### 10.13.5 Case studies

In each of these case studies, we expose a problem in pure properties, a solution, and the pros and cons of this solution.

### Time signatures

A time signature needs to prevent accidentals from passing over or under it, but its extent does not necessarily extend to the Y-position of accidentals. LilyPond’s horizontal spacing sometimes makes a line of music compact and, when doing so, allows certain columns to pass over each other if they will not collide. This type of passing over is not desirable with time signatures in traditional engraving. But how do we know if this passing over will happen before line breaking, as we are not sure what the X positions will be? We need a pure estimation of how much extra spacing height the time signatures would need to prevent this form of passing over without making this height so large as to overly-distort the Y-extent of an system, which could result in a very ‘loose’ looking score with lots of horizontal space between columns. So, to approximate this extra spacing height, we use the Y-extent of a time signature’s next-door-neighbor grobs via the pure-from-neighbor interface.

• pros: By extending the extra spacing height of a time signature to that of its next-door-neighbors, we make sure that grobs to the right of it that could pass above or below it do not.
• cons: This over-estimation of the vertical height could prevent snug vertical spacing of systems, as the system will be registered as being taller at the point of the time signature than it actually is. This approach can be used for clefs and bar lines as well.

### Stems

As described above, Stems need pure height approximations when they are beamed, as we do not know the beam positions before line breaking. To estimate this pure height, we take all the stems in a beam and find their pure heights as if they were not beamed. Then, we find the union of all these pure heights and take the intersection between this interval (which is large) and an interval going from the note-head of a stem to infinity in the direction of the stem so that the interval stops at the note head.

• pros: This is guaranteed to be at least as long as the beamed stem, as a beamed stem will never go over the ideal length of the extremal beam of a stem.
• cons: Certain stems will be estimated as being too long, which leads to the same problem of too-much-vertical-height as described above.