Interval family: Difference between revisions

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 Sets of integer harmonics contain intervals of the form ''a/1'' with ''a'' being an arbitrary integer inside some limit.
-=== Primodality ===
+{| class="wikitable"
+|+ Family table
-{{main|Primodality}}
+|-
+! Family
-In contrast to other interval sets individual primodes are not defined by a limit and do not necessarily contain all previous sets. Rather the denominator of all of the primode's intervals simply has to be equal to a specific integer while the numerator is free to vary.
+! Example
+! Notes
+|-
+| [[Odd limit]]
+| 6-Limit: 1/1, 2/1, 3/1, 3/2, 4/1, 4/3, 5/1, 5/2, 5/3, 5/4, 6/1, 6/5, 8/1, 8/3, 8/5, 10/1, 10/3, 12/1, 12/5, 16/1, 16/3, 16/5, ... + inverse ratios 1/2, 1/3, 2/3, ...
+| Interval set is infinite, 6-odd-limit identical to 5-odd-limit
+|-
+| [[Odd limit#Integer limit|Integer limit]]
+| 6-Limit: 1/1, 2/1, 3/1, 3/2, 4/1, 4/3, 5/1, 5/2, 5/3, 5/4, 6/1, 6/5 + inverse ratios
+|
+|-
+| Octave complemented integer limit {{idio}}
+| 6-Limit: 1/1, 2/1, 3/1, 3/2, 4/1, 4/3, 5/1, 5/2, 5/3, 5/4, 6/1, 6/5, 8/1, 8/3, 8/5, 10/1, 10/3, 12/1, 12/5 + inverse ratios
+| Interger-limit with one factor of 2 ignored from every interval
+|-
+| Larger-than-1/1-Integer-limit {{idio}}
+| 6-Limit: 2/1, 3/1, 3/2, 4/1, 4/3, 5/1, 5/2, 5/3, 5/4, 6/1, 6/5
+| Integer limit with only ratios larger than 1/1
+|-
+| [[Odd prime sum limit]] {{idio}}
+| 6-Limit: 1/1, 2/1, 3/1, 3/2, 4/1, 4/3, 5/1, 5/2, 5/3, 5/4, 6/1, 6/5, 8/1, 8/3, 8/5, 9/1, 9/2, 9/4, 9/5, 9/8, 10/1, 10/3, 10/9, 12/1, 12/5, 16/1, 16/3, 16/5, 16/9, ... + inverse ratios
+| Interval set is infinite
+|-
+| [[Harmonic]]s
+| 6-Limit: 1/1, 2/1, 3/1, 4/1, 5/1, 6/1
+|
+|-
+| [[Harmonic#Prime Harmonic|Prime harmonics]]
+| 5-Limit: 2/1, 3/1, 5/1
+|
+|}