Where does sequence collide?

An ordered list of terms, one for each counting number, so that there is a first term, a second term, a third, and so on without end: formally it is a function whose inputs are the natural numbers. Rudin's 1976 Principles of Mathematical Analysis defines it this way and builds on it the idea of convergence, where the terms settle ever closer to a single limit value. The referent here is a pure ordering of abstract elements and the question of what it tends toward, and it is not the order of building blocks in a molecule, a repeated musical figure, or a run of scenes in a film.[1]

Unit

One indexed list of terms, written as its general term and its index range

Recovery means

Not applicable

Measured by

Studied by whether its terms approach a limit, tested with the epsilon definition of convergence and criteria such as being Cauchy or monotone and bounded

The exact linear order of the building blocks strung along a biological chain: the order of the four bases in DNA or RNA, or the order of amino acids in a protein. Determining that order is called sequencing, and Sanger, Nicklen, and Coulson's 1977 DNA sequencing with chain-terminating inhibitors gave the method that made reading a genome's base order routine. The referent is a physical string of chemical units in a molecule, aligned and compared across organisms, and it has nothing to do with an abstract list of numbers, a musical restatement, or a stretch of film.[2]

Unit

One ordered string of residues, written base by base or amino acid by amino acid

Recovery means

Not applicable

Measured by

Read off by sequencing chemistry and instruments, then compared by aligning two or more strings to score how well their orders match

The immediate restatement of a short melodic or chord pattern at a higher or lower pitch, so the same shape is heard again shifted up or down the scale. Aldwell and Schachter's Harmony and Voice Leading treats it as one of the basic devices of tonal music, a way of spinning a passage forward by repeating a figure at successive pitch levels. The referent is a musical repetition defined by pitch shift, and it is a different thing from an unending list of numbers, the order of units in a molecule, or a block of scenes in a film. In older usage the same word also names a kind of medieval chant, another meaning again.[3]

Unit

One statement of a pattern plus its repetitions, counted by how many pitch steps it moves each time

Recovery means

Not applicable

Measured by

Identified by ear and in the score by spotting the repeated figure and the constant interval by which each restatement is transposed