29edo/Unque's compositional approach: Difference between revisions

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 One benefit of using extraclassical intervals is that the art and tendo thirds (unlike their diatonic counterparts) do not crowd one another when used in a chord together, being separated by a whole tone rather than a chroma.
+=== Harmonic Approximations ===
+Critics of 29edo have often said that it fails to approximate most ratios beyond the 3-limit; primes 5, 7, 11, and 13 are all of relatively high error, and as such the tuning does not provide the necessary colors to suffice as an introductory system to tunings beyond 12edo.
+Assuming for the sake of the argument that approximating JI is somehow the only thing that one may want of a tuning, and further assuming that one even knows what that entails on their first venture into xenharmonic tunings, 29edo does not fall quite as flat as some would have you believe.  Notably, the aforementioned error on primes 5, 7, 11, and 13 are all in the same direction and of roughly the same amount, which leads their difference tones to be tuned quite well.
+{| class="wikitable"
+|+13-limit difference tones
+! colspan="2" |Interval
+!7/5
+!11/5
+!13/5
+!11/7
+!13/7
+!13/11
+|-
+! rowspan="2" |Error
+!Absolute (¢)
+| -3.2
+| +0.5
+| +1.0
+| +3.7
+| +4.2
+| +0.5
+|-
+!Relative (%)
+| -7.7
+| +1.2
+| +2.3
+| +8.9
+| +10.0
+| +1.1
+|-
+! colspan="2" |Steps
+(Reduced)
+|14
+(14)
+|33
+(4)
+|40
+(11)
+|19
+(19)
+|26
+(26)
+|7
+(7)
+|}
+Additionally, 4\29 can be interpreted as 32/29, adding prime 29 to the subgroup; this allows the chromatic semitone to be interpreted as the simple and accurate 29/27, the supraminor third as 29/24, and the submajor third as 36/29.
 == Chords of 29edo ==