How to determine frequency characteristics of a single tone car horn.
The idea is to be able to play tunes on the horn. The horn is a 12V DC
device having an electro-mechanical mechanism which vibrates a metal
diaprahm to produce a single tone. Will changing current generate
different tones? What is the bill of materials for a 12V car horn.

The frequency characteristic of a standard car horn is relatively
insensitive to voltage and current, and therefore not suitable for a
musical horn application.  Judge this for yourself by listening for a
frequency difference when you turn your headlights off and on (engine
not running) or comparing the horn frequency between engine off and
on.  These conditions cause a few volt change to the horn.

Horns designed for musical applications are actually horn-loaded
loudspeakers.

Well, I don't know about the engineering aspects. However, I can tell
you that the "frequency characteristics" you might be looking for are
the harmonics of the standard scale. First of all, most car horns, at
least in the U.S., beep in the key of F (about 349.23 Hz). If you
could theoretically figure out how to make the horn play different
tones, then you would need to know how much to change the frequency.
The octave going from the A below middle C to the A above (commonly
used to tune instruments) is as follows (once again in Hertz):

A  = 220.00
A# = 233.08
B  = 246.94
C  = 261.63 (Middle C)
C# = 277.18
D  = 293.66
D# = 311.13
E  = 329.63
F  = 349.23
F# = 369.99
G  = 392.00
G# = 415.30
A  = 440.00

To get a higher or lower octave, you essentially need only multiple or
divide by two. The A lower than the one before middle C is given by
110 Hz. The next G# is given by about 830.6 Hz. Hope this helps you
somewhat.

- Entropix