Hey Francis, thanks for your wonderfully thought out question.

There are many variables involved in your question.

As you would have seen in SPS Screech Pedals, what people think they are doing vs what is really happening comes to mind. Also the psychological impact of solution 1 is more often than not extremely destructive.

Firstly “the speed of air for pitch change” is a terrible psychology. This suggests “blowing faster” to play higher. As I have demonstrated throughout the course, this is not the case.

There is the speed of oscillation of the air column which is pitch determined by the aperture and then there is the amount of flow which is the amount of displacement per/sec which requires one to support the airflow faster.

This is murky and complicated. Telling someone to blow faster to change pitch creates all kinds of over exertion issues.

Keeping the flow steady, changing SHAPE and then gradually adding volume to an efficient system creates efficient habits.

Solution 1. Suggests playing the note at the same volume. The “contraction of the muscles of the mask” will stimulate the pitch change. The compression of the air thanks to the expiratory muscles is the volume.

Solution 2.
“Changing the configuration of the mouth with the same compression” will result in higher pitches but the volume will be decreased; see how the two solutions are not actually going to achieve the same outcome?!

The reason for my approach? Learning the correct “configuration” i.e. SHAPE allows the student to efficiently find the pitch.

Teaching a student to blow faster with no awareness of SHAPE requires massive force to blow or force the lips into the required configuration. This is generally a futile approach.

My approach? Find pitch, add volume.

As the Singing C suitably demonstrates, you can discover an extremely high register with the only exertion from the body being that of the inhalation.

The speed of air (the amount per second: blow faster) is volume.

The speed of oscillation of the air column, determined at the aperture is the frequency/pitch.

All I really care about is the psychological impact a suggestion or command has on a student.

I spend my life re-teaching people who are looking for “solutions” by blowing harder to back off and play efficiently then change SHAPE to find notes they have never been able to find due to overblowing and the resulting pinching the lips, or vice versa.

Cheers.