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"We'd have most of what we predicted of the conquest of space, if we hadn't ignored parasite control."
- Larry Niven

Sound Analysis  
  Improving language teaching by showing the waveform of a spoken word or phrase, and comparing it to standard speech.  

In the novella Gulf, the main characters of the story use a special language called Speedtalk, an artificial language that greatly improved the speed with which people could communicate with each other.

To help Joe learn to speak, Gail makes use of a special kind of analysis.

Gail started teaching him to hear by speaking to him single words from the odd language, requiring him to repeat them back. "No, Joe. Watch." This time whenshe spoke the word it appeared on the screen in sound analysis, by a means basically like the one used to show the deaf-and-dumb their speech mistakes. "Now you try it."

He did, the two arrays hung side by side. "How's that, teacher?" he said triumphantly.

"Terrible ... try again."

She shifted the controls; he tried again. This time his analysis array was laid down on top of hers; where the two matched, they canceled. Where they did not match, his errors stood out in contrasting colors.

From Assignment in Eternity, by Robert Heinlein.
Published by Signet in 1953
Additional resources -

It's not clear exactly what appears as an "array", but it sounds like the waveform corresponding to the spoken word. Computer-based language teaching systems have appeared in the last 5-10 years that make use of personal computers to do exactly this. The student speaks the word or phrase into the microphone, and has a chance to compare his work with that of the teacher by comparing the two waveforms.

To the best of my knowledge, this method was never used to teach deaf people to speak. As far as I know, most of this teaching is done using anatomical references, and watching your own tongue and palate in a mirror, after watching the teacher.

(Thanks to Kate Gladstone for this one!)

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Additional resources:
  More Ideas and Technology from Assignment in Eternity
  More Ideas and Technology by Robert Heinlein
  Tech news articles related to Assignment in Eternity
  Tech news articles related to works by Robert Heinlein

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