“The lecture is clearly structured and very instructive.”
“Everything (contributed most to my learning,) he was an incredible instructor.”
“The lectures were very rich, often times too rich that we had to push back several lectures for later and thus change the syllabus throughout the quarter. Overall though, the lectures were good.”
“I really enjoyed lecture. It was super informative and helpful for my projects.”
“Dongryul was very helpful and accommodating, and he made sure that students from all levels of musical background were getting a lot out of the course.”
– Course Evaluation notes from students
MUSI103, Introduction to Music: Materials and Design, The University of Chicago, Spring 2021
– Center for Innovation in Teaching and Learning
Spring/2015, Spring/2016, The University of Illinois Urbana Champaign
On Goethe's Garden:36 min. video lecture on the algorithmic process of controlling time and frequencies by using Chaotic Dynamical System in my composition, Goethe’s Garden for two pianos tuned a quarter-tone apart (May 2021)
A Presentation on the acoustical models of bell sounds and the modelling of virtual bell shapes and their spectra by synthesizing engineering physics and campanology with music, by using the Finite Element Method (FEM) technique.
A DMA dissertation presentation at the IRCAM Forum Workshops, "Spatialization, Orchestration, Perception, hors les murs"
Montreal (online), February 4–5–6 and 11–12, 2021
Interval Training - P4 in Aural Skills(Making Intervals Independent)
Tritone in Music Theory and History
This is my lecture on Tritone in Music Theory which runs about 40 min. (Sectional link in comment)
It covers the following topics:
- Tritone in Different Tuning Systems
- Tritone in Counterpoint
- Tritone in Messiaen
- Tritone in the Overtone Series
- Tritone in Hindemith
- Tritone in Functional Harmony
- Tritone in Mussorgsky
- Tritone in Wagner
- Tritone in Rage Against the Machine
- Tritone In Jazz Harmony: Tritone Substitution
* Please note that Hindemith wrote that for the minor third interval, there exists a virtual fundamental (combination tone), which will be a major third lower than the lower tone of minor third, and a perfect 5th lower than the lower tone of a major 6th. However, because of a "practical" reason in composition, he put this interval in his Series 2 category and set the lower pitch of minor 3rd as the root, and the upper pitch of major 6th interval as the root. Here is what he wrote:
"Here theory comes into conflict with the practice of composition, which likes to deal with things that are clearly to be heard and seen, and would therefore like to take one of the two tones of the directly produced interval as its root. Practice could perfectly well yield to the theoretical requirement without the slightest hindrance, as long as the minor third and the major sixth appeared alone–that is, in two-part writing only. But as soon as these intervals appear in combination with others, which is by far the most usual practice in our music, the observance of this theoretical requirement would make our analysis far too difficult and too different from our habitual point of view, so that it seems more advantageous to treat both intervals according to the pattern which we have derived from their predecessors in the series. This would make the lower tone of the minor third, and the upper tone of the major sixth. the root."
Based upon the scalar interpretation, a tritone chord can be resolved in multiple ways. Here are different interpretations and resolutions of the tritone:
Ex) Chord: G-dom7 (tritone will be B and F)
The solfège syllables/ scalar degrees follow B here
1) V-I in C maj / G-C (Ti-Do, 7-1)
2) V-i in C minor / G-Cm (Si-La, 7-1)
3) V-vi in C maj / G-Am (Ti-Do: B goes to C, 7-1)
4) V-VI in C minor / G-Ab (Si-La: B goes to C, 7-1)
5) German aug6 - V - i in B minor / G-F#64-F#7-Bm (La-la-si-la: B goes to B to A# to B, 1-1-7-1)
6) German aug6 - V - I in B ma / G-F#64-F#7-B (doi-do-ti-do: B goes to B to A# to B, 1-1-7-1)
In addition to these progressions, if the B and F are interpreted in the opposite way, e.g., B and F can be scale degree 4 and 7 of F# major if F is enharmonically respelled as E-sharp, we can have 6 more solutions (progressions), e.g., V-I in F# major or F# minor etc. Here the pivotal chord will be C# dom7 (C#-E#(=F)-G#-B) instead of Gdom7.
Please also note that there are other ways to interpret the tritone as other than members of a dominant seventh or German aug 7th chord. For example, altered dominant chords also can have a tritone. Here the B and F can be interpreted as scale degree flat-2 and 5 of B-flat key, so the chord progression and resolution will be F dominant 7 flat-5 (F-A-B(=C-flat)-E-flat, same as French aug chord), which will be resolved to B-flat. If this is the case, the B and F can be interpreted as scale degrees flat-2 (C-flat) and 5(F) which will go to 1(B-flat) and 5. (F stays and C-flat goes to B-flat).
Wagner resolved the tritone in his Tristan (half dim 7th) chord in an unusual way which became the most famous example among all musical excerpts. He used a half-diminished chord instead of the French augmented 6th chord, which is resolved to the dominant 7th chord. Here the tritone was resolved in the same way from the French augmented chord, and what Wagner did was changing the lower major third interval (F and A) to a minor third interval (F and A-flat). This changed the quality of the initial chord from French aug 6th chord to the half diminished 7th chord.
Mussorgsky used the tritone in a brilliant way. Without resolving it, he juxtaposed two different dominant seventh chords by using the enharmonic respelling and maintained the tritone dyad. For example, by using F and B here as a common tone pivot tritone, you can alternate G Dom 7 chord and C# Dom 7th chord, which happened in his well-known opera, Boris Godunov’s Coronation scene. So if we can be creative, we can write a progression by juxtaposing three or more chords which include the same tritone. (e.g., G-dom 7th - F half dim 7th - C# Dom 7th - B half dim 7th - G# full dim 7th etc.)
Because from the late Romantic period many composers deployed their harmonic progressions in linear chromatic motions largely driven by the tritone resolution (not always though, it will be more proper to say that was driven by the common voice-leading practice, including the chromatic “creeping”), Hindemith regarded the tritone as one of the most important elements in his harmonic progressions and musical language, naming it as “guiding tones” to be resolved in the linear harmonic motion and musical context. Check his book, The Craft of Musical Composition (Schott, 1984) for more details.
Complex Rhythmic Layers in Ferneyhough's Music
BPM calculation and Metric Modulation
Circle of Fifths in Music Theory
SuperCollider Fundamentals 1
SuperCollider Fundamentals 2
Loudness, Decibel, and Sound Intensity Level in Acoustics and Music
Understanding musical meter as a representation of frequency and period
