Acoustic analysis with soundgen

Andrey Anikin

2020-02-06

1 Purpose

There are numerous programs out there for performing acoustic analysis, including several open-source options and R packages. For in-depth analysis of individual mammalian sounds it’s hard to beat PRAAT (batch processing is possible, but a bit tricky, because PRAAT uses its own, rather unusual scripting language). For bird sounds, a sophisticated tool is Sound Analysis Pro. In R, the most general-purpose acoustic toolkit is the seewave package. Soundgen builds upon the functionality of seewave, adding high-level functions for sound synthesis (see the vignette on sound synthesis), manipulation, and analysis.

Reasons to use soundgen for acoustic analysis might be:

  1. User-friendly approach: a single call to the analyzeFolder function will give you a dataframe containing dozens of commonly used acoustic descriptors for each file in an entire folder. So if you’d rather get started with model-building without delving too deeply into acoustics, you are one line of code away from your dataset.
  2. Flexible pitch tracking: soundgen uses several popular methods of pitch detection in parallel, followed by their integration and postprocessing. While the abundance of control parameters may initially seem daunting, for those who do wish to delve deeply this makes soundgen’s pitch tracker very versatile and offers a lot of power for high-precision analysis.
  3. An interactive app for manual correction of pitch contours - pitch_app().
  4. Audio segmentation with in-built optimization: the tools for syllable segmentation and detection of energy bursts are fast and simple (based on smoothed intensity contours) but quite flexible. Control parameters can also be optimized automatically as long as you have a manually segmented training sample.
  5. Additional specialized tools for acoustic analysis such as modulation spectra and self-similarity matrices.

Many of the large variety of existing tools for acoustic analysis were designed with a particular type of sound in mind, usually human speech or bird songs. Soundgen’s pitch tracker was written to analyze human non-linguistic vocalizations like screams and laughs. These sounds are much harsher and noisier than ordinary speech and stand much closer to the vocalizations of other mammals than to human speech. In addition, the original corpus (Anikin & Persson, 2017) was collected from online videos, so that both sampling rate and microphone settings varied tremendously. From the very beginning, the focus has thus been on developing a pitch tracker and a segmenting tool that would be robust to noise and recording conditions. This makes soundgen highly suitable for performing acoustic analysis of animal vocalizations. You can of course apply soundgen to speech, but note that it was not optimized for speech, unlike specialized phonetic software like Praat.

To summarize, you might want to look at soundgen’s tools for acoustic analysis if you are extracting a large number of acoustic predictors from a large number of audio files, for example:

The most relevant functions are:

TIP Soundgen’s functions for acoustic analysis are not meant to be exhaustive. MFCC extraction is readily available in R (e.g., with tuneR::melfcc), so there was no need to duplicate it in soundgen. Linear predictive coding (LPC) is also implemented in R (see phonTools::lpc and phonTools::findformants). As a convenience, soundgen::analyze shows the output of phonTools::findformants, but for serious formant analysis you might want to use an interactive program like PRAAT and check everything manually. A good approach may be to start with soundgen::analyze to get a table of many common acoustic predictors and then add some more using other R packages, software, or manual measurements.

This vignette is designed to show how soundgen can be used effectively to perform acoustic analysis. It assumes that the reader is already familiar with key concepts of phonetics and bioacoustics.

TIP This vignette mostly covers acoustic analysis with soundgen. In many cases, there are related R functions from other packages. For a tour-de-force overview of alternatives together with highly accessible theoretical explanations of sound characteristics, see Sueur (2018) “Sound analysis and synthesis with R”

2 Acoustic analysis with analyze

To demonstrate acoustic analysis in practice, let’s begin by generating a sound with a known pitch contour. To make pitch tracking less trivial and demonstrate some of its challenges, let’s add some noise, subharmonics, and jitter:

library(soundgen)
## Loading required package: shinyBS
s1 = soundgen(sylLen = 900, temperature = 0,
              pitch = list(time = c(0, .3, .8, 1), 
                           value = c(300, 900, 400, 1300)),
              noise = c(-40, -20), 
              subDep = 100, jitterDep = 0.5, 
              plot = TRUE, ylim = c(0, 4))

# playme(s1)  # replay as many times as needed w/o re-synthesizing the sound

The contour of f0 is determined by our pitch anchors, so we can calculate the true median pitch:

true_pitch = getSmoothContour(anchors = list(time = c(0, .3, .8, 1),
                                             value = c(300, 900, 400, 1300)),
                              len = 1000)  # any length will do
median(true_pitch)  # 633 Hz
## [1] 633.2559

2.1 Basic principles

At the heart of acoustic analysis with soundgen is the short-time Fourier transform (STFT): we look at one short segment of sound at a time (one STFT frame), analyze its spectrum using Fast Fourier Transform (FFT), and then move on to the next - perhaps overlapping - frame. As the analysis window slides along the signal, STFT shows which frequencies it contains at different points of time. The nuts and bolts of STFT are beyond the scope of this vignette, but they can be found in just about any textbook on phonetics, acoustics, digital signal processing, etc. For a quick R-friendly introduction, see seewave vignette on acoustic analysis.

Putting the spectra of all frames together, we get a spectrogram. analyze calls another function from soundgen package, spectrogram, to produce a spectrogram and then plot pitch candidates on top of it. spectrogram is a modified version of seewave::spectro with added routines for removing background noise, controlling contrast and brightness, adding median smoothing, etc (see the examples in ?spectrogram). To analyze a sound with default settings and plot its spectrogram, all we need to specify is its sampling rate (the default in soundgen is 16000 Hz):

## Scale not specified. Assuming that max amplitude is 1
## [1] 633.2559
## [1] 433.6764

There are several key parameters that control the behavior of STFT and affect all extracted acoustic variables. The same parameters serve as arguments to spectrogram. As a result, you can immediately see what frame-by-frame input you have fed into the algorithm for acoustic analysis by visually inspecting the produced spectrogram. If you can hear f0, but can’t see individual harmonics in the spectrogram, the pitch tracker probably will not see them, either, and will therefore fail to detect f0 correctly. The first remedy is thus to adjust STFT settings, using the spectrogram for visual feedback:

2.2 Basic spectral descriptives

Apart from pitch tracking, analyze calculates and returns several acoustic characteristics from each non-silent STFT frame:

2.3 Custom spectral descriptives

The function soundgen::analyze returns a few spectral descriptives that make sense for nonverbal vocalizations, but additional predictors may be useful for other applications (bird songs, non-biological sounds, etc.). One way to obtain extra predictors is to add the necessary code to the internal function soundgen:::analyzeFrame() and to soundgen::analyze(). If you want deltas, they can be extracted directly from the output of analyze(..., summary = FALSE). But in many cases the easiest solution may be to just extract the spectra and then process them manually, without calling analyze(). In fact, many popular spectral descriptors are mathematically trivial to derive - all you need is the spectrum for each STFT frame, or perhaps even the average spectrum of the entire sound. Here is how you can get these spectra.

For the average spectrum of an entire sound, go no further than seewave::spec or seewave::meanspec:

##            x            y
## [1,] 0.00000 9.717651e-05
## [2,] 0.03125 1.542056e-04
## [3,] 0.06250 2.438498e-04
## [4,] 0.09375 4.312115e-04
## [5,] 0.12500 5.819006e-04
## [6,] 0.15625 6.976463e-04

If you are interested in how the spectrum changes over time, extract frame-by-frame spectra - for example, with spectrogram(..., output = 'original'):

##  num [1:400, 1:77] 4.61e-04 3.57e-04 1.78e-04 1.09e-04 7.31e-05 ...
##  - attr(*, "dimnames")=List of 2
##   ..$ : chr [1:400] "0.005" "0.0250250626566416" "0.0450501253132832" "0.0650751879699248" ...
##   ..$ : chr [1:77] "0" "15" "30" "45" ...

Let’s say you are working with frame-by-frame spectra and want to calculate skewness, the 66.6th percentile, and the ratio of energy above/below 500 Hz. Before you go hunting for a piece of software that returns exactly those descriptors, consider this. Once you have normalized the spectrum to add up to 1, it basically becomes a probability density function (pdf), so you can summarize it in the same way as you would any other distribution of a random variable. Look up the formulas you need and just do the raw math:

## Warning in min(which(cumsum(df$d) >= 2/3)): no non-missing arguments to min;
## returning Inf
##       skew            quantile66         ratio500       
##  Min.   : 0.04044   Min.   :0.02503   Min.   :  0.0016  
##  1st Qu.: 0.24907   1st Qu.:0.90613   1st Qu.: 13.5314  
##  Median : 0.62426   Median :1.12640   Median : 34.0669  
##  Mean   : 1.52400   Mean   :1.00309   Mean   : 81.9872  
##  3rd Qu.: 1.16263   3rd Qu.:1.24655   3rd Qu.:114.1721  
##  Max.   :13.74199   Max.   :1.58698   Max.   :583.3943  
##  NA's   :1          NA's   :1         NA's   :1

If you need to do this analysis repeatedly, just wrap the code into your own function that takes a wav file as input and returns all these spectral descriptives. You can also save the actual spectra of different sound files and add them up to obtain an average spectrum across multiple sound files, work with cochleograms instead of raw spectra (check out tuneR::melfcc), etc. Be your own boss!

2.4 Loudness

The digital representation of a sound is a long vector of numbers on some arbitrary scale, say [-1, 1]. Values further from zero correspond to a higher amplitude - in physical terms, to greater pertubations of sound pressure level caused by the propagating sound wave. A smoothed line following peak amplitude values is known as an amplitude envelope. However, there is no simple correspondence between the absolute height of amplitude peaks and the subjectively experienced loudness of the corresponding sound. A commonly reported measure of sound intensity is its root mean square (RMS) amplitude, which takes into account the average value of sound pressure, and not only the height of peaks. More sophisticated estimates of loudness also take into account the relative sensitivity of human hearing to different frequencies, masking of adjacent tones in the time and frequency domains, etc.

To illustrate the differences between these estimates, let’s look at a pure tone sweeping with fixed absolute amplitude from 100 to 4000 Hz over 2 s:

Smoothed absolute amplitude envelope (flat):

RMS amplitude per STFT frame, as returned by analyze(), column “ampl”:

## Scale not specified. Assuming that max amplitude is 1

An estimate of subjectively experienced loudness in sone, column “loudness”:

Soundgen also has a dedicated function for calculating the loudness and plotting the output, getLoudness(). Loudness values are overlaid on the spectrogram - observe how the loudness peaks as f0 reaches about 2-3 kHz and then drops. The absolute values in sone are only an approximation, since they are dictated by the playback device (e.g. your headphones), but the change of loudness within one sound, or across different sounds analyzed with the same settings, is informative.

## Warning in getLoudness(sweep, samplingRate = samplingRate): Scale not specified.
## Assuming that max amplitude is 1

2.5 Pitch tracking

If you look at the source code of soundgen::analyze() and embedded functions, you will see that almost all of this code deals with a single acoustic characteristic: fundamental frequency (f0) or its perceptual equivalent, pitch. That’s because pitch is both highly salient to listeners and notoriously difficult to measure accurately. The approach followed by soundgen’s pitch tracker is to use several different estimates of f0, each of which is better suited to certain types of sounds. You can use any pitch tracker individually, but their output is also automatically integrated and postprocessed so as to generate the best overall estimate of frame-by-frame pitch. There are four currently implemented classes of pitch estimates in soundgen: autocorrelation, lowest dominant frequency, cepstrum, and spectrum (ratios of harmonics). These four methods of pitch estimation are not treated as completely independent in soundgen. Autocorrelation is performed first to provide an initial guess at the likely pitch and harmonics-to-noise ratio (HNR) of an STFT frame, and then this information is used to adjust the expectations of the cepstral and spectral algorithms. In particular, if autocorrelation suggests that the pitch is high, confidence in cepstral estimates is attenuated; and if autocorrelation suggests that HNR is low, thresholds for spectral peak detection are raised, making spectral pitch estimates more conservative.

The plot below shows a spectrogram of the sound with overlaid pitch candidates: yellow circles = autocorrelation pitch estimate (pitchAutocor), red triangles = spectral pitch estimate (pitchSpec), orange crosses = lowest dominant frequency band (dom). The size of each point shows the certainty of estimation: smaller points are calculated with lower certainty and have less weight when all candidates are integrated into the final pitch contour (blue line). To specify which pitch tracking methods should be employed, use pitchMethods. For example, we can also include cepstral estimates (violet “envelope” symbols):

## Scale not specified. Assuming that max amplitude is 1

2.5.1 General settings

analyze has a few arguments that affect all methods of pitch tracking:

  • entropyThres: all non-silent frames are analyzed to produce basic spectral descriptives. However, pitch tracking is both computationally costly and can be misleading if applied to obviously voiceless frames. To define what an “obviously voiceless” frame is, we set some cutoff value of Weiner entropy, above which we don’t want to even try pitch tracking. To disable this feature and track pitch in all non-silent frames, set entropyThres to 1.
  • pitchFloor, pitchCeiling: absolute thresholds for pitch candidates. No values outside these bounds will be considered.
  • priorMean and priorSD specify the mean and sd of gamma distribution describing our prior knowledge about the most likely pitch values. The prior works by scaling the certainties associated with particular pitch candidates. If you are working with a single type of sound, such as speech by a male speaker or cricket sounds, specifying a strong prior can greatly improve the quality of the resulting pitch contour. When batch-processing a large number of sounds with analyzeFolder(), the recommended approach is to set a vague, but still mildly informative prior. priorMean is specified in Hz, but the expected deviation from this typical value is calculated on a musical scale, so priorSD is in semitones. For example, if we expect f0 values of about 300 Hz plus-minus half an octave (6 semitones), a prior can be defined as priorMean = 300, priorSD = 6. For convenience, the prior can be plotted with getPrior:

TIP The final pitch contour can still pass through low-certainty candidates. You can think of the prior as a soft alternative (or addition) to the inflexible bounds of pitchFloor and pitchCeiling

  • nCands: maximum number of pitch candidates to use per method. This only affects pitchAutocor, pitchCep, and pitchSpec. dom never returns more than one candidate per frame, since it doesn’t make sense to consider several lowest dominant frequency bands - this simply drags the final pitch contour upwards without improving the accuracy.
  • minVoicedCands: minimum number of pitch candidates that have to be defined to consider a frame voiced. It defaults to ‘autom’, which means 2 if dom is among the candidates and 1 otherwise. The reason is that dom is usually defined, even if the frame is clearly voiceless, so we want another pitch candidate in addition to dom before we classify the frame as voiced.

2.5.2 Pitch tracking methods

Having looked at the general settings, it is time to consider the theoretical principles behind each pitch tracking method, together with arguments to analyze that can be used to tweak each one.

2.5.2.1 Autocorrelation

Time domain: pitch by autocorrelation, PRAAT, pitchAutocor.

This is an R implementation of the algorithm used in the popular open-source program PRAAT (Boersma, 1993). The basic idea is that a harmonic signal correlates with itself most strongly at a delay equal to the period of its fundamental frequency (f0). Peaks in the autocorrelation function are thus treated as potential pitch candidates. The main trick is to choose an appropriate windowing function and adjust for its own autocorrelation. Compared to other methods implemented in soundgen, pitch estimates based on autocorrelation appear to be particularly accurate for relatively high values of f0. The settings that control pitchAutocor are:

  • autocorThres: voicing threshold, defaults to 0.7. This means that peaks in the autocorrelation function have to be at least 0.7 in height (1 = perfect autocorrelation). A lower threshold produces more false positives (f0 is detected in voiceless, noisy frames), whereas a higher threshold produces more accurate values f0 at the expense of failing to detect f0 in noisier frames.
  • autocorSmooth: the width of smoothing interval (in bins) for finding peaks in the autocorrelation function. If left NULL, it defaults to 7 for sampling rate 44100 and smaller odd numbers for lower sampling rate.

To use only autocorrelation pitch tracking, but with lower-than-default voicing threshold and more candidates, we can do something like this (prior is disabled so as not to influence the certainties of different pitch candidates):

## Scale not specified. Assuming that max amplitude is 1

2.5.2.2 Dominant frequency

Frequency domain: the lowest dominant frequency band, dom.

If the sound is harmonic and relatively noise-free, the spectrum of a frame typically has little energy below f0. It is therefore likely that the first sizable peak in the spectrum is in fact f0, and all we have to do is choose a reasonable threshold. Naturally, there are cases of missing f0 and misleading low-frequency noises. Nevertheless, this simple estimate is often surprisingly accurate, and it may be our best shot when the vocal cords are vibrating in a chaotic fashion (deterministic chaos). For example, sounds such as roars lack clear harmonics but are perceived as voiced, and the lowest dominant frequency band often corresponds to perceived pitch.

The settings that control dom are:

  • domThres (defaults to 0.1, range 0 to 1): to find the lowest dominant frequency band, we look for the lowest frequency with amplitude at least domThres. This key setting has to be high enough to exclude accidental low-frequency noises, but low enough not to miss f0. As a result, the optimal level depends a lot on the type of sound analyzed and recording conditions.
  • domSmooth (defaults to 220 Hz): the width of smoothing interval (Hz) for finding the lowest spectral peak. The idea is that we are less likely to hit upon some accidental spectral noise and find the lowest harmonic (or the lowest spectral band with significant power) if we apply some smoothing to the spectrum of an STFT frame, in this case a moving median.

For the sound we are trying to analyze, we can increase domSmooth and/or raise domThres to ignore the subharmonics and trace the true pitch contour:

## Scale not specified. Assuming that max amplitude is 1

2.5.2.3 Cepstrum

Frequency domain: pitch by cepstrum, pitchCep.

Cepstrum is the FFT of log-spectrum. It may be a bit challenging to wrap one’s head around, but the main idea is quite simple: just as FFT is a way to find periodicity in a signal, cepstrum is a way to find periodicity in the spectrum. In other words, if the spectrum contains regularly spaced harmonics, its FFT will contain a peak corresponding to this regularity. And since the distance between harmonics equals the fundamental frequency, this cepstral peak gives us f0. Actually, in soundgen the FFT is applied to raw spectrum, not log-spectrum, since it appears to produce better results. Cepstrum is not very useful when f0 is so high that the spectrum contains only a few harmonics, so soundgen automatically discounts the contribution of high-frequency cepstral estimates. Cepstral pitch tracking is disabled by default, since this method is both slower and less robust for human non-linguistic vocalizations. Depending on the type of analyzed audio, however, both the accuracy of different pitch tracking methods and their optimal parameters may change (see the section on optimization below).

The settings that control pitchCep are:

  • cepThres: voicing threshold (defaults to 0.3).
  • cepSmooth: the width of smoothing interval (in Hz) for finding peaks in the cepstrum. If left NULL, it defaults to 31 for sampling rate 44100 and smaller odd numbers for lower values of sampling rate.
  • cepZp (defaults to 0): zero-padding of the spectrum used for cepstral pitch detection (points). Zero-padding may improve the precision of cepstral pitch detection, but it also slows down the algorithm.
## Scale not specified. Assuming that max amplitude is 1
## Warning in analyze(s1, samplingRate = 16000, plot = TRUE, ylim = c(0, 4), : 
## cepSmooth should be between 10 and 1000; resetting to 400

2.5.2.4 Spectrum

Frequency domain: ratios of harmonics, BaNa, pitchSpec.

All harmonics are multiples of the fundamental frequency. The ratio of two neighboring harmonics is thus predictably related to their rank relative to f0. For example, (3 * f0) / (2 * f0) = 1.5, so if we find two harmonics in the spectrum that have a ratio of exactly 1.5, it is likely that these are the first two harmonics, making it possible to calculate f0 (Ba et al., 2012). This is the principle behind the spectral pitch estimate in soundgen, which seems to be particularly useful for noisy, relatively low-pitched sounds.

The settings that control pitchSpec are:

  • specThres (0 to 1, defaults to 0.3): voicing threshold for pitch candidates suggested by the spectral method. The scale is 0 to 1, as usual, but it is the result of a rather arbitrary normalization. The “strength” of spectral pitch candidates is basically calculated as a sigmoid function of the number of harmonic ratios that together converge on the same f0 value. Setting specThres too low may produce garbage, while setting it too high makes the spectral method excessively conservative.
  • specPeak (0 to 1, defaults to 0.35), specHNRslope (0 to Inf, defaults to 0.8): when looking for putative harmonics in the spectrum, the threshold for peak detection is calculated as specPeak * (1 - HNR * specHNRslope). For noisy sounds the threshold is high to avoid false sumharmonics, while for tonal sounds it is low to catch weak harmonics. If HNR (harmonics-to-noise ratio) is not known, say if we have disabled the autocorrelation pitch tracker or if it returns NA for a frame, then the threshold defaults to simply specPeak. This key parameter strongly affects how many pitch candidates the spectral method suggests.
  • specSmooth (0 to Inf, defaults to 150 Hz): the width of window for detecting peaks in the spectrum, in Hz. You may want to adjust it if you are working with sounds with a specific f0 range, especially if it is unusually high or low compared to human sounds.
  • specMerge (0 to Inf semitones, defaults to 1): pitch candidates within specMerge semitones are merged with boosted certainty. Since the idea behind the spectral pitch tracker is that multiple harmonic ratios should converge on the same f0, we have to decide what counts as “the same” f0.
  • specSinglePeakCert: (0 to 1, defaults to 0.4) if apitchSpec candidate is calculated based on a single harmonic ratio (as opposed to several ratios converging on the same candidate), its weight (certainty) is taken to be specSinglePeakCert. This mainly has implications for how much we trust spectral vs. other pitch estimates.
## Scale not specified. Assuming that max amplitude is 1

TIP As you can guess by now, any pitch tracking method can be tweaked to produce reasonable results for any one particular sound (read: to agree with human intuition). The real trick is to find settings that are accurate on average, across a wide range of sounds and recording conditions. The default settings in analyze are the result of optimization against manually verified pitch measurements of a corpus of 260 human non-linguistic vocalizations. For other types of sounds, you will need to perform your own manual tweaking and/or formal optimization.

2.5.3 Missing fundamental

The perception of pitch does not depend on the presence of the lowest partial corresponding to the actual fundamental frequency: even if it is removed or masked by low-frequency noise, the pitch remains unchanged. By definition, the “dom” estimate of pitch cannot function when this lowest partial is missing (it works by literally tracking the lowest dominant frequency band). However, the remaining three pitch tracking methods - autocorrelation, cepstrum, and BaNa - have no problem dealing with a missing fundamental frequency because they take the entire spectrum into account, not only the lowest partial.

A sound with four partials at 300 Hz (f0), 600 Hz, 900 Hz, and 1200 Hz:

The pitch is tracked correctly:

## Scale not specified. Assuming that max amplitude is 1

The same sound, but without the first partial (f0).

Again, no problem with pitch tracking, although now the pitch contour is following a partial that is no longer there:

## Scale not specified. Assuming that max amplitude is 1

The implications are as follows: if the lower part of your signal is degraded (wind noise, an engine running, somebody else talking in the background, etc.), you can apply a high-pass filter to remove low frequencies. Even if you filter out the first partial by doing so, pitch tracking is not going to suffer. BUT: do NOT use the “dom” pitch estimate if the f0 is either filtered out or invisible because of noise!

2.6 Postprocessing of pitch contour

Pitch postprocessing in soundgen includes a whole battery of distinct operations through which the pitch candidates generated by one or more tracking methods are integrated into the final pitch contour. We will look at them one by one, in the order in which they are performed in analyze. But first of all, here is how to disable them all:

## Scale not specified. Assuming that max amplitude is 1

When the sound is not too tricky and enough pitch candidates are available, postprocessing actually makes little difference. In terms of the accuracy of median estimate of f0, you are likely to get a good result even with postprocessing is completely disabled. However, if you are interested in the actual intonation contours, not just the global average, postprocessing can help a lot.

2.6.1 Continuous voiced fragments

It often makes sense to make assumptions about the possible temporal structure of voiced fragments, such as their minimum expected length (shortestSyl) and spacing (shortestPause). If these two parameters are positive numbers, the first stage of postprocessing is to divide the sound into continuous voiced fragments that satisfy these assumptions. The default minimum length of a voiced fragment is a single STFT frame. If shortestSyl is longer than a single frame, then we need at least two adjacent voiced frames to start a new voiced fragment. A single voiced frame surrounded by unvoiced frames then gets discarded (assumed to be unvoiced). If two voiced fragments are separated by less than shortestPause, they are merged. What this means is simply that they are processed as a single syllable by pathfinder() (see below). No interpolation takes place at this stage.

The next few blocks of postprocessing are performed by an internal function, soundgen:::pathfinder(). Its input is a matrix of pitch candidates for each frame of a single voiced syllable, usually with multiple candidates per frame. Each candidate is also associated with a different certainty. We want to find a good path through these candidates - that is, a pitch contour that both passes close to the strongest candidates and minimizes pitch jumps, producing a relatively smooth contour. The simplest first approximation is to take a mean of all pitch candidates per frame weighted by their certainty - the “center of gravity” of pitch candidates - and for each frame to select the candidate that lies closest to this center of gravity. This initial guess at a reasonable path may or may not be processed further, depending on the settings described below.

2.6.2 Interpolation

To make sure we have at least one pitch candidate for every frame in the supposedly continuous voiced fragment, we interpolate to fill in any missing values. The same algorithm also adds new pitch candidates with certainty interpolCert if a frame has no pitch candidates within interpolTol of the median of the “center of gravity” estimate over plus-minus interpolWin frames. The frequency of new candidates is equal to this median. For example, if interpolTol = 0.05, new candidates are calculated if there are none within 0.95 to 1.05 times the median over the interpolation window. You can also enable interpolation to fill in unvoiced frames, but without adding new pitch candidates in voiced frames. To do so, set interpolTol = Inf.

Here is an example (interpolated segments are shown with a dotted line)

## Scale not specified. Assuming that max amplitude is 1
## Scale not specified. Assuming that max amplitude is 1

2.6.3 Pathfinding

The next step after interpolation is pathfinding proper - searching for the optimal path through pitch candidates. If pathfinding = "none", this step is skipped, so we just continue working with the path that lies as close as possible to the (possibly interpolated) center of gravity of pitch candidates. If pathfinding = "fast" (the default option), a simple heuristic is employed, in which we walk down the path twice, first left to right and then right to left, trying to minimize the cost measured as a weighted mean of the distance from the center of gravity and the deviation from a smooth contour. The key setting is certWeight, which specifies how much we prioritize the certainty of pitch candidates vs. pitch jumps / the internal tension of the resulting pitch curve. Low certWeight (close to 0): we are mostly concerned with avoiding rapid pitch fluctuations in our contour. High certWeight (close to 1): we mostly pay attention to our certainty in particular pitch candidates. The example below is intended as an illustration of how pathfinding works, so all other types of smoothing are disabled, forcing the final pitch contour to pass strictly through existing candidates.

## Scale not specified. Assuming that max amplitude is 1
## Scale not specified. Assuming that max amplitude is 1

The final option is pathfinding = 'slow', which calls stats::optim(method = 'SANN') to perform simulated annealing. This is a more powerful algorithm than the simple heuristic in pathfinding = 'fast', but it is called “slow” for a good reason. In case you have plenty of time, it does improve the results, but note that this algorithm is stochastic, so each run may produce different results. Use an additional argument, annealPars, to control the algorithm. See ?stats::optim for more details.

2.6.4 Snake

What is here esoterically referred to as the “snake” can be seen as an alternative to the pathfinding algorithms above, although both can also be performed sequentially. Whereas pathfinding attempts to find the best path through existing pitch candidates, the snake wiggles the contour under a weighted combination of (a) elastic forces trying to snap the pitch contour to a straight line and (b) the pull of high-certainty pitch candidates. In a sense the snake is thus a combination of interpolation and pathfinding: like interpolation, it can add new values different from existing candidates, and like pathfinding, it balances the certainty in candidates against the smoothness of the resulting contour.

The only new control parameter in the snake module (apart from certWeight) is snakeStep, which controls the speed of adaptation (the default is 0.05). The higher it is, the faster the snake “wiggles”. This reduces processing time, but introduces a risk of “overshooting”. If snakeStep is too low (close to 0), the snake moves too slowly and may fail to reach its optimal configuration. To disable the snake module, set snakeStep = NULL. You can also produce a separate plot of the snake by setting snakePlot = TRUE, as in the example below (again, all other postprocessing is disabled to show what the snake alone will do). The zigzagging line is the initial contour (the path through pitch candidates that lie as close as possible to the center of gravity of each frame), the smooth blue line is the pitch contour after running the snake, and the green lines trace the progress of iterative snake adaptation. Note that at certWeight = 0.1 the snake is heavily biased towards producing a smooth contour, regardless of its distance from high-certainty pitch candidates.

## Scale not specified. Assuming that max amplitude is 1

TIP Should you use pathfinding, the snake, or both? Pathfinding makes more sense if you want the final contour to pass strictly through existing candidates, say if there are relatively few candidates, most of which are right on target and some completely off. In these conditions the snake will not do much (but not much harm, either). The snake becomes attractive if you have a lot of candidates from different pitch tracking methods, many of which are slightly off and should be averaged. In addition, the more garbage you expect among your pitch candidates, the more you might want to interpolate and apply median smoothing

2.6.5 Median smoothing

The final postprocessing stage is median smoothing. It is conceptually similar to interpolation, except that by now there is only a single f0 value left per frame, so we can forget about the multiple candidates and their certainties. It wouldn’t make much sense to apply kernel smoothing to this curve: the snake can usually do this in a smarter way, since it does know about the multiple candidates and their certainties. What we want from the smoothing algorithm is to detect and correct only outliers: the values that stick out from the surrounding frames. The parameters that control this module are smooth and smoothVars.

If smooth is a positive number, contours of the variables in smoothVars are smoothed using a customized version of median smoothing. This modifies only the values that deviate considerably from the moving median and preserves all other values (so this is a bit different from applying a moving median or kernel smoothing). smooth controls both the tolerated deviance and the size of the window for calculating a moving median. smooth = 1 (the default) corresponds to a window of ~100 ms and tolerated deviation of ~4 semitones. This smoothing can be applied to any measured value, not only the final pitch contour. The default is smoothVars = c('pitch', 'dom'). To turn off the median smoothing, set smooth = 0 or smoothVars = NULL.

## Scale not specified. Assuming that max amplitude is 1
## Scale not specified. Assuming that max amplitude is 1

TIP Pathfinding (“slow”, “fast” or “none”) is the only postprocessing module that does not deviate from pitch candidates actually returned by pitch tracking algorithms. Interpolation, snake, and median smoothing produce new pitch values per frame, which may be quite different from any actual candidates

2.7 Customization of pitch plotting

When analyzing a sound, and even when batch-processing an entire folder, it is often helpful to plot both the final pitch contour - perhaps overlaid on a spectrogram - and individual pitch candidates. You can easily do so from analyze, as in all the examples above. The default plotting parameters can also be customized, for example:

## Scale not specified. Assuming that max amplitude is 1

You can also suppress plotting any of these three components: the spectrogram, the final pitch contour, or individual pitch candidates. To suppress plotting the spectrogram, set plotSpec = FALSE. To suppress plotting the pitch contour, set pitchPlot = NULL. To suppress plotting pitch candidates, set candPlot = NULL.

To save the plot, specify a valid path, for example:

This creates a file called ‘sound.png’ 900 x 500 pixels in size in the indicated folder. This is mostly useful when you do batch processing of multiple files with analyzeFolder and want to save the plots for manual checking of extracted plot contours (see below).

2.8 Batch processing with analyzeFolder

You may not feel too excited to learn that soundgen contains a wrapper around analyze that is meant for analyzing all .wav files in a folder. Indeed, calling analyze in a loop will achieve the same result. However, analyzedFolder can save you a bit of manual coding. If you want to preserve frame-by-frame information for each file in a folder, you can either loop through the files manually or call analyzeFolder(myfolder, summary = FALSE), which returns a list of dataframes. In contrast, analyzeFolder(myfolder, summary = TRUE) returns a single dataframe, in which each acoustic predictor is summarized as the mean, median, and SD of frame-by-frame measurements. Since this is the kind of data you would normally use as input for things like classification of sounds or cluster analysis, this is a convenient shortcut for generating an acoustic dataset for further statistical modeling. In addition, analyzeFolder allows you to simultaneously save the plots and prints out estimated time to completion.

TIP Processing time varies a lot depending on the exact settings and input, but expect up to a few seconds of machine time per second of audio. The surest way to speed things up is to reduce step and to avoid pathfinding = 'slow' (other types of postprocessing have very little effect on processing time)

2.9 Manual correction of pitch contours with pitch_app()

Just like soundgen_app() is an interactive shiny app for sound synthesis, pitch_app() provides a wrapper around analyze() with an option to step in and manually correct the intonation contour. The app runs in a browser; you can load one or more wav or mp3 files, adjust the settings, verify and correct the pitch contours, and save the output as a .csv file. Please see ?pitch_app for more information.

3 Audio segmentation

3.1 Bursts and syllables

3.1.1 Segmenting a single sound: segment

In addition to measuring spectral characteristics and fundamental frequency, it is often important to analyze the temporal structure of a sound. In particular, it is often helpful to divide a sound into separate “syllables” - continuous acoustic fragments separated by what we consider to be “silence”. If this “silence” was not full of background noise and breathing, the task would be trivial: we could simply define syllables as continuous segments with ampiltude above some threshold. As it is, with non-studio material it is problematic to find a single threshold that would accurately coincide with the beginning and end of syllables in different sounds (presuming that we are interested in batch processing multiple sounds without manually adjusting the settings for each sound).

Sometimes we are more interested in the rate of syllables per second and in their regularity, rather than the absolute duration of each syllable. In this case it makes more sense to look for bursts of acoustic energy - local maxima in amplitude envelope that are high enough both in absolute terms (relative to the global maximum) and with respect to the surrounding region (relative to local mimima). The spacing between bursts - the interburst interval - can allow us to recover the perceptually salient temporal structure of a bout of vocalizing, such as the number of syllables in a bout of laughing, their average frequency, and regularity.

Soundgen package contains a function called segment, which uses both these approaches: it looks for both syllables and bursts. These two algorithms are not independent: syllables are found first, and then the median length of a syllable becomes the expected interburst interval, guiding burst detection. segment operates with amplitude envelopes - smoothed contours of sound intensity. To demonstrate how it works, we will look at the example from ?segment and go through the control parameters.

This synthesized laugh-like sound contains 8 syllables, each 50 ms long and separated by 70 ms of unvoiced fragments with some overlapping aspiration noise (NOT silence!). With default settings, segment finds 5 syllables of median length median(a$syllables$sylLen, na.rm = TRUE) = 66 ms separated by median(a$syllables$pauseLen, na.rm = TRUE) = 57 ms. The syllables are shown by blue line segments in the plot above. The last syllables are missed either because they are below the default detection threshold sylThres (90% of the global mean amplitude) or because their apparent duration falls below the default shortestSyl of 40 ms due to its low amplitude. All 8 bursts are correctly detected. The interburst interval is estimated to be median(a$bursts$interburstInt, na.rm = TRUE) = 123 ms (the correct number is 120 ms), with SD = sd(a$bursts$interburstInt, na.rm = TRUE) = 4 ms (the correct number is 0, since we set temperature to 0). Note that, just as with many real-life sounds, the question of when each syllable starts and ends is pretty meaningless, given the continuous and loud breathing noise. In contrast, the spacing of bursts is both perceptually meaningful and objectively measurable.

Some other settings worth mentioning are:

  • windowLength, overlap: length (ms) and overlap (%) of the smoothing window used to produce the amplitude envelope. See ?seewave::env, which is called with the argument msmooth = c(smooth_points, smoothOverlap), where smooth_points = ceiling(windowLength * samplingRate / 1000). Setting the overlap too low makes the enveloped jagged and imprecise, while setting the window length too low produces insufficient smoothing:

  • shortestSyl and shortestPause incorporate our prior knowledge by expecting the syllables and pauses between them to be at least 40 ms long (by default). Setting shortestSyl and shortestPause too low may inflate the number of discovered syllables, but burst detection should not be affected as much. If shortestSyl is too high, excluding shorter fragments, we won’t find any syllables, but burst detection can still succeed. The most damaging mistake is to set shortestPause too high, because separate syllables are then merged and the expected interburst interval becomes inflated, preventing the algorithm from recognizing closely spaced bursts (see the example below).

  • burstThres and peakToTrough control how high a burst has to be in absolute terms (compared to the global maximum of the envelope) and in relative terms (compared to the local minimum). So a burst is a local maximum that is at least burstThres high and at least peakToTrough times higher than the local minimum. The size of the analysis window for finding local maxima and minima is controlled by interburst, which defaults to the median length of detected syllables times interburstMult. By default the local minimum is only calculated to the left of the candidate burst (troughLeft = TRUE, troughRight = FALSE). The left-right distinction is irrelevant with this artificial, perfectly symmetrical example, but it appears to improve performance with real-life sounds, which often display assymmetrical attack with sharp onset and more gentle decay.

3.1.2 Batch processing: segmentFolder

Just as analyzeFolder is a wrapper around analyze that simplifies looping through a whole folder of .wav files, segmentFolder provides a convenient wrapper around segment. It accepts the same arguments as segment and can optionally save segmentation plots in the designated folder (e.g., savePath = ~/Downloads/). It also reports estimated time left (verbose = TRUE). You can save either detailed stats on individual syllables and bursts (summary = FALSE) or produce a summary table with means, medians, and SDs (summary = TRUE).

TIP If you are analyzing a single sound and are willing to adjust the settings manually, you can measure both syllables and bursts accurately. For batch processing without manual adjustments, bursts are more robust

3.2 Self-similarity matrices

The basic idea behind self-similarity matrices (SSMs) is to compare different parts of the same sound with each other and present their pairwise similarity indices as a square matrix with time along both dimensions. The diagonal going from bottom-left to top-right represents the similarity of each fragment with itself. For example, at (100, 100) we have the similarity of the fragment at 100 ms with itself, while at (100, 200) we have the similarity of the fragments at 100 ms and 200 ms. Let’s begin with an example taken from ?ssm:

Look at the upper panel first. There are three main regions: the large red square in the lower left corner, which corresponds to the first bout; the red square in the center, which corresponds to the long pause between the bouts; and the checkered field in the upper right corner, which corresponds to the second bout. Observe the characteristic diagonal. The SSM clearly shows periodicity within the second bout, which confirms that these syllables are very similar to each other in terms of their spectral characteristics. Now look at the lower panel of the plot. This is a spectrogram overlaid with so-called “novelty”: peaks show when something changes in the sound, based on the SSM.

The results of SSM analysis can vary dramatically, depending on how it is performed. We begin by extracting some form of spectrogram of the entire sound, then we somehow compare each frame to each other frame, and finally we calculate a measure of novelty. At each step there are crucial decisions to make, which can dramatically alter the result. Let’s look at the settings that control each step. As you play with these settings, don’t be surprised if your SSM suddenly looks completely different!

  1. Spectrogram extraction is controlled by some already familiar settings such as windowLength and overlap (or step if you prefer). However, it can often be helpful to base the SSM on some other spectral characteristics than the usual spectrogram. Under the hood, ssm calls tuneR::melfcc to return the power spectrum (as in a spectrogram, input = 'spectrum'), mel-transformed spectrum (auditory spectrum, which is supposed to be closer to how humans perceive sounds, input = 'audiogram'), or mel-frequency cepstral coefficients (MFCCs - a popular choice of input for automatic sound classification, as in speech recognition software, input = 'mfcc'). There are also several arguments that are passed to tuneR::melfcc: maxFreq controls the highest frequency analyzed, MFCC controls the number of mel-frequency cepstral coefficients to extract, and nBands basically controls the frequency resolution.

  2. SSM calculation starts with the spectrogram (or the MFCCs matrix) produced at the previous stage. This input is divided into windows, each of which can be one or several STFT frames in length, and then each window is compared to each other window using either cosine similarity (simil = 'cosine') or Pearson’s correlation (simil = 'cor'). Prior to this the input matrix can be normalized column-wise, so as to level out the differences in sound intensity across frames (norm = TRUE). The size of analysis window is controlled by the argument ssmWin, ms. Note that as you increase ssmWin, the resulting SSM literally shrinks in size, reducing its resolution. This is a great feature if your sound is very long, but it is seldom needed for shorter sounds. As you decrease ssmWin, it ultimately reaches the size of a single STFT frame (step) and can’t go down any further, unless you improve time resolution of the spectrogram itself by reducing windowLength and/or increasing overlap.

  3. Novelty calculation starts with the SSM computed at the previous step. Here the idea is to move along the diagonal and multiply the SSM by a Gaussian checkerboard matrix, so as to detect changes in the spectral structure (see Foote, 2000). The settings that control this algorithm are kernelLen and kernelSD. The crucial parameter is kernelLen (ms): a large kernel is good for detecting global changes in the sound, such as transitions between different vocalizations, whereas a small kernel is good for detecting rapid changes, such as individual bursts in a laugh. If you are curious about the kernel itself, take a look at ?soundgen:::getCheckerboardKernel().

TIP The output of segment can potentially be combined with novelty from ssm and perhaps also with pitch tracking to improve audio segmentation using all these sources of information. At present this integration has not been implemented

4 Modulation spectrum

Acoustic analysis in the context of phonetic or bioacoustic research tends to begin with a spectrogram. However, there is a complementary perspective on visualizing and analyzing sounds, which looks at the joint distribution of temporal and spectral modulation known as “modulation spectrum”. The principal insight is the idea that a sound can be represented as a sum of sinusoidal spectrotemporal ripples. In case this concept is difficult to grasp, here are two intuitive explanations (for a rigourous scientific presentation, please refer to Singh & Theunissen, 2003). The first way to understand the modulation spectrum is to think of it as a two-dimensional Fourier transform of the spectrogram. For those familiar with image processing, this is the standard way of representing any two-dimensional image as a sum of sinusoidal components (ripples) that differ in their frequency and direction. When the image in question is a spectro-temporal representation of a sound, such as a spectrogram or wavelet transform, the result is the modulation spectrum. The second basic insight is to link the modulation spectrum to spectro-temporal receptive fields (STRFs) of auditory neurons. Some neurons respond to rapid upward sweeps, others to broadband noise pulses at a particular frequency, and so on. The modulation spectrum maps nicely onto STRFs, in the sense that it shows which spectro-temporal patterns are prevalent in a particular sound.

The basic function for obtaining a modulation spectrum in soundgen is modulationSpectrum. It accepts one or more numeric vectors or one or more audio files as input, prepares a spectrogram via STFT, takes its two-dimensional FFT, and optionally performs some additional post-processing and plotting. For multiple inputs, a separate modulation spectrum is initially extracted for each one, and then they are averaged into a single output. For processing a number of audio files separately and saving their individual modulation spectra, please use the function modulationSpectrumFolder.

The first and crucial thing to remember when working with modulation spectra is that they are extremely sensitive to the initial step of transforming a sound into a spectrogram, especially the window length and step used in STFT. In order to detect temporal modulation at 20 Hz, for example, the step of a spectrogram has to be under 50 ms (1/20 s). Likewise, spectral modulation of 10 cycles/KHz cannot be resolved unless the window length is long enough (~20 ms). Here is a simple illustration:

s = soundgen(pitch = 70, amFreq = 25, amDep = 80, rolloff = -15)
ms = modulationSpectrum(s, samplingRate = 16000, logWarp = NULL,
                        windowLength = 25, step = 25)
## Warning in modulationSpectrum(s, samplingRate = 16000, logWarp = NULL,
## windowLength = 25, : roughRange outside the analyzed range of temporal
## modulation frequencies; increase overlap / decrease step to improve temporal
## resolution, or else look for roughness in a lower range

In this example we missed both spectral modulation at ~14 cycles/KHz corresponding to the f0 of 70 Hz (1000/70 = 14.3) and temporal modulation at 25 Hz. To increase the resolution in both directions, we can simultaneously increase the window length (to capture spectral modulations) and decrease STFT step (to capture temporal modulations):

ms = modulationSpectrum(s, samplingRate = 16000, logWarp = NULL,
                        windowLength = 40, step = 10)

Now we can see both spectral modulations at 14 Hz (f0) and temporal modulations at 25 Hz, as expected. When working with sounds for which you don’t know the ground truth, however, the point is not to take the first modulation spectrum you happen to produce at face value - play around with different settings and compare the results. This is really the same indeterminacy principle as the more familiar tradeoff between frequency and time resolution in spectrograms.

Beyond these basic settings, there are several other options:

ms = modulationSpectrum(
  s, samplingRate = 16000, windowLength = 40, step = 10,
  logSpec = FALSE,  # log-transform the spectrogram before 2D FFT?
  power = 2,  # square amplitudes in modulation spectrum ("power" spectrum)
  roughRange = c(15, 35),  # temporal modulations in the "roughness" range
  logWarp = 2,  # log-transform axes for plotting
  kernelSize = 7,  # apply Gaussian blur for smoothing
  quantiles = c(.5, .8, .95, .99),  # customize contour lines
  colorTheme = 'terrain.colors'  # alternative palette
)
ms$roughness  # percent of energy in the roughness range
## [1] 10.05026

5 Optimization

The results of acoustic analysis are sensitive to the chosen settings: the size and overlap of Fourier windows, the method(s) of pitch tracking and their parameters, etc. The default settings of the two main functions presented in this vignette, analyze and segment, have been optimized for human non-linguistic vocalizations. If you analyze other types of sounds, such as human speech or whale songs, you can probably improve the accuracy by changing some settings. In many cases the required changes are obvious: for example, to analyze f0 in ultrasonic whistles of dolphins or rodents you will obviously want to record at a much higher sampling rate, use shorter FFT windows, raise pitch_ceiling and / or prior_mean, etc. Other settings are not so obvious or even downright opaque, inviting some form of automatic optimization.

All that you need in order to run optimization is a training sample - that is, a few hundred sounds for which you know the right answer (average pitch, the number of syllables, or whatever it is that you wish to measure). You can start by analyzing this training sample with some reasonable settings, and then you can check the measurements manually, correcting any mistakes. This gives you a “key”, and then you can fiddle with the settings trying to reproduce this key as closely as possible, but now without manual interventions. Once you have found the optimal settings, you can use them to analyze future samples of acoustically similar material. More sophisticated methods of optimization involving cross-validation are also possible, but even the simplest check against manual measurements can cause a dramatic improvement in the quality of your measurements.

R has excellent optimization tools, notably stats::optim. It can also be done manually; for example, you can specify a grid with combinations of several control parameters and repeat the analysis for each combination, each time comparing the result with your “key”. Since I have gone through this process when optimizing the default settings in analyze and segment, I believe it may be helpful to share some code and tips specific to this particular optimization problem.

Soundgen package contains two vectors containing “keys” for the optimization of segmentation (segmentManual) and pitch tracking (pitchManual) of 260 sounds in the corpus of human vocalizations described in Anikin & Persson (2017). segmentManual contains manually verified syllable counts, and pitchManual the average pitch of these 260 sounds. These numbers are by no means intended to represent the absolute truth: in many cases it is very hard to objectively count the syllables or even determine the “true” pitch (if you doubt it, listen to the sounds, which can be downloaded here). Nevertheless, these manual measurements should not be too far off the mark, so they are acceptable targets for training the algorithm.

The easiest, “out-of-the-box” solution is to use the soundgen function optimizePars, which is essentially a wrapper around stats::optim tailored to this particular task. There are extensive examples in the documentation for this function: see ?optimizePars.

TIP The parameters of segment can be optimized within an hour or two with 260 sounds (total audio duration ~9 min), but pitch tracking is really too slow to be optimized head-on. Try a few parameters at a time and use grid optimization instead of optim whenever possible. Even so, this might take a few nights

If you prefer to optimize manually, without calling opitmizePars, here are a couple of examples.

# checking combinations of pitch tracking methods
myfolder = 'path.to.260.wav.files'  
key = log(pitchManual)
p = c('autocor', 'cep', 'spec', 'dom')
pp = c(list(p),
       combn(p, 3, simplify = FALSE),
       combn(p, 2, simplify = FALSE),
       combn(p, 1, simplify = FALSE))
out = list()
res = data.frame('pars' = sapply(pp, function(x) paste(x, collapse = ',')),
                 cor1 = rep(NA, length(pp)),
                 cor2 = rep(NA, length(pp)))
# repeating the analysis for each combination of methods in pp
for (i in 1:length(pp)) {
  out[[i]] = analyzeFolder(myfolder, plot = FALSE, verbose = FALSE, step = 50,
                           pitchMethods = pp[[i]])$pitch_median
  res$cor1[i] = cor(log(out[[i]]), log(pitchManual), use = 'pairwise.complete.obs')
  res$cor2[i] = cor(log(out[[i]]), log(pitchManual), use = 'pairwise.complete.obs') *
    (1 - mean(is.na(out[[i]]) & !is.na(key)))
  print(res[i, ])
}
res[order(res$cor1, decreasing = TRUE), ]  # max correlation regardless of NA
res[order(res$cor2, decreasing = TRUE), ]  # max correlation penalized for NA

And another example, for a grid of two parameters of analyze:

myfolder = 'path.to.260.wav.files'
key = log(pitchManual)
out = list()
pars = expand.grid(windowLength = c(17, 35, 50),
                   smooth = c(0, 1, 2))
for (i in 1:nrow(pars)) {
  out[[i]] = suppressWarnings(analyzeFolder(myfolder, plot = FALSE, verbose = FALSE, step = 25,
               pitchMethods = c('autocor','dom','spec'),
               windowLength = pars$windowLength[i],
               smooth = pars$smooth[i]))$pitch_median
  print(cor(log(out[[i]]), key, use = 'pairwise.complete.obs'))
  print(cor(log(out[[i]]), key, use = 'pairwise.complete.obs') *
          (1 - mean(is.na(out[[i]]) & !is.na(key))))
}
pars$r1 = sapply(out, function(x) {
  cor(log(x), key, use = 'pairwise.complete.obs')
})
pars$r2 = sapply(out, function(x) {
  cor(log(x), key, use = 'pairwise.complete.obs') *
    (1 - mean(is.na(x) & !is.na(key)))
})
pars

v = 6  # pick some combination of par values to explore
trial = log(out[[v]])  
cor (key, trial, use = 'pairwise.complete.obs')
cor (key, trial, use = 'pairwise.complete.obs') * (1 - mean(is.na(trial) & !is.na(key)))
plot (key, trial)
abline(a=0, b=1, col='red')

6 References

Anikin, A. & Persson, T. (2017). Non-linguistic vocalizations from online amateur videos for emotion research: a validated corpus. Behavior Research Methods, 49(2): 758-771. Text and sounds available here

Ba, H., Yang, N., Demirkol, I., & Heinzelman, W. (2012, August). BaNa: A hybrid approach for noise resilient pitch detection. In Statistical Signal Processing Workshop (SSP), 2012 IEEE (pp. 369-372). Boersma, P. (1993). Accurate short-term analysis of the fundamental frequency and the harmonics-to-noise ratio of a sampled sound. In Proceedings of the institute of phonetic sciences (Vol. 17, No. 1193, pp. 97-110).

Foote, J. (2000). “Automatic Audio Segmentation using a measure of audio novelty.” In Proceedings of IEEE International Conference on Multimedia and Expo, vol. I, pp. 452-455.

Singh, N. C., & Theunissen, F. E. (2003). Modulation spectra of natural sounds and ethological theories of auditory processing. The Journal of the Acoustical Society of America, 114(6), 3394-3411.

Sueur, J. (2018). Sound analysis and synthesis with R. Heidelberg, Germany: Springer.