quotes from liner notes, natural trumpet, etc.

From the liner notes of Naxos 8.553593...

"
The natural trumpet itself, a trumpet without valves, is restricted to the
notes of the harmonic series, the so-called partials. Some of these notes
are impure and cause problems with intonation, especially if the trumpet is
played together with an instrument of fixed pitch, like the organ. The 11th
harmonic is too high for F' and too low for F#"; the 13th is too low for A"
and is nearer to G#"; the 7th and 14th harmonics are slightly too low for
Bb' and Bb", respectively. In mean-tone temperament, however, the impure
notes are less conspicuous and an experienced performer can reduce these
problems by his embouchure. This is also easier on an old trumpet because
of irregularities in the tubing. The matter is complicated by modern
replicas, with even tubing which makes the pitch of every harmonic more
stable. As the harmonics in the upper register lie very close together, it
is difficult to achieve secure attack. With the modern valve trumpet
lower harmonics are used, making the attack more secure. The modern trumpet,
with its six valve combinations, is, in fact, a combination of seven
natural trumpets. On the other hand the valve trumpet needs more wind than
the natural trumpet, the player will, therefore, have to be prepared to
adjust his technique to achieve a secure attack with the natural instrument.
In order to help the modern performer shift between the valve and natural
trumpet a finger-hole system was devised in 1960 by Otto Steinkopf. By
opening one hole all even-numbered harmonics are excluded and by opening
another all the odd ones. In this way, by opening one of the holes the
nearest harmonic can be excluded, giving greater security of attack. . .
Trumpets with such holes may be call Baroque trumpets, to distinguish them
from pure natural trumpets.

...In the first years of the 17th century trumpet parts were confined to
a limited number of notes, as, for example, in the 5-part trumpet _Toccata_
in Monteverdi's _Orfeo_. The melodic part ... consisted only of the notes
C", D", E", F", and G", and less often A". Fantini broke with this
tradition and developed a use of the solo trumpet in its entire range, from
the 2nd to the 16th harmonic, from C to C'".
"