Superpartient ratio: Difference between revisions

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 == Definitions ==
 In ancient Greece, fractions like 3/1 and 5/1 were not considered to be epimeric ratios because of their additional restriction that [[Harmonic|multiples of the fundamental]] cannot be epimeric. Epimeric ratios were considered to be inferior to epimoric ratios.
+== Delta-N terminology ==
+The delta of a [[ratio]] is simply the difference between its numerator and its denominator. (Delta is also known as degree of epimoricity.) A ratio with a delta of N is called a delta-N ratio.
+{| class="wikitable" style="text-align:center;"
+|+
+examples
+!delta-1 ratios
+|2/1
+|3/2
+|4/3
+|5/4
+|6/5
+|7/6
+|etc.
+|-
+!delta-2 ratios
+|3/1
+|5/3
+|7/5
+|9/7
+|11/9
+|13/11
+|etc.
+|-
+!delta-3 ratios
+|4/1
+|5/2
+|7/4
+|8/5
+|10/7
+|11/8
+|etc.
+|-
+!delta-4 ratios
+|5/1
+|7/3
+|9/5
+|11/7
+|13/9
+|15/11
+|etc.
+|}
+Thus [[superparticular]] ratios are delta-1 ratios, and [[Superpartient ratio|superpartient ratios]] are all ratios except delta-1 ratios. The delta-N terminology was coined by [[Kite Giedraitis]].
 == Superpartient subcategories ==