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If you have a series of crotchets (quarter notes), and you want to effect an approximate ritardando by using tempo markings, which of the following would sound more natural:

  • Arithmetic Progression: decrease tempo by a fixed value for successive crotchets, e.g. 100, 90, 80, 70; or

  • Geometric Progression: either decrease tempo by a applying a fixed ratio of the previous tempo for successtive crotchet, .e.g 100, 90, 81, 73; or alternatively decrease tempo by a fixed value for a geometrically increase duration, e.g. for crotchets 1,2,4,8, use tempo 100, 90, 80, 70?

NB: For context, this is used as a workaround to achieve a rit effect during playback for some sequencers.

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    It might depend on software. I've always drawn a curve in the master track & fiddled til it felt right, but that's Cubase-only, perhaps. – Tetsujin Mar 29 '20 at 18:02
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I would say neither would sound more “natural”, music is subjective, one might sound better or worse to you. If I am reading a piece I’m not looking for numerical patterns in tempo changes so I would opt for 100 90 80 etc. for simplicity. If you played the sequence for others both ways I would guess 95% of them wouldn’t notice a difference so sequence it the way it sounds good to you but keep it simple for sight readers.

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I sometimes use 100-90-80-70 ... *1)

but mind this is not arithmetical because this is actually -1/10 ...-1/9...-1/8...-1/7 ...

1*) well, just because I am to lazy to try out other BPM ;)

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  • 100, 90, 80, 70, ... : is an arithmetic sequence. – Elements in Space Mar 30 '20 at 7:04
  • Of course, but not its effect in the proportion times and BPM – Albrecht Hügli Mar 30 '20 at 7:06
  • It'll be a Harmonic Sequence when you're talking wrt Time. – RishiNandha Vanchi Apr 2 '20 at 14:43
  • The speed (or velocity) is in an arithmetic progression (AP). This corresponds to constant acceleration, similar to what we study in physics. The inverse of the velocity follows a harmonic progression, and is proportional to the time taken for each beat. – Hypergeometricx Apr 3 '20 at 13:57

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