc/number/8mu.aspx ~~Tonalsoft Encyclopedia | ''~~8mu / oktamu'']

* [http://tonalsoft.com/enc/number/8mu.aspx 8mu / oktamu] on [[Tonalsoft Encyclopedia]]

[[Category:Listen]]

@@ Line 1: / Line 1: @@
 {{Infobox ET}}
-{{EDO intro|3072}}
+{{ED intro}}
 == Theory ==
@@ Line 8: / Line 8: @@
 === As a tuning standard ===
-edo's step is known as '''octamu''' (eighth MIDI-resolution unit, 8mu, 2<sup>8</sup> = 256 equal divisions of the [[12edo]] semitone). The internal data structure of the 8mu 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, and 5 other bits which are not 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 3072edo is known as an '''octamu''' (eighth MIDI-resolution unit, 8mu, 2<sup>8</sup> = 256 equal divisions of the [[12edo]] semitone). The internal data structure of the 8mu 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, and 5 other bits which are not 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 ===
@@ Line 18: / Line 18: @@
 == Regular temperament properties ==
 {| class="wikitable center-4 center-5 center-6"
+|-
 ! rowspan="2" | [[Subgroup]]
 ! rowspan="2" | [[Comma list]]
@@ Line 30: / Line 31: @@
 | {{monzo| 37 25 -33 }}, {{monzo| 161 -84 -12 }}
 | {{mapping| 3072 4869 7133 }}
-| -0.002
+| −0.002
 | 0.003
 |
@@ Line 37: / Line 38: @@
 | 250047/250000, {{monzo| -2 -25 1 14 }}, {{monzo| -53 -1 9 12 }}
 | {{mapping| 3072 4869 7133 8624 }}
-| 0.006
+| +0.006
 | 0.013
 |
@@ Line 44: / Line 45: @@
 | 9801/9800, 151263/151250, 184549376/184528125, 73525096183/73466403840
 | {{mapping| 3072 4869 7133 8624 10627 }}
-| 0.013
+| +0.013
 | 0.019
 |
@@ Line 51: / Line 52: @@
 | 9801/9800, 140625/140608, 151263/151250, 196625/196608, 3327500/3326427
 | {{mapping| 3072 4869 7133 8624 10627 11638 }}
-| 0.006
+| +0.006
 | 0.022
 |
@@ Line 77: / Line 78: @@
 == External links ==
-* [http://tonalsoft.com/enc/number/8mu.aspx Tonalsoft Encyclopedia | ''8mu / oktamu'']
+* [http://tonalsoft.com/enc/number/8mu.aspx 8mu / oktamu] on [[Tonalsoft Encyclopedia]]
 [[Category:Listen]]