The first disc is much more interesting, combining the monochord
with improvisations from Stan Sulzmann and Paul Clarvis among others.
In the Musurgia universalis (Rome, 1650) Kircher presents different divisions (arithmetical and geometric) of the monochord
, reproduces drawings of keyboards with octave divisions of more than 12, describes (superficially) the temperament with the octave divided into 12 equal parts, and considers the use of logarithms for the measurement of intervals (although he only applies them to the octave).
Pendulums in Radiesthesia detect vibrations in a way that is analogous to the monochord
. In the Monochord
, there is amplitude and wavelength as shown in Figure 13; in operating the pendulum, the same concept of amplitude and wavelength applies.
However, Ulrich's hypothesis linking the monochord
with the hummel is almost solely based on shared similar appearances.
This group works by marked points within the twinned totals of 108 that represent -- but again proportionally -- perfect musical intervals seen either as "a group of poems, differentiated at each end by some structural mark (the ends of a sequence, say, or the ends of a series of poems in the same stanzaic pattern)" (71) along a monochord
or, inversely, as harmonic divisions of the whole such as "an octave that could be divided by similar means into tetrachords, or tones, by counting equal divisions of the whole -- under this scheme, the fifth would occur seven-twelfths of the way through the group" (71).
Proportionally related geometrical figures (circles, triangles etc.), architectural principles and design, and proportions ultimately related to the divisions of the monochord
were all proposed.
The staff and clefs are covered in just over two pages and a full-page example; solmization and mutation occupy seven pages of text and four and a half pages of examples; the transposition of clefs takes up little more than one page, including its example; the modes are allotted twelve pages of text, six and a half of tables and eight of examples; and the volume ends with four pages on the division of the monochord
. The result cannot stand alone like its German progenitor but depends crucially on the teacher's filling in its outlines in his lectures.
[GREEK TEXT OMITTED] or lute, the basic instrument of Arabic music theory; the Greek sources will have thought of the kithara, or the monochord
.(14) In addition, since our concern is with Varro's medici musici and not with the
This process of becoming, the struggle of growth, is represented by a monochord
throughout On the Way to Becoming; it creates constant tension.
The House of Life sequence is replete with terminology related to musical performance, including references to instruments (hautboy, harp, lute, monochord
), performers (minstrel, daughters of the daybreak, bird, sirens), techniques (modulation, choral consonancy, wave, echoes, silence), and compositions (voluntary, air, tune, strain, song, ditties, dirges, vesper-song) in addition to musical titles ("Broken Music," "The Song-Throe," "The Monochord
," "Death's Songsters").
The temple, presided over by Apollo (the god of rational music) and Thalia (the joyous muse), contains within its structure representations of the various aspects of musical knowledge--a clock representing the durations of musical time, a monochord
tower signifying the proper divisions, a lower vestibule showing Pythagoras and the smithy, graffiti on the walls presenting musical notation, two entryways representing the portals of the ears, and a spiral near the top signifying air set in motion by sound.
Following the Pythagorean divisions of the monochord
discussed by Boethius and Jacques Le Febvre, Bermudo includes a detailed description of how to divide the fingerboard precisely with the help of the compass.