By Jon Chappell
In the last newsletter?s tech installment ?Converting Tempo to Real Time, Musical Time and Delay Time,? we looked at the relationship between tempo and real time. Common everyday applications of this conversion include knowing exactly how many bars 10 seconds of music is if your groove has a tempo of q = 96 (6 bars and one 16th note) and which part of the beat you?ll be on after exactly 11.5 seconds of music at q = 120 (beat 4 of bar 6). The former case lets you know how much music you can fit into your looper at a given tempo, and the latter case is good for scoring sound effects cues for film and video.
But probably the most common usage for musicians converting tempo into real time is to find the subdivision (part of the beat) value of a note on a digital delay or arpeggiator. Many plug-ins, pedals, and outboard effects do this conversion for you right from the interface, by offering you note-value icons (8th notes, triplets, etc.) as choices, but they don?t always give you the subdivision you need. If you have a millisecond read-out, and you want to plug in the numbers yourself, you just need to learn the simple formulas for deriving subdivisions from the tempo.
Following are the most common subdivisions you?ll want to set your delay to:
Now for the math. The numbers corresponding to beat subdivisions are all simple and easy to remember. For each desired subdivision, you take a different number and divide it by 60 to get the millisecond readout. The subdivisions and their numbers are as follows:
That?s not too hard to remember, considering everything filters down from 60 in a logical, proportional way (e.g., for computing 8th notes, you use 30, which is half 60, etc.). Here?s the formula for calculating the ms time for a given tempo (T = tempo):
Let?s try it with the common tempo of 120. Plugging that number in and solving for the right side of the equation, we get this:
So all the numbers seem pretty reasonable and standard stuff for a DDL, except perhaps those numbers to the right of the decimal. But you can ignore those, or rather round them up or down and it won?t make that much of a difference.
The ?x 1,000? bit is to get rid of the decimal point and put the units into milliseconds instead of thousandths of a second. You can skip this part and just ignore the decimal, but it gets tricky when there are fractions of a ms. I like to know where the decimal is for ms, and many DDLs don?t show fractional ms, so you often have to round this number up or down. For example, at q = 120, an 8th-note triplet is 166.67 ms. I?d rather see the number presented that way than 0.16667 seconds. So keep in the ?x 1,000? part.
By the way, the easiest way to do a lot of these calculations is to use a DDL calculator (there are lots of them online) or do what I did, and set up an Excel spreadsheet. It?s simple; just use Figure 1 as a guide, and write the formulas this way for each cell in column B:
But you don?t have to know the formulas if you just want download my little utility yourself. Check it out at Delay Calculator.
Here?s one case where you could calculate subdivision and use a multi-tap delay to produce a ?fake tremolo??a rapid repeating of precisely timed notes, with one note strike (if on a guitar) or note press (for a keyboard instrument).
16th-note triplets are good for a tremolo effect because they?re faster than 16ths and therefore sound more like a rapid-fire tremolo than 16ths would. To use our tempo from above (120), you?d derive the values of 83, 166, 250, and 233. If we have a 4-tap multi-tap delay, our first note, the one we strike, would be 0. The second note is the first tap (83 ms), the third note is the second tap (166 ms), etc. Using a plug-in, shown in the screen shot in Figure 2, here?s how we?d plug in the numbers.
You can vary the other parameters to taste, but a tremolo would require a Feedback of 0, and an effect volume of 100%, or equal to the played or struck note.
Fortunately, many delays now come with a tap tempo, and DAW plug-ins have extensive synching and subdivision functionality. Tap tempo not only relieves you from doing the math, it means that even if the tempo changes, you can still stay in sync by just retapping the tempo. Even delay pedals, like the Tech 21 Boost D.L.A., Line 6 Echo Park, and Empress Super Delay offer subdivision modes as well. But knowing how to derive the subdivisions yourself means you can create these effects anywhere, anytime?on a DAW, and on a delay with only a millisecond readout, and using just your noggin to achieve any subdivision-based delay you can dream up.
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