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178:). To use the organum, you would remove the rods you needed, manipulate them or rearrange them as needed to perform your calculation, and then return the rods to the box. Some of the rods were simple tables, as one might find in an almanac. Other rods, in particular the music, cryptography, and arithmetic rods, were more complex in design and intended to be used in combination.
207:, who was Kircher's pupil. The book includes numerous excerpts from the original manual. There is also a portrait of the young Charles Joseph who had died four years earlier. There are no surviving Organums which closely resemble the device illustrated in Schott's book, but there are three known devices, likely of Jesuit manufacture, which contain essentially the same content.
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There are few surviving examples of the
Organum. There are no surviving Organums which closely resemble the device illustrated in Schott's book, but there are three known 17th-century devices which contain essentially the same content. Most of them appear to have been built to impress important
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This compartment had tablets which resembled those found in an almanac. For each day of the year, the length of the day and night, the times for sunrise and sunset, and the duration of morning and evening twilight were provided. All the information was based on measurements taken at 48 degrees
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was a music composing device of similar design to the
Organum. The content of the rods was essentially the same as the musical rods in the Organum (although there was room for more of them). The Organum can be thought of as an improved and generalized version of the Arca.
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The
Organum Mathematicum was a box or chest divided into nine or more compartments. Each compartment was filled with wooden rods or slats (called "tariffa" by Kircher). The compartments were organized according to the nine functions they performed (see
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This
Organum has a steep slope which presents all the rods attractively. There is a dial in the front which can be used to find local time in 24 different cities around the world (the dial duplicates an illustration from Kircher's
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This
Organum is the 'odd man out' - it is very different in appearance from the Florence and Prague devices, which are essentially identical. The chest is not sloped, and there are a lot of extra drawers on the pedestal.
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The rods in this section could be used to determine the date of Easter and other church holidays which were positioned relative to it. These rods simply contained a table of upcoming dates.
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Kircher, Athanasius: Letter to
Gottfried Aloys Kinner, containing instructions for operation of Organum Mathematicum, reprinted in Schott, 1668, translated to German by Dr. Peter Frieß
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This section had tables describing movements for the visible planets, and the constellation Draco, and also provided astrological interpretations for the 12 zodiac signs.
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The rods in this section could be used by non musicians to compose church music. The system used was the same as that used for
Kircher's previous device, the
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This
Organum appears identical to the Florence model. Some photos show an additional metal frame which may have been added later for protection.
304:. They contained sets of musical phrases which could be combined randomly to set verses to music, producing millions of hymns in 4-part harmony.
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in the middle of the 17th century. With proper instruction and use, the device could assist in a wide assortment of calculations, including
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The device described in Schott's book was divided by functionality into 9 main sections, each of which contained approximately 24 rods.
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The rods in this section could be used to encrypt and decrypt text using a cyclic transposition cypher, based on a keyword.
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was an information device or teaching machine that was invented by the Jesuit polymath and scholar
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The rods in this section could aid in determining the design of bulwarks in fortification plans.
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The rods in this section could aid in determining heights, by use of a geometric square.
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Kircher adopted some of the ideas in the
Organum from preexisting inventions like
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Another view of the
Organum Mathematicum at the Museo Galileo in Florence, Italy.
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The Organum Mathematicum was later described in a 1668 book of the same title by
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161:. Like other calculating devices of the period, the Organum prefigures modern
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The rods in this section contained information needed to construct sundials.
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patrons to the Jesuits. It is unclear if any of them saw regular use.
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Organum Mathematicum information at University of Würzburg
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The Organum Mathematicum at the Museo Galileo in Florence
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465:Organum Mathematicum at Museo Galileo, Florence
214:Front and back of one of Kircher's musical rods
122:The Organum Mathematicum of Athanasius Kircher
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448:Haub, Vollrath: Organum Mathematicum Website
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