Tempo changes [was Re: ]

On 2026-02-24 22:36, metachromatic wrote:
> "We don't require this level of detail in music expressions for dynamic
> ramps."
> 
> You don't -- many other composers do.

I want to correct some misinformation in Metachromatic's message for the 
sake of bystanders who might otherwise be thrown off track.

Arnold proposed this scenario:

     you specify the total duration (e.g. 4 measures),
     the frequency (e.g. each  quarter an update)
     and the relative final tempo (e.g. 2/3)

This describes a ramp in tempo.  LilyPond MIDI output already supports 
ramps in dynamics (i.e., decrescendo and crescendo) without users having 
to do the math and insert absolute levels periodically in the music 
expression.  At the moment, I don't see anything that would stand in the 
way of doing something similar for tempo changes.  To a person 
interested in trying that, I'd also encourage thinking about slowing the 
MIDI tempo by a parameterized amount for a parameterized time at \caesura.


> inability to specify tempo changes as real numbers (from tempo
> 73.241 to tempo 74.856, for example)

Rational numbers are sufficient for these examples, and LilyPond 
supports rational numbers.

https://lilypond.org/doc/v2.25/Documentation/notation/displaying-rhythms#metronome-marks

The MIDI output uses an approximation constrained by the MIDI design.

The default metronome mark rounds to an integer, which is reasonable for 
music of the era that LilyPond's defaults usually target.  As for many 
other things, the user can override the stencil or add text to describe 
a tempo change in any way that can be put into writing.
-- 
Dan