16edo: Difference between revisions

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== Theory ==
== Theory ==
{| class="wikitable center-all"
{{Odd harmonics in edo|edo=16}}
!
! prime 2
! prime 3
! prime 5
! prime 7
! prime 11
! prime 13
! prime 17
! prime 19
|-
! error (¢)
| 0
| -27.0
| -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.
'''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.