The document summarizes a video about analyzing the Tristan chord through Fourier analysis and the Karplus-Strong algorithm. The Tristan chord is a dissonant chord composed by Wagner that appears in his opera Tristan und Isolde. Fourier analysis was used to break down the chord into its frequency components. The Karplus-Strong algorithm then synthesized each note separately and combined them to recreate the full chord, though it did not perfectly match due to ignoring timbre. The video demonstrated applying digital signal processing techniques to analyze the musical properties of the famous Tristan chord.

1. SY BTECH (2017-18)
Programming Assignments Submission
Applied Mathematics Practical using MATLAB
Name of student: Omkar Rane
Branch & Block: 1 and 1
Cycle No.: 2
Roll No.: SETB118
Summary of the video:
1. Title / topic of the video:
Digital Signal Processing/signal processing on Tristan Chord through Fourier analysis
approach. Tristan chord is ancient musical chord composed by Wilhelm Richard Wagner.
was a German composer, theatre director, polemicist, and conductor who is chiefly
known for his operas (or, as some of his later works were later known, "music dramas").
2. The video is about what:
The video is about Tristan chord. The Tristan chord is a chord made up of the notes F, B,
D♯, and G♯. More generally, it can be any chord that consists of these
same intervals: augmented fourth, augmented sixth, and augmented ninth above a bass
note. It is so named as it is heard in the opening phrase of Richard Wagner's opera Tristan
und Isolde as part of the leitmotif relating to Tristan.
3. Main idea covered in video:
Tristan chord appears in four bars prelude of opera music. It was first performed in 1865
Tristan chord is dissonance chord so it might not be pleasing to listen it. Main idea
behind this video is to analysis various frequency produced by chords through Fourier
analysis spectrum showed in video.

2. 4. Analysis / summary:
Fourier spectrum analysis:
In western music convention there are various notes like A3
#
, C3
#
, D4
#
, f4
#
, G4
#
, A4
#.
Each note has a unique frequency associated with it. A4=440 Hz is taken as
reference note. A3=220 Hz and A5=880 Hz. There is one octave situated between each
frequency. for e.g.: A3, B3, C3, D3, E4, F4, G4 are notes between frequency 220 Hz to
440 Hz this range forms 1 octave similarly octaves are present for different notes.
An Octave corresponds to doubling or halving of frequencies. Octaves are spaced into 12
halves evenly spaced half tones.
Karplus-algorithm analysis:
Then using fast Fourier Transform algorithm the frequencies are components are
segregated in spectrum from. Various chords corresponding to specific frequency are
represented on frequency through fast Fourier transform analysis. Components present in
spectrum are F4, B3, D#
4, F4, G#
4, B4. The B and F one octave higher are simply
harmonic overtones of fundamental notes in chord and they don’t affect analysis part.

3. Further Karplus strong algorithm is used for part by part analysis of different frequencies
components. This algorithm allow synthesis each note separately by setting frequency at
with it works. In order to synthesize all notes, we use four Karplus algorithm in parallel
combinations to get complete Tristan chord note effect. Even after playing this together
does not matches original Tristan chord version. This is because only one component of it
is played and timbre of instrument is ignored while doing it. timbre determines that way
in which several frequency component decays with base frequencies. timbre also
determines base frequency of instrument such whether the musical instrument is plucked,
pinched etc. Timbre can be excited to original instrument by electro-mechanical devices.
5. Conclusion:
Tristan chord has its own influence on western musical era particularly in opera domain
of music in its prelude.
The chord appears in all parts of opera but its resolution appears in end.
The Tristan Chord was used to understand fast Fourier transform analysis of a spectrum
of chord through which we could analyze different frequency components in it.
Further Karplus strong algorithm was used to break down different components of notes
in various small parts. these algorithms were connected in parallel to see combine effect
of notes together. We could see that it almost matched original Tristan chord. Due to
timbre effect it’s not exactly similar to original chord. According to author of video we
can reproduce original timbre produced by instrument by analyzing base frequency of it.
We have understood the application of Tristan chord in signal processing and digital
signal processing domain through this video.