Adding some rather random factoids to what's been said, the paper used
for music rolls is "Machine Glazed Bleached Kraft", about 60 grammes
per square metre.  There's more to it than that, of course...

One major attribute of music-roll paper is that it must run straight
and not wander from side to side -- known to its makers as "runnability".
When paper is put under tension it will straighten along the grain
because that is the direction which it stretches least: if the grain
is consistently biassed to one side the paper will pull to that side
(a rare fault), and if the grain wanders then the roll will wander and
eventually fray to destruction (a common fault).

The best music-roll papers run extremely true.  I would imagine that
there were many trade details that an experienced operator could adjust
to achieve this kind of behaviour -- such as by careful forming of the
wire mesh on which the paper is formed in a Fourdrinier machine, the
consistency and contents of the pulp and the manner in which the pulp
was laid onto the wire, the consistency of heating of the drying
rollers, the tension put on the drying paper -- whatever controls such
machines have.

Another major attribute of a music roll is dimensional stability.
Paper is hygroscopic (absorbs moisture) and changes dimension according
to its humidity.  This is controlled by manufacturers by the addition
of material to the pulp: modern makers use synthetic resins to bind the
fibres in the resulting paper and give both stability and "wet strength"
(think of paper cups).

Older books on paper indicate that the key additive was natural resin
obtained from pine trees, mixed with alkalis such as sodium silicate
and alum: "the cementing action of the silicate on the fibres keeps
down fluff, and this is also very beneficial in papers which have to
be clearly punched..." (Modern Paper-Making, Clapperton & Henderson,
Blackwell, 1947).

Roll paper also mustn't produce fluff which clogs up the innards of
player mechanisms.  However, resin decays, and, as is very well known,
the adoption of resin-sized wood-pulp for paper in the early 1800s
introduced paper decay along with it.

Another approach to reduce hygroscopic behaviour is to wax the paper.
Waxing roll paper was very rare in the heyday of mechanical music,
certainly for domestic instruments.  Modern American recuts have tended
to use waxed paper, with some shift to resin-impregnated paper.

Most roll papers have one shiny side, achieved by "machine glazing"
-- passing the paper over a heated smooth roller under heavy pressure.
Too shiny is not good, though, as the paper should not slip when on the
take-up spool because this causes pauses in the music.

Paper needs to be fray-resistant but not so strong that it cannot be
perforated.  This generally relates to the length of fibre used in the
pulp.  Longer fibres give greater strength -- makers refer to "burst
strength".  There is a grade of paper sold as "butcher paper" which is
poor for making rolls because its fibres tend to close holes... which
is intentional, so that bones don't puncture the paper.

In Germany, at least two makers of music rolls purchased their own
paper mills.  They located a company that made good paper and then
bought it!  The largest maker by far was Hupfeld, and their older
rolls are on paper watermarked "H&E" for Hoffman & Engelmann of
Neustadt-on-Haardt.  Hupfeld purchased them and changed the watermark
to "Phonola".  This paper was, and remains, of superb quality.  The
other German firm that purchased their own paper mill was Welte -- the
famous "red" rolls.

Julian Dyer
Wokingham, Berkshire, UK