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So in most accents of English, /r/ is fricated when it follows /t/ and /d/ word-initially, and in some it has become a full affricate /tʃ/. If you were going to look at a spectrogram of this, how could you measure the degree of frication of /r/? I'm looking at the affrication of /tr/ and /dr/ and need to know how it differs from just /r/ being fricated.

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The short answer is that there is no difference. Phonetically speaking, an affricate is just a stop closure followed by a period of frication, so [t] plus frication is the same as an affricate. The distinction between an affricate and a stop-fricative sequence is really a phonological one, where the former behaves as a single phoneme and the latter behaves as a sequence of two phonemes. See the related question: Is there a difference between an affricate and a plosive+fricative consonant cluster?

In the case you are talking about, we know there are two phonemes at play--/t/ and /ɹ/. Following the conventions that linguists use for bracketing, this sequence doesn't strictly speaking "become" /tʃ/, since that would indicate one phoneme sequence becoming another phoneme entirely, which only makes sense in a discussion of diachronic change; in a synchronic context, it's more accurate to say that the underlying sequence /tɹ/ is sometimes realized as something like [tʃɹ] (note the square brackets, indicating a phonetic realization). See the related question: Why are /t/ and /d/ sometimes affricated before /ɹ/ in English? Technically, it is the aspiration associated with the initial /t/ that is turning into a fricative, so from a phonological point of view it might make more sense in all cases to think of this process as the affrication of the /t/ rather than the "fricativization" (or spirantization) of the /ɹ/. In practice, however, it might be difficult to say where the /t/ ends and where the /ɹ/ begins in the spectrogram, since the tongue usually gets in position for the /ɹ/ before voicing kicks in, i.e., during the apiration/fricative noise.

As for how to "measure" the degree of frication in the /tɹ/ on a spectrogram, it's not clear how you would quantify such a property, but the main visual difference between frication noise and aspiration noise is that formant structure is visible in the latter but not in the former.

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  • In that case, since /ɹ/ is phonetically [ɚ̥], there should be visible formants in the spectrgram of [tʃɹ]. Also, both /ʃ/ and /ɹ/ are rounded, and the onset and length of lip rounding should be visible as well, and measurable, as well. My guess -- based on zero experimental experience -- is that the individual variation will swamp the /tɹ/ ~ /tʃ/ variation, which is to say some people consistently hear the difference and some never do and some can under certain conditions. And everybody's convinced they do, so nobody notices the difference; like /θ/ ≠ /ð/, which always comes as a shock.
    – jlawler
    May 18, 2014 at 14:25
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    I do have experimental experience with this phenomenon, and it's true that there is a lot of variation from speaker to speaker. It is also true that there is often formant structure visible after the frication noise, but often the formant structure is only apparent in the transition from the consonant cluster into the following vowel (so if the following vowel is [i], for example, F2 and F3 are steeply rising coming out of the frication noise). Depending on one's labeling scheme, that transition could be considered part of the /ɹ/ or not.
    – musicallinguist
    May 18, 2014 at 23:32
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    It is also true that the degree of lip rounding and retroflexion will affect both the distribution of frication noise and the loci of the formants, and often one sees a downward-sloped center of gravity in the noise that "fades into" the second and third formants, which tend to bunch together at a relatively low part of the spectrum under these conditions. It is thus not always straightforward to decide whether noise in the spectrogram should be characterized as frication or aspiration, and even when it is clear that both are present, it is not always clear where to draw a line between them.
    – musicallinguist
    May 18, 2014 at 23:44
  • I have another question which is more specific about the same subject. When you look at a spectrogram of an affricated realisation of "tree", you can see the period of frication and then there (at least in the examples I'm looking at) is the /r/ which is showing formants as is usual for an approximant. However, all the literature I've read has said that if the /r/ follows a voiceless stop (i.e. /t/), it becomes devoiced. When I look up what a devoiced approximant looks like, it says it's more like a fricative and less like an approximant. But in 'tree', I'm still seeing it as approximant. Why?
    – user3604
    May 19, 2014 at 7:15
  • @user3604 I have some ideas, but it might be best for you to post this as a separate question and include some screen caps of the spectrograms in question.
    – musicallinguist
    May 19, 2014 at 14:15

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