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n.1.An instrument for measuring angles for determining elevations, distances, etc.
Webster's Revised Unabridged Dictionary, published 1913 by G. & C. Merriam Co.
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Among these instruments was a pantometer, or sector, calibrated in such a way as to indicate various tuning systems.
Illus.2 shows the bronze pantometer calibrated by Zaragoza.
It is significant that Zaragoza refers to the pantometer as a `military pantometer' in the main part of the book, but as a compas harmonico (`musical compass') in the final section.
It is possible that these `tables' referred to the lines dividing up the octave on a bronze pantometer (or a proportional ruler, as discussed below) similar to that in Zaragoza's box.
215-17).(30) Illus.3b shows the double line of commas on the inside of both legs of the pantometer; immediately below the point marked `56' is the marking `Oct' or octave.
The last part of Fabrica y uso is dedicated to the explanation of the tetrachord and the pantometer, the two methods for working out the temperaments outlined in the book.
Finally, Zaragoza describes the use of the pantometer or `harmonic compasses' (pp.
Table 4 Authors and sources on music theory and the pantometer Date General Jesuits 1544 Stifel (ML) 1569 Ramus c.1584-c.
Two manuscript volumes in Naples and Antwerp include his treatise on the pantometer and other mathematical instruments written in Spanish and for use in the peninsula from 1618.(37) These provide the earliest evidence for the pantometer in Spain or, at least, in Castilian-speaking areas dependent on the Spanish crown.
Galileo, possibly taking Coignet's pantometer as his model, wrote his own highly influential treatise Le operazioni del compasso geometrico et militare (Padua, 1606), with followers such as B.
Sometime after 1626 an unknown Spanish writer translated the treatises on the pantometer and proportional ruler by Henrion and Metius: both can be found in a single volume in the Real Academia de la Historia in Madrid.(43) This, then, is the second piece of evidence (Coignet's treatises in Spanish being the first) of the introduction of the pantometer to Spain, but the scientific instruments clearly were known in Spain earlier than this, especially in the royal place in Madrid, where Philip II had founded a mathematics academy between 1582 and 1584.
As far as the contribution of the Jesuits is concerned, it would appear that Antonio Possevino was the first to include in a clearly defined way music among the mathematical disciplines (and these, in turn, in the broader Jesuit programme, the Ratio studiorum); his Bibliotheca selecta de ratione studiorum (Rome, 1593) has a valuable bibliography, as well as a critical edition of the treatises attributed to Euclid entitled Musica and Sectio canonis.(48) Christophorus Clavius (Geometria practica, Maguncia, 1606, pp.4-13) describes the use of the pantometer, although he does not specifically mention musical lines.