Uploaded January 2022 | Updated September 2026, 2 weeks ago
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0:00 : Who was Hugo Riemann?
1:38 : What's This Theory Trying to Do?
3:50 : Basic Neo-Riemannian Transformations (P, R, and L)
6:52 : Some Secondary Transformations (N, S, and H)
8:27 : Uniform Triadic Transformations (UTTs)
12:15 : Why Isn't This Taught?
📚 Selected Further Reading:
"Uniform Triadic Transformations" by Julian Hook (Journal of Music Theory, 46:1/2, Spring–Autumn 2022)
"Alfred Schnittke's Triadic Practice" by Christopher Segall (Journal of Music Theory, 61:2, Oct. 2017)
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Classical Nerd is a video series covering music history, theoretical concepts, and techniques, hosted by composer, pianist, and music history aficionado Thomas Little.
----------
Music:
- Thomas Little: Dance! #2, performed by Rachel Fellows, Michael King, and Bruce Tippette
- Thomas Little: Invasion of the Minor Seconds for Pierrot Ensemble and Percussion
----------
Contact Information:
Questions and comments can be directed to:
nerdofclassical [at] gmail.com
Facebook:
facebook.com/classicalnerd
Instagram:
instagram.com/the_classical_nerd
----------
All images and audio in this video are for educational purposes only and are not intended as copyright infringement. If you have a copyright concern, please contact me using the above information.
🎶 Support the channel:
🎼 lentovivace.bandcamp.com
🎼 patreon.com/classicalnerd
0:00 : Who was Hugo Riemann?
1:38 : What's This Theory Trying to Do?
3:50 : Basic Neo-Riemannian Transformations (P, R, and L)
6:52 : Some Secondary Transformations (N, S, and H)
8:27 : Uniform Triadic Transformations (UTTs)
12:15 : Why Isn't This Taught?
📚 Selected Further Reading:
"Uniform Triadic Transformations" by Julian Hook (Journal of Music Theory, 46:1/2, Spring–Autumn 2022)
"Alfred Schnittke's Triadic Practice" by Christopher Segall (Journal of Music Theory, 61:2, Oct. 2017)
----------
Classical Nerd is a video series covering music history, theoretical concepts, and techniques, hosted by composer, pianist, and music history aficionado Thomas Little.
----------
Music:
- Thomas Little: Dance! #2, performed by Rachel Fellows, Michael King, and Bruce Tippette
- Thomas Little: Invasion of the Minor Seconds for Pierrot Ensemble and Percussion
----------
Contact Information:
Questions and comments can be directed to:
nerdofclassical [at] gmail.com
Facebook:
facebook.com/classicalnerd
Instagram:
instagram.com/the_classical_nerd
----------
All images and audio in this video are for educational purposes only and are not intended as copyright infringement. If you have a copyright concern, please contact me using the above information.
![Robert Carl on Postmodernism, Spectralism, Studying with Xenakis, and More
🎶 Support the channel: http://www.patreon.com/classicalnerd
Visit Dr. Carls web site at http://www.robertcarlcomposer.com
0:00 Introduction
0:54 Why Xenakis isn’t postmodern
3:15 Postmodernism as movement vs. stance
4:18 How Xenakis “blew [Carl’s] mind”
5:18 Postmodernism as restructuring
7:29 Having “outsiders” as teachers
11:30 Betsy Jolas and French “cultural self-awareness”
13:02 Spectralism and serialism in 1980s Paris
15:04 How studying history impacted Carl’s music
18:46 Non-teleological music (Zimmermann, Stockhausen, Oliveros)
21:15 Carl’s harmonic approach
23:44 Overtones as a structural device
25:21 Cowell’s “unified field theory”
27:00 “From the Ground Up” (2002)
30:18 When overtones meet equal temperament
31:31 “Changing My Spots” (2005)
37:12 Choosing an intonation system
39:08 “Night Garden” (2012–13)
41:58 The “harmonic ladder”
46:05 Modulation between harmonic series
47:46 Fixed and frozen register
48:30 Composers should be theorists, too
51:00 Transcendentalism vs. humanism
54:25 Young composers’ diverse inspiration
55:53 How artificial intelligence will impact music industry
58:06 Concert music’s appeal
59:52 Values in popular music
1:01:07 Recent work
1:02:21 Quasi-improvised “Infinity Avenue” (2017)
1:03:19 Symphony No. 7 “Infinity Avenue” (2020)
1:04:09 “Infinity Avenue” as a continuing project
1:05:16 Only writing what’s necessary
1:05:39 Conclusion
📚 Sources/further reading:
Music Composition in the 21st Century: A Practical Guide for the New Common Practice by Robert Carl (Bloomsbury, 2020)
Temporal and Harmonic Concerns in the Music of Robert Carl by Daniel Morel (MM thesis, UMKC, 2018): https://mospace.umsystem.edu/xmlui/handle/10355/64180
Music:
Bernd Alois Zimmermann: Stille und Umkehr (1970), performed by the Frankfurt Radio Symphony conducted by Hans Zender: https://www.youtube.com/watch?v=UeteD0zHMqo
Robert Carl: From the Ground Up (2002), performed by John McDonald: https://www.youtube.com/watch?v=Zpe2w8pd8jo
Robert Carl: Changing My Spots (2005), premiere recording
Robert Carl: Night Garden (2012–13)
Robert Carl: Infinity Avenue, quasi-improvised version (2017), performed by Henry Birdsey, Adam Buffington, Robert Carl, Zach Rowden, Trevor Saint, and Matt Sargent: https://www.youtube.com/watch?v=HXw-InMYbKA
Robert Carl: Symphony No. 7 Infinity Avenue (2020), performed by Foot in the Door conducted by Edward Cumming: https://www.youtube.com/watch?v=1X2eX2z5r5U
Robert Carl: White Heron (2012), performed by the Boston Modern Orchestra Project conducted by Gil Rose: https://www.youtube.com/watch?v=NoDfLsfaiAA
Contact Information:
Questions and comments can be directed to:
nerdofclassical [at] gmail.com
Facebook:
https://www.facebook.com/classicalnerd/
Instagram:
https://www.instagram.com/the_classical_nerd/
All images and audio in this video are for educational purposes only and are not intended as copyright infringement. If you have a copyright concern, please contact me using the above information. Robert Carl on Postmodernism, Spectralism, Studying with Xenakis, and More](https://i.ytimg.com/vi/TuVNxkV7ULA/mqdefault.jpg)
![Alan Belkin on Salience, David Diamond, and More
Thanks again to Dr. Belkin for his time! Check him out at https://alanbelkinmusic.com/ or his YouTube channel at https://www.youtube.com/channel/UCUQ0TcIbY_VEk_KC406pRpg
Classical Nerd is a video series covering music history, theoretical concepts, and techniques, hosted by composer, pianist, and music history aficionado Thomas Little.
Music:
- Thomas Little: Dance! #2 in E minor, performed by Rachel Fellows, Michael King, and Bruce Tippette
Contact Information:
Questions and comments can be directed to:
nerdofclassical [at] gmail.com
Facebook:
https://www.facebook.com/classicalnerd/
Instagram:
https://www.instagram.com/the_classical_nerd/
All images and audio in this video are for educational purposes only and are not intended as copyright infringement. If you have a copyright concern, please contact me using the above information. Alan Belkin on Salience, David Diamond, and More](https://i.ytimg.com/vi/UFUjfPgTgJk/mqdefault.jpg)
![Great Composers: Giacinto Scelsi
A look at the final Count of Ayala Valva.
This was a viewer request from YouTuber BASSOONISTFROMHELL. Please note that requests for future videos are on hold for the time being, given the extraordinary number of requests Ive already received. See the current request queue at http://lentovivace.com/requestqueue.html.
Classical Nerd is a weekly video series covering music history, theoretical concepts, and techniques, hosted by composer, pianist, and music history aficionado Thomas Little.
Music:
- Giacinto Scelsi: Four Pieces on a Single Note, performed by the Vienna Radio Symphony Orchestra conducted by Peter Rundel [original upload: MfTjz6emd7c]
- Thomas Little: Dance! #2 in E minor, Op. 1 No. 2, performed by Rachel Fellows, Michael King, and Bruce Tippette
Contact Information:
Questions and comments can be directed to:
nerdofclassical [at] gmail.com
Tumblr:
classical-nerd.tumblr.com
All images and audio in this video are for educational purposes only and are not intended as copyright infringement. If you have a copyright concern, please contact me using the above information. Great Composers: Giacinto Scelsi](https://i.ytimg.com/vi/UX_8DJeaGaU/mqdefault.jpg)
![Tuning: An Introduction
🎶 Support the channel: http://www.patreon.com/classicalnerd
📚 Sources/further reading:
Info on quarter-comma meantone and Werkmeister III were sourced from tables on Kyle Ganns web site [https://www.kylegann.com/histune.html], which in turn comes from Tuning: Containing the Perfection of Eighteenth-Century Temperament, the Lost Art of Nineteenth-Century Temperament, and the Science of Equal Temperament by Owen Jorgensen (Michigan State University Press, 1991).
The video featuring split sharps may be found at https://www.youtube.com/watch?v=7GhAuZH6phs
Additionally, I highly recommend the book How Equal Temperament Ruined Harmony (and Why You Should Care) by Ross W. Duffin (Norton, 2007).
Music:
- Thomas Little: Dance! #2, performed by Rachel Fellows, Michael King, and Bruce Tippette
Contact Information:
Questions and comments can be directed to:
nerdofclassical [at] gmail.com
Facebook:
https://www.facebook.com/classicalnerd/
Instagram:
https://www.instagram.com/the_classical_nerd/
All images and audio in this video are for educational purposes only and are not intended as copyright infringement. If you have a copyright concern, please contact me using the above information. Tuning: An Introduction](https://i.ytimg.com/vi/Uikxrhl5w2E/mqdefault.jpg)
![Rethinking Dissonance (A Theory of Harmonic Symmetry)
🎶 Support the channel:
🎼 https://lentovivace.bandcamp.com
🎼 https://www.patreon.com/classicalnerd
Classical Nerd is a video series covering music history, theoretical concepts, and techniques, hosted by composer, pianist, and music history aficionado Thomas Little.
Music:
- Thomas Little: Dance! #2 in E minor, performed by Rachel Fellows, Michael King, and Bruce Tippette
Contact Information:
Questions and comments can be directed to:
nerdofclassical [at] gmail.com
Tumblr:
https://classical-nerd.tumblr.com
Facebook:
https://www.facebook.com/classicalnerd/
Instagram:
https://www.instagram.com/the_classical_nerd/
All images and audio in this video are for educational purposes only and are not intended as copyright infringement. If you have a copyright concern, please contact me using the above information. Rethinking Dissonance (A Theory of Harmonic Symmetry)](https://i.ytimg.com/vi/VARBs7_K2z8/mqdefault.jpg)
![Great Composers: Imogen Holst
A look at the second-most-famous Holst.
This was a viewer request from YouTuber classicalmusic26. If youve got a question or request for a future video, leave a comment, shoot me a message through YouTube, or use the email/Tumblr links below.
Classical Nerd is a weekly video series covering music history, theoretical concepts, and techniques, hosted by composer, pianist, and music history aficionado Thomas Little.
Music:
- Imogen Holst: “Phantasy” Quartet, performed by the London Conchord Ensemble [original upload: a5wokRknTRE]
- Thomas Little: Dance! #2 in E minor, Op. 1 No. 2, performed by Rachel Fellows, Michael King, and Bruce Tippette
Contact Information:
Questions and comments can be directed to:
nerdofclassical [at] gmail.com
Tumblr:
classical-nerd.tumblr.com
All images and audio in this video are for educational purposes only and are not intended as copyright infringement. If you have a copyright concern, please contact me using the above information. Great Composers: Imogen Holst](https://i.ytimg.com/vi/VHcMU5D41TI/mqdefault.jpg)
![Musical Sudoku: Serialisms History and Techniques
Math in music? Its more likely than you think.
This was a viewer request from YouTuber Quinn Roberts. See the current request queue at http://lentovivace.com/requestqueue.html.
Classical Nerd is a weekly video series covering music history, theoretical concepts, and techniques, hosted by composer, pianist, and music history aficionado Thomas Little.
Music:
- Arnold Schoenberg: Piano Suite, Op. 25, performed by Peter Bradley-Fulgoni and available on IMSLP: https://tinyurl.com/yarg6ygr
- Thomas Little: Dance! #2 in E minor, Op. 1 No. 2, performed by Rachel Fellows, Michael King, and Bruce Tippette
Contact Information:
Questions and comments can be directed to:
nerdofclassical [at] gmail.com
Tumblr:
classical-nerd.tumblr.com
All images and audio in this video are for educational purposes only and are not intended as copyright infringement. If you have a copyright concern, please contact me using the above information. Musical Sudoku: Serialisms History and Techniques](https://i.ytimg.com/vi/VhA3W3PAb5g/mqdefault.jpg)
![Confronting Stillness: The Life and Works of Morton Feldman
🎶 Support the channel:
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📚 Sources/further reading:
http://www.cnvill.net/mfhall.pdf
http://nilsvigeland.com/writings-interviews/morton-feldman-ii
http://www.cnvill.net/mf-interview-with-Nils-Vigeland.pdf
https://www.researchgate.net/publication/242758215_Morton_Feldman_and_Abstract_Expressionism_Time_and_sound_construction_in_his_piano_miniatures_of_the_1950s_and_1960s
https://publications.lakeforest.edu/cgi/viewcontent.cgi?article=1007&context=seniortheses
http://rohandrape.net/ut/rttcc-text/Hanninen2004a.pdf
https://www.youtube.com/watch?v=BKyW2Ua_9YY
http://www.good-music-guide.com/community/index.php/topic,28007.20.html
https://fsu.digital.flvc.org/islandora/object/fsu:175589/datastream/PDF/view
https://portal.rcs.ac.uk/mdonohue/wp-content/uploads/sites/261/2017/02/Vertical_thoughts-morton-feldman.pdf
http://www.ex-tempore.org/mpaccione/MPACCIONE.htm
This was requested by Ryan Edwards, Chlamydius Spearmint, Joe Rhodes, Harrison Koley, Stavroula Mi, and Zachary Detrick. See all requests at http://www.lentovivace.com/classicalnerd.html.
Classical Nerd is a video series covering music history, theoretical concepts, and techniques, hosted by composer, pianist, and music history aficionado Thomas Little.
Music:
- Thomas Little: Dance! #2 in E minor, performed by Rachel Fellows, Michael King, and Bruce Tippette
- Morton Feldman: Coptic Light, performed by the Royal Concertgebouw Orchestra conducted by Peter Eötvös [original upload: PgS37X4P2hM]
- Morton Feldman: The King of Denmark, performed by Colin Frank [original upload: rZpa0WWAK5c]
- Morton Feldman: Rothko Chapel, performed by the Ensemble Intercontemporain and Les Cris de Paris conducted by Gregor A. Mayrhofer [original upload: ks_mZJR-lAQ]
- Morton Feldman: Between Categories, performed by Frank Wolff, Wilhelm Schulz, Christoph Keller, Morton Feldman, Hans-Peter Friedrich, Ulf Klausenitzer, Burkhard Wissemann, and Michael Dietz [original upload: XUnT3FOg0tI]
- Morton Feldman: Piano and Orchestra, performed by John Tilbury and the BBC Scottish Symphony Orchestra [original upload: r_gzPtMuKRw]
- Darude: Sandstorm, clip originally from Wikipedia [http://tinyurl.com/y2cch3md]
Footage:
- Morton Feldman, Ursula Oppens, and Elliott Carter in conversation: https://www.youtube.com/watch?v=DZzEnuUJEsA
Contact Information:
Questions and comments can be directed to:
nerdofclassical [at] gmail.com
Tumblr:
classical-nerd.tumblr.com
Facebook:
https://www.facebook.com/classicalnerd/
Instagram:
https://www.instagram.com/the_classical_nerd/
All images and audio in this video are for educational purposes only and are not intended as copyright infringement. If you have a copyright concern, please contact me using the above information. Confronting Stillness: The Life and Works of Morton Feldman](https://i.ytimg.com/vi/VpL80kd9qcY/mqdefault.jpg)

![Great Composers: Edgard Varèse
A look at the stratospheric colossus of sound.
This was a request from Tyson Davis. See all current requests at http://www.lentovivace.com/requestqueue.html
Classical Nerd is a weekly video series covering music history, theoretical concepts, and techniques, hosted by composer, pianist, and music history aficionado Thomas Little.
Music:
- Edgard Varèse: Amériques, performed by the Royal Concertgebouw Orchestra conducted by Riccardo Chailly [original upload: 8zXaEwWFbnA]
- Thomas Little: Dance! #2 in E minor, Op. 1 No. 2, performed by Rachel Fellows, Michael King, and Bruce Tippette
Contact Information:
Questions and comments can be directed to:
nerdofclassical [at] gmail.com
Tumblr:
classical-nerd.tumblr.com
All images and audio in this video are for educational purposes only and are not intended as copyright infringement. If you have a copyright concern, please contact me using the above information. Great Composers: Edgard Varèse](https://i.ytimg.com/vi/WnJNTNg9IF0/mqdefault.jpg)
![Why Viola Jokes?
🎶 Support the channel:
🎼 https://lentovivace.bandcamp.com
🎼 https://www.patreon.com/classicalnerd
Why one instrument gets a bad rap.
Classical Nerd is a weekly video series covering music history, theoretical concepts, and techniques, hosted by composer, pianist, and music history aficionado Thomas Little.
Music:
- Thomas Little: Gossamer Limerence, Op. 9b, performed by Wooram Kwon and Thomas Little
- Thomas Little: Dance! #2 in E minor, Op. 1 No. 2, performed by Rachel Fellows, Michael King, and Bruce Tippette
Contact Information:
Questions and comments can be directed to:
nerdofclassical [at] gmail.com
Tumblr:
classical-nerd.tumblr.com
All images and audio in this video are for educational purposes only and are not intended as copyright infringement. If you have a copyright concern, please contact me using the above information. Why Viola Jokes?](https://i.ytimg.com/vi/WtmlybCRplY/mqdefault.jpg)