Correct predictions are in blue. If we detect only a subset of a labelled sentence, we highlight the caught part as blue, the missing part light blue. False positives are in green and false negatives are in red.

Problem 007 (All-interval series) — Constraint detection

Given the twelve standard pitch-classes -LRB- c , c# , d , - -RRB- , represented by numbers 0,1 , -,11 , find a series in which each pitch-class occurs exactly once and in which the musical intervals between neighbouring notes cover the full set of intervals from the minor second -LRB- 1 semitone -RRB- to the major seventh -LRB- 11 semitones -RRB- . That is , for each of the intervals , there is a pair of neigbhouring pitch-classes in the series , between which this interval appears . The problem of finding such a series can be easily formulated as an instance of a more general arithmetic problem on $ \ mathbb Z_n $ , the set of integer residues modulo $ n $ . Given $ n \ in \ mathbb N$ , find a vector $ s = -LRB- s_1 , - , s_n -RRB- $ , such that $ s $ is a permutation of $ \ mathbb Z_n = -LCB- 0,1 , - , n-1 -RCB- $ ; and the interval vector $ v = -LRB- | s_2-s_1 | , | s_3-s_2 | , - | s_n-s _ -LCB- n-1 -RCB- | -RRB- $ is a permutation of $ \ mathbb Z_n \ setminus \ -LCB- 0 \ -RCB- = \ -LCB- 1,2 , - , n-1 \ -RCB- $ . A vector $ v $ satisfying these conditions is called an all-interval series of size $ n $ ; the problem of finding such a series is the all-interval series problem of size $ n $ .

Problem 007 (All-interval series) — Detection of the decisions and objects to be modeled

Given the twelve standard pitch-classes -LRB- c , c# , d , - -RRB- , represented by numbers 0,1 , -,11 , find a series in which each pitch-class occurs exactly once and in which the musical intervals between neighbouring notes cover the full set of intervals from the minor second -LRB- 1 semitone -RRB- to the major seventh -LRB- 11 semitones -RRB- . That is , for each of the intervals , there is a pair of neigbhouring pitch-classes in the series , between which this interval appears . The problem of finding such a series can be easily formulated as an instance of a more general arithmetic problem on $ \ mathbb Z_n $ , the set of integer residues modulo $ n $ . Given $ n \ in \ mathbb N$ , find a vector $ s = -LRB- s_1 , - , s_n -RRB- $ , such that $ s $ is a permutation of $ \ mathbb Z_n = -LCB- 0,1 , - , n-1 -RCB- $ ; and the interval vector $ v = -LRB- | s_2-s_1 | , | s_3-s_2 | , - | s_n-s _ -LCB- n-1 -RCB- | -RRB- $ is a permutation of $ \ mathbb Z_n \ setminus \ -LCB- 0 \ -RCB- = \ -LCB- 1,2 , - , n-1 \ -RCB- $ . A vector $ v $ satisfying these conditions is called an all-interval series of size $ n $ ; the problem of finding such a series is the all-interval series problem of size $ n $ .

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