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The Little Harmonic Labyrinth - BWV 591 Harmony and Counterpoint Analysis 

TheKantor
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A labyrinth is distinct from a maze in that a maze has different paths to choose from with the intent of causing confusion. A labyrinth has only a single path with many convolutions that eventually arrives to a center.
Bach metaphorically directs us through a tour of the keys in this harmonic labyrinth. Beginning in the key of C, we traverse to distant keys until we eventually arrive at the center of the labyrinth. We see him use tools such as diminished seventh chords to pivot into different tonal landscapes throughout the three movements. We encounter a fugue in the center of the labyrinth which features the rectus and inversus of the fugue superimposed upon each other, as well as the signature of his name implied musically at the end of the fugue. In the final movement, we traverse similarly back into the labyrinth until reaching a restatement of the entrance of the labyrinth.
The harmonic guide is intended to follow typically the bass line, or whatever note is doubled at a particular instance in the work. Following the harmonic guide, we can attempt to see the logic in the way Bach chooses to pivot into different chords and tonal centers. We can see that oftentimes the harmonic guide dictates a kind of planetary center from which neighboring notes are chosen for melodies and chords.
Performed by Wolfgang Stockmeier.

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7 сен 2024

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Комментарии : 42   
@flizt.9061
@flizt.9061 2 года назад
So that's what Achilles and the Tortoise heard in the Labyrinth of the Majotaur.
@KemTrivedi
@KemTrivedi 2 года назад
Thats page 123 of GEB which brought me here 🙂
@flizt.9061
@flizt.9061 2 года назад
Nice! I thought no one would understand the reference. Hope you are enjoying the book.
@KemTrivedi
@KemTrivedi 2 года назад
@@flizt.9061 Yes, thx, had first read and enjoyed it in the 80s when i was a kid and there was no youtube to hear the music! Picked it up again yesterday, and 'somehow' getting a lot more out of it. Couldnt find the audio of the Sloth Canon though 🙂 Cheers
@M419.99
@M419.99 2 года назад
Whoa I'm also reading it. Eric is a genius for mapping our thought processes. My brain exploded multiple times, and that's just the first 3 chapters!
@Geopholus
@Geopholus Год назад
This video is truly extraordinary. This is the first time I see someone who understands music and Bach in a very similar way to the way I do! Many years ago when I was around the age of 12 or so,.. I became aware of chords, chord progressions, and roots of chords. In High School I took a course in music theory, with a teacher (John Hanulik) who sent many of his students off to Julliard, Oberlin, & Boston Conservatory. At that time students returned from those colleges and informed him that their college professors complained that his students had already the equivalent of 2nd year college theory. I remember the discussions I had with a few friends who also loved Bach,... his music suggests an underlying structure that informs the notes chosen without spelling out the structure of the beams behind the walls. I spent quite a lot of time working out the mathematics of the tempered scale, and how western counterpoint seemed to often involve pivoting on 5 or 7 chords, or 4 chords. or 5 of 5 chords or 4 of 4 chords of chords to a one chord,,..or one that could be substituted for these by changing one note a half step.. I even worked out a way of coloring the 12 chromatic tones of a keyboard so that the color relationships consistently mapped onto the harmonic relationships, and used a math matrix similar to Your tone matrix here, that would allow one to map the note changes, as, what, I called a "MEANDER" pattern, somewhat like the structures used by that fellow on Scientific American who wrote puzzles, and described game theory. The result is so SIMILAR to what You have!!!, though my pattern was listed as points on graph paper with a systematic way of mapping simple fractions of whole numbers! I have been using my understanding to write counterpoint now for 50+ years. The sad thing is computers keep getting aged out of the communication system and I have run out of money to keep upgrading ,.... so though I have a few hundred pieces sequenced into a couple of old sequencer programs that are now around 30 years old. I am not updated enough to get them onto YT so far ! Also around 30 years ago I wrote some AI that allowed me to select a few parameters, and allow the computer to generate some pretty plausible music, based on those structures I had inferred from Bach. Because my system wasn't based on statistically gathering up data from extant works, it was not so much the plagiarist as "Emily" (David Chope's program). I hope to upload some of my work with a completely different 'visualization program, one that is based on actually mapping the waveforms of the notes playing together as polar plots of those whole number ratios,... this is based on work that i did at Cooper Union with video feedback around the early 1970's a couple of which were shown at "the kitchen" video /electronic music gallery in NYC . I still wonder where the inspiration for Win Amp came from which was also pretty similar to my video feedback work. So glad to see this GREAT WORK !
@ArtHistoryMemes-fi6op
@ArtHistoryMemes-fi6op 2 месяца назад
@Geopholus I think you should check the amazing channel of The Lost Art Of Counterpoint!
@joannescouchet7038
@joannescouchet7038 3 года назад
Really incredible visualization!
@thekantor1964
@thekantor1964 3 года назад
Glad you could enjoy it!
@robertosaviano9270
@robertosaviano9270 3 года назад
wow... I'm without words
@OutbackBoy
@OutbackBoy 3 года назад
The cheeky bugger! A convincing bVII to I in G major with cadential ornamenti and all, only to transform into a V7 to I in C major for the final cadence. This really is a harmonic labyrinth
@peteryu8711
@peteryu8711 2 года назад
Learning this on the piano, I wish one day I will get a chance to play this on an organ
@jasonwilbermusic
@jasonwilbermusic Год назад
What software or app did you use to generate the tonnetz and the circle animations?
@emrevone
@emrevone 7 месяцев назад
I feel Majotaur is behind me
@OutbackBoy
@OutbackBoy 3 года назад
The fugal subject 2:32 is just BACH in retrograde and overlapping itself, repeated a lot. Becomes more apparent at 2:59 when the inversion appears since you get the classic descending semitones.
@thekantor1964
@thekantor1964 3 года назад
If you like that, check out the first movement of the Bm mass i made a few days ago ru-vid.com/video/%D0%B2%D0%B8%D0%B4%D0%B5%D0%BE-tgmmyfX4LPo.html
@OutbackBoy
@OutbackBoy 3 года назад
@@thekantor1964 hehe the Kyrie is one of my all time favourites. You're a legend
@handavid6421
@handavid6421 2 года назад
How wonderful.
@kp2kpx
@kp2kpx 10 месяцев назад
Here while reading GEB.
@henrykwieniawski7233
@henrykwieniawski7233 3 года назад
Wow... Bach was way ahead of his time!
@marcossidoruk8033
@marcossidoruk8033 2 года назад
Stupid comment.
@incription
@incription Год назад
How are the path keys chosen? for example it goes C, G, D, A upwards... why not C, C#, D? Is it chosen for the piece? Edit: I get it, any hexagon contains two sets of notes seperated by a semitone...
@ericmoon8043
@ericmoon8043 Год назад
This is the first instance I have ever encountered of anyone else besides myself mapping the circle of fifths onto the color wheel. Is this visualization software available?
@handavid6421
@handavid6421 Год назад
I'm quite convinced this is by heinichen. a brilliant composer, who invented the circle of fitfhs ( the concept at least)
@AndreaJobPicanello
@AndreaJobPicanello 3 года назад
Very very interesting! Could you explain a bit more how the graphic analysis works?
@thekantor1964
@thekantor1964 3 года назад
ru-vid.com/video/%D0%B2%D0%B8%D0%B4%D0%B5%D0%BE-zyOoZInEeIo.html
@thekantor1964
@thekantor1964 3 года назад
The graph analysis allows us to see the chords used in better detail, as well as how they are related. A bit of music theory knowledge is required to gain information from it.
@AndreaJobPicanello
@AndreaJobPicanello 3 года назад
​@@thekantor1964 thank you! A new world is opening to my eyes, I didn't know anything about the riemannian transformations. I have some music basis, I absolutely want to deepen the subject and then watch your video again on the basis of what I have learned 👍
@thekantor1964
@thekantor1964 3 года назад
The red "guide" i put in the video has errors, just a warning. I meant to have it track the doubled bass notes predominantly, but failed in a lot of cases in the animation. Please forgive me!
@AndreaJobPicanello
@AndreaJobPicanello 3 года назад
@@thekantor1964 I hope to be able to catch those errors! I will tell you later... 😁
@frankmiller9301
@frankmiller9301 2 года назад
Absolutely wonderful work! May I reprint this to another video website?
@thekantor1964
@thekantor1964 2 года назад
Sure thing, not like i own the music. It would be cool if you linked it back so more people could find the other works too
@frankmiller9301
@frankmiller9301 2 года назад
@@thekantor1964 thank you very much!!! I'd make more people know this!
@benoitarliaud1349
@benoitarliaud1349 3 года назад
Very nice vizualisation of harmony ! Do you know if the harmonic guide has any other name ? (can't find out anywhere)
@thekantor1964
@thekantor1964 3 года назад
Admittedly I added the "harmonic guide" as an attempt to map the progression of the harmony. It works often but it's quite unscientific so to say. The closest thing i can think of it representing is either a tonal center or a map of guide tones. It often follows pedal points as well.
@nahuelguzman
@nahuelguzman 3 года назад
Maybe Tonnetz is what you are looking for
@OutbackBoy
@OutbackBoy 3 года назад
Love it. 1:24 should be f min not F Maj (Ab not A). There might be other mistakes too :(
@thekantor1964
@thekantor1964 3 года назад
Plenty of mistakes I will admit. It was the first time I made such an animation
@OutbackBoy
@OutbackBoy 3 года назад
@@thekantor1964 it is a truly amazing animation. A great study aid. Thank you so much
@4stringed
@4stringed 7 месяцев назад
That's not Bach, I'm sorry. I couldn't express how helpful this video is though, thank you for putting gigantic time and effort into it!
@iosnoob8046
@iosnoob8046 3 года назад
Ganggg
@isaiasramosgarcia9771
@isaiasramosgarcia9771 3 года назад
es una especie de tiento?
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