Set Theory: An Introduction

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I learned this material from private composition lessons during my undergrad and then from a theory professor who was a student of Dr. Allen Forte at Yale. Additional information has come from private composition lessons during discussions of serial techniques.

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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.

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Music:

- Thomas Little: Dance! #2 in E minor, performed by Rachel Fellows, Michael King, and Bruce Tippette

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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.

[ClassicalNerd]

This video attempts to distill a good chunk of a 20th-century analysis class into about twenty minutes. If there are sufficient questions, I'll try to cover them in a segment of my next _Composition Masterclass_ video.

[TheSutov]

I was honored to have studied with prof. Forte. It is necessary to add three facts to this fine introduction: 1) Set theory offers insight into super/sub set relations within ATONAL and MODAL structures not just 12-tone. (This is how to progress in analysis of larger pieces of music) Master Forte already in the 90ies combined Set theory with schenkerian approach in observing the counterpoint and marginal pitches within atonal or modal texture. (Set theory serves us to ANALYZE and LISTEN with good knowledge of the material) 3) Interval vector information offer an incredible tool for composers: I call it THE GOLDEN RULE of invariant pitch classes under certain transpositions or inversions (two rules, actually). And, the interval vector accounts also for the INVERSIONS of interval classes: m2/M7, M2/m7 etc.(also, the set-table offers a comprehensive overview of ALL possible complementary sets within 12 tones!). I wrote my doctoral thesis (DMA) on Messiaen's harmony (Harmonic Density in Messiaen, Cornell 99', mentor R. Sierra) precisely with set theory tools. In Messiaen's bibliography (I think by Vincent Benitez) my last name Savli is misspelled into Salvi. (dyslexia not allowed here!)

[loganm]

Pure maths students, this isn’t what you were looking for

[redvine]

Fun fact about those all interval tetrachords 0146 and 0137 as they relate to tonality:

If you think of 0146 as the scale degrees of the harmonic minor scale you get #7, 1, 3, and 4 (I.e. G#, A, C, and D). If you think of 0137 as the scale degrees of its relative major scale you get scale degrees 3, 4, 5, and 7 (I.e. E, F, G, and B). That’s all 8 notes of the major/relative harmonic minor scale (aka the “bebop scale”) appearing once and only once.

Just goes to show how colorful the good old fashioned major scale really is.

[sanchopanza]

I'm studying fundamental mathematics and find this very interesting and natural. Related terms might include modular arithmetic, reduced binary quadratic forms and, of course, prime numbers.

[doricdream]

i just recently finished up my general music theory studies, and set theory was by far my favorite part. it also resonates with me greatly because my musical background comes from chiptune and demoscene, which are usually written in programs called trackers. trackers actually make use hex values, and as a result one actually ends up thinking about and applying intervals in terms of set theory. the music is vastly more tonal in these circles so its not serial by any means, but its a fun parallel that made learning set theory enjoyable for me.

[aakashchakrabarty]

Hey this is the most comprehensive tutorial on set theory.
I would also be interested in a video where you show your book collection.😆

[edgarmatias]

Really great summary. I learned this stuff 30 years ago, and did some work building on it at the time. Agree with you that the IC vector is the most useful part of it all — especially ic5 and ic6, since all commonly used scales can be derived from some combination of ic5 and ic6 intervals. Love your channel!

[theodoremann]

I was at Eastman when Howard Hanson wrote the book that supposedly initiated interest in this approach. Although I majored in music theory, I didn't understand it then, and I don't understand it now. However, I have no doubt at all that it's a legitimate and significant contribution to music analysis.

[jareddavismusic]

Great video and presentation! You have compressed a lot of info into a short digestible and entertaining clip! Bravo 👏

[pawncube]

I loved it! The explanation and the concept. I remember I always wanted to analyse music using something like this

5:32 Programmers will be pleased. The only thing is using A and B instead of T and E

18:46 I remember 12tones did a video on this. He explained basically all of this without using any of the terminology or mentioning set theory

[neocleouscomposer]

Great video! Would love to see a similar explanation of Schenkerian analysis!

[musicalintentions]

Thank you so much for sharing this. It has helped a lot!

[Owofbfbajfbsnsn]

Wow! I love how humans can "feel" these mathematical intervals as different sensations. I wonder what else we sense with our bodies that we have yet to explain

[RobertWildling]

Great to find a video about set theory here! In Austria, were I am from, and maybe even in Europe, set theory is not accepted very well. The most common statement is "Set theory looks at music as if it was Switzerland without mountains." – BTW, there is **only one set** that has a different number on each interval class position. Who knows which one that is?

[marcmosteirin]

I think there's an error in the graphic at 8:18 - IC2 should say m7, not m6?

[ToneCanyon]

Im still confused, but this is the best one ive seen on the subject! I gotta bust out some manuscript paper!, !

[rafaellazo]

Love your videos bro, you inspire me! thank you for bringing classical music closer to people!

[grayson]

Hi there, I was wondering if you could do a biography on the composer Thomas Little?

[amorpheousstone]

Hi, Great video! Would you recommend George Perle's book 'Serial Composition and Atonality' ? Many Thanks.