Music teaching and computation device

A music teaching and computation device in the form of a slide rule has a first display part on which are set out, by means of indicia the characteristic structures of five different modes of music. A second relatively movable display part co-operating with the first display part has indicia thereon representing notes of a musical keyboard, separated by spatial intervals in proportion to the musical intervals of pitch between the notes represented thereby. The first and second indicia can be brought into registry with each other, so as to compute the chords and scales in any of the presented given modes of music.

FIELD OF THE INVENTION 
This invention relates to devices for assisting in musical composition, and 
for assisting in the study and learning of music principles and harmony. 
In the teaching of music, and at least at the elementary level, it is 
normal to instruct the pupil to learn the notes of a key-board by letter 
and to locate the representation of the respective notes as musical 
notations on the familiar pair of five lined staffs. By this means, the 
pupil learns to play the key-board, normally of a piano, by reading the 
music written down in conventional manner and transposing written notes to 
the correct notes of the keyboard. Conventional written musical notations 
include symbols denoting key, key signatures, sharps, flats, note 
durations etc. In such teaching, little attention is paid to the inherent 
structure of music, the various modes of music or the relationship of the 
notes making up a mode of music to each other. The pupil therefore tends 
to learn to play music as written, but not to play "by ear", i.e. by 
location of the notes of melodies and harmonies on an instrument by 
recognition of sounds and patterns, without use of written notations of 
the music. 
BACKGROUND OF THE INVENTION 
There are a number of different modes of music, each of which comprises a 
series of diatonic scales. Each diatonic scale comprises a series of seven 
steps, rising from one tone to its octave. The steps between the degrees 
(notes) of a scale are either a semitone or a tone in magnitude. Each of 
the different modes of music has its own characteristic sequence of tone 
and semitone steps or intervals between successive degrees of its scales. 
All of the diatonic scales of a given mode of music have the tone-semitone 
sequence characteristic of that mode. 
The most familiar modes of music in Western culture are the major scale 
(also known as the Ionian Mode), and the Aeolian or minor mode (from which 
Western minor scales are derived). The major mode has the following 
sequence of steps: 
EQU tone-tone-semitone-tone-tone-tone-semitone 
Thus in a major scale which starts and finishes on the note C (i.e. in 
which C is the tonic or keynote), known as the scale (key) of C major, the 
degrees which must comprise the scale are dictated by the above interval 
sequence, and are as follows: 
______________________________________ 
tone tone semitone 
tone tone tone semitone 
C- D- E- F- G- A- B- C- 
tonic tonic 
______________________________________ 
If D is chosen as the tonic note, the resulting scale of D major uses F 
sharp as the third note or degree instead of F natural and C sharp as the 
seventh note or degree instead of C natural, thereby maintaining the 
characteristic tone-semitone interval sequence of the major mode. 
Other modes of music have different sequences of tone-semitone intervals 
between adjacent degrees of their diatonic scales. A thorough familiarity 
with the sequences characteristic of various modes of music facilitates 
playing by ear. 
In the past, musical compositions in the Western culture have generally 
been written and played in accordance with one mode of music, at least for 
long passages of the composition. Any change from one mode, e.g. major, to 
another mode, e.g. Aeolian has normally represented a distinct transition 
point in the music, between separate passages thereof, except for 
occasional use of chords from another mode. It is seldom that more than 
two different modes of music are incorporated into the same composition. 
There is currently, however, more and more attention being paid by 
composers and musicians alike to other modes of music, in addition to the 
familiar major and Aeolian minor modes, in particular the Phrygian mode, 
the Mixolydian mode and the Dorian mode. Numerous other modes of music are 
known, but the other modes do not fit the accepted harmonic patterns of 
music found in the Western culture. Up until fairly recently, the 
aforementioned modes have been regarded as archaic musical forms, and have 
not had a significant role in Western Culture. However, as composers and 
musicians continually strive for new and varied effects in their music, 
these previously disregarded modes are being used to a greater extent. 
There is also a tendency, in modern music, to "mix" the various modes of 
music in a single composition, and to make frequent and abrupt changes 
from one mode to another in the composition. One way of achieving this is 
to introduce into a musical passage written in a given mode, one or more 
chords which are derived from another mode. These chords thereby provide 
transition points for changing from one mode of music to another. 
Accordingly, for the student of music, as well as for the composer, there 
is an increasing need to study and understand at least the five different 
modes of music referred to above, namely major (Ionian), Aeolian, 
Mixolydian, Dorian and Phrygian, and their relationship with one another. 
It is also helpful to know the various chords and characteristics thereof 
which can be used in different modes of music. 
BRIEF DESCRIPTION OF THE PRIOR ART 
There have been previous proposals for display devices for teaching various 
aspects of musical theory and structure. However, none of these display 
devices, as far as is known, have paid attention to the various different 
modes of music and the relationship between them. Further, they have not 
attempted to assist the music student or composer in understanding and 
working in all these various modes and in transposing music between the 
various modes Ionian (major), Aeolian, Dorian, Phrygian and Mixolydian. 
SUMMARY OF THE INVENTION 
The present invention provides a teaching device for use by a music student 
which assists the student in learning to play music by ear, by emphasising 
and exhibiting inherent musical patterns and forms, and by displaying 
graphically musical patterns and forms of a variety of different modes of 
music. Preferred embodiments of the invention also provide for the 
teaching of harmonics, and chords, and the computation thereof, in a 
variety of different modes of music, and can be used to assist in musical 
composition. 
According to the present invention, there is provided a music teaching and 
computation device in the form of a slide rule. The device has a first 
relatively movable display part and a second relatively movable display 
part, each of which bear respective indicia. The first relatively movable 
display part is divided into at least three sectors, each sector 
representing a given, different mode of music, and each sector bearing a 
first series of indicia representing the notes of diatonic scales of the 
mode of music represented thereon, the indicia of the first series being 
spaced from one another a first distance representative of a musical 
interval of pitch of a tone or a second distance, substantially half the 
first distance, and representative of a musical interval of pitch of a 
semitone the sequence of first distances and second distances between 
adjacent notes corresponding to the tone-semitone sequence characteristic 
of the mode of music represented thereby; 
the second relatively movable display part bearing a second series of 
indicia representing in sequence the notes of a musical keyboard, the 
distances between adjacent indicia of the second series being proportional 
to the musical interval of pitch between the notes represented by the 
respective indicia, the distance representing a musical interval of one 
tone in the second series of indicia being substantially the same as the 
distance representing a musical interval of one tone in the first series 
of indicia, 
the first and second relatively movable display parts being movable with 
respect to one another to allow the first and second series of indicia to 
be moved into registry with one another. 
By suitable adjustment of the first and second display parts relative to 
each other, the first and second series of indicia can be registered with 
one another to allow the determination from their alignment of all the 
notes or degrees comprising a given diatonic scale, in any of modes of 
music presented by the sectors in the first display part. For example when 
the first and second series of indicia are aligned so that the indicia 
representing the note C of the second series of indicia coincides with the 
indicia of the first series representing the first note of a diatonic 
scale, the notes comprising the diatonic scales of C in all of the modes 
of music presented can be read off, by reading the coincidences of the 
indicia of the first series with the indicia of the second series, through 
all the sectors of the first display part. 
DESCRIPTION OF THE PREFERRED EMBODIMENTS 
Preferably, the first display part has at least four sectors, and most 
preferably five sectors, representing respectively the major (Ionian), 
Dorian, Phrygian, Mixolydian and Aeolian modes of music. 
In a preferred embodiment of the invention, there are also provided third 
and fourth relatively movable display parts, bearing respectively third 
and fourth series of indicia, both the third and fourth series of indicia 
being essentially similar to the second series of indicia, and 
representing in sequence the notes of a musical keyboard, the distances 
between adjacent indicia of the respective third and fourth series being 
proportional to the musical interval of pitch between the notes 
represented by the respective indicia of the series, the distance 
representing a musical interval of one tone in the third and in the fourth 
series of indicia being substantially the same as the distance 
representing a musical interval of one tone in the first series of 
indicia. This preferred embodiment of the invention permits the 
construction of triad chords, in all of the various modes of music 
represented by respective sectors of the first display part. 
An integral part of any musical composition is the triad chords present in 
the composition, which are largely responsible for conferring melodic and 
harmonic characteristics to the composition. A triad chord consists of 
three notes, comprised of alternate notes of the diatonic scale of the 
composition within its particular mode of music. The chord is generally 
referred to by its base note, i.e. the lowest note of the triad of which 
it is comprised. The chords of the C-major diatonic scale are thus 
CEG(first), DFA(second), EGB(third), FAC(fourth), GBD(fifth), ACE(sixth), 
and BDF(seventh chord). 
Such a triad chord may be a major chord, a minor chord or a diminished 
chord. The type of chord is determined by the interval of pitch between 
the adjacent notes making up the triad chord. Since triad chords use notes 
found in a diatonic scale in a mode of music, the intervals of pitch 
between the notes of the chord, and hence their type as regards major, 
minor and diminished, is determined firstly by the mode of music under 
consideration and secondly by the base note of the chord. For example, in 
the case of the diatonic scale of C in the major mode, the first chord is 
CEG, and the intervals between the notes are respectively C-E two tones 
and E-G one and a half tones, which are characteristic intervals of a 
major chord. This is the C-major chord. 
The second chord of the diatonic scale of C in the major mode, DFA, 
however, has corresponding intervals of one and a half tones (D-F) and two 
tones (F-A) which are the characteristic intervals of minor chords. This 
is the D minor chord. The seventh chord of the diatonic scale of C in the 
major mode BDF, has corresponding intervals of one and a half tones and 
one and a half tones, characteristic of a diminished chord. This chord BDF 
is thus called the B diminished chord. 
Each note of a diatonic scale within a given mode of music can thus be 
assigned a designation major, minor or diminished, which denotes the 
character of the triad chord within the mode of music which uses the note 
as the base note. Since the character of the triad chord indicates its 
type of structured sound and harmony, a familiarity with the character of 
chords derived from a given base note in a particular mode of music is 
helpful in understanding musical structures, and making and understanding 
musical compositions and their melodic forms. 
In the preferred form of the present invention, the first series of indicia 
on the first relatively movable display part include a further series of 
indicia which denotes the character of the triad chord which uses the note 
represented by the respective indicia as its base note. Such further 
indicia are included on the first series of indicia in all the sectors of 
the first display part, i.e. for all the modes of music represented 
thereon. Thus the device according to the invention permits not only the 
construction of triad chords in all the various modes of music represented 
thereon, but also a determination of their character, so as to assist in 
preparing musical compositions. 
The device of the present invention permits the composer or student to move 
with ease between the various modes of music presented, and to recognize 
the relationships between them. Once the various display parts have been 
aligned to give information with respect to one mode of music, they are 
thereby aligned to give corresponding information with respect to all the 
other modes of music presented. 
It has been discovered that, for any given diatonic scale of music, across 
all five of the different modes of music under consideration, there are 
nineteen possible chords (3 note triads) which can be used whilst 
maintaining the accepted melodic and harmonic characteristics of the music 
in the given diatonic scale. All of these nineteen chords can fit 
harmonically and melodically within the scheme of music of the given 
diatonic scale. Departure from these nineteen chords, in a composition in 
the given diatonic scale, gives a degree of dissonance. A composer 
generally selects the chords in his composition by ear, without being 
aware of the 19 possible chords open to him. The present invention 
provides a means of determining the 19 possible chords in any given 
diatonic scale and thus enlarges the scope of chord selection for the 
composer. Some of the chords of the nineteen possibilities are in one 
modality of music, whilst some are in another. The use of these chords, in 
a composition in a given diatonic scale, enables the composer to move 
between the different modalities of music within the composition, thereby 
increasing the range of melodic and harmonic characteristics of the 
composition. 
Preferably, each of the display parts of the present invention is in the 
form of a disc, and the distances between indicia of a series are angular 
distances. The display parts are pivotally connected together at a common 
center, so that they overlie one another. The first display part is thus 
opaque, whilst the other display parts which overlie it may be 
transparent, with their respective indicia inscribed thereon. 
In another embodiment of the invention, the first relatively movable 
display part is an opaque disc and bears the first indicia around its 
outer perimeter, and the second relatively movable display part is also an 
opaque disc, pivotally connected to the first part at a common center. The 
second disc is of smaller diameter than the first disc, so as to leave 
visible the first indicia when the second disc overlies the first disc. 
The second disc bears the second indicia around its periphery, for 
registration with the first indicia. The second disc, in this embodiment, 
may also bear, radially inwardly of the first indicia, notations of the 
notes comprising the triad chords of the respective base note indicated by 
the second indicia thereon. A third disc may be provided pivotally 
connected to the common center, and bearing the fourth-note indicia 
representing notes of a musical keyboard and angularly spaced from one 
another by an angular interval representing the appropriate musical tone 
or semitone interval. The third disc can be aligned so that the fourth 
note indicia thereon compute 4-note chords (6th or 7th) with the triad 
chord indicia on the second disc. Finally in this embodiment, there is 
provided a cover disc, fixed with respect to the first display part, 
generally opaque but provided with apertures therein which can be 
registered with the triad chord notations on the second display part. The 
apertures in the cover disc and the triad chord notations on the second 
disc may be presented in three circumferential sets in respective 
registration, the sets corresponding respectively to major, minor and 
diminished chords displayed on the thiad chord notations through the 
apertures when correctly aligned. Thus the character of a given triad 
chord may be indicated, according to the set of apertures through which it 
is displayed. 
In a further alternative, the display parts can be made rectangular and 
relatively slidable with respect to one another, in the form of an 
elongated rectangular slide rule. In such form, the first relatively 
movable display part comprises the slide rule base, and the second, third 
and fourth display parts are slidably received in side-by-side 
relationship in a mounting recess in the first display part. 
Other items of musical information may additionally be presented on the 
various display parts of the device according to the present invention. 
For example the first display part or first disc, may include fifth 
indicia comprising a series of equiangularly spaced notations, separated 
by an angular distance representing two and one half tones, and the second 
display part may include sixth indicia for registration with the fifth 
indicia, the sixth indicia representing notes of a musical keyboard and 
separated from one another by an angular distance representing the 
appropriate musical interval of a tone or a semitone. The notes 
represented by the sixth indicia in registry with the fifth indicia then 
progress in the clockwise direction by 4ths. and in the anti-clockwise 
direction by 5ths. Triad chords based upon notes separated by such 4th 
intervals and 5th intervals have harmonic relationship to one another and 
commonly follow one another, or progress harmonically into one another, in 
musical passages, in one specific mode of music, e.g. major(Ionian). Such 
fifth indicia in registry with sixth indicia also indicate to the composer 
or student major seventh chords which contain a common tritone, which is 
useful for the operator to know in understanding musical forms and 
compositions, and composing music. A major seventh is a four note chord 
comprising a major triad and the seventh of the scale. 
Further, appropriate ones of fifth indicia may be joined together by 
suitable graphic means, to show the harmonic resolution of chords based on 
the note indicated by registry of the fifth and sixth indicia, into the 
prime chord of the tonic note under consideration.

The illustrated embodiment of the invention comprises a plurality of 
indicia bearing display parts movable with respect to one another into 
various alignments and registrations with one another. The movable display 
parts are in the form of indicia bearing circular disc, pivotally 
connected at a common center. 
With reference to FIG. 1, there is a first relatively movable display part 
in the form of a base disc 30 which is divided by bold radial lines 31 
into five substantially equal sectors 32, 33, 34, 35 and 36. The sectors 
represent respectively the modes of music Major, Dorian, Phrygian, 
Mixolydian and Aeolian as marked. Each sector is divided into six 
equiangular divisions, e.g. 37 by means of five equally spaced broken 
radial lines e.g. 38. Each space represents a musical interval of one 
tone, so that each entire sector represents a musical interval of six 
tones or one octave. The disc 30 is provided with a peripheral tab 39 to 
assist in angular movement of it. 
The disc 30 is provided around its perimeter with a first series of indicia 
40, marked as blocks and adjacent associated notation on the drawing, 
representing notes of a scale of a given mode of music. Thus the indicia 
40 in the sector 32 are angularly spaced according to the sequence of 
intervals of a scale of major mode of music, and lie either on or midway 
between the broken lines 38. In the other sectors 33, 34, 35 and 36, the 
block indicia 40 are arranged corresponding to the characteristic 
tone-semitone interval sequence of the respective mode of music Dorian, 
Phrygian, Mixolydian and Aeolian. The block indicia also include a 
notation of the tonic -- soh -- fah characteristic of the respective note, 
by initial letter, i.e. D represents doe R represents ray etc. 
The first series of indicia 40 also include further indicia in the form of 
notations 41, some of which are circled. The notations 41 indicate the 
type of triad chord which will be based on the respective note of the 
scale represented by the corresponding block of indicia 40. Thus, when the 
chord is to be major the symbol m is used. When the chord is to be minor, 
the symbol - is used. When the chord is to be diminished, the symbol o is 
used. 
The center 20 of disc 30 is apertured to receive a suitable pivotal 
mounting connection. Extending radially outwardly from the center 20 are 
fifth indicia 21 in the form of equiangularly spaced radial lines, 
separated from one another by an angular distance representing 2 and one 
half tones. There are 11 of these lines in all, a space of 5 tones being 
left between lines 22 and 23 of the series, i.e. the line opposed to the 
base line 24 of the series 21 is omitted. 
FIG. 2 illustrates the front view of a second relatively movable display 
part in the form of a second disc 42 for use in conjunction with the base 
disc 30 of FIG. 1. The second disc 42 has a peripheral tab 43 to assist in 
angular movement of it. Disc 42 is transparent and bears a second set of 
angularly spaced indicia 44, marked with letters corresponding to the 
notes they represent, in the sequence in which the notes appear on a 
musical keyboard and spaced apart by an angular interval corresponding to 
the interval of musical pitch between the notes which they represent. The 
angular interval representing a semitone on disc 42 and second indicia 44 
thereon is the same as that representing a semitone on disc 30 of FIG. 1. 
Thus when disc 42 is assembled on disc 30 with their centers coinciding, 
the second indicia 44 fall on or midway between lines 38 of disc 30, and 
by angular adjustment can be brought into registry with block indicia 40 
of disc 30. The set of indicia 44 are arranged to be spaced a short 
distance inwardly of indicia 40, 41 of disc 30, for ease of reading when 
the discs are superimposed. 
A sixth set of indicia 55 is provided near the center of disc 42, 
representing notes and corresponding to the second set of indicia 44. 
These are positioned to register with the ends of lines 21 on disc 30, 
i.e. the fifth indicia. 
Disc 42 has a further set of lettered indicia 45, disposed radially 
outwardly of the series 55 and registering with individual ones of the 
series 55. These indicate the related minor scale having the same key 
signature as the major scale represented by the corresponding indicia of 
series 55. Thus indicia C of series 55 registers with indicia A of series 
45, showing that the C major scale has the same key signature as the A 
minor scale, namely no sharps or flats. A further series 56 of indicia on 
disc 42 indicates the respective key signatures of the indicia on series 
45 and 55 in registry therewith. Thus it is shown that both the key of G 
major (series 55) and E minor (series 45) have the key signature of one 
sharp. 
FIG. 3 illustrates a third relatively movable display part comprising a 
third disc 46, having a peripheral tab 47 for assisting in its angular 
movement, and bearing a third set of lettered indicia 48. The lettered 
indicia 48 are essentially the same as the second set of lettered indicia 
44 appearing on disc 42 of FIG. 2. They represent notes of a keyboard, are 
spaced apart by an angular distance corresponding to the musical interval 
between the adjacent notes, and the angular distance between notes of set 
48 representing a semitone is the same as the angular distance 
representing a semitone on discs 42 and 30. The set of indicia 48 on the 
disc 46 of FIG. 3 is spaced radially inwardly, as compared with the set of 
indicia 44 on disc 42, so that when the discs 30, 42 and 46 are assembled 
with their centers coinciding, indicia 48 appear inwardly of indicia 44 
for ease of reading. Disc 46 is made of transparent material. 
FIG. 4 is a front view of a fourth relatively movable display part in the 
form of a fourth disc 49. The disc 49 has a peripheral tab 50 for ease of 
movement thereof, and bears a fourth set of indicia 51. In essential 
respects, the disc 49 is the same as disc 46, being made of transparent 
material, and bearing the set of indicia 51 representing the notes of a 
keyboard, spaced apart according to the musical interval between adjacent 
notes, the angular distance representing a semitone on disc 49 being the 
same as that representing a semitone on discs 46, 42 and 30. Indicia 51 
are spaced inwardly with respect to the indicia 48 on disc 46, so that 
when disc 49 is assembled on top of disc 46 with centers coinciding, the 
set of indicia 51 is disposed within the set of indicia 48 for ease of 
reading. 
FIG. 5 shows the discs 30, 42, 46 and 49 superimposed in working 
relationship. They can be operated to determine notes of scales and 
construct chords. They are pivotally connected at their common center 20. 
Thus, considering discs 30 and 42 in the sector representing the major mode 
of music, it will be seen that if the indicia representing note C on the 
second set of indicia 44 of disc 42 is set to correspond to the block 
indicia 40 on the base disc 30 representing the first note of the scale, 
i.e. bold line 31, the remainder of the note designations D,E,F,G,A, B and 
C on the indicia 44 register with the remaining block indicia, thereby 
reading the notes in the major scale of tonic C. 
Similarly, in the Dorian mode, in sector 33, the notes comprising the scale 
of C-Dorian can be read off by the registry of indicia 40 with indicia 44, 
to be C,D,E flat, F,G,A,B flat. Similar computations can be made for the 
tonic C scale in the Phrygian,Mixolydian and Aeolian modes, by reading the 
same registries in sectors 34, 35 and 36 respectively. 
If the second disc 42 were to be moved one tone to the left 
(anti-clockwise) of its position shown in FIG. 5, so that note D 
registered with the first block indicia of the set 40 of the major mode, 
the disc would be set to read the notes of the D Major scale, in 
correspondence with the block indicia 40, namely the notes E,F sharp, G,A, 
B, C sharp and D. Notes of the tonic D scale cal also be read off for the 
other modes of music, using indicia 40 and 44 on the first and second 
discs, respectively, with the discs in this relatively position. 
The third indicia 48 and the fourth indicia 51 on the third and fourth 
discs 46, 49 respectively are used to compute triad chords. Thus in the 
position of the discs illustrated in FIG. 5, the third disc 46 is placed 
so that the E indicia on the set 48 is in line with the C indicia on the 
set 44 of disc 2, and the fourth disc 49 is placed so that the G indicia 
of the set 51 is in line with the E indicia of the set 48 on the third 
disc 46. This arrangement therefore puts in line the letters C E G on the 
discs, the prime chord in the scale of C-major. 
In all modes of music and in all scales, there are three primary chords, 
which are those using as base notes the first, fourth and fifth notes of 
the scale, and comprising internally a triad of the aforementioned base 
note, the next but one note of the scale, and the note next but one up the 
scale from the second note. Thus, in the key of C major, the three primary 
chords are C E G, F A C and G B D. These are all major chords, since the 
intervals between adjacent notes have the major characteristics. From 
these primary chords, derivative secondary chords can be determined. One 
seconeary chord in C major is the chord E G A, another is B D F, another 
is A C E, and the fourth one is D F A. The device of the invention as 
illustrated allows the secondary chords to be computed. These various 
chords may be major, minor, or diminished. The notations 41 of the indicia 
40 indicate whether the triad chord based on the respective note will be 
major, minor or diminished. 
In the position of the various discs shown in FIG. 5, the note C of the 
second indicia 44 is set to the base line 31, so as to put the device into 
position for scale of tonic C in all the displayed modes of music. The 
other discs are aligned so that note E of the third indicia and note G of 
the fourth indicia are aligned with the base line 31, constructing the 
major chord CEG of tonic scale C. Proceeding clockwise around the discs, 
it will be observed that all the other major chords of tonic scale C, in 
all of the five displayed modes of music, have also been aligned by these 
indicia and can be read off -- FAC (major or Ionian), GBD (major or 
Ionian), E flat GB flat (Dorian), FAC (Dorian) etc. The composer can thus 
derive all of the major chords for tonic scale C for consideration for 
inclusion in a composition, crossing back and fourth between the modes. 
Further, the device will give the composer all the minor chords in tonic 
scale C, by a small angular adjustment of the third disc 46. The third 
indicia 48 on the third disc 46 effectively represent the middle note of 
the triad chord. To change from major chords, set out in the position 
shown in FIG. 5, to minor chords, by definition the middle note must be 
lowered one semitone, i.e. third disc 46 must be moved clockwise an 
angular distance equivalent to one semi-tone. By so doing, all of the 
minor chords of tonic scale C, in all of the presented modes of music, are 
aligned under the minor notations 41 of first indicia 40, by the indicia 
44, 48, 51. These are DFA (major or Ionian mode), EGB(major or Ionian 
mode), ACE(major or Ionian mode), CE flat G(Dorian), FA flat C(Phrygian) 
etc. These are now available for the composers selection. In the same 
manner, all the diminished chords can be obtained by suitably aligning the 
discs to correspond to the musical intervals of pitch between adjacent 
notes characteristic of a diminished chord. 
The computation of chords can be repeated at will for other tonic scales 
throughout the presented modes, by adjusting the discs to bring the 
desired tonic note on indicia 44 into registry with base line 31, and 
suitable adjustment of the other discs for major, minor etc. chord 
intervals. It turns out that for any given tonic scale, there are nineteen 
different chords throughout the five presented modes. The location of 
these is indicated on the base disc 30 by a further series of indicia 
namely circling the respective notations 41 of the indicia 40. Chords 
falling under a non-circled notation 41 are duplicates of those falling 
under the circled notations. By inclusion of the identification of the 19 
chords the range of selection of chords available to the composer is 
clearly presented, and a further indication of the relationship between 
the various modes of music is given. 
The sixth series of indicia 55 on the second disc 42 register with the 
fifth set of indicia 21 on the base disc 30. This registry gives 
information concerning triad chord progressions in the major mode of 
music. The notes indicated by registry of indicia 21 with indicia 55, and 
hence chords (major, minor or diminished) based on these notes, progress, 
in the clockwise direction by 4th intervals, and in the anti-clockwise 
direction by 5th intervals. Thus, in the alignment shown in FIG. 5, the 
interval C to F is a fourth, F to B flat is a fourth, etc, and the 
interval C to G is a fifth, G to D is a fifth etc. This registration of 
indicia also gives the student or composer valuable information about 
chord progressions. When working in the key of C major, as the discs are 
aligned in FIG. 5, these alignments indicate that, in a musical 
composition, the chord of one base indicated by the alignment can 
naturally and harmonically be followed by the chord indicated by the 
adjacent alignment, i.e. the E chord can be naturally followed by the A 
chord or the B chord. The indicia 21 also include broken lines 25, 26 
indicating possible chord resolution and progression back to the prime 
chord based on the tonic note of the scale. Thus in the FIG. 5 alignment, 
the chord of B may be acceptably followed by the tonic chord of C. 
The alignment also indicates that a chord may be followed by the chord 
represented by the registration at the radially opposite end of a line of 
indicia 21. Thus in the alignment of FIG. 5, i.e. C major, it is indicated 
that the triad chord B can be followed by chord F. The composer is thus 
presented with the various commonly accepted chord progressions, for 
returning in the composition from one chord to the base chord of the 
scale, in commonly accepted manner. From the chord of E, for example, when 
playing in the C major scale shown in FIG. 5, the music may return to the 
tonic -- C chord via the A, D and G chord sequence, or via the B -- chord 
or via the B flat and F sequence. These are the chord progressions 
commonly found and accepted in Western music. The device according to the 
invention graphically illustrates this, and teaches familiarity with it. 
By suitable alignment of the indicia 21 and 55, these chord progressions 
for any major diatonic scale may be illustrated and computed. In addition, 
the opposite ends of the radial lines of series 21 join together two 
dominant seventh chords sharing the same tritone, which is significant in 
understanding musical structures and making musical compositions. 
The primary chords of a given major tonic scale are presented by 
coincidence of indicia 21 and 55. The prime chord based on the tonic note 
is presented at the base line 31 coincidence. The other two primary 
chords, based on the fourth and fifth notes of the scale, are presented by 
the coincidences of series 21 and 55 immediately adjacent to, and on 
either side of, the base line 31, no matter which tonic scale is set to 
the base line 31.