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Confused
"but not 11/9 (11 is a prime greater than 9) nor 15/7 (since 15 is 3*5, both leas then 9, but with product greater than 9)"
Ok, so what odd limit are these? 11/9 is 11 odd-limit? 15/7 is 15 odd-limit?
Is 3/1 in 3 odd-limit?
is 12/1 in 3 odd-limit?
is 10/3 in 3 odd-limit or 5 odd-limit?
- Omegatron September 02, 2014, 06:48:54 AM UTC-0700
and why does the primeness of 11 in 11/9 matter? the odd limit of 15/7 is 15 while the odd-limit of 11/7 is 11? so primeness is irrelevant?
- Omegatron September 02, 2014, 06:57:49 AM UTC-0700
A distinction is made between prime limits (p-limits) and odd limits. As I understand it, odd limits define diamonds of intervals, whereas a prime limit defines the highest "dimension" of an interval space by dimensions (here is also a rank considered). I also think these definitions in this wiki could be improved.
As for your actual questions, I think:
3/1 is in 3 odd-limit and in the 3 p-limit
12/1 is in the 13 odd-limit and in the 3 p-limit
10/3 is in the 11 odd-limit and in the 5 p-limit
- xenwolf September 02, 2014, 08:37:20 AM UTC-0700
I was wrong. As Wikipedia describes it, the factor 2 (and each of its powers) is irrelevant. So 12/1 should be in the 3 odd-limit and 10/3 in the 5 odd-limit.
- xenwolf September 02, 2014, 08:41:38 AM UTC-0700
Ok so are these lists correct? They are generated from Calkin-Wilf sequence:
1 prime-limit includes {1:1}
2 prime-limit includes {1:1, 1:2, 2:1, 1:4, 4:1, 1:8, 8:1, 1:16, 16:1, ...}
3 prime-limit includes {1:1, 1:2, 2:1, 1:3, 3:2, 2:3, 3:1, 1:4, 4:3, 3:4, 4:1, 3:8, 8:3, 1:6, 9:4, 9:2, 2:9, 4:9, 6:1, ...}
5 prime-limit includes {1:1, 1:2, 2:1, 1:3, 3:2, 2:3, 3:1, 1:4, 4:3, 3:5, 5:2, 2:5, 5:3, 3:4, 4:1, 1:5, 5:4, 3:8, 8:5, ...}
1 odd-limit includes {1:1, 1:2, 2:1, 1:4, 4:1, 1:8, 8:1, 1:16, 16:1, ...}
3 odd-limit includes {1:1, 1:2, 2:1, 1:3, 3:2, 2:3, 3:1, 1:4, 4:3, 3:4, 4:1, 3:8, 8:3, 1:6, 6:1, 1:8, 16:3, 3:16, 8:1, ...}
5 odd-limit includes {1:1, 1:2, 2:1, 1:3, 3:2, 2:3, 3:1, 1:4, 4:3, 3:5, 5:2, 2:5, 5:3, 3:4, 4:1, 1:5, 5:4, 3:8, 8:5, ...}
- Omegatron September 11, 2014, 08:18:45 PM UTC-0700
Seems so, although 1 prim-limit looks a bit strange.
...and "Calkin-Wilf sequence" means this? http://en.wikipedia.org/wiki/Calkin%E2%80%93Wilf_tree#Breadth_first_traversal
- xenwolf September 12, 2014, 03:58:41 AM UTC-0700
Yeah, I read some page that said "1-limit is just the unison", but I can't find it now.
Yes, that sequence.
- Omegatron September 12, 2014, 08:07:35 AM UTC-0700