tetrachords

Each mode or scale was composed of two sets of four notes, called tetrachords, probably derived from the ancient form of the lyre, which in Homer's time is known to have had four strings.

Critical and Historical Essays Lectures delivered at Columbia University Edward MacDowell 1884

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).

Archytas Huffman, Carl 2007

Can any sense be made of this criticism in light of Archytas 'tetrachords?

Archytas Huffman, Carl 2007

Archytas influenced the Sectio Canonis, since Proposition 3 is based on a proof by Archytas (A19), but the treatise cannot be by Archytas, because its theory of pitch and its account of the diatonic and enharmonic tetrachords differ from those of Archytas.

Archytas Huffman, Carl 2007

The crucial point is that Archytas 'account of the tetrachords in each of the three genera can be shown to correspond to the musical practice of his day; Ptolemy's criticisms miss the mark because of his ignorance of musical practice in Archytas' day, some 500 years before Ptolemy (Winnington-Ingram 1932, 207).

Archytas Huffman, Carl 2007

Second, Ptolemy, who is our major source for Archytas 'tetrachords (A16), argues that Archytas adopted as a principle that all concordant intervals should correspond to superparticular ratios.

Archytas Huffman, Carl 2007

There are several puzzles about the tetrachords which Archytas adopts in each of the genera.

Archytas Huffman, Carl 2007

It discusses the science of sound, intervals, tetrachords, instruments, and compositions, and outlines a lute fretting that incorporated two newly introduced neutral or microtonal intervals in addition to the basic diatonic arrangement of Pythagorean intervals.

b. Iran, Iraq, and Anatolia 2001

Berger, however, contends that in serial terms the F in question could be interpolated into a scale that would consist of two congruent tetrachords.

Griffes Disharmony Maisel, Edward 1985

I observed in passing that the tonality of the Sonata, because it contains an F rather than an F#, does not consist of two congruent tetrachords.

Griffes Disharmony Maisel, Edward 1985