16edo: Difference between revisions

m JI approximation: -> approximation to JI
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== Approximation to JI ==
== Approximation to JI ==
=== Selected just intervals by error ===
=== Selected just intervals by error ===
The following table shows how [[15-odd-limit intervals]] are represented in 16edo (ordered by absolute error).
{{Q-odd-limit intervals|16}}
 
{| class="wikitable center-all mw-collapsible mw-collapsed"
|+style=white-space:nowrap| 15-odd-limit intervals by direct approximation (even if inconsistent)
|-
! Interval, complement
! Error (abs., in [[cent]]s)
|-
| [[12/11]], [[11/6]]
| 0.637
|-
| [[13/10]], [[20/13]]
| 4.214
|-
| '''[[8/7]], [[7/4]]'''
| '''6.174'''
|-
| [[13/11]], [[22/13]]
| 10.790
|-
| '''[[5/4]], [[8/5]]'''
| '''11.314'''
|-
| [[13/12]], [[24/13]]
| 11.427
|-
| [[15/11]], [[22/15]]
| 11.951
|-
| [[9/7]], [[14/9]]
| 14.916
|-
| [[11/10]], [[20/11]]
| 15.004
|-
| '''[[16/13]], [[13/8]]'''
| '''15.528'''
|-
| [[6/5]], [[5/3]]
| 15.641
|-
| [[7/5]], [[10/7]]
| 17.488
|-
| [[9/8]], [[16/9]]
| 21.090
|-
| [[14/13]], [[13/7]]
| 21.702
|-
| [[15/13]], [[26/15]]
| 22.741
|-
| '''[[11/8]], [[16/11]]'''
| '''26.318'''
|-
| '''[[4/3]], [[3/2]]'''
| '''26.955'''
|-
| [[11/9]], [[18/11]]
| 27.592
|-
| [[15/14]], [[28/15]]
| 30.557
|-
| [[10/9]], [[9/5]]
| 32.404
|-
| [[14/11]], [[11/7]]
| 32.492
|-
| [[7/6]], [[12/7]]
| 33.129
|-
| [[18/13]], [[13/9]]
| 36.618
|-
| [[16/15]], [[15/8]]
| 36.731
|}
{{15-odd-limit|16}}


It's worth noting that the 525-cent interval is almost exactly halfway in between 4/3 and 11/8, making it very discordant, although playing this in the context of a larger chord, and with specialized timbres, can make this less noticeable.
It's worth noting that the 525-cent interval is almost exactly halfway in between 4/3 and 11/8, making it very discordant, although playing this in the context of a larger chord, and with specialized timbres, can make this less noticeable.