Hi David,
Quote:

Here's the way I do it.. Maybe wrong but it's closer to what John said.
1/4. note = 96 b/m. That's three 1/8 notes equal to 32 b/m. 2X 1/8 = 1/4 note which you are playing in 4 beats per measure. This would put the tempo = 64 b/m for a 1/4 note and 96 b/m for a dotted 1/4 note. therefore, I think the tempo is, John says, 64 b/m. Hope this helps.


The largest value note that divides as a integer value into both a dotted quarter note and a quarter note is the eighth note (i.e. the dotted quarter note contains 3 x eighth notes and the quarter note contains 2 x quarter notes).

This means that if the two time signatures correlate, the length of time that an eighth note lasts in each time signature must be the same. If the eighth notes are not the same duration in each time signature then the two time signatures cannot possibly equate.

96 BPM
In one minute (60 secs) 96 dotted quarter notes play. This means that in 60 secs, the equivalent of 288 eighth notes must have been played. (3 x 96 = 288)

Therefore the length of a single eighth note = (60 secs) ÷ (288 notes) = 0.208 secs

64 BPM
In one minute (60 secs) 64 quarter notes play. This means that in 60 secs, the equivalent of 128 eighth notes must have been played. (2 x 64 = 128)

Therefore the length of a single eighth note = (60 secs) ÷ (128 notes) = 0.469 secs.

Overall, at 64 BPM (quarter note), the eighth note has a duration of over twice that of the eighth note at 96 BPM (dotted quarter note). This means that a quarter note = 64 BPM is a slower tempo than a dotted quarter note = 96 BPM.

The concept of converting beats per minute from one note value to another another note value confuses many people. It's the "beats per minute" bit that adds a layer of complexity and takes the conversion process into a more complicated sphere of mathematical reasoning.

Regards,
Noel

Last edited by Noel96; 01/27/11 05:32 AM.
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