DESIGN AND MAKE A NOVEL MUSICAL INSTRUMENT “BAM-SAZ ...

DESIGN AND MAKE A NOVEL MUSICAL INSTRUMENT
“BAM-SAZ or TONDAR (Bass Satour)”
Mohammad Reza Shajarian
Head of High Council of music, Iran House of Music
Tehran-Iran
S.Shajarian@gmail.com
Shabnam Ataei
Electronic Engineer
Shahid Beheshti University ( National University)
Shabnam.ataei@gmail.com
Mohammad Reza Shajarian is the most famous Iranian vocalist, composer and the musical instruments maker.
His works are brilliant in the history of Persian music. In 1999, UNESCO in France presented him with the
prestigious Picasso Award, one of the Europe's highest honors. He has many international awards. He was
Nominated for Grammy award in Best World Music 2004 and 2006. Also he has won Mozart award in 2007 in
Moscow.
He is the Head of High council of music in Iran House of Music, that most of the Persian music Masters are
members of there.
Shabnam Ataei : Electronic Engineer from Shahid Beheshti (National) University, Tehran – Iran. She has
worked on music theory and physics of music for many years.
She has many publications and researches on signal processing and a patent on a digital tuner of musical
instruments. She has also many Journals or Conferences papers on Electrical engineering.
She has contributed for writing some books and research projects.

Abstract
The issue of gaining the most harmonious sound from a musical instrument has always been a concern for Musical Maestros
and Musical instrument makers. “ Since 1960 I have been preoccupied with enhancing the harmony of some of iranian
musical instruments and in particular Santoor.” Said Mohammad Reza Shajarian, renowned Iranian Maestro and the author of
this paper. The opinions regarding the aspect of Harmony, however, tends to be diverse. The fact that has resulted in various
designs and Makings of Musical Instruments. This paper specifically aims at analyzing one of the Iranian Musical
instruments called the Santoor and introduces a newly-made instrument, Tondar, which is designed to produce a sound of a
better quality in addition to enhancing the sound capacity of the Santoor.
Introduction
An outline of the concept of harmony in Musical
Instruments
In order to understand why certain combinations of notes
make harmony and others don’t, we will study the simplest
instrument, a single string. The formula for the frequency
of a vibrating string is:
1 ⎛
f = ⎜
2l
⎝
T
D
Frequency=(1/2*length)(tension/line density)^0.5
When:
Frequency is in Hertz=1/sec
Length is in meters
Tension is a force in Newton=kg*m/sec^2
Line density is the string thickness, in kg/m
⎞
⎟
⎠
(1)
Bam-Saz (Bass Santour Or “Tondar”): The Design and
structure
This fact has many physical manifestations in Musical
Instruments design, such as:
_ Low-sound instruments must be much larger than highsound
ones. In general, an instrument which is an octave
lower must be twice as large. For example, in the stringed
instruments, a simple comparison yields the obvious fact
that Contrabass is larger than cello and the others are viola
and violin respectively.
_ Lower Sounds are also to be produced through
thickening the string or winding metal or fishing-nylon
strings around it.
In the next chapter, the design of the Santoor and the
introduction of Tondar is further discussed
Regarding the above-mentioned facts.
Bam-Saz (Bass Santour)
Persian musical instruments cover about 3-4 octaves in a
moment with a specific tune. Besides, low frequencies and
bass notes cannot be fully produced by the available
instruments. Santoor is a Persian musical instrument that
covers about 3 octaves. However, it cannot provide the
ideal homogeneity which a Musician desires and the
produced sound is not sharp enough, Therefore a need for
an instrument with a much lower frequency coverage is
observed.
“BAM-SAZ” introduced in this paper is designed and
made through a novel method of designing and measuring

of resonating strings including new measurements and
designing method in addition to new braces sizes. It covers
about 4.5 octaves, from A2 to G6 which grants us a choice
of low frequencies that were unique among all of its
Persian precursors.
We, hereby, shed light on the techniques used for devising
this instrument:
The Modification of strings
As we have already stated for strings measurements we use
this formula:
Frequency=(1/2*length)(tension/line density)^0.5
350.0
300.0
250.0
200.0
f
150.0
D
l
100.0
50.0
0.0
0 5 10 15 20 25
G6 G4
G3 G5
F6 F4
F3 F5
E6 E4
E3 E5
D6 D4
D3 D5
C6 C4
C3 C5
B6 B4
B3 B5
A6 A3
A3 A5
G5 G3
G2 G4
F5 F3
f
F2 F4
D E5 E3
l
E2 E4
D5 D3
D2 D4
C5 C3
C2 C4
15 20 25
B5 B3
B2 B4
G6
F6
E6
D6
C6
B6
A6
G5
F5
E5
D5
C5
B5
Because of the bass sounds and long length of strings it can
be used with damper.
The classic Santoor and the Tondar can be compared in
Figure No.2.
G4
G3 G5
F4
F3 F5
E4
E3 E5
D4
D3 D5
C4
C3 C5
B4
B3 B5
A3
A3 A5
G3
G2 G4
F3
F2 F4
E3
E2 E4
D3
D2 D4
C3
C2 C4
B3
B2 B4
Fig.2 Iranian santoor compare with “Tondar”
The Design of the body
The classic santoor cannot produce an absolutely
harmonious sound since due to its trapezoidal geometry the
distance from the bridges to rails varies. Therefore the
pressure applied on soundboard will be different because
of the difference in Normal coordinate of the tensile Force.
The solution offered in the design of the Tondar is to
harmonize this coordinate through applying height to the
ribs. (Fig. 3)
The strings diameter sizes are between .035 and .070 and
all of them are steel and without wounding and wrapping
on the left hand and the right side strings diameters are
between .24 and .070 with wrapping cover.

In addition, a modification has also been applied to the
previous inner braces in order to reach the optimum
efficiency in harmonizing sound by balancing the pressure
on Soundboard and also preventing the redundant
harmonics through dividing the inner space of sound box.
(Fig. 4)
Conclusion
Fig. 2D & 3D figure of Bam Saz
References
1- Mathematical Harmonies, Mark Petersen, 2001.
2- Johnston, Ian, Measured Tones, The interplay of
physics and music, Hilger, NY, 1989.
3- Pierce, John R., the Science of Musical Sound,
Scientific American Library, NY, 1983.
The figures below provide the wave forms and frequencies
of the same note produced by classic Santoor and the
Tondar.
The frequencies are the same because the notes are the
same. A note has one frequency and a frequency as a
number is relate to one note.
Waveforms of two notes (sol), 97 and 196 Hz Santoor &
Tondar are shown in figures below