[freixas]

This topic relies on background information in The Compressibility of Air and Mass Flow, Speed, and Pressure, Pressure Waves, and Mouthpiece Length and “Responsiveness”

Latency is the time between two related events. With respect to this post, the events are:

• Air is blown into a mouthpiece.
• Air moves into the melodica’s air chamber.

This is somewhat imprecise. Let’s assume the air in the mouthpiece is still;  that is, the average velocity of the molecules in the air is 0. When we blow in, we are generating an airflow; the average velocity of the air is no longer 0. We never really blow at an absolutely steady velocity, nor can we instantly change from a 0 velocity to some higher value—airflow increases from 0, varies over time and eventually decreases back to 0.

So the question is really: if we could record the velocities at the mouthpiece of the tube and as it reaches the air chamber, how much latency would there be between matching portions of the recordings?

The background articles listed above, particularly the one on pressure waves, answer the question: the latency is determined by the speed of sound. The speed of sound in dry air at 20° C is about 2.92 milliseconds per meter. It is faster in humid air and faster in warmer air, both typical of the air coming from the lungs, so a latency of 2.92 ms/s might be taken as the “worst case”.

If you blow directly into a melodica, the latency of the mouthpiece is 0. If you use a 57 cm tube, the latency is about 1.66 ms.

Musicians are interested in the latency of the entire system, from when they begin an action (blowing) until they can hear the results (a change in the volume of a note). The mouthpiece latency is just part of the system. For the moment, let’s assume a reed is already vibrating and that it can change its vibration almost instantly in response to a change in airflow. The total latency would then be the total distance from mouthpiece entrance to reed and back to the ear.

Every aspect of this latency is determined by the speed of sound. A typical tube mouthpiece is about ½ meters long.The total path from the mouthpiece entrance to the highest reed is roughly 1 meter. Let’s add another meter for the return trip to the ear. The total system latency would then be 5.84 ms. This latency is undetectable by even the most sensitive musician. Shortening the mouthpiece length would not yield a perceivable change in latency.

We could lengthen the mouthpiece. The distance from the melodica back to the ear is unlikely to change much (we need to be able to reach the keys to play it). If we assume that a sensitive musician could detect latencies greater than 12 ms, then we could add another 6.16 ms of latency for a total mouthpiece length of 2.6 meters and still perceive no latency.

I omitted the reed latency. That remains an open question to be investigated elsewhere.

There appears to be no reason to limit oneself to a mouthpiece tube length of 57 cm, at least not for latency reasons. I’ve discovered that I can make tubes of any length by taking the fittings from a melodica tube and inserting them into a vinyl (PVC) tube with an inner diameter of 3/8″ (14 mm). This makes it more comfortable to play the melodica placed on a flat surface.

There is also little latency penalty in connecting two or more melodicas together using a Y-connector as shown by Akeo Minamikawa (pianonymous) in this video:

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