Subject: Re: Nodes, intonation, pedals and super R#.
Well the number of nodes inside a trumpet depends on which harmonic is being played.
I will discuss a Bbtrumpet using no valves. (The use of valves changes which harmonic is being sounded as in the use of alternate fingerings.)
The note 2 octaves under low c has only 1/4 of a complete wavelength in the trumpet. It also has only 1 node in the horn.
Pedal c has 1/2 of a wavelength and 2 nodes in the horn.
Low c has a complete wavelength in the trumpet and 3 nodes.
Second line g has 1.5 wavelengths and 4 nodes in the horn.
Middle c has 2 wavelengths and 5 nodes in the horn.
4th space e has 6 nodes.
G has 7,
Bb has 8 and
high c has 4 complete wavelengths and 9 nodes in the horn.
Super c has 8 wavelengths and 17 nodes while
2 octaves over high c (triple high c) has 16 wavelengths and 33 nodes in the horn.
(This accounts for the leadplayer that misses his super** and hits some weird unknown note. There are a lot of slots in this register.)
The vast difference in sound between the pedal tones and low c is caused by pedals not having a complete wavelength in the horn.
The nodes in a cylindrical tube are spaced evenly apart.
In conical tubing they shift toward the smaller end. That is one reason why more people can play pedals on flugelhorn than on trumpet. And why some trumpets resist sounding pedals.
If only cylindrical (straight) tubing were used then every note would require an adjustment by pulling a slide to fix intonation problems.
If the inside diameter of conical tubing is altered at a nodal point then every note that has a node at that point would have it’s intonation altered. Some good and some bad.
Therefore to fix intonation you must only alter nodal points that either correspond to only one note or to several that are out of tune the same direction.