Definitions
from The American Heritage® Dictionary of the English Language, 4th Edition
 n. Music A series of four diatonic tones encompassing the interval of a perfect fourth.
from Wiktionary, Creative Commons Attribution/ShareAlike License
 n. In music a tetrachord is any set of four different pitch classes.
from the GNU version of the Collaborative International Dictionary of English
 n. A scale series of four sounds, of which the extremes, or first and last, constituted a fourth. These extremes were immutable; the two middle sounds were changeable.
from The Century Dictionary and Cyclopedia
 n. In music: An instrument with four strings.
 n. The interval of a perfect fourth.
 n. A diatonic series of four tones, the first and last of which are separated by a perfect fourth.
Etymologies
Examples

Now then, these intervals of tones and semitones of the tetrachord are a division introduced by nature in the case of the voice, and she has defined their limits by measures according to the magnitude of the intervals, and determined their characteristics in certain different ways.

Thus it appears that it was Didymus, and not Ptolemy, who proposed the tuning of the tetrachord which is now accepted as correct.
A Popular History of the Art of Music From the Earliest Times Until the Present

With the Greeks the tetrachord was the unit of analysis as the octave is with us today, and all Greek scales are capable of division into two tetrachords, the arrangement of the intervals between the tones in each tetrachord differentiating one scale from another, but the tetrachords themselves always consisting of groups of four tones, the highest being a perfect fourth above the lowest.] [Illustration: Fig. 53.]

It strikes me that there's a joke to be made about The Clash being an allinterval tetrachord, but I'll leave that for another day.

This treatise began with a discussion of the basic principles of acoustics (B1), defined the three types of mean which are of importance in music theory (B2), and went on to present Archytas 'mathematical descriptions of the tetrachord (the fourth) in the three main genera (chromatic, diatonic, and enharmonic  A16A19).

Archytas 'enharmonic tetrachord is composed of the intervals 5: 4, 36: 35 and 28: 27 and his chromatic tetrachord of the intervals 32: 27, 243: 224, and 28: 27.

One genus was called the diatonic; one example of this is the Pythagorean diatonic described above, which is built on the tetrachord with the intervals 9: 8, 9: 8 and 256: 243 and was used by Philolaus and Plato.

The ratios in Archytas 'diatonic and enharmonic tetrachords are indeed superparticular, but two of the ratios in his chromatic tetrachord are not superparticular (32: 27 and 243: 224).

The unusual numbers in Archytas 'chromatic tetrachord do correspond to a chromatic scale in use in Archytas' day.

There is no doubt that Archytas knew of this diatonic scale, but his own diatonic tetrachord was somewhat different, being composed of the intervals 9: 8, 8: 7 and 28:
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