16edo: Difference between revisions

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 ==Selected just intervals by error==
 The following table shows how [[Just-24|some prominent just intervals]] are represented in 16-EDO (ordered by absolute error).
+===Best direct mapping, even if inconsistent===
+{| class="wikitable"
+|-
+! | Interval, complement
+! | Error (abs., in [[cent|cents]])
+|-
+| style="text-align:center;" | [[12/11|12/11]], [[11/6|11/6]]
+| style="text-align:center;" | 0.637
+|-
+| style="text-align:center;" | [[13/10|13/10]], [[20/13|20/13]]
+| style="text-align:center;" | 4.214
+|-
+| style="text-align:center;" | [[8/7|8/7]], [[7/4|7/4]]
+| style="text-align:center;" | 6.174
+|-
+| style="text-align:center;" | [[13/11|13/11]], [[22/13|22/13]]
+| style="text-align:center;" | 10.790
+|-
+| style="text-align:center;" | [[5/4|5/4]], [[8/5|8/5]]
+| style="text-align:center;" | 11.314
+|-
+| style="text-align:center;" | [[13/12|13/12]], [[24/13|24/13]]
+| style="text-align:center;" | 11.427
+|-
+| style="text-align:center;" | [[15/11|15/11]], [[22/15|22/15]]
+| style="text-align:center;" | 11.951
+|-
+| style="text-align:center;" | [[9/7|9/7]], [[14/9|14/9]]
+| style="text-align:center;" | 14.916
+|-
+| style="text-align:center;" | [[11/10|11/10]], [[20/11|20/11]]
+| style="text-align:center;" | 15.004
+|-
+| style="text-align:center;" | [[16/13|16/13]], [[13/8|13/8]]
+| style="text-align:center;" | 15.528
+|-
+| style="text-align:center;" | [[6/5|6/5]], [[5/3|5/3]]
+| style="text-align:center;" | 15.641
+|-
+| style="text-align:center;" | [[7/5|7/5]], [[10/7|10/7]]
+| style="text-align:center;" | 17.488
+|-
+| style="text-align:center;" | [[9/8|9/8]], [[16/9|16/9]]
+| style="text-align:center;" | 21.090
+|-
+| style="text-align:center;" | [[14/13|14/13]], [[13/7|13/7]]
+| style="text-align:center;" | 21.702
+|-
+| style="text-align:center;" | [[15/13|15/13]], [[26/15|26/15]]
+| style="text-align:center;" | 22.741
+|-
+| style="text-align:center;" | [[11/8|11/8]], [[16/11|16/11]]
+| style="text-align:center;" | 26.318
+|-
+| style="text-align:center;" | [[4/3|4/3]], [[3/2|3/2]]
+| style="text-align:center;" | 26.955
+|-
+| style="text-align:center;" | [[11/9|11/9]], [[18/11|18/11]]
+| style="text-align:center;" | 27.592
+|-
+| style="text-align:center;" | [[15/14|15/14]], [[28/15|28/15]]
+| style="text-align:center;" | 30.557
+|-
+| style="text-align:center;" | [[10/9|10/9]], [[9/5|9/5]]
+| style="text-align:center;" | 32.404
+|-
+| style="text-align:center;" | [[14/11|14/11]], [[11/7|11/7]]
+| style="text-align:center;" | 32.492
+|-
+| style="text-align:center;" | [[7/6|7/6]], [[12/7|12/7]]
+| style="text-align:center;" | 33.129
+|-
+| style="text-align:center;" | [[18/13|18/13]], [[13/9|13/9]]
+| style="text-align:center;" | 36.618
+|-
+| style="text-align:center;" | [[16/15|16/15]], [[15/8|15/8]]
+| style="text-align:center;" | 36.731
+|}
+===Patent val mapping===
 {| class="wikitable"
@@ Line 399: / Line 481: @@
 | style="text-align:center;" | 60.084
 |}
-It's worth noting that the 525-cent interval is almost exactly halfway in between 4/3 and 11/8, making it EXTREMELY discordant.
+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.
 [[File:16ed2-001.svg|alt=alt : Your browser has no SVG support.]]