Different Fade Shapes
There are a number of different “shapes” (or curves) that can be used for fades and cross-fades. These shapes are basically a reference to the rate at which the level change happens over the length of the fade. While many DAWs offer you the option to fine-tune or customize the fade curves, here we will be looking only at the commonly offered “preset” curves. There are four main types to consider: linear (sometimes referred to as equal gain), logarithmic (sometimes referred to as equal power), exponential, and S-curve. In order to fully understand the subtleties of difference between the different fade shapes, it might be wise to explain the decibel scale (dB) and the differences between sound levels in your DAW and perceived volumes.
The simplest of all fade curves, linear, represents an equal rate of gain increase or decrease throughout the duration of the fade. As we have already stated, though, an equal rate of change of gain doesn’t equate to an equal rate of change of the perceived volume. If you look at the diagram above, you will see the gain curves (for fade-in and fade-out) on the left and the associated perceived volume curve on the right. As you can see, this “linear” fade-in curve actually sounds like it stays quite quiet to start with, and then the rate of volume increase builds toward the end. Conversely, the fade-out would sound like there was quite a large drop in volume initially, and then it would seem more consistent toward the end of the fade.
This is quite often the default fade shape in DAWs and for shorter fade-ins and-outs, the kind we might use at the beginning or end of a region, just to ensure that there are no digital clicks at the region borders; these linear fades are perfectly acceptable. Equally, in situations where your audio has a natural ambience or reverb to it that you want to minimize, the quick initial drop in perceived volume of these linear curves could work quite well to seem to shorten the ambience.
This fade curve would do nicely in some situations where longer fades are needed. If you had a sound that you wanted to give the effect of accelerating toward you, then a linear curve might work. An exponential curve (see below) could be used if you wanted to further emphasize this acceleration effect. But for a natural-sounding, longer fade-in or -out, then a linear curve probably isn’t the best choice.
The story with cross-fade is slightly different, though. Because the perceived volume drops more quickly at the beginning of the fade, you can see that, at the halfway point in time (halfway across from left to right), the perceived volume is noticeably below 50%. The effect of this on a linear cross-fade is that, at the midpoint of the fade, both sounds are below half of their maximum perceived volume, and as a result the sum of the two will be below the maximum level of either. If the two sounds are both of different levels anyway, and the cross-fade time is long enough, then this might not be a problem, but if you are using a short cross-fade for an edit that is perhaps in the middle of a single note of a performance, then you could have a perceptible dip in volume in the middle of the cross-fade.
With this in mind, it is advisable to at least consider one of the other fade curves for short cross-fades between similar levels’ audio regions.
The perceived volume of a sound has a logarithmic relationship with its level in decibels, so it seems sensible to assume that having a fade that works on a logarithmic scale would counteract the curve of the linear fades, and, if you look at the diagram above, you will see that it does do exactly that. If you now compare these curves with the ones for linear fades, you may notice a similarity. In the case of the fade-ins, the shape of the perceived volume curve looks like we have taken the level in decibels curve and pulled the middle of the line toward the bottom right corner. Similarly with the fade-out curves, it looks like we have pulled the line toward the bottom-left corner. In the case of linear fades, it takes the straight line and introduces a curve, and in the case of the logarithmic fades, it takes an already curved line and straightens it out.
The sound of a logarithmic fade should be that of a consistent and smooth increase in (perceived) volume over the whole duration of the fade, and because of this it makes sense that this curve shape can be used for most general-purpose fading tasks. Logarithmic fades are often a good choice for long fade-outs (at the end of songs for example) because of the perceived linear nature of the fade. If you are applying fade-outs to regions with natural ambience, then logarithmic fades would seem very “neutral,” in that they wouldn’t tend to reduce the sound of the ambience, as a linear fade would.
They are also very useful for creating natural cross-fades, especially when you are cross-fading in the middle of a sustained note or word. When you apply a logarithmic cross-fade, the perceived volume at the midpoint of the fade is around 50% of the maximum, so, when the two regions being cross-faded are summed together, you get an output volume that seems pretty much constant.
Exponential fade curves are in many ways the exact opposite of logarithmic curves, in that the fade-ins seem to start off increasing in volume very slowly and then only shoot up really quickly at the very end of the fade, and the fadeouts seem to drop very quickly from the maximum volume and then seem to decrease only very slowly over the rest of the duration. The diagram above illustrates this and also shows that in many ways the perceived volume of an exponential fade could be seen as an exaggerated version of a linear fade. Naturally, it isn’t quite as simple as that, but thinking of it in those terms can help to establish what it might be used for. Fading in with an exponential curve would give the impression of a sound accelerating rapidly toward you, which could be useful in certain situations. Equally, using an exponential fade-out at the end of regions with a natural ambience will certainly help to suppress that ambience, and that is very useful in many situations.
Given the shape of the perceived volume curve, it isn’t hard to imagine that exponential curves are much less suitable for both sides of cross-fades, unless a very specific effect is required, simply because, at the center point of the crossfade, both signals are quite low in level, so the resulting cross-fade will have a definite dip in the middle. Again, how much of a problem this is depends very much on the length and context of the cross-fade. Longer cross-fades on more ambient sounds may sound fine, with the associated dip giving a little “breathing space” in the middle of the cross-fade, but, if you are trying to use them in the middle of notes or words or for very quick transitions in general, the resulting dip may be very off-putting.
The S-curve is quite a difficult one to think about, because it has attributes of each of the previous three types and is further complicated by the fact that there are two different types of S-curves. Like a linear curve, at the midpoint, the level of the sound (decibel level) is at 50%, but the shape of the curve before and after this midpoint is not linear in nature. As you can see from the diagram above, you could almost view S-curves as a combination of a logarithmic and an exponential curve (although mathematically it isn’t quite that). In the case of the first example (which I have called Type 1), one that I would consider a more traditional S-curve, you could view fade-ins as an exponential curve up to the midpoint, followed by a logarithmic curve from the midpoint to the end, and fade-outs as logarithmic up to the midpoint and then exponential from the midpoint to the end. Conversely, in the second example (Type 2), the situation is reversed, and the fade-ins are more like a logarithmic fade up to the midpoint and then an exponential fade from there to the end, and fade-outs are exponential to the midpoint and logarithmic from the midpoint to the end.
When considering applications for S-curves in cross-fading, it can be helpful to think of the Type 1 curves as a kind of halfway house between a linear cross-fade and a simple “cut” between two files. If we had two files directly adjacent to each other with no cross-fades, then the second would start playing at the exact moment the first one finished. If we are lucky, and if we have made sure our regions all start and end at zero-crossing points, the result will be a very abrupt transition from one region to the other. If the edits regions aren’t trimmed nicely to zero-crossing points, then we could well get unwelcome glitches or pops. In order to avoid this, we could use any of the cross-fade methods described above, but, in all but the very shortest of cross-fade times, there would be a period when both sounds were audible simultaneously. The same applies with S-curve cross-fades. If there were no point when both sounds were playing simultaneously, then it wouldn’t be a cross-fade after all. But what the S-curve (Type 1) does is to minimize the amount of time that both sounds are playing simultaneously. This allows to make edits that sound like direct “cuts” from one sound to another but which have that little extra smoothness and polish to them.
Type 2 S-curves, on the other hand, are generally more suitable for longer crossfades, where we want the smoothness of a cross-fade and the consistency of a cross-fade in terms of overall level but the ability to have both of the crossfading sounds audible for as long as possible. In essence what happens is that there is a relatively short period at the start of each cross-fade where the outgoing sound drops quickly toward 50% and the incoming sound rises correspondingly to around 50%. The rate of changeover then slows, and both sounds will appear to stay at almost the same level for most of the middle half of the crossfade, and then, toward the end, there is a final quick changeover for the final few percent of the fade.
Excerpt from Digital Audio Editing: Correcting and Enhacing Audio in Pro Tools, Logic Pro, Cubase, and Studio One by Simon Langford © 2013 Taylor & Francis Group. All Rights Reserved.