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WikispacesArchive>Mike Battaglia |
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| What would be the counterpart of odd limit for tritave equivalence named? | | What would be the counterpart of odd limit for tritave equivalence named? |
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| : Good question. I don't think there's a name for it. What would you like to call it? Mod-3 limit? [[User:Mike Battaglia|Mike Battaglia]] ([[User talk:Mike Battaglia|talk]]) 21:10, 27 September 2018 (UTC) | | : Good question. I don't think there's a name for it. What would you like to call it? Mod-3 limit? [[User:Mike Battaglia|Mike Battaglia]] ([[User talk:Mike Battaglia|talk]]) 21:10, 27 September 2018 (UTC) |
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| = ARCHIVED WIKISPACES DISCUSSION BELOW =
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| '''All discussion below is archived from the Wikispaces export in its original unaltered form.'''
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| <span style="color:#800000">'''PLEASE MAKE ANY NEW COMMENTS <u>ABOVE</u> THIS SECTION.'''</span> Anything below here is for archival purposes only.
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| == Confused ==
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| "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)"
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| Ok, so what odd limit are these? 11/9 is 11 odd-limit? 15/7 is 15 odd-limit?
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| Is 3/1 in 3 odd-limit?
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| is 12/1 in 3 odd-limit?
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| is 10/3 in 3 odd-limit or 5 odd-limit?
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| - '''Omegatron''' September 02, 2014, 06:48:54 AM UTC-0700
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| 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?
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| - '''Omegatron''' September 02, 2014, 06:57:49 AM UTC-0700
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| 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.
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| As for your actual questions, I think:
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| 3/1 is in 3 odd-limit and in the 3 p-limit
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| 12/1 is in the 13 odd-limit and in the 3 p-limit
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| 10/3 is in the 11 odd-limit and in the 5 p-limit
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| - '''xenwolf''' September 02, 2014, 08:37:20 AM UTC-0700
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| 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.
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| - '''xenwolf''' September 02, 2014, 08:41:38 AM UTC-0700
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| Ok so are these lists correct? They are generated from Calkin-Wilf sequence:
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| 1 prime-limit includes {1:1}
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| 2 prime-limit includes {1:1, 1:2, 2:1, 1:4, 4:1, 1:8, 8:1, 1:16, 16:1, ...}
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| 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, ...}
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| 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, ...}
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| 1 odd-limit includes {1:1, 1:2, 2:1, 1:4, 4:1, 1:8, 8:1, 1:16, 16:1, ...}
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| 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, ...}
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| 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, ...}
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| - '''Omegatron''' September 11, 2014, 08:18:45 PM UTC-0700
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| Seems so, although 1 prim-limit looks a bit strange.
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| ...and "Calkin-Wilf sequence" means this? http://en.wikipedia.org/wiki/Calkin%E2%80%93Wilf_tree#Breadth_first_traversal
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| - '''xenwolf''' September 12, 2014, 03:58:41 AM UTC-0700
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| Yeah, I read some page that said "1-limit is just the unison", but I can't find it now.
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| Yes, that sequence.
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| - '''Omegatron''' September 12, 2014, 08:07:35 AM UTC-0700
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