Multimedia project by Zoran Scekic

in partnership with EUROMicroFest 2015

premiered 10-12 of April, 2015; CH V. Lisinskog, Zagreb


Some years ago I’ve started to explore the world of Just intonation after a simple question that has occurred to me: “If we change the sides of some specific geometrical shape (right triangle etc.) with piano or guitar strings, what kind of chord could be heard?
 Since that time I’ve explored characteristics, possibilities and restrictions of natural intervals that I’ve described in my book ‘Five limit intervals – theory & praxis’. I’ve been coauthor of the book ‘Mathematics and music’ with professor Zvonimir Sikic.
 For further exploring and composing music in Just intonation, I’ve constructed microtonal keyboard that has been built in San Diego and wrote several pieces for solo piano in Just intonation. Premiers and seminars were in Helsinki, Warsaw, Vienna, Maribor and Osijek. Last two years I’m working on international multimedia project about objective connection between art and science. The project is called ‘Panmonism’.


‘Panmonism’ shares four major aspects. Art, science, engineering and education are introduced through concert, animation, exhibition, and a lecture.
Opening of the event is a  concert première of microtonal compositions for solo piano, followed by short animated film Exhibition consist of photography, pictures and 3D prints. Special part of exhibition introduces drawings made by machines. Machines in working mode will be installed as a part of exhibition as well.
Lecture and seminar consist of music, mathematics and engineering including historical background, analyses and explanations of all introduced works and exhibits.

The project takes its title from Greek ‘pan’ – ‘all’ and ‘monos’ – ‘single’. Panmonism shows in a very simple way that the difference between music and mathematics is not in structure but in our perception. What is common to both is endless possibilities of use and, unfortunately misuse.


Historical background

In 19 th century, French physics discovered that if a beam of light is bounced off a mirror attached to a vibrating tuning fork, and then reflected off a second mirror attached to a perpendicularly oriented vibrating tuning fork (usually of a different pitch, creating a specific harmonic interval), results in a very regular and complex geometric figure – the curve. (Figure 1). The scientist name is Jules Antoine Lissajous and figures are called Lissajous curves.

This discovery led to the invention of other apparatus such as pendulum harmonograph (Figure 2). These mechanisms from the 19th and early 20th century were very popular but limited to relatively simple forms of drawing.

Click here to learn more

Pendulum harmonograph is a mechanical apparatus that employs pendulums to create a geometric image. The drawings created typically are Lissajous curves, or related drawings of greater complexity. The devices, which began to appear in the mid-19th century and peaked in popularity in the 1890s, cannot be conclusively attributed to a single person, although Hugh Blackburn, a professor of mathematics at the University of Glasgow, is commonly believed to be the official inventor (Wikipedia).

harmonograph-with-vibrating-tuning-forks               pendulum-harmonograph

Figure 1. Lissajous vibrating tuning forks                         Figure 2. – Pendulum harmonograph


Today, there are software capable of drawing more complex drawings. However there are a number of people who are trying to build a mechanical drawing machine for complex Lissajaus curves (Figure 3).

versatileFigure 3: – This modern, versatile yet complex harmonograph is derived from a Meccano harmonograph after a design by ir. Hans van den Berg. The Meccano model was described in Meccano Nieuws nr. 14.4 (1996), nr. 15.3 (1997) and in Constructor Quarterly nr. 36, June 1997. A harmonic motion is a general term applied to a reciprocating motion like that of a piston or a pendulum of a clock. The records obtained by this instrument are valuable to the scientific investigator as a means of studying the laws of vibration in relationship with time.

Lira Spectrum (Figure 7.) is harmonograph constructed by Z. Scekic ; prototype is designed and build by GIOSPINI Studios  and financed by City of Zagreb/ City Council for culture.  While drawing, Lira Spectrum is simultaneously producing music in the rhythm patterns and intonation analogue to the picture. Another innovation in the world of harmonograph introduced by Lira Spectrum is ability to draw Lissajous curves generated by four frequencies with independently adjustable amplitude (ascending, descending or constant) and 360 degrees phase shift.

Project characteristics:

Panmonism is promotional-artistic-educational multimedia project.

The base of the project Panmonism is concert performance of microtonal pieces, exhibition of ‘Lira Spectrum’ prototype and seminar with workshop based on the books mentioned in the introduction. The main aim of the project is promotion  of microtonal music to the professional as well as to the public by exposing direct link between art and science.  The disciplines involved in the project are: microtonal music, mathematics, physics, photography, animation, 3D printing, engineering and knowledge sharing. Panmonism is very mobile project including machines and instruments prototypes. Every performance is an open invitation for artists and scientists to collaborate in the project.

  •  Project program: 


– solo piano –

‘Music for piano in five limit Just intonation’ – comp. and arr. – Z. Scekic, solo piano – Ana Zgur (Figure 4.)


Figure 4. Piano player – Ana Zgur

‘Music for piano in five limit Just intonation’ is an open series of compositions aiming to explore the harmony of non tempered microtonal system based on integer harmonics, also called Just intonation. It has been released in album JUST MUSIC. All music intervals used in these compositions are built on prime numbers 2, 3 and 5, which is usually called the five limit intervals.



Aims to show the different perceptions of the same phenomena such as intonation, frequencies, Lissajous curve and length of the musical string.

“Introduction to Panmonism”
– synopsis & storyboard by Z. Scekic, animation by Marko Ivezic, sound design by Kristijan Funaric

* Introduction to Panmonism was among accepted works for the 2015 Bridges Short Movie Festival featured at the Bridges Conference 2015 in Baltimore, USA




„Lissajous tuning forks“ (figure 1.)

„Pendulum harmonograph“ (figure 2.)

Z-board prototype (figure 6.)

 „Lira Spectrum” prototype (figure 7.)

Harmonograph drawings (figure 8.)

Photos of Lissajous curves (figure 9.)

Lissajous 3D models (figure 10.)




Figure 6. Z-board – master keyboard custom-made by StarrLabs, San Diego/USA, based on Z. Scekic specification; financed by the “Entrepreneurship in the Culture” program


Figure 7. Lira Spectrum – harmonograph constructed by Z.Scekic ; prototype is designed and build by GIOSPINI Studios  and financed by City of Zagreb/ City Council for culture (photo by K. Godina)


                      harmonograph-drawings                       ZoranScekic_10042015_fotoAnastazijaVrzina-2743

                Figure 8. Harmonograph drawings                              Figure 10. Lissajous curve 3D models;

                                                                                                             print by SMARTEH, photo by A.Vrzina


Figure 9. Lissajous Curve – image from a laser harmonograph – construction of a laser pendulum by Z. Scekic, photo by Aleksandar Bellian



 “Historical intersection”  (aliquots, tuning, tempering, Lissajous, etc.)  – based on the book “Mathematics and Music”, published by Profile (Figure 11.)

 “Nowadays” – promotion of the book “Five Limit Intervals – Theory & Praxis,” (Figure 12.) and prototype of the micro tonal electronic keyboard “Z-Board”


             Figure 11. “Mathematics and music”, Profil         Figure 12. “Five Limit Intervals – theory &  praxis”



Figure 13. – Z.Scekic holding seminar ‘When future meets the past’ at Fryderyk Chopin University of Music, Warsaw; 2010.




Zvonimir Šikić, Ana Žgur, Zoran Šćekić

SPECIAL THANKS TO: Miroslav Stodić, Ana Žgur, Mišo Uštulica, Miroslav Šimeg and Krešimir Godina