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Yordan Kamdzhalov
Conducting Berlin Philharmonic in 2007
Born	October 16 1980 Turgovishte, Bulgaria
Website	https://kamdzhalov.com/

A superellipse, also known as a Lamé curve after Gabriel Lamé, is a closed curve resembling the ellipse, retaining the geometric features of semi-major axis and semi-minor axis, and symmetry about them, but defined by an equation that allows for various shapes between a rectangle and an ellipse.

In two dimentional Cartesian coordinate system, a superellipse is defined as the set of all points $(x,y)$ on the curve that satisfy the equation

$$\left|{\frac {x}{a}}\right|^{n}\!\!+\left|{\frac {y}{b}}\right|^{n}\!=1,$$

where $a$ and $b$ are positive numbers referred to as semi-diameters or semi-axes of the superellipse, and $n$ is a positive parameter that defines the shape. When $n=2$, the superellipse is an ordinary ellipse. For $n>2$, the shape is more rectangular with rounded corners, and for $0<n<2$, it is more pointed.

Generalizations

The generalizations of the superellipse in higher dimensions retain the fundamental mathematical structure of the superellipse while adapting it to different contexts and applications.

Superellipsoid

A superellipsoid extends the superellipse into three dimensions, creating shapes that vary between ellipsoids and rectangular solids with rounded edges. The superellipsoid is defined as the set of all points $(x,y,z)$ that satisfy the equation:

$$\left|{\frac {x}{a}}\right|^{n}\!\!+\left|{\frac {y}{b}}\right|^{n}\!+\left|{\frac {z}{c}}\right|^{n}\!=1,$$

where $a,b$ and $c$ are positive numbers referred to as the semi-axes of the superellipsoid, and $n$ is a positive parameter that defines the shape.

Hyperellipsoid

A hyperellipsoid is the $d$-dimensional analogue of an ellipsoid (and by extension, a superellipsoid). It is defined as the set of all points $(x_{1},x_{2},\ldots ,x_{d})$ that satisfy the equation:

$$\left|{\frac {x_{1}}{a_{1}}}\right|^{n}\!\!+\left|{\frac {x_{2}}{a_{2}}}\right|^{n}\!+\ldots +\left|{\frac {x_{d}}{a_{d}}}\right|^{n}\!=1,$$

where $a_{1},a_{2},\ldots ,a_{d}$ are positive numbers referred to as the semi-axes of the hyperellipsoid, and $n$ is a positive parameter that defines the shape.

Related Shapes

Using different powers can represent more general class of curves. For two-dimentional case the equation is $\left|{\frac {x}{a}}\right|^{m}\!\!+\left|{\frac {y}{b}}\right|^{n}\!=1;m,n>0,$ where $m$ either equals to or differs from $n$. If $m=n$, it is the Lamé's superellipses. In the general case $m\neq n$, the curve possesses more flexibility of behavior, and is better possible fit to describe some experimental information.

Likewise, for the three-dimensional case, three different positive powers $m$, $n$ and $p$ can be used in the equation $\left|{\frac {x}{a}}\right|^{m}\!\!+\left|{\frac {y}{b}}\right|^{n}\!+\left|{\frac {z}{c}}\right|^{p}\!=1$. If $m=n=p$, a super-ellipsoid is obtained. If any two or all three powers differ from each other, a solid is obtained that may possess more flexibility in representing real structural data than the super ellipsoid. A three-dimensional super-ellipsoid with $m=n=2.2$, $p=2.4$ and the semi-diameters $a=b=1$,  $c=0.5$ represents the structure of the National Centre for the Performing Arts in China.

In the general $N$–dimensional case, the equation is $\left|{\frac {x_{1}}{a_{1}}}\right|^{N_{1}}\!\!+\left|{\frac {x_{2}}{a_{2}}}\right|^{N_{2}}\!+\ldots +\left|{\frac {x_{N}}{a_{N}}}\right|^{N_{N}}\!=1$, where In general, $n_{1},n_{2},\ldots ,n_{N}$ may differ from each other. It is the superellipsoid only if $n_{1}=n_{2}=\ldots =n_{N}=n$.

Superquadrics are a family of shapes that include superellipsoids as a special case. They are used in computer graphics and geometric modeling to create complex, smooth shapes with easily adjustable parameters.

While not a direct generalization of superellipses, hyperspheres (defined by $\textstyle \sum _{i=1}^{d}\displaystyle x_{i}^{2}=r^{2}$) share the concept of extending geometric shapes into higher dimensions.

The related shapes demonstrate the versatility and broad applicability of the fundamental principles underlying superellipses.

The standard equation for a superellipsoid in 3D is: (​ax​​r+​by​​r)rn​+​cz​​n=1 where a, b, and c are the semi-axes, and r and n are parameters that control the shape. For r=n=2, the superellipsoid is an ordinary ellipsoid. Different values of r and

n can create a variety of shapes, from more cuboid to more spheroidal forms.In the polar coordinate system, the superellipse equation is (the set of all points $(r,\theta )$ on the curve satisfy the equation) :

Yordan Kamdzhalov (Bulgarian: Йордан Камджалов) is a Bulgarian conductor and music director.

Kamdzhalov is a laureate Jorma Panula and Gustav Mahler international conducting competitions and served as General Music Director of Theater & Orchester Heidelberg. Throughout his career he has collaborated with a range of international orchestras including the Los Angeles Philharmonic, Philharmonia Orchestra London, German Symphony Orchestra Berlin, Tonhalle Orchestra Zurich, Konzerthausorchester Berlin and New Japan Philharmonic. In the opera sector, he conducted performances at, among others, Komische Oper Berlin and Theater Magdeburg, earning him a nomination as 'Best Opera Conductor of the Year' by Deutschlandradio Kultur. As of 2015, Kamdzhalov is the Artistic Director and Principal Conductor of the Bulgarian Genesis Orchestra and Music Laboratory for the Human Self.

Early life

Education

Kamdzhalov began piano lessons as a child at the cultural community center in Turgovishte, guided by his mother, a music teacher. In 1999, Kamdzhalov began to study conducting at the Sofia Conservatory under Vassil Kazandjiev and continued at the Hanns Eisler University of Music in Berlin under Christian Ehwald, simultaneously completing training as a choir conductor. He was selected to work over an extended period with the Philharmonia and London Philharmonic Orchestras, which led to his collaboration with well-established conducting mentors including Lorin Maazel, Vladimir Jurowski and Esa Pekka Salonen. During his training he also served as a lecturer in Early music at the National Academy of Music (Bulgaria). In 2007, he began to develop his own mathematical interpretation of musical scores by transforming them into structures of eighths, which facilitated memorization and allowed him to focus on communication while conducting.

Career

In 2006, Kamdzhalov became Artistic Director and Principal Conductor of the international Berlin Ensemble Innorelatio and served as musical director at the Schlosstheater Rheinsberg from 2007 to 2009. In 2011, he was appointed Chief Conductor of the opera, the philharmonic orchestra and the Schloss festival in Heidelberg. The seasons realized during his tenure were the most financially successful in the history of Theater & Orchester Heidelberg. He chose not to extend his contract beyond 2014, but he remained as Principal Guest Conductor for the following season. His rendition of Bruckner’s Symphony No.3 at his final concert in Heidelberg as General Music Director prompted a critic from Bachtrack to write: “I have now heard many performances of the finale, including that by Sir Simon Rattle and the Berlin Philharmonic, but at this point Kamdzhalov outshone them all.” In 2014, IAU and NASA named a minor planet 52292 Kamdzhalov, stating that "he connects the world of music with the fascination for the universe." The same year the publishing house Sagner released the book "Sound Worlds: Conductor Yordan Kamdzhalov" about Kamdzhalov's music and philosophy. As of 2018 he has been appointed Music Director & Chief Conductor of the opera house in Rijeka, Croatian National Theatre Ivan Zajc.

Аwards (Highlights)

• 2009 - first prize at the fourth international orchestra conducting competition 'Jorma Panula' in Vaasa (Finland)
• 2010 - third prize at the third international conducting competition 'Gustav Mahler' in Bamberg (Germany)
• 2010 - nominated as 'Best Opera Conductor of the Year' by Deutschlandradio Kultur for conducting the production "Carmen" at the Theater Magdeburg
• 2011 - 'Musician of the Year' award from the Bulgarian National Radio
• 2013 - nominated from Opernwelt in the category of 'best performance' for the premiere of Wolfgang Rihm's opera 'Dionysos' at the Heidelberg Opera
• 2014 - "Music Critics’ Award" at the 24th Central European Music Festival (Slovakia)
• 2015 - Honorary award 'Ambassador for Bulgarian Culture Worldwide' from Superbrands

Work at Foundation Yordan Kamdzhalov

Yordan Kamdzhalov at work in Bulgaria

Kamdzhalov is the co-founder and president of the Foundation Yordan Kamdzhalov, established in 2010 with a stated goal of supporting young Bulgarian talents and preserving Bulgaria's musical traditions. The foundation's activities gradually led to the creation of the socio-cultural platform, including theYoung Artists Competition, Music Laboratory for the Human Self, Genesis Orchestra, Academia Musica, and Interdisciplinary Artists.

Genesis Orchestra

In 2016, Kamdzhalov became Artistic Director and Chief Conductor of the new Genesis Orchestra, featuring musicians and soloists from Bulgaria, Europe, America, and Asia. The orchestra's debut concert at Gasteig, recorded for the German label cpo, was perceived as 'a new chapter in our cultural heritage'.

Music Laboratory for the Human Self

In 2014, Kamdzhalov assumed the roles of Artistic Director and Principal Conductor as well as participant in the Music Laboratory for the Human Self, a conceptual platform unfolded in three choral formats: Choir, Ensemble and Bulgaria Sings. The Choir acts as the resident choir for the symphonic Genesis Orchestra. The vocal Ensemble's repertoire includes music styles from antiquity to the 21st century, interwoven with fragments and motifs of Bulgarian folklore. Bulgaria Sings provides a platform for people to gather, sing, and collaborate at significant historical and cultural-educational sites across Bulgaria.

Academy for the Human Self

In 2024, the "Yordan Kamdzhalov" launched the Academy for the Human Self - an interdisciplinary educational center comprising of training on Science (mathematics and physics), Art (theory of music, piano, violin, percussion instruments and dance) and Sport (chess and table tennis). The academy is envisioned to provide free comprehensive training for individuals of all ages.

In 2017, Kamdzhalov received the Echo Klassik prize for Concerto Recording of the Year (20th/21st Century category), alongside the piano duo Genova & Dimitrov. In 2018 he led the Genesis Orchestra for a concert in National Palace of Culture, Bulgaria, featuring Lisa Gerrard in Górecki’s Symphony No.3 and Vehadi improvisation on music by Beinsa Duno, later released internationally on CD. In 2018, Kamdzhalov conducted the debut Music Laboratory for the Human Self (Chore and Ensemble) accompanied by the Genesis Orchestra, at Wiener Musikverein in an sound-spatial performance featuring motifs and music by Peter Deunov. In April 2024, he announced the latest concert-spectacle with Genesis Orchestra, and the Music Laboratory (Choir and Ensemble), titled Mystery and Freedom.

Vision

Kamdzhalov lecturing on Beinsa Douno's music at Seven Rila Lakes, Bulgaria, 2016

Recognizing the potential of Bulgarian music and talent to enrich global culture, Kamdzhalov considers the expansion of his projects in Bulgaria in recent years a paramount endeavor. He established the Genesis Orchestra with the mission to 'create pulses' in cultural space, uncovering deeper layers within individuals and tapping into the inner power of the human self. He perceives Music Laboratory for the Human Self as a platform for surpassing conventional performance paradigms by shifting the focus from the musical elements to the interpreter. Kamdzhalow regards the interpretation of Deunov's music in the project Etudes of the Future as a pinnacle of creative freedom and the the work of his life. Describing his nearly two-decade exploration as "music of absolute content", he continues to shape his visionary ideas into reality.