Tools required: One protractor.
Directions (for homemade version):
To prepare coat hangers:
Unbend coat hangers. Join ends of straightened
wires end to end with tape or weld to provide a 8 to
10 metres continuous length of wire.
Construction from wire: Bend wire around
a conveniently sized cylindrical tin (can) to form spiral
spring shape of 8-12 inch (200-400mm) diameter.
Position, place or tie 31 elastic bands
for markers at intervals of 208.65 degrees around the
spiral spring using protractor.
Label thirty-one clothes pegs (pins).
One for each note name: Fbb Cbb Gbb Dbb Abb Ebb Bbb
Fb Cb Gb Db Ab Eb Bb F C G D A E B F# C# G# D# A# E#
B# F## C## G##.
Attach labeled clothes pegs: Suspend
the wire spiral with its elastic band markers by a loop
bent from the wire after your last mark. Eg. From a
lamp or ceiling. Attach the clothes pegs in the above
sequence (at the marks, beginning at the end you started
your angle measurements from. (the bottom of the spiral),
and ascending by one fifth (208.65 degrees) each step.
There are many possible modifications
for this basic design, eg. paint markings, color code
pegs. blue tack, or chewing gum instead of elastic bands,
although the angle and spiral shape should be precise.
Display various scales
1. Greek Modes and Indian equivalents
using only naturals, attach a length of string to join
the pegs: C-D-E-F-G-A-B and back to C.
You will notice that the Large intervals
move upwards and one radian around the spiral. The small
intervals move downwards and 68.45 degrees around the
Starting at each of the points and listing
them in ascending order will give you the seven Greek
modes (Indian names in brackets):
starting from C=Ionian (Indian Bilaval
Scale); D=Dorian (Kafi); E=Phrygian (Bhairavi); F=Lydian
(Kalyan); G=Mixolydian (Khamaj); A=Aeolian (Asavari;
and B=Locrian Mode.
2. Sharps and flats Attach second and
third strings of different colours in the following
You will see that you have generated
the same shapes, but higher and lower on the spiral
and with a small phase shift between them of (2s-L)=54.084"
or 16.2252 degrees
(1) Up into the sharp tonalities [G#
Major scale (Ionian) i.e. 8 sharps]
(2) Down into the flat tonalities [Ab
Major (Ionian) Scale i.e. 4 flats]
3. Hindi Scale Tie strings to connect
the following sequence: C-D-E-F-G-Ab-Bb-C
This produces the shape of one of the
fundamental Hindi scales. You will notice that it follows
the sequence of the Ionian mode up to G but diverges
after that as though it was a flat Western scale having
three flats. You could consider it as an Ab Major with
the Eb sharpened to E in Western terms or as the root
of five further modes following the pattern of four
adjacent Large intervals and a single Large separated
by two separate small intervals. (LLsLsLL).
4. The Mysterious Middle Eastern Interval.
East of a line North/South from about where the Iron
Curtain used to stand, there is a cultural area which
uses an interval absent from Western music. This interval
is called the sharp second and is the difference between
two Large and one small interval (2L-s). Examples of
this interval are found in many Indian, Hungarian, and
Romanian scales. You can represent it on your model
by joining Ab and B; Db and E; Eb and F#, or any other
way which gives the same angles or phase.