INDICATORS FOR DETERMINING CHORDS AND MUSICAL INTERVALS OF THE DIATONIC SCALE, ALSO LATITUDE, LONGITUDE, AND RELATIVE TIME OF PLACES ON EITHER TERRESTRIAL OR CELESTIAL PLANI- SPHERES.
Year: 1874

page_text: LETTERS PATENT to Samuel Dyer Tillman, of Jersey City, in the
County of Hudson, and State of New Jersey, in the United States
of America, for the Invention of "INDICATORS FOR DETERMINING CHORDS
AND MUSICAL INTERVALS OF THE DIATONIC SCALE, ALSO LATITUDE, LONGITUDE,
AND RELATIVE TIME OF PLACES ON EITHER TERRESTRIAL OR CELESTIAL PLANI-
SPHERES.
"
Sealed the 10th March 1874, and dated the 26th January 1874.
COMPLETE SPECIFICATION filed by the said Samuel Dyer Tillman at
the Office of the Commissioners of Patents, with his Petition and
Declaration, on the 26th January 1874, pursuant to the 9th Section
of the Patent Law Amendment Act, 1852.
5 TO ALL TO WHOM THESE PRESENTS SHALL COME, I, SAMUEL
DYER TILLMAN, of Jersey City, in the County of Hudson, and State of
New Jersey, in the United States of America, send greeting.
WHEREAS I am in possession of an Invention for "INDICATORS FOR
DETERMINING CHORDS AND MUSICAL INTERVALS OF THE DIATONIC SCALE, ALSO

page_text: LATITUDE, LONGITUDE, AND RELATIVE TIME OF PLACES ON EITHER TERRESTRIAL
OR CELESTIAL PLANISPHERES," and have petitioned Her Majesty to grant
unto me, my executors, administrators, and assigns, Her Royal Letters
Patent for the same, and have made solemn Declaration that I am the
first and true Inventor thereof.
5
NOW KNOW YE, that I, the said Samuel Dyer Tillman, do hereby
declare that the following Complete Specification, under my hand and
seal, fully describes and ascertains the nature of the said Invention, and
in what manner the same is to be performed, in and by the following
statement :-
The first part of the Invention relates to a new and improved instru-
ment for indicating all musical intervals and common chords.
1
The object of this part of the Invention is to indicate and measure,
by means of musical scales, the diatonic intervals and common chords
belonging to any required tonic in the major mode, and at the same 1
time to show separate and distinct from these the proper intervals and
common chords belonging to the same tonic in the minor mode; also to
make the instrument embracing fixed and movcable scales in a cheap
and effective form.
An instrument patented by me in the United States of America, 2
dated November 8th, 1853, was designed especially to show the true
and tempered intervals of the diatonic scale in the major mode. In
practice however it was found impracticable to solve all musical
problems with that instrument, because it was quite impossible to
represent with clearness on one and the same surface all the intervals 2
and the common chords belonging to the same tonic in the minor as
well as in the major mode. This radical defect I have remedied in my
Invention herein-after described.
Both Inventions are based on the same conception of the progression
of pitch represented by the projection of a spiral, each ring of which a
embraces all the intervals of the diatonic scale.
In this present Invention all the octaves of a given sound are found
at the points where the same radius rector intersects the spiral, thus
obviating the difficulty encountered in measuring intervals on a con-
tinuous right line, which requires the addition of the eighth note in
order to measure seven intervals. The rings of the spiral represent
all the octaves of each sound in the musical series, therefore it is only

page_text: necessary to use one ring of the spiral for illustrating and measuring
musical changes produced by a change in the pitch of the tonic. This
ring or single revolution of the spiral is made a true circle for con-
venience, and on this circle all the intervals within the octaves are
represented as herein described.
I employ a ring or annular plate made of metal or other suitable
material, one side of which shows the intervals of the diatonic scale,
usually called the fixed scale (see Figure 1 in the accompanying
Drawing) which are represented by divisions of a circle, and designated
by the first seven letters of the alphabet, also the five intermediate
intervals, indicated by flats and sharps, and as made with instruments
played by means of keys. These twelve equal parts represent the
twelve so-called semitone intervals within the octave; I call them the
twelve ascending grades of pitch, one grade being the measure of a
semitone, and two grades being the measure of a tone interval. These
twelve grades or semitone intervals are numbered like the hours on
the dial of a watch 12, 2, 4, 5, 7, 9, 11, correspond respectively to
C, D, E, F, G, A, B, representing both the intervals and the sounds
of the fixed musical or diatonic scale, and the remaining numbers
1, 3, 6, 8, 10, represent divisions of the five tones, intervals respectively,
into semitone intervals, which are designated by either a sharp or a
flat added to one of those letters. Within this ring is a disc of metal
or other suitable material which is held in place and arranged so as to
rotate freely within the ring. On one side of this disc, as shown in
Figure 1, are divisions of a spiral which measure the intervals of a
movable diatonic scale. The length of these seven intervals corresponds
to those of the fixed diatonic scale, and is measured in twelfths of the
circle. These measurements on the rotating disc are made clear by a
combination of inverted curves, and further designated by the solfeggio
syllables do, re, mi, fa, sol, la, si. The "do" nearest the centre
designates the tonic or key note, a second "do" is added above the
first to show the octave, but this second do" is in fact the first
note of a second series of sounds, which if made would be corre-
sponding octaves of the seven sounds which form the first series.
As the six remaining solfeggio syllables have a fixed relation to
the tonic "do" it is evident that any change in the position of
"do" in relation to the fixed scale of the ring would require a cor-
responding change in the pitch of other sounds belonging to this
"6

page_text: tonic. The rotation of the disc shows the changes which may be given
to the position of the tonic, and the relations of the movable scale to the
fixed scale.
In order to show with distinctness the sounds which produce the
common chords belonging to each key I place within the scale three
portions or segments of circles which measure these major triads; on
each portion are marks in a radial line with those solfeggio syllables by
which the chord is known and distinguished. As major triads are
measured by four grades followed by three grades there can be three
different common chords in the diatonic series, namely, as shown in
Figure 1, do, mi, sol; sol, si, re; fa, la, do.
All the changes arising from a change of tonic in the major mode,
and all the major common chords which can be made, are shown on the
face of the ring and disc, as represented in Figure 1, by altering their
relative positions.
On the reverse side of the ring and disc, as represented in Figure 2,
are the measurement of intervals required in the minor mode. The
measurement of the fixed scale by divisions of a circle on the annular
plate or ring into twelve parts is precisely like that shown in Figure 1.
The seven letters are omitted for convenience, but can be added when
required. The corresponding numerals on cach side of the ring aro
exactly opposite each other, so that 12, 2, 4, 5, 7, 9, 11, indicate the
same sounds in the minor and major modes. On the disc however, as
shown in Figure 2, the divisions marking the intervals are different,
"la" being taken as the tonic in the minor mode; this syllable has the
same position on the circle as "do" in the major mode, therefore these
syllables are exactly opposite each other. From the inner "la," see
Figure 2, the progression of pitch on the diatonic scale is shown, and la
above is the octave of the tonic. In descending the scale only diatonic
intervals are indicated, but in ascending the scale the last two notes of
the scale are commonly raised a semitone. These measurements are
shown by inverted curves, and the arrow heads connected therewith
point out the notes used in ascending and descending the scale.
To illustrate the use of this instrument it is only necessary to fix the
revolving disc D in a given position, so that "do" on the side showing
the intervals in the major mode shall be on one of the sounds indicated
on the fixed scale R, all the intervals are then pointed out; and on

page_text: looking at the reverse side all the intervals used in the minor mode with
the same tonic sound are also shown.
Figures 1 and 2 show the two sides of the instrument, when "do" is
on C, thus it is seen that all the diatonic intervals in the major mode
are indicated by letters, this being designated as the natural key; yet
the same tonic in the minor mode requires the sounds or intervals
belonging to the key of E flat, but in ascending the series 9 or A may
be substituted for 8 or A flat, and 11 or B for 10 or B flat. The
relative tonics are also shown for each key, for example, Figure 1
exhibits the order of the diatonic scale intervals used in the major
mode, O being the tonic of the natural key, if to use the minor mode
in the samo key the tonic must be changed from C to A, the relative
minor tonic is A or 9, three grades below C or 12. This gives us the
rule for finding the relative minor tonic in given key, namely, subtract
from the number indicating the tonic in the major modo three, and the
remainder will be the number indicating the minor mode tonic in the
same key. If the major mode tonic is indicated by a number less than
three, then twelve is added to it before the subtraction is made, for
example, in the key of five flats the major mode tonic is onc, con-
sequently the minor tonic is ten. In the same manner the relative
major tonic is found by adding three to the number indicating the tonic
in the minor mode. As shown in Figure 2 the tonic in the minor mode
is 12, by adding three grades we find that the relative major tonic is 3
or E flat.
The common chords in the minor mode are made up of an interval
measured by three grades, followed by one of four grades, consequently
there can be formed on the diatonic scalo only three regular minor
common chords; these are indicated on Figure 2 by portions of circles
and marks, which show these chords to be, first, la, do, mi; second, re,
fa, la; and third, mi, sol, si.
There is an imperfect chord or triad made up of two intervals, each
measured by three grades, this is shown by the inner portion of a circle
in Figure 2, to be si, re, fa; and is the only case where a triad chord
embraces six grades or one half of the whole circle.
Another method of indicating on the rotating discs diatonic intervals
and chords is by means of a combination of triangles. The triangle
points out the common chord, those with thick lines being the most

page_text: important; thus Figure 3 represents the intervals and chords in the
minor mode. The triangle formed by dotted lines measures the imperfect
triad.
It may be found in practice that the use of these triangles in place of
the curves and portions of circles on the rotating disc will give the
student a better idea of harmony.
Interesting problems relating to modulation may be solved by the use
of the numerals designating the grades or semitones within the octaves;
the ring or annular plate is made of thick copper metal, but to economize
metal I have invented a mode of stamping out from metal the ring and
using the circular plate cut out of the inside of the ring, as the rotating
disc. To accomplish this I form a tongue on the periphery of the disc
and along the middle of the plate of such width as to allow metal to
overlap each side without projecting beyond the thickness of the disc;
then on the inner and lower edge of the ring and in the same planc I
form a lip or slight projection extending inward, and on the inner and
upper edge of the ring I form another projection or lip extending
upwards or at right angles with the other lip; these lips are made
so small as to form when finished a diminutive groove on the inside
of the ring, in which moves the small tongue already described. After
the disc is placed within the ring so that its tongue rests on the lower lip
of the ring, the upper lip is bent from its upright position so as to have
the same direction as the lower lip, thus forming a groove within which
the tongue of the disc will freely rotate. Figure 5 shows a cross section
of the ring and disc before the upper lip has been bent over the tongue.
D is the disc; t, t¹, the tongue resting on the lower lip 1, 1, of ring R,
and,, is the upper lip ready to be bent over the tongue so as to prevent
the escape of the disc D. In practice it may be found more convenient
to form the tongue on the inside of the ring, and the lips for the groove
on the outside edges of the disc; this is only a modification of the same
device for securing within a ring a disc of equal thickness so that it may
move freely therein. This combination of ring and disc having the
appearance of a medal I have designated the instrument as a "music
medal." The most rapid method of forming the tongue and lips
described is by means of pressure in the same dies which form the
characters and figures found on the faces of the instrument.
The second part of the Invention relates to an instrument for a

page_text: different purpose. I use the rotating circular disc differently engraved or
marked to ascertain or show readily the latitude and longitude and
relative time of any place on the earth's surface. To adapt the disc to
this purpose on one side is firmly fastened a map of the Northern
hemisphere, and in like manner on the other side a map of the Southern
hemisphere; in these maps the pole is represented at the centre and tho
equator at the circumference. The best map for this use is a modifica-
tion of the globular projection in which degrees of latitude are measured
by equal distances on a radial line. This map is preferably not
disfigured by circles of latitude or by radial lines of longitude.
on
Figure 6 represents a plan of the instrument in its simplest form ;
Figure 7 is a vertical or transverse section at the middle. In theso
Figures D is the disc covered on either side by a map and rotating on
the pin P, which pin is sustained in its position by the two arms A, A³.
For the purpose of a hand map these arms are firmly fastened to a
handle H. Each arm is so constructed that one of its sides or edges is
a right line or radial line from the pin P, which represents the pole.
The arm on each side is graduated and numbered from opposite the
equator to the pole on the map so as to denote the degrees of latitude.
The degrees of longitude are indicated by graduations on the circle E, E',
which represents the equator; these are numbered from 1 up to 180,
both east and west from a given meridian, the place almost universally
on the zero of the scale being Greenwich Observatory, England. Outsido
of the circle E, E¹, representing the equator is another circle T, T¹,
which are graduations indicating intervals of time. First the circle is
divided into twenty-four equal parts, which measure hours; these are
numbered from 1 up to 12 on either side of a given meridian, which
may be that of London or the capital of any country in which the map
is used. Time graduations may be in parts of hours and minutes. On
the largest discs thus far made the graduations are so frequent as to
indicate half minutes. The principal use of this instrument being to
determine the latitude, longitude, and time of any place these are all
shown on the same right line. For example, selecting New York as
the point to be defined, turn the disc until New York is on the radial
line of the arm,
and there the graduation will indicate its latitude, its
longitude shown where the arm intersects the equator, and its difference
in timo is indicated where the arm crosses the outer circle. Thus the
latitude, longitude, and time of any place in either hemisphere is shown
on the same right line. Furthermore the shortest distance between

page_text: any two places of different latitudes in the same hemisphere is easily
found. The difference in longitude and the difference in latitude
estimated in miles give the two sides of a right angled spherical triangle,
the hypothenuse of which is the distance required.
On each of the large maps is placed the length, in miles, of a degree
of longitude at each degree of latitude; also the length of the longest
day and night at degrees of latitude is placed on the large maps.
The actual velocity of the carth's rotation on its axis at any place
is given in miles per minute by dividing the length of a degree of
longitude at that point by four. It is obvious that other geographical
problems may be solved more rapidly by the aid of my terrestrial plani-
sphere than by the ordinary globe.
When a larger planisphere, say of two feet diameter is required, the
arms instead of being united to a handle, as shown in Figures 6 and 7,
are connected with a single vertical standard, which may be sustained on
three or four legs. The largest planisphere yet made, the disc is thirty-
seven inches in diameter, may be sustained by a pair of horizontal bars,
one of which A, B, is shown in Figure 8 by means of a pin at C. This bar
is graduated each way from where its two ends cross the equator to its
centre the pole, with the degrees of latitude; a similar graduation is on
the opposite side of the disc. These bars are sustained by two vertical
pillars or posts which rest on the feet G and H, and are strengthened by
the lower bar E, F. On this bar may be fixed a wheel W, in the grooved
end of which the edge of the disc revolves. Similar wheels may be
used at A and B if required to keep the disc in the same plane.
Another plan of using the large planisphere is to sustain it by a
graduated fork, that is, by inverting the instrument as shown in Figure 6,
and sustain it by connecting the handle with a cord and pulley hung to
the wall, so arranged that the disc may be raised and lowered or turned
over. This plan is especially adapted for schools and seminaries of
learning. For use on shipboard two discs may be employed, one for
each hemisphere. The disc D, with a graduated arm A, is sustained by
a pin P, which is fastened in a board or a wall, as shown in Figure 9.
Either the disc or arm may be rotated on the pin P.
An arrangement similar to the above may be used as a celestial atlas
by substituting for the terrestrial maps celestial maps of the stars seen
in the northern and southern hemispheres. Such maps may have also
in connection with the radial arm an oval ring to exactly define the

page_text: limit of vision, and the stars visible at any time indicated on a graduated
time circle. It is obvious that portions of a hemisphere may be used
when required instead of a complete one.
Having thus fully described my Invention, I would have it understood
that I claim with regard to the first part of the Invention the combi-
nation of the ring R with the inner movable disc D, provided upon their
obverse and reverse faces with indexes of the major and minor intervals
respectively, the whole forming a music medal, substantially as and for
the purpose described.
Also a medal consisting of the ring R and rotating disc D, such parts
being struck up from one piece of metal substantially as described, with
or without the musical indexes herein-before mentioned.
I claim with regard to the second part of the Invention the combi-
nation of the circular disc covered by a map either of the northern or
the southern hemisphere of the earth, with a graduated arm or bar
indicating degrees of latitude, which arm may be stationary when the
disc is rotated, or which may be revolved on its supporting pin when the
disc is stationary.
Also the combination of a graduated circle measuring intervals of
time, with a map of the northern or southern hemisphere of the earth,
having its circumference graduated for the degrees of longitude, the
whole being so arranged that the latitude, longitude, and time of any
place on the earth's surface may be shown at once.
In witness whereof I, the said Samuel Dyer Tillman, have hereunto
set my hand and seal, this Thirteenth day of January, in the
year of our Lord One thousand eight hundred and seventy-four.
SAMUEL DYER TILLMAN. (L.S.)
Witness,
ARNOLD HÖRMANN,
Mechanical Engineer,
16, Murray Street,
New York City,
U. S. A.