User:CompactStar/Ordinal interval notation: Difference between revisions
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Left and right can be used multiple times to produce more complex directions. For example, leftleft is flatter than left, leftright is between left and central, rightleft is between central and right, and rightright is sharper than right. Adding a left always means to go flatter, and adding a right always means to go sharper, with each new left/right having less and less of an impact. Formally, if k is a degree, X and Y are any sequence of lefts/rights: | Left and right can be used multiple times to produce more complex directions. For example, leftleft is flatter than left, leftright is between left and central, rightleft is between central and right, and rightright is sharper than right. Adding a left always means to go flatter, and adding a right always means to go sharper, with each new left/right having less and less of an impact. Formally, if k is a degree, X and Y are any sequence of lefts/rights: | ||
* Xleft k-th = the simplest just k-th whose direction starts with X and is flatter than the X k-th | * Xleft k-th = the simplest (with respect to Tenney height) just k-th whose direction starts with X and is flatter than the X k-th | ||
* Xright k-th = the simplest just k-th whose direction starts with X and is sharper than the X k-th | * Xright k-th = the simplest (with respect to Tenney height) just k-th whose direction starts with X and is sharper than the X k-th | ||