Properties of a very low pitched natural horn?

Question

I would like to acquire a natural horn to play a very low pitched tone. I am not educated in music, so I don't even know how to describe the tone in a correct way (is it "low pitched"?), but I found a fitting tone in a YouTube video:

I have not succeeded in finding out which properties will affect the tuning of such an instrument (diameter, length, form, material, etc.), so I was hoping to find some advice here. Best case information for me would be the name of a specific instrument and a link to a video or sound file. But it would also help me to get a hint how to better phrase my requirement (in technical more correct terms).

Answer 1

You mean the pedal note or fundamental note?

„Certain low brass instruments such as trombone, tuba, euphonium, and alto horn are whole-tube and can play the fundamental tone of each harmonic series with relative ease. . Trombone and tuba in particular are often called upon to play pedal notes (fundamental notes) and so-called "false harmonics" and "false tones" below their normal range.“

https://en.wikipedia.org/wiki/Pitch_of_brass_instruments

Edit:

The sound and tone depends

a) from the length

b) the pressure of the lips

c) the angle of the air stream (from the lips to the mouthpiece, embouchure)

you can try this out with a simple garden hose:

Note:

If you’re asking about:

(diameter, length, form, material, etc.)

This answer implies: material and form ... they don‘t matter, but the length. (I‘ve been playing for over 60 years all kind of brass instruments. You can produce a pedal tone on all of them, even without a mouth piece, with loose lips. But with one it’s easier, of course.)

Answer 2

It's really pretty simple: for a horn (aka brass instrument or equivalent), you've got a tube with a vibrator at one end and the other end open. The fundamental pitch has wavelength (ideally) 4 times the tube length. Quoting from a random thesis paper on brass instruments: (The Physics of the Trumpet - Berkopec)

The trumpet is considered in first order as [a] tube[,] closed at one end with a pressure antinode at the playing end. This results in standing-wave solutions with an odd number of 1/4-wavelength[s] between the two ends, such that k_n = nπ/2L, where n is [an] odd integer value. The corresponding modal frequencies are therefore in the ratios 1:3:5:7: etc.
The assumption that Z=0 at x=L is not perfect, because the open end of the pipe radiates into the surrounding air which has mass and [thus] also its own impedance.

Quoting from wikipedia,

Whole tube vs half tube The ease with which a player produces the fundamental note of each harmonic series for each tubing length of a modern brass instrument varies with the instrument's design. As bore width increases relative to length, it becomes easier for the player to resist the instrument's tendency to jump to the second harmonic instead of producing the fundamental frequency. Brass instruments with sufficient bore to allow the "whole tube" to vibrate easily, as opposed to "half the tube" (i.e., the second harmonic), are called "whole-tube" instruments.