Riemannian Transformations: Part 1 Schillinger Caught in the Tonnetz
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- Опубліковано 5 чер 2024
- An essential aspect of Neo-Riemannian Theory is chord transformation. This tutorial presents the 3 elementary Riemannian transformations (Parallel, Relative and Leading-tone exchange) and the compound transformations (PL, LP, PR, RP). Each of these is shown for major and minor triads in the Tonnetz diagram and staff notation. Transformations are interpreted in terms of the equivalent Schillinger Symmetric Harmony System Root Cycle, and demonstrated with a very short musical application example. Companion booklet and blank Tonnetz diagram template for your chord progression at
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Contents:
00:00 What this video is about
00:25 Section 1. Introduction, Neo-Riemannian Theory, Tonnetz, Schillinger Root Cycles
03:18 Section 2. Elementary Riemannian Transformations
04:16 Section 2.1. P-transformation, major triad- parallel minor
06:21 Section 2.2. R-transformation, major triad - relative minor
07:43 Section 2.3. L-transformation, major triad - mediant minor
08:52 Section 2.4. P', R' and L' inverse transformations, minor - major
10:41 Diatonic root cycles
11:16 Section 3. Compound Riemannian Transformations, chromatic mediants, film music narrative
13:48 Section 3.1. PL-transformation, C to Ab
15:06 Section 3.2. PR-transformation, C-Eb
16:09 Section 3.3. RP-transformation, C-A
17:20 Section 3.4. LP-transformation, C-E
18:20 Section 3.5. LP-trensformation, Cm-Abm
19:30 Section 3.6. RP-transformation, Cm-Ebm
20:53 Section 3.7. PR-transformation, Cm-Am
22:09 Section 3.8. PL-transformation, Cm-Em
23:20 Section 3.9. Triad combinations and symmetric scales
25:47 Summary and conclusion
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#NeoRiemannianTheory #TriadTransformations #SchillingerSystemOfMusicalComposition
Holy F... cant believe I'm finally understanding all of these concepts took me around 10 years as a hobby musician to get to this point lol thank you so much
@bk8biokiller8 You're welcome; glad my videos were helpful in understanding these NRT aspects. Maybe you'll discover more useful content in the other episodes.
Muuuuuuuuuuuuchas graciiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaas
Incredibly underrated video.
@whiskyngeets Thank you for the kind words. From the YT analytics I know this video has the most views and likes on this channel. So I assume my attempt at showing the equivalence between Riemannian Transformations and the Schillinger Systems of Harmony has found some appreciation. Currently underrated on a global scale, yes that may be the case. Let's wait and see.
I'd say criminally underrated.
Outstanding as always. Thank you, Frans!
Thank you for the continual support and encouragement!
Excellent video! I’m grateful for your in depth analysis as well as the terrific examples.
@omnaraiya Thanks for the positive feedback, you're welcome. I assume you also watched the other episodes in this series, and found the link in the description to the companion booklet on my website with all diagrams and reduced score examples.
Clear, exhaustive tutorial! Thanks!
@mauro marion bizzotto You're welcome. Hope you appreciate the other episodes in this series equally well. Thanks for the feedback.
GRACIAS. MUY BUEN VIDEO FELICITACIONES.
💯💯💯
@Yimy Robles. Sorry, somehow missed or forget to respond to this comment. Thank you for the kind words.
love it!!
@udomatthiasdrums5322 This turned out to be a tutorial subject that received quite a bit of viewer interest. Glad you liked it. Thanks for the comment.
Merci for this. This is out of my pay grade, but you gave me some hints on where to start.
@Lawrence Taylor Best of luck with the learning process. If you need help don't hesitate to ask.
I really appreciate your videos!! Thanks
@Tristan Paxton, You're welcome. Glad you like these tutorials.
Great video! Thank you!
You're welcome! Sorry for the late reply; YT does not signal all comments, so I may miss some of the feedback.
Thank you for this video. Impressive.
You're welcome. Hopefully you will enjoy watching other content on this channel.
Thank you for discussing Schillinger
@el ba I hope I succeeded to connect aspects from Neo-Riemannian Theory to corresponding elements in the Schillinger System of Musical Composition. Thanks for your comment!
@@FransAbsil Yes. I see you have some other Schillinger videos. I look forward to watching them in the future
Great video, and excellent examples.
The latest in a series of very pragmatic applications of what for some could be abstract concepts buried in obtuse academic language.
FYI: Another reference to look for and add to your next video is Frank Lehmans "Hollywood Harmony". Between what you are doing in this specific video and the first 10 or so pages of section 3 of that book, there is an excellent breakdown of the neo-riemannian system and what this very interesting tool can do. He then proceeds to many deep theoretical dives into cinematic examples using this "Harmonic toolkit" that are worth looking at.
Thanks for pointing out the Lehman book. I had read his 2018 Music Analysis journal paper on Film-as-Concert-Music. I will order the book.
This is so amazing thank you so much! :)
@Mary You're welcome. Hope you'll find the other episodes in this series equally useful.
Wonderful. Isn’t it interesting how nineteenth-century performers created systems to understand complex musical structures as aids to their performance-Schenkerian graphic analysis, Riemann’s agogic theories, etc.-when they have evolved, through theory and analysis specialists, to be understood today strictly as ways to improve compositional technique? Most performers’ eyes glaze over if required to study systems originally designed by their predecessors as guides to their own craft!
@mylesjordan9970 If I may add: the development of music theory in general lags behind the application phase by a number of years. First there is the creative composer (risk-taking, full of surprise), then later the musicologists start to identify the building blocks and general principles. The exception is dodecaphony where 'rules' came before or at the same time music was composed (and we all know how well that idiom is received). For me studying music theory speeds up the learning process as I can skip the music analysis phase and start experimenting with the principles right away. Thank you for your observations!
Well put-and true also of performance. Haydn wrote dozens of string quartets at Eszterház, but not a single one appears in the historical record as having being performed there. Why? The art of string quartet performance hadn’t yet begun to evolve, so they actually sounded horrific. He actually ends one with a fugue, then appends to the manuscript “Sic amicus amici fugit”-thus do friends flee from one another!
@mylesjordan9970 Thanks for sharing your views on the Haydn string quartet writing and performance. Didn't know about the fuga annotation. And wouldn't we all want to hear a recording from the Classical and Romantic Music era? And then, foremost, some JS Bach live improvisations! Alas, some great art predates technology.
@@FransAbsil Can you believe we have Immanuel Kant to thank for killing off improvisation in classical music? Because there were no recordings yet, Kant insisted that all music was without form, couldn’t be contemplated like a Greek vase for its proportions, so it was therefore worth less “than wall papers.” E.T.A. Hoffmann had to show him musical manuscripts and explain Haydn’s plan: exposition, development, recapitulation, so formal aspects were clear to him. He then agreed that music was an art-but only in its printed form. That’s why, since the early 19th century, all “serious” study of music has been only in the contemplation of its written form, taking primacy over its sound-a development Bach would have found completely absurd.
@mylesjordan9970 Surely, (German 18th-19th century) philosophers did make many outspoken statements on art; we are entering the domain of "Goethe hat gesagt ...". Dangerous terrain, at times. The value of the score is obvious for studying many musical aspects, most of all form and harmony. Predicting the overall sound and thus the emotional response is trickier though. I remember a statement by conductor Bernard Haitink who admitted that although he studied scores in great detail, he was unable to grasp the full orchestral timbre and sectional balance, until hearing the music during rehearsal. That's where he instantiated the musical message. You must be doing a lot of meta-musical reading. Thanks for your contribution.
Wonderful stuff. Got to find time to practice this stuff
Thanks for the comment. Don't hurry, this video will remain online unless UA-cam has different plans. Hopefully it is sufficiently practical to get you started on this subject.
@@FransAbsil I have a music degree and feel comfortable with theory, counterpoint, and am learning orchestration. Where should I start in terms of Riemannian Transformation? Is there a current composition book to study?
@Jonathan Parham In answer to your question, may I suggest the following references?:
- If you would like to compose with triads using the Neo-Riemannian Theory (NRT) principles download the Ms Thesis by Laura Felicity Mason that I mention in the video (2:17). I am sure the Lehman book on Hollywood Harmony suggested by Erik Hiser will be an excellent textbook.
- For a more modern style (extended chords, dissonance handling, etc) read Ludmila Ulehla Contemporary Harmony, Romanticism through the Twelve-Tone Row (I used this book for my series on Chord Tension Level control) or Twentieth Century Harmony by Vincent Persichetti (see my tutorial on modal harmonies. Recently I discovered that this book is an Adam Neely favourite).
- Or go for the 2 volumes of the Schillinger System of Musical Composition, with a wealth of generalizations and techniques in a wide range of styles. NRT is not mentioned explicitly, but there are many analogies in his diatonic and symmetric harmony system root cycle approach.
Probably you know most of these sources already. I just listed the books in my library that I find useful 'starters' for musicians with a good music theory background. Hope this helps.
@@FransAbsilThanks. Only a couple of them I've heard of. I like what I'm hearing in your mock ups in the video looking for written exercises. Thanks
Such great content, I appreciate your time and efforts on such an endevour.
You're welcome. I take inspiration from Sisyphus, rolling my personal rock up a steep slope ;-)
@@FransAbsil :D I know that feeling lol
It seems like you can spend a whole lifetime studying music , with an infinite amount ahead. Yet somehow its the journey that's rewarding more than a destination.
I'm always looking for more polytonal and atonal language info, as well as polymeter and polyrhythm simply because its a little more hard to come by .
But I am curious as your feelings about a intermediate difficulty music vocabulary like Charlie Parker?
Thank you so much Frans! I learnt so much new stuff! Could you think about doing a series of videos about orchestration? It would be very very helpful. And I really enjoy your orchestrations here
Thanks for the positive feedback; always pleased to hear that the effort is being appreciated. Indeed, orchestration is not explicitly covered in the videos in this playlist, that is about composition techniques. There is some coverage of orchestration for jazz big band, studio orchestra and wind/concert bands in my Arranging by Examples e-book. Be aware that the demos created with sample libraries and virtual instruments are not representative of a real acoustic recording, since the DAW mixing process will modify the (tonal) balance. As a book I do recommend Blatter, Instrumentation and Orchestration, Schirmer Books, Thomson Learning, 1997. I use that as a handbook, and have many others in my library. Above all, study classical music scores and listen to recordings or live performances (not possible these days, though). Try asking yourself: how would the sound change in case of a different instrumentation, a different voicing, what is typical for this composer, etc? Each page of a Ravel score is a treasure of information (my copies are full of annotations, valve position, fingering and voicing diagrams, range/register markings, mostly in awe). Hope this helps.
At roughly 14:06 (§3.1) you've played Cm - AbM, an L transformation vs what is the intended demonstration CM P Cm L AbM. You may wish to amend that as it will likely confuse others with good relative pitch skills.
@Mark Hoover You're absolutely right about the audio error in the CM-AbM transformation. I'll go and whip myself for this quality control failure. At the final tutorial production stage I do discover errors, some of which are easy to repair. However sometimes I am simply too busy fighting ScreenFlow and miss a few. When PayPal donations get to a level where I can afford a senior reviewer plus a fresh pair of ears before uploading, you've got the job! Thanks.
Great video Frans!! Only one detail i noticed: at 7:58 in the audio example sounds a Cm instead of a C major triad.
@Fabio Zurita thanks for this detailed observation. You're right and there's been reported another blunder at 14:06. Sorry, while fighting software hurdles there are concentration lapses, when creating these multimedia projects. My sincere apologies.
Doctor Absil, thank you for your excellent lecture, and may I know whether the Tonnetz diagram is a picture or an exe?
@Cloud Dai thank you for the feedback. I assume you are referring to the companion document; it is a 28 pages PDF file with text, diagrams and score examples from the 4-part tutorial series on Riemannian Transformations. At the end there are two blank Tonnetz template diagrams (triangles and node points), the first of which is centered around C-Cm. The Tonnetz diagrams are NOT an interactive program; they have been designed for pencil drawing. The document is part of a book series (currently, Nov 2022, 18 documents with more than 300 pages in total), that is available to my Patrons. Does this answer the question?
@@FransAbsil Sure! Thank you for replying to me.
@Cloud Dai I am responding to your more recent report (Nov 7, 2022) about comments not becoming visible. This is indeed the case and has also been happening with others occasionally. They show up as notifications when I sign in to UA-cam, but neither do they become regular comments, nor can I reply. I tried to find reasons for this behavior, and did online searches, but there seems not to be a reason for or solution to this problem. I just happens randomly and I apologize for the inconvenience. I do welcome comments and discussion, and do my best to answer all questions.
Tried to do sensefully program this on my synth (#3 on my channel). Close enough. ;D
@isosthenie Just watched your video. Most interesting, generating the Neo-Riemannian transformations in the Tonnetz with a rack module! Almost makes the composer superfluous. How did you control the timing of these transitions (random number multiples of a smallest duration unit)?
@@FransAbsil Good question! Thanks for listening! :) I've used an euclidian pattern I programmed in the digital module on the right called "Pamela's New Workout". It allows for complex, even random and very well timed LFOs or clocks and gates (long and short specific control voltage outputs in controlled patterns). This I used to control the dark module with the triangular shape on the screen, called Ornament & Crime (this one I built myself, so it looks a little different from others). It has two rows of inputs and one row of outputs. The upper row defines when a new tone in form of a specific control voltage is put out in the lower row and when a transformation takes place. The middle row defines what tone should be put out (high, low, key, interval) and which transformation is going to take place. These signals I send to the sound sources, 2 analogue and 1 digital voltage controlled oscillator (VCO). In the Ornament & Crime module, as it is digital, I made some specific settings for this to sound alright. Of course you need to tune the VCOs, filter them (for example the fading in/out is done with a so called low pass gate controlled by Pam's) etc. :D For additional randomness, I patched a so called sample and hold control voltage into an attenuverter, which changed the polarity of two LFOs hitting the Ornament & Crime. I could go into more details, but this is already too much to take in I guess. The machine takes over some parts of the creative process, it is a dispositive in a certain way, but I have to know how to use it an accept to be surprised by it nonetheless. ;) The composer is also the listener and the audience of the machine! That is the beauty of modular synthesizers. And if you want a new instrument with different "presets" and signal paths, just plug all the cables and patch anew.
@isosthenie Many thanks for the detailed answer. I will revisit your page and inspect the video with your written information; if I have further questions/comments I will write them there.
I’m still trying to fully understand !! What does SM and R4i means ?
@Dante Gh Thanks for asking. Sorry to hear that the notation is not clear. This video is about triad transformations that yield non-diatonic pairwise combinations. I use the symbol S for a chord Structure (with unspecified root pitch): S5 is a triad {1,3,5}. Riemannian transformations in this episode use major triads SM and minor triads Sm. The notation R4i indicates a Root movement type. In diatonic harmony we find the root moving by multiples of 3rds: R3 is a descending minor/major 3rd (e.g., C to Am), R5 the fifth and R7 means that the root moves a diatonic 7th down (or, equivalently an ascending 2nd). In order to obtain non-diatonic triad pairs, also called chromatic mediants, we move by either 3 or 4 semitones up/down. So R4i means that the root descends by 4 semitones, a major 3rd (e.g., Cm-Abm, a non-diatonic combination). May I suggest the videos on nomenclature in Schillinger diatonic/symmetric harmony? Hopefully this answers the question.
I love the internet
ok. 21.14
@Kasper Westberg, sorry, but I failed to decipher this message. How may I help?
Hello. It was actually to remind me which part i understood. This requires a good level of knowledge in harmonic analysis. Thank you for posting anyway!