Alright, this might be an odball question, so here goes. This question is part music, part mathematics, but mostly mathematics.
I am an audio engineer and I want precise delay times in certain pan positions in the stereo spectrum. I am trying to calculate delay time in milliseconds, I already have the main formula for calculating times for certain note lengths, but there are a few that are quite tricky and beyond my knowledgeable grasp and I am unsure how I would go about figuring out how to calculate these values. Here is what I have so far; please bare with me, as I am doing the best I can to provide as much information as possible.
- There are 60,000 milliseconds in a minute
- We need to take into consideration the BPM (Beats Per Minute) of the current track
- By default, all calculations result in quarter note values
So, the formula is:
- 60,000 / BPM (140 for example) = 428.5 ms, you always round upwards, so we actually end up with 429 ms
So that is the basic formula with a default note value of quarter notes, as 1 quarter note = 1 beat
But, what if we want a delay time other than quarter note values? To answer this, we first need to understand basic note comparisons
- A Basic quarter note would have a value of 100%
- Next we have 8th notes, you can fit 2 8th notes in a quarter note, making an 8th note have a value of 50% or 0.50 more precisely
- Next, 16th notes, you can fit 4 in a quarter note, giving a 16th note a value of 0.25
- 32nd notes, 8 in a quarter, a value of 0.125
- 64th notes, 16 in a quarter, a value of 0.0625
Let's do another calculation with a different note, say 16th notes
- 60,000 / 140 = 429 x 0.25 = 107 ms
Here is where it gets tricky, we also have dotted notes, and triplet notes indicated by (. & T)
Let's start with dotted notes
- .8th, if you compare a .8th note to a regular quarter note, you will see that it's 75% of the length of a quarter note or equivalent in length to 3 regular 16th notes, making 75%, or more precisely 0.75 (Please refer to the chart I have created below)
This is where I stop as I am unable to figure out what percentage or in decimal form the values of the rest of the notes would be in comparison to a regular quarter note or 4 16th notes (using 4 16th notes as a comparison is easier in the chart I have created)
So with that said, I would like to know the values for:
- .16th, .32nd, .64th (These would be the dotted notes)
- 8thT, 16thT, 32ndT & 64thT (These would be triplet notes)
If you would like to inquire more information I will do my best, but I am not sure what I can provide
A dotted note takes 50% longer than the plain note. For example, a dotted eighth note at 140 bpm (quarter note rate) would require a delay of $$ \frac{60}{140}\cdot \frac{1}{2} \cdot 1.5 = 0.32142857... $$ seconds, or $321.42857..$ msec.
A triplet of eighth notes contains $3$ notes in the space of $2$ normal eighth notes, so the delay is 2/3 of of the usual. So a triplet of eighth notes at 140 bpm would require $$ \frac{60}{140} \cdot \frac{1}{2} \cdot 2 \cdot \frac{1}{3} = 0.142857142... $$ seconds, or $142.857142..$ msec. That is, there are three eight notes per quarter note, so delay needed is 1/3 the delay for a quarter note.
For other notes, just change the $1/2$ factors above to the appropriate power-of-2 fraction (e.g., 1/4 for sixteenth notes, 1/8 for 32nd notes, etc.)