Beep: Difference between revisions

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 If using brittle beep (23cd, 14edo, etc.), one might want to consider using this as a guideline. With this spectrum, no partials are more than 25 cents above or below their perfectly harmonic values, and when using 14edo, no intervals will be more than 26 cents out of tune. This is only a guideline, and only with synthesized tones would it be possible to achieve this perfectly. With physical idiophones (celestas, gamelans, etc.) it should still be possible to get a great approximation using CAD (or trial and error).
-Fundamental (1st): just
+* Fundamental (1st): just
+* Octave (2nd): just
+* 3rd: -12.5
+* 4th: just
+* 5th: +25
+* 6th: -12.5 cents
+* 7th: -25 cents
+* 8th: just
+* 9th: -25 cents
+* 10th: +25 cents
+* 11th: -25 cents
+* 12th: -12.5 cents
+* 13th: +15 cents
+* 14th: -25 cents
+* 15th: +12.5 cents
+* 16th: just
-Octave (2nd): just
+== Tunings ==
+=== Tuning spectrum ===
-rd: -12.5
+{| class="wikitable center-all left-4"
+|-
-th: just
+! Edo<br>Generator !! Eigenmonzo<br>(Unchanged-interval) !! Generator (¢) !! Comments
+|-
-th: +25
+| || 5/3 || 884.3 ||
+|-
-th: -12.5 cents
+| 3\4 ||  || 900.0 || Lower bound of 7-odd-limit diamond monotone
+|-
-th: -25 cents
+|  || 7/5 || 908.7 ||
+|-
-th: just
+| 10\13 ||  || 923.1 ||
+|-
-th: -25 cents
+|  || 5/4 || 928.8 || 5- and 7-odd-limit minimax
+|-
-th: +25 cents
+|  || 7/6 || 933.1 ||
+|-
-th: -25 cents
+| 7\9 ||  || 933.3 ||
+|-
-th: -12.5 cents
+| 11\14 ||  || 942.9 ||
+|-
-th: +15 cents
+| || 9/7 || 945.0 || 9-odd-limit minimax
+|-
-th: -25 cents
+| || 3/2 || 951.0 ||
+|-
-th: +12.5 cents
+| 4\5 ||  || 960.0 || Upper bound of 7-odd-limit diamond monotone<br>9-odd-limit diamond monotone (singleton)
+|-
-th: just
+| || 7/4 || 968.8 ||
+|-
+| || 9/5 || 1017.6 ||
+|}
 [[Category:Temperaments]]