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Re: Decorated interval operations: still a problem



John Pryce wrote:
2.4. An arithmetic operation on bare intervals is obtained by promoting the bare intervals to decorated intervals whose decorations are all-0 and then performing the operation with the resulting decorated intervals.

At an abstract level, this is false as stated, because the bare intervals are closed under arithmetic operations.

The simplest solution IMO is to assume you meant
2.4. An arithmetic operation having some bare interval operands and some decorated interval or bare decoration operands is obtained by promoting the bare intervals to decorated intervals whose decorations are all-0 and then performing the operation with the resulting decorated intervals.

(Where "all-0" now becomes 4 for the bare empty set, 2 for all other bare intervals, according to Arnold's prescription.)

Is that correct?


Yes.

We are clarifying these various issues in our new position paper, which will describe the algebraic structure of bare intervals, bare decorations, and decorated intervals as an ADT at Level 2.

Nate Hayes