I am a music theorist (PhD Louisiana State University, 2019) who uploads educational videos on topics of music composition, music theory, and music analysis.
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Great question. Fux was writing in a time before the modern solfege syllables were invented. In his time, the syllables only covered a six-note transposable hexachord: Do (or Ut), Re, Mi, Fa, Sol, and La. So the tritone between F and B, for instance, must be sung with syllables from two different hexachords. F would be Fa in the hexachord built on C (the natural hexachord) and B would be Mi in the hexachord built on G (the hard hexachord).
Thank you, that is a very flattering thing to say. Of course I still have lots of room to improve the content and the presentation. I cannot recommend your channel highly enough to anyone who is interested in my videos. The stuff you put out is excellent.
I think that video lectures are very difficult pedagogically. You are presenting with only the information you have taken from theory books. You should be very explanatory for beginners. If you are preparing these lectures for those who know and advanced students, why should they follow these lectures if they know? You should be able to convey something to people rather than so much content. Thanks for our efforts anyway.!
I come from Taneyev's lineage. Be baffled by the 100 or so compositions I've done on my channel. Be baffled chiefly by how bad they are, considering I apparently come from Taneyev's (and Tchaikovsky's and Beethoven's) lineage. Tchaikovsky was apparently scared of Taneyev. You can see from this video how frighteningly obscure Taneyev's treatment of music was. No wonder he was.
Thanks for the video ive always considered schenkerian analysis to be astrology for music theory not as something trying to solve the "discrepancy problem"
In 20:00 there is a fourth on the third measure (beetwen A and D) which is allowed in upper voices but, is it still a consonance when the lower voices aren't being played at the same time, leaving those two upper voices alone? And, is it the same rule for piano and strings, where, in the second case, the lower notes keep sounding, unlike with piano?
I have been needing some help with triple counterpoint, so you making a video about it is great!!!. Regarding the last video, you could make one about the melodic rules stated by Jeppesen, i feel he really cared about melodic rules, even more than Gladstone or Schubert, so a full rundown of that text would be awesome. 💟
Absolutely fantastic work. This is not an easy book to summarise and make digestible in video form, even for a non-lay audience. Excellently presented, and it must have been a lot of work making all the example transcriptions from the book. I really think this could be one of the most important video series on music theory side in the future in terms of how many people will get to encounter Taneyev'v theories for the first time, and hopefully read his books, who wouldn't have even heard of him otherwise.
",,,Rachmaninov described him as 'the personification of truth on Earth' ... Once, distressed by Rachmaninov's laziness when it came to studying the rudiments of composition, Taneyev hit on a novel idea. He sent his cook to Rachmaninov's house with a musical problem, and strict instructions not to return until Rachmaninov had solved it. Rachmaninov, knowing that Taneyev could not have his dinner until the cook went home, and begged by the servants in his own house to get rid of their unwanted visitor, was obliged to do the work required, and to do it quickly. Taneyev was prepared even to wait for his food if necessary, such was his inexhaustible devotion to his pupils."
I have made a PDF of all the vertical shifting indices possible in Taneyev's notation: drive.google.com/file/d/1wMZ6e_MMRJqmMDs09E8H6jkLnqInhW7M/view?usp=sharing The intervals are labelled according to his cardinal numbering system (i.e. scale steps); numbers with squares around them are intervals that are consonant if one admits the consonant 4th; the superscript numbers 1 and 2 before each Jv mean that they belong to Taneyev’s categories of group 1 or group 2 indices respectively: group 1 consists of indices where perfect intervals become perfect in their derivatives (and imperfect become imperfect), and group 2 refers to indices where imperfect intervals become perfect (and vice versa). See the third paragraph of my very long comment about Jv=-8 for more information.
Ordinarily, Jv=-8 is incredibly restrictive because the only fixed consonance it has is a 5th (which becomes another 5th), but if you admit the 4th as a consonance in relation to upper voices, then you can employ both the 4th and the 6th as fixed consonances (which invert to each other), and parallel and similar motion is allowed for these intervals (which they ordinarily aren't for imperfect and dissonant intervallic shifting indices). This is why the Bach example in the video works so well. Likewise, the JJv -12, 1 and -1 open up a wide array of fixed consonances with parallel and similar motion if one admits the consonant 4th, making them in fact very useable in their own right. I should mention one more general principle which is invaluable to know (I've alreaded alluded to it): indices of perfect intervals allow for parallel and similar motion for imperfect consonances, since imperfect intervals shift to imperfect intervals (likewise, perfect to perfect); in contrast, indices of imperfect and dissonant intervals forbid parallel and similar motion, since, imperfect intervals become perfect and vice versa. Jv=-8 is the only exception to this, where the 5th becomes a 5th (both perfect), but since its only fixed consonance (without admitting the 4th) is perfect, parallel and similar motion can't be employed anyway. Admitting the consonant 4th inverts these principles (where 4ths are admitted): in perfect indices (-3, 4, -7, -10), 4ths cannot be approached in parallel or similar motion, since they become perfect intervals; for imperfect and dissonant indices except for Jv=1 (-1, 2, -5<, -12, -13), 4ths can be approached with parallel and similar motion, since they become imperfect consonances (Jv=-13 results in 4ths becoming 4ths, which can be treated according to the rules of simple counterpoint as imperfect). Amazing work with your videos, by the way; I look forward to seeing this series unfold over the summer!
Exactly! Indices like ±6 and -8 feel horrid to write in 2-voice combis as per the book where you're writing for outer-voice-pair to outer-voice-pair swaps, but if you're writing for situations where either the original or derivative combis are upper voice pair then suddenly it's much more manageable and pretty broadly useful. When writing I came up with a method that's a little more compact, easier to reason around and potentially more accurate than Taneyev's: instead of using a single row of interval conditions for the original and derivative pair and then introducing liberties after the fact for multi-voice situations like permitting 4ths etc., you can use different rows of interval conditions for upper and lower voice pairs and simply use the appropriate rows for whatever voice pairs your original and derivative combis are meant to function in. It's a slight simplification, but I just write 4ths as consonant (no suspension signs) for upper voice pair condition rows, and extend the "..." from 3rds to 6ths instead of just 5ths and 6ths. Using different rows has the advantage that you can handle fairly complex cases and have the correct conditions simply "baked in". Still need to handle the edge cases as Taneyev does though. You can also gain liberties with direct motion (not parallel) at 2JJv even without this trick, since Taneyev doesn't really touch on the fact that, in practice, hidden 5ths/8ves are only really a concern in the outer voice pair, and only when the sop leaps (or in 2 voice texture more generally). If either the original or the derivative pairs are non-outer voice pairs, then you don't have to worry about directly approaching perfect consonances in them. Even if it's outer-to-outer, if your combi will be deployed in 3+ voice texture you can for instance approach a 6th in Jv = -9 if the bass moves by step and the sop by leap in the same direction, as the derivative will be a correctly approached direct 5th for 3+ voices.
@@hex5499 Of course, the rules of similar motion are relaxed under various conditions of real polyphonic writing, but you're right, Taneyev should have been more clear on the case of consonant 4ths, along the lines you describe (though I filled in some of those gaps myself as I was writing exercises).
It continually amazes me, as a composer for 50 + years that all treatises or studies on counterpoint seemed to be poised like guns at composers in the crosshairs, ready to shoot down any ideas the composer has,.. with a rule, that makes the idea untenable. Wouldn't it be so much better to teach us HOW to BUILD a composition rather than how to tear it down. Let the critic of J S Bach, Johann Adolf Scheibe, study these strict rules, so that he may heap more coals on his own head as he languishes in HELL ! You know there is something wrong when Palestrina's works are cited as BAD EXAMPLES of counterpoint, while many describe his pieces as among the most perfect ever written. For those who want to WRITE COUNTERPOINT rather than develop a serious imposter syndrome complex. I will give a couple of helpful hints. Think about the harmonic series, (and sub harmonic series, made up of divisions by whole number ratios, as guide points for voice leading. Use different rhythmical divisions for different counterpoint voices, use contrary motion often, rather than parallel motion for everything other than 3rds or 6ths, if the result of breaking rules sounds really appealing, in context, always break the rule (it serves no purpose). Rules don't make music, people who love what they are doing, make music. As Peter Schickele said: " if it sounds good, IT IS GOOD ! ! ! " Don't be afraid of down beat passing tones, dominant 7ths, seconds, and 9ths, etc but keep in mind the incremental building or release of tensions. Parallel 4ths or fifths are pretty much the same (one tone is inverted by an octave). All dominant 7th chords contain tritones, ... Bach often used them generously in two part counterpoint, just be aware of where they came from and where they are going. Lavish use of diminished 7th chords, makes modulation to different keys quite workable. George Harrison of the Beatles loved them for that. Have fun !!! If You are looking for an excuse, to hate the prospect of music composition, read this guy: Taneev .....or Schenker.
I am afraid you greatly underestimate the genius of Sergei Taneyev. Listen to his one and only prelude and fugue in g-sharp minor (6minutes). Or his piano quintet op. 30. Taneyev was greatly admired by his students Rachmaninoff, Scriabin, Gliere, his teachers Rubinstein and Tchaikovsky, many other contemporaries such as Koussevitzky, Glazunov, L. Auer Rimsky Korsakov, Turgenev and many others as a composer, virtuoso pianist, teacher, theoretician, ethnomusicologist as well as a man of incredible kindness, integrity and wisdom. Taneyev points out exceptions to common practice of renaissance counterpoint. Taneyev‘s approach of music is much more profound than listing rules and prohibitions. It would suffice to read his 3 page introduction to his book „convertible counterpoint“ to realize this. The afterword/ conclusion also explains a lot.
I’m an old guy with a masters in music comp I received years ago and just recently discovered your videos. Your lectures are great, you cover every essential component combined with a refresher in college music theory which in my case came in handy. Please keep doing them.
About voice crossing to avoid violations of parallel prohibitions. I often hear resistance to rules or hear flouting of them in the claim that you can break them after mastering them. I think these attitudes miss the point that rules are based on how music sounds. Rules are tools of prediction; do this and it will sound like this. Rules are not merit badges. They don’t confer virtue because you comply with them, they tell you what to expect about how your music will sound. If your mistake sounds like this when you do it the first time, it sounds the same on the hundredth time whether or not you “mastered” the rule by otherwise producing a thousand compliant settings. I said that to set up an observation about the synth playback of the voice crossing examples. Since we don’t hear actual linear events of voice motion, these examples still sound like parallelisms. The voice crossing isn’t apparent and the twinge of parallels is still evident. It doesn’t matter for the example! I only wish for better cultivation of listening acuity. It disappoints me when I observe working composers and arrangers fail to internalize the point that mastery of craft helps them sound better and don’t discern how neglecting predictors of unpleasant effects undermines the quality of their work.
A few people can look up at the end of a mathematics lecture and follow a board full of algebraic-type equations. Most can't. This is how I've always felt about strict counterpoint.( But I love the musical outcomes.) Thick individuals like me so, so, so need people like you. Many thanks
"No one laughed, but I think that is because I had not instituted the proper permission structure." Amazing. Great video, my students will benefit tremendously from your channel, I'm very happy to have stumbled upon you.
Forgive me for going on a nerd rant after watching only 45 seconds of your video but it spurred an impulse in me to comment. I love music theory, and learning how counterpoint was fundamental to the historical development of composition was a big revelation to me at the time, particularly because of how most contemporary musicians think in terms of chord progression in isolation. What I'm trying to say is that I'm the kind of person who likes to sit and think about how music works. I recently started to imagine intervals as having a kind of "potential energy", or something similar to how in highschool chemistry you learn about the push and pull of electrons due to the atoms trying to achieve a stable set of valence electrons. This isn't a perfect metaphor, but I hope the point still comes across. Each interval has its own sense of inertia which creates a feeling of anticipation that can either be delayed, reconciled, or subverted. I believe there is a similar principle to rhythm and phrasing in relation to the subdivision of each measure. Anyway, let me abandon this diatribe before I ramble incoherently, even more so than I already have.
Your comment is one of the MOST COHERENT things I have ever heard.! ! ! Yes, melodies suggest where they are going, as they fly, and so does each chord progression or combination have "inertia",.. but also "aspirations", which are sort of like the arc of a narrative, they know where they want to go, to reach a successful resolution, and they use their experience (of where they have been) to inform their flight. So much more interesting and inspiring than rules about what NOT to do ! And just like in chemistry, it really is like a mathematical thing. Like consider the valence of an element to figure out what it would like to combine with,... like if it has extra valence electrons it wants to join with something with a deficit of electrons in the outer shell. Maybe a noble gas is like the tonic of the key ( 1 chord ) and an oxidizing agent is like a five-seventh chord, and a two chord is kinda like a metal that seeks out an oxidizing agent ! Maybe a six chord is sorta like something that can have a covalent bond, it's valence changes with context ! That's fun to think about !
almost every rule of counterpoint has exceptions. These rules are designed just to develop sensitivity to all the important aspects of polyphony. And then you can forget them and follow your ear.
Some of the rules stated still makes a lot of sense to me. I studied music in the 1980s and much of what you address reminds me of what I learned back then. With the advent of time, our modern ears have begun to accept some of the voicings that were discouraged in the past. Even Beethoven has been known to say that he used parallel octaves at time. How is this addressed when studying Sergei Taneev's theories? Is strict counterpoint still valid in this case? Thanks for posting.
The English translation of Convertible Counterpoint by Ackley Brower is available on Google Books as a free downloadable PDF, and Paul Grove's dissertation, in which he translated Taneyev's Doctrine of Canon (along with excerpts of other Russian theorists that discuss things such as double canon), can be found on the University of Arizona repository website.
I am admittedly less than a minute in ... but ... from the point of view of a mathematician, music notation is awful. Mathematicians spend an age with notation as it eventually melds with intuition and should serve to aid further development. Music notation is an ad hoc legacy. It is something you get used rather than having a function.
This is a common sentiment I see with folks with maths-y backgrounds and usually ends up being a bunch of premature conclusions after all of 5 minutes exposure to (tonal) music theory, so I'd be interested in what your specific criticisms are. As far as I'm concerned, standard notation is excellent precisely *because* of how well it aids with the development of strong intuitions about the behaviour of notes in a tonal/modal context. It's "ad hoc" in the same way your liver is an ad hoc result of evolution, yet replacing it with a carbon filter because you know better and like the highly logical design would be naive. There is definitely music where the diatonic lens of standard notation is a hindrance though, but it's not tonal/modal-adjacent.
@Jacob Gran: Thank you for this great video! I’ve tried to find that book online. I could find it only in Russian. Has this book ever been translated into English or German? I would like to purchase it.
@@TobiasTimKlingbiel I do have a physical copy of Convertible Counterpoint published by 'Forgotten Books', but it appears to be just a cheap scan, with several diagrams and notation poorly rendered (the last horizontal exercises were completely mangled). I noticed RU-vidr CGP Grey had the same issue with the publisher for another historical book, so it's not an isolated incident. Thank God for PDFs!
As @PiersHudsonComposer mentioned, the English translation by Ackley Brower ("Convertible Counterpoint in the Strict Style" Bruce Humphries 1962) is unfortunately out of print. However, it is available on Google Books as a free downloadable PDF, with legible appendices. A scan of the original Russian is available on IMSLP.org. I do not know whether there is a German version.
@@TobiasTimKlingbiel And Paul Grove's dissertation, in which he translated Taneyev's Doctrine of Canon (along with excerpts of other Russian theorists that discuss things such as double canon), can be found on the University of Arizona repository website.
I’m just about to watch the video but first I’d like to say that it is Great that you are making videos again! Your content is excellent and extremely helpful.
Wow, what a find!!! As a pianist I haven’t looked beyond Taneyev’s Piano Trio, Quartet and Quintet, but these works have cemented my opinion of him as a truly great composer, coupled with the knowledge of all the famous pupils he’s had one can only admire the man. Thanks for your efforts in making this video.
Matthew Marvuglio, who was dean of performance at Berklee, also studied with Norden. He called the idea of two-voice counterpoint being central as the principle diaphony.
It seems to me that many of these euphonic counterpoint rules can be determined purely aurally since trangressing these rules simply sounds 'clumsy' or 'tasteless' even. Presumably this is how these rules were first established and codified. The earliest reference to the avoidance of parallels fifths I have encountred was atributed to the advice of English composer Leonel Power (1380-1445). It is a shame Henry VIII's Reformation destroyed many of his and others pre-renaissance works (espeicially considering Henry VIII was himself an amateur composer).
Music is not just tones, but also the rhythm, texture, number pf voices. If you compose for an organ and it already is set to play 5ths, you just won't hear parallel fifths at all. If low string and high strings play parallels - you won't even notice because the brain won't connect extreme registers. If there is a lot of voices going in contrary motion, then parallel 5ths won't even be noticeable. And there are lots of ways to use parallel fifths to mimic medieval chant, for example. It all depends on what you're trying to express at the moment. What is heard is more important than what's written!
@@alexkha In a sense, these idiomatic parallelisms you describe only confirm the rules of counterpoint; they are admonished precisely because perfect intervals blend in with each other, which defies the intention of polyphonic music to have independent vocal lines and harmonic variety. In other idioms, perfect parallels in organ registration or string arrangement are a matter of creating a single 'enriched' line, rather than two lines that happen to have parallel octaves and 5ths along with other intervals (though other musical idioms do exhibit such a tendency).
@@PiersHudsonComposer exactly! "vocal" is the keyword here. Counterpoint assumes SATB voices. Once you mix in different instruments, it's a different ball game altogether!
@@alexkha Different idioms and instrumentation certainly confer different conditions, but my point is that the principles of vocal counterpoint still carry over into many other idioms such as organ or string arrangement, with parallel perfect intervals acting as singular 'enriched' lines. This confirms the principle that 'if parallel perfect intervals are used, the voices will blend in with each other, effectively becoming one voice'. The mere use or disuse of parallel perfect intervals doesn't break the dialectic.
@@alexkha Presumably these developments were a reaction against the hollow tones of the then prevalent plainsong and organ registers. A little prior to the time of Power and Dunstable there was the beginning of an English choral innovation of replacing 5ths with 3rds which quickly caught on in Continental Europe as the 'English Style'. I'm sure many organists are aware that although Organ registers can and do include 3rds (e.g. the 'Mixture' stop) they don't work satisfactorily in solo since euphonic scales rely on a mix of major and minor 3rds / 6ths. Adding a 5th interval tends to be less intrusive as one is just bolstering the 2nd harmonic which is typically quite prevalent anyway. Speaking of which it is interesting that the modern fascination with valve (tube) amps relies on a subtle boost in the 2nd harmonic - i.e. adding a hint of flattering artificial complexity to the music. The one rule of 4 part harmony I find most difficult to grasp in a euphonic sense is the avoidance of the 2nd Inversion as illustrated in Taneyev's treatise - It seems like splitting hairs as, in context, it sounds sufficiently harmonious and avoiding it restricts one's options greatly. Perhaps I am missing the point and it's just a guide in a similar sense to composers preferring contrary motion since, as a side effect, one then inevitably avoids parallel 5ths by avoiding parallel motion in general. I have read Taneyev's book previously and even started weiting a Forth program to automatically generate harmonies in the purely mathematical way he lays out. Judging by some other comments I am not the only one to think of this. Perhaps after this series I will dust it off and complete it AI music software is all very well but it is hard to tweak and refine a black box system.
Thank you for providing an explication of this important work. My counterpoint teacher, Hugo Norden, was a friend of translator Ackley Bower, who died with the manuscript had seen its way through the publication process. Dr. Norden saw it through to completion,
I did not know that! I have read three of Dr. Norden's books and I admire them. Very concise, no matter how complex the subject matter. His book on canon in particular is one of the very few American scholarly works from that time period that is clearly Taneev inspired. Thank you for your comment!
Woah, you studied under Norden? I didn't know about his history with Ackley Bower, that's such a cool bit of information. So basically we all owe Norden a debt for even being able to read an English translation of Moveable Counterpoint?
@@JacobGran Right? I felt the same reading the counterpoint and fugue books: really concise and practically focused. The canon one's great because it covers basically all the canon types Taneyev never treats in DoC, so they really complement each other.
@@JacobGran I regret that I lost my notebooks from Norden's classes. His unpublished ideas open up all sorts of possibilities for things no one else even talks about
Thanks! So difficult theme, But I understood Something) One question - where is hidden octave in example on 4.57? As I know from college course - hidden octaves detected on edges voices
Notes: - Suspensions can be elaborated with re-articulations, anticipations, embellishing tones, escape tones, or mordent thingies 1:58 - Embellishing tones can influence shape of melody and delay resolution 2:55 - Quavers can fill in fourths but only on weak beats 3:36 - Dotted minims can be used on beat one to add rhythmic interest to 2:1 relations 4:37 - Rhythms should start slow, accelerate to climax, hold, accelerate again, and then glide back into the cadence, but should be well blended too 5:01 - Work from 4th species basis to maintain more equal interest 7:44
You mentioned the book's reputation of being difficult. As Taneyev writes in the Preface, "if one uses this book as a teaching handbook, one must make sure to understand what is really important to the student and what is further examination of the topic". "if one uses this book as a teaching handbook" - this means it ain't mainly a teaching handbook, but a treatise. Therefore, one must make an effort to contextualize his reading or teaching, otherwise it will turn up chaotic. I think that's a reason why it's considered to be difficult and has a limited reputation among english-speaking theorists. According to various sources, Taneyev's own teaching in his classes at the Moscow Conservatory used to be well-organized and properly contextualized in a way that fascinated all the students, even the ones with little or no interest in music theory. So nice that you made this introductory video, and I'm so glad to hear that it's gonna be a part of a series.
