User:CompactStar/Overtone scale: Difference between revisions

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-An '''ADO''' (arithmetic divisions of the octave) or '''overtone scale''' is a tuning system which divides the octave arithmetically rather than logarithmically. This is equivalent to taking an octave-long subset of the harmonic series and make it repeat at the octave.  For any C-ADO system, the m-th degree is equal to the ratio (C+m)/C. For example, in [[12ado]] the first degree is [[13/12]], the second is 14/12 ([[7/6]]), and so on. For an ADO system, the distance between interval ratios is equal, rather than the distance between their logarithms like in EDO systems. All ADOs are subsets of [[just intonation]]. ADOs with more divisors such as [[Highly_composite_equal_division|highly composite]] ADOs generally have more useful just intervals.
+An '''ADO''' (arithmetic divisions of the octave) or '''overtone scale''' is a tuning system which divides the octave arithmetically rather than logarithmically. This is equivalent to taking an octave-long subset of the harmonic series and make it repeat at the octave.  For any C-ADO system, the m-th degree is equal to the ratio (C+m)/C. For example, the [[5ado]] system consists of the 5th to 10th harmonics:
+{| class="wikitable"
+|-
+| harmonic
+| 5
+| 6
+| 7
+| 8
+| 9
+| 10
+|-
+| JI ratio
+| [[1/1]]
+| [[6/5]]
+| [[7/5]]
+| [[8/5]]
+| [[9/5]]
+| [[2/1]]
+|}
+For an ADO system, the distance between interval ratios is equal, rather than the distance between their logarithms like in EDO systems. All ADOs are subsets of [[just intonation]]. ADOs with more divisors such as [[Highly_composite_equal_division|highly composite]] ADOs generally have more useful just intervals.
 If the first division is <math>R_1</math> (which is ratio of C/C) and the last , <math>R_n</math> (which is ratio of 2C/C), with common difference of d