Doublings

The above is the instrumentarium of Richard Strauss's Elektra, from the 1916 edition published by Adolph Fürstner. I took a photo from my score, which I got in 1979, a lifetime ago.
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​It's in glorious 'Germtalian', typical of the time: an eclectic mixture of Italian, German, and a few bits of Latin thrown in for good measure. Nothing unusual, and contrabassi is still acceptable today, just meno corretto according to modern Italian dictionaries: the preferred spelling is contrabbassi. And nowadays, the Italians prefer controfagotto to contrafagotto. But 'secundi', on the other hand, is pure Latin and plain wrong. Whether this comes from Strauss himself or from his German publishers is difficult to determine. 

This demonstrates that correct and incorrect are the wrong axes for score conventions, which have deep cultural roots encompassing multiple truths simultaneously. All depending on the understanding of everybody involved, from composer to publisher to engraver.

And then there's of course the wholly absurd. Every musician is familiar with the term con sordini, with mutes. But when you see 'senza con sordini' in a score, you know you're dealing with an amateur, or at least with someone who's misunderstood something very basic. But the masters themselves are not exempt: I think it was Stockhausen who wrote So schnell wie möglich (as fast as possible) in a piano piece (possibly Klavierstück X) only to follow it by Noch schneller (even faster) a few bars later. Correctness in music is a many-faceted thing. Logic can be obscure, conventions are multi-dimensional and clearly overlap, and instructions can be psychological rather than factual, as in the Stockhausen example. All this must be embraced.

But I'm digressing, for the purpose of this post is to illustrate how musicians are numbered: first flute, second flute, and so on. That's one dimension. But then musicians can play more than one instrument: they have a primary instrument and then they double on one or more auxiliary instruments. That's the second dimension. And the numbers in one dimension don't map directly onto the other.
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Look at the very first two lines. There's a dedicated piccolo player (ottavino) and then there are three normal flutes. Strauss numbers them Flute I, II, III. But then the first flautist also doubles on piccolo. The dedicated piccolo player is Ottavino I, and the first flautist doubles on Ottavino II. Two dimensions.

You see the same thing in several places: Oboe III doubles on Cor Anglais, which takes no number since there's only one. On the other hand, the four Wagner Tubas in B♭ and F double on French Horns V, VI, VII, and VIII.

All these things must be correctly numbered in the score and parts, whether you choose to use Arabic or Roman numerals. Strauss uses Roman numerals as was the custom at the time, but conventions varied and do so still.

This can be time-consuming and complicated to set up in traditional scorewriters and involve modes requiring you to do some parts of your setup in one tool and other parts in other tools or dialogs. Ooloi does it for you automatically while you drag and drop. The following video shows how, using the Piece Window.

For the technical specification, see ADR-0054: Automatic Semantic Naming and Numbering of Musicians and Instruments. It is written to be readable by musicians and engravers, not only by programmers.

It was designed and implemented in a single day. That's possible because the architecture underneath it was already there: immutable data, a transactional model, and a gesture layer that composes structural edits atomically.

It works in the other direction as well, of course