User:BudjarnLambeth/Tritavesque: Difference between revisions

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The '''tritavesque intervals'''{{idiosyncratic}} are all those intervals a/b, where b is the largest possible integer that is less than half of a, and shares no common ~~factirs~~ with a.

The '''tritavesque intervals'''{{idiosyncratic}} are all those intervals a/b, where b is the largest possible integer that is less than half of a, and shares no common factors with a.

The first few tritavesque intervals are:

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As tritavesque intervals get more complex, they usually but not always get closer to [[2/1]].

Many of these intervals see use as [[~~equave~~]]s for [[edonoi]] and other [[nonoctave]] scales.

Many of these intervals see use as [[period]]s for [[edonoi]] and other [[nonoctave]] scales. They also see use as ninths of scales in edonoi, especially [[EDT]]s.

The more complex

The more complex of these intervals can also be used as [[pseudo-octave]]s.

== List of tritavesque intervals ==

The numerators are the integers starting from 3 (3, 4, 5, 6, 7...). The denominators are [https://oeis.org/A116921 OEIS sequence A116921] — ''a(n) = largest integer <= n/2 which is coprime to n'' — but skipping the first entry (0).

# [[3/1]]

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# [[29/14]]

# [[30/13]]

# [[31/15]]

# [[32/15]]

# [[33/16]]

# [[34/15]]

# [[35/17]]

# [[36/17]]

# [[37/18]]

# [[38/17]]

# [[39/19]]

# [[40/19]]

And so on...

== See also ==

* [[Taxicab distance]]

[[Category:Lists of intervals]][[Category:Nonoctave]][[Category:Edonoi]]

@@ Line 1: / Line 1: @@
-The '''tritavesque intervals'''{{idiosyncratic}} are all those intervals a/b, where b is the largest possible integer that is less than half of a, and shares no common factirs with a.
+The '''tritavesque intervals'''{{idiosyncratic}} are all those intervals a/b, where b is the largest possible integer that is less than half of a, and shares no common factors with a.
 The first few tritavesque intervals are:
@@ Line 7: / Line 7: @@
 As tritavesque intervals get more complex, they usually but not always get closer to [[2/1]].
-Many of these intervals see use as [[equave]]s for [[edonoi]] and other [[nonoctave]] scales.
+Many of these intervals see use as [[period]]s for [[edonoi]] and other [[nonoctave]] scales. They also see use as ninths of scales in edonoi, especially [[EDT]]s.
-The more complex
+The more complex of these intervals can also be used as [[pseudo-octave]]s.
 == List of tritavesque intervals ==
+The numerators are the integers starting from 3 (3, 4, 5, 6, 7...). The denominators are [https://oeis.org/A116921 OEIS sequence A116921] — ''a(n) = largest integer <= n/2 which is coprime to n'' — but skipping the first entry (0).
 # [[3/1]]
@@ Line 41: / Line 42: @@
 # [[29/14]]
 # [[30/13]]
+# [[31/15]]
+# [[32/15]]
+# [[33/16]]
+# [[34/15]]
+# [[35/17]]
+# [[36/17]]
+# [[37/18]]
+# [[38/17]]
+# [[39/19]]
+# [[40/19]]
 And so on...
+== See also ==
+* [[Taxicab distance]]
 [[Category:Lists of intervals]][[Category:Nonoctave]][[Category:Edonoi]]