80edo: Difference between revisions

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The '''80 equal temperament''', often abbreviated 80-tET, 80-EDO, or 80-ET, is the scale derived by dividing the octave into 80 equally-sized steps. Each step is exactly 15 [[~~cent|~~cent]]s.

The '''80 equal temperament''', often abbreviated 80-tET, 80-EDO, or 80-ET, is the scale derived by dividing the octave into 80 equally-sized steps. Each step is exactly 15 [[cent]]s.

== Theory ==

80et is the first equal temperament that represents the [[19-limit]] [[tonality diamond]] [[consistent~~|consistently~~]], though it barely manages to do so.

80et is the first equal temperament that represents the [[19-limit]] [[tonality diamond]] [[consistent]]ly, though it barely manages to do so.

80et [[Tempering_out|tempers out]] 176/175 and 540/539 in the [[11-limit]], 169/168, [[325/324]], [[351/350]], [[352/351]], [[364/363]] and 1001/1000 in the [[13-limit]], 136/135, 221/220, 256/255, 289/288, 561/560, 595/594, 715/714, 936/935, 1275/1274 in the [[17-limit]], 190/189, 286/285, 361/360, 400/399, 456/455, 476/475, 969/968, 1331/1330, [[1445/1444]], 1521/1520, 1540/1539 and 1729/1728 in the 19-limit, not to mention such important non-superparticular commas as [[2048/2025]], 4000/3969, 1728/1715 and 3136/3125.

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41&80 <<7 26 25 -3 -24 -33 20 ... ||

In each case, the numbers joined by an ampersand represent 19-limit [[~~Patent_val|~~patent ~~vals~~]] (meaning obtained by rounding to the nearest integer) and the first and most important part of the wedgie is given.

In each case, the numbers joined by an ampersand represent 19-limit [[patent val]]s (meaning obtained by rounding to the nearest integer) and the first and most important part of the wedgie is given.

== Intervals ==

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== Just approximation ==

{| class="wikitable center-all"

! colspan="2" |

! colspan="2" |

! prime 2

! prime 3

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| -5.04

|-

![[Relative error|relative]] (%)

! [[Relative error|relative]] (%)

| 0.0

| +20.3

@@ Line 1: / Line 1: @@
-The '''80 equal temperament''', often abbreviated 80-tET, 80-EDO, or 80-ET, is the scale derived by dividing the octave into 80 equally-sized steps. Each step is exactly 15 [[cent|cent]]s.
+The '''80 equal temperament''', often abbreviated 80-tET, 80-EDO, or 80-ET, is the scale derived by dividing the octave into 80 equally-sized steps. Each step is exactly 15 [[cent]]s.
 == Theory ==
-et is the first equal temperament that represents the [[19-limit]] [[tonality diamond]] [[consistent|consistently]], though it barely manages to do so.
+et is the first equal temperament that represents the [[19-limit]] [[tonality diamond]] [[consistent]]ly, though it barely manages to do so.
 et [[Tempering_out|tempers out]] 176/175 and 540/539 in the [[11-limit]], 169/168, [[325/324]], [[351/350]], [[352/351]], [[364/363]] and 1001/1000 in the [[13-limit]], 136/135, 221/220, 256/255, 289/288, 561/560, 595/594, 715/714, 936/935, 1275/1274 in the [[17-limit]], 190/189, 286/285, 361/360, 400/399, 456/455, 476/475, 969/968, 1331/1330, [[1445/1444]], 1521/1520, 1540/1539 and 1729/1728 in the 19-limit, not to mention such important non-superparticular commas as [[2048/2025]], 4000/3969, 1728/1715 and 3136/3125.
@@ Line 28: / Line 28: @@
 &amp;80 &lt;&lt;7 26 25 -3 -24 -33 20 ... ||
-In each case, the numbers joined by an ampersand represent 19-limit [[Patent_val|patent vals]] (meaning obtained by rounding to the nearest integer) and the first and most important part of the wedgie is given.
+In each case, the numbers joined by an ampersand represent 19-limit [[patent val]]s (meaning obtained by rounding to the nearest integer) and the first and most important part of the wedgie is given.
 == Intervals ==
@@ Line 210: / Line 210: @@
 == Just approximation ==
 {| class="wikitable center-all"
-! colspan="2" |
+! colspan="2" | <!-- empty cell -->
 ! prime 2
 ! prime 3
@@ Line 237: / Line 237: @@
 | -5.04
 |-
-![[Relative error|relative]] (%)
+! [[Relative error|relative]] (%)
 | 0.0
 | +20.3