User:BudjarnLambeth/Tritavesque: Difference between revisions
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As tritavesque intervals get more complex, they usually but not always get closer to [[2/1]]. | As tritavesque intervals get more complex, they usually but not always get closer to [[2/1]]. | ||
Many of these intervals see use as [[ | 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 of these intervals can also be used as [[pseudo-octave]]s. | |||
== List of tritavesque intervals == | == 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]] | # [[3/1]] | ||
| Line 39: | Line 42: | ||
# [[29/14]] | # [[29/14]] | ||
# [[30/13]] | # [[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... | And so on... | ||
== See also == | |||
* [[Taxicab distance]] | |||
[[Category:Lists of intervals]][[Category:Nonoctave]][[Category:Edonoi]] | [[Category:Lists of intervals]][[Category:Nonoctave]][[Category:Edonoi]] | ||
Latest revision as of 02:55, 7 May 2025
The tritavesque intervals[idiosyncratic term] 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:
3/1, 4/1, 5/2, 6/1, 7/3, 8/3, 9/4, 10/3, 11/5...
As tritavesque intervals get more complex, they usually but not always get closer to 2/1.
Many of these intervals see use as periods for edonoi and other nonoctave scales. They also see use as ninths of scales in edonoi, especially EDTs.
The more complex of these intervals can also be used as pseudo-octaves.
List of tritavesque intervals
The numerators are the integers starting from 3 (3, 4, 5, 6, 7...). The denominators are OEIS sequence A116921 — a(n) = largest integer <= n/2 which is coprime to n — but skipping the first entry (0).
- 3/1
- 4/1
- 5/2
- 6/1
- 7/3
- 8/3
- 9/4
- 10/3
- 11/5
- 12/5
- 13/6
- 14/5
- 15/7
- 16/7
- 17/8
- 18/7
- 19/9
- 20/9
- 21/10
- 22/9
- 23/11
- 24/11
- 25/12
- 26/11
- 27/13
- 28/13
- 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...