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Beats Per Minute Conversion

• To: mathgroup at smc.vnet.net
• Subject: [mg8471] Beats Per Minute Conversion
• From: "Benjamin R. Tubb" <brtubb at cybertron.com>
• Date: Tue, 2 Sep 1997 16:15:08 -0400
• Sender: owner-wri-mathgroup at wolfram.com

Can anyone determine the Mma function for the following problem whose
variables and some known solutions are:

Determine the MIDI Coarse and Fine Tuning values for converting to any BPM
playback from a given Sample Rate, MIDI Note and BPM (beats per minute) rate.

GIVEN:
SampleRate = 44100 kHz
Orginal BPM = 52 (beats per minute)
MIDI Note = C4 (i.e. Middle C)
Coarse Tuning = 0 (from a range, in semitones, of +/- 48)
Fine Tuning = 0 (from a range, in cents, of +/- 50)

Four known solutions for different BPM values are:

40 BPM
Coarse Tuning = -05
Fine Tuning   = +46

100 BPM
Coarse Tuning = +11
Fine Tuning   = +32

130 BPM
Coarse Tuning = +16
Fine Tuning   = -14

180 BPM
Coarse Tuning = +21
Fine Tuning   = +50

Benjamin Tubb
brtubb at cybertron.com