16edo: Difference between revisions

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@@ Line 9: / Line 9: @@
 | Prime factorization = 2<sup>4</sup>
 | Subgroup = 2.5.7.13.19.27
-| Step size = 75.000
+| Step size = 75¢
-| Fifth type = [[Mavila]] 9\16 675¢
+| Fifth type = [[Mavila]] 9\16 = 675¢
+| Major 2nd = 2\16 = 150¢
+| Minor 2nd = 3\16 = 225¢
+| Augmented 1sn = -1\16 = -75¢
 | Common uses = mavila, metallic harmony
 | Important MOS = [[mavila]] anti-diatonic 2L5s 2223223 (9\16, 1\1)<br/>[[mavila]] superdiatonic 7L2s 222212221 (9\16, 1\1)<br/>[[gorgo]] 5L1s 555551 (3\16, 1\1)<br/>[[lemba]] 4L2s 332332 (3\16, 1\2)
@@ Line 16: / Line 19: @@
 == Theory ==
-'''16-EDO''' is the [[Equal_division_of_the_octave|equal division of the octave]] into sixteen narrow chromatic semitones each of 75 [[cent|cent]]s exactly. It is not especially good at representing most low-integer musical intervals, but it has a [[7/4|7/4]] which is only six cents sharp, and a [[5/4|5/4]] which is only eleven cents flat. Four steps of it gives the 300 cent minor third interval, the same of that 12-EDO, giving it four diminished seventh chords exactly like those of [[12edo|12-EDO]], and a diminished triad on each scale step.
+{| class="wikitable" style="text-align:center;"
+!
+!prime 2
+!prime 3
+!prime 5
+!prime 7
+!prime 11
+!prime 13
+!prime 17
+!prime 19
+|-
+!error (¢)
+|0¢
+|  -26.96¢
+|  -11.3¢
+|  +6.2¢
+|  -26.3¢
+|  -15.6¢
+| -30.0¢
+|2.5¢
+|-
+![[relative error]] (%)
+|0%
+| -36
+| -15
+|8
+| -35
+| -21
+| -40
+|3
+|-
+![[nearest edomapping]]
+|16
+|9
+|5
+|13
+|7
+|11
+|1
+|4
+|-
+![[fifthspan]]
+|0
+|  +1
+|  -3
+|  +5
+|  -1
+|  +3
+| -7
+|4
+|}
+'''16-EDO''' is the [[equal division of the octave]] into sixteen narrow chromatic semitones each of 75 [[cent]]s exactly. It is not especially good at representing most low-odd-limit musical intervals, but it has a [[7/4]] which is only six cents sharp, and a [[5/4]] which is only eleven cents flat. Four steps of it gives the 300 cent minor third interval, the same of that 12-EDO, giving it four diminished seventh chords exactly like those of [[12edo|12-EDO]], and a diminished triad on each scale step.
 ==Intervals==
@@ Line 439: / Line 495: @@
 ==Selected just intervals by error==
-{| class="wikitable" style="text-align:center;"
-!
-!prime 2
-!prime 3
-!prime 5
-!prime 7
-!prime 11
-!prime 13
-|-
-!error
-|0¢
-| -26.96¢
-| -11.3¢
-| +6.2¢
-| -26.3¢
-| -15.6¢
-|-
-![[fifthspan]]
-|0
-| +1
-| -3
-| +5
-| -1
-| +3
-|}
 The following table shows how [[Just-24|some prominent just intervals]] are represented in 16-EDO (ordered by absolute error).
@@ Line 872: / Line 903: @@
 ==Commas==
-EDO [[tempering_out|tempers out]] the following [[Comma|comma]]s. (Note: This assumes [[val|val]] &lt; 16 25 37 45 55 59 |.)
+EDO [[tempering_out|tempers out]] the following [[comma]]s. (Note: This assumes [[val|val]] &lt; 16 25 37 45 55 59 |.)
 {| class="wikitable"