# 'confusion matrix' for English phonemes

Is there a measure of distance somewhere that tells me that certain phoneme A is more "distant" or "different" to phoneme B than it is to phoneme C in English?

For example, that the phoneme /k/ is more close to phoneme /t/ that it is to /a/. (random values to create an example)

Edit: As suggested by @Mitch, this is actually a 'confusion matrix' for English phonemes. Can anyone point to one of such tables?

• I think you should ask first whether it is true that some phonemes are closer. How do you know that /k/ and /t/ are closer than /k/ and /a/? Feb 27, 2015 at 15:40
• You can think of the English phonemic chart as kind of a periodic table of the phonemes, with separate tables for consonants and vowels. One can actually envision a phonetic space, and measure distances (in millimeters or frequencies) between individual phones. But phonemes form simpler systems, more like the set of all the chemical elements than (say) the abstract space of all possible organic compounds, which is more like the set of all possible phones. Feb 27, 2015 at 15:43
• Obviously, /t/ is closer to /k/ than it is to /a/ because /a/ is in a different chart than /t/ and /k/ are. Both of them are consonants, while /a/ is a vowel. However, this is not a vast improvement in measurement, and it's not clear what "distance" between discrete entities should be measured, not in which dimensions, nor how many dimensions are necessary. Probly the best that can be achieved with phonemes is to say 'X is closer to Y than it is to Z' or else 'X is about as close to Y as it is to Z' Feb 27, 2015 at 15:47
• You are looking for a 'confusion matrix' for English phonemes. There exist these kinds of things used within speech recognition software. I'm not sure if there are any publicly available. Feb 27, 2015 at 16:01
• Feb 27, 2015 at 16:31

After googling for a while for "confusion matrix", found this resource:

http://people.cs.uchicago.edu/~dinoj/research/confmat.html

Perhaps is interesting to learn how to read a confusion matrix here:

http://en.wikipedia.org/wiki/Confusion_matrix

Edit: Thanks to J Trana for also pointing out the following papers:

• This answer has, unfortunately, suffered from link rot, and is no longer useful.
– Joe
Jun 6, 2016 at 1:29
• This and this have not only consonant but also vowel confusion matrices; I found them to be useful. Feb 17, 2018 at 15:49
• @J Trana: This is useful. Why not make the comment an answer? Feb 17, 2018 at 19:02
• Thanks! I felt your answer was a good one and already accepted long ago; this merely acts as a helpful addendum in the spirit of your answer rather than as a new standalone one. With these types of resource-finding questions, I tend to find there is a natural trend towards a community wiki-style answer over time. Feb 17, 2018 at 20:52
• I see, in that case, I will add your comment to my answer. With your permission, of course. Feb 20, 2018 at 17:18

The confusion matrix is highly dependent on the native language of the listener.

For example, a German speaker once asked me why we pronounce the German composer Bach's name with a /k/, when [bɑf] is clearly closer to [bɑx] than [bɑk]. It's not to modern English speakers. But it might have been closer in Middle English: the word laugh, which was originally pronounced with /x/, is now pronounced with an /f/ and not a /k/.

Similarly, this question and its answers show that Spanish speakers perceive /ɛ/ as the closest English phoneme to /e/, while American English speakers think it's /eɪ/.

And I suspect that /z/, /d/, and /v/ are the closest phonemes to /ð/ in various languages, because these are all substituted for /ð/ by foreigners learning English.

And even among native English speakers, people from California can't tell the difference between Don and Dawn, while people from the U.K. think they sound nothing alike.

• Good point. Does that mean there is no standard or objective measure of distances between phonemes within a language? But this is often desirable for computational purposes. Apr 3, 2021 at 7:58
• With my answer, I was saying that there's no objective measure of distance between phonemes that holds across various languages. But I wouldn't be surprised if speakers of a single dialect of a language perceived there's a consistent measure of distance between phonemes. I don't know whether anybody has studied this. Apr 3, 2021 at 11:47
• Actually, the links in El Marce's answer see to imply that speakers of a single dialect have a reasonably consistent measure of distance between phonemes, although I'd like to see a study confirming that. Apr 5, 2021 at 12:57