How Kapustin Maximizes Harmonic Contrast: Brightness, Darkness, and Modal Interchange

Here I explain a harmonic space of so called "brightness" and "darkness", which corresponds intuitively to the circle of fifths. The examples in this video are from Nikolai Kapustin's Piano Sonata No. 2. Kapustin's compositions display virtuosic jazz language and harmony within classical forms. In the space of "harmonic luminosity" as shown on the Tonnetz, we can explore Kapustin's harmonic choices that create captivating contrasts in perceived color, tonality, and "brightness/darkness".

00:00 Intro
03:00 Circle of Fifths = Brightness/Darkness
03:42 Scales
05:00 Chords
06:09 The Tonnetz
09:42 Harmonic Continuum
11:39 Lum Transformation
13:52 Lum7 = Flip = Modal Interchange
18:24 Example 1
21:17 Example 2: Maximal Harmonic Contrast - Lum13
23:43 Lum Space
26:16 Conclusion

[CalebCarman]

This video is a revelation. I’ve always loved Kapustin! 🥰

[pariah]

This is about the best presentation of tonnetz I've ever seen. I started taking notes on tonnetz transformations and didn't really follow through but this lesson really reawakened the fire of revisiting tonnetz. I was feeling like it would be useful but I had yet to see a direct representation of how it could be applied and digested until now. And the app just compounds on the helpful visual representation. So glad I found you and this fantastic video. Now I have tons of study to do. 😂 Can't thank you enough for creating this!

[calebw]

This is one of the best videos on music theory I've ever watched - I want to thank you for how articulately you've managed to make this concept 'click' for me after I've been confounded by a lot of other explanations!

[bryanchristopher]

Never heard of tonnetz before, I really appreciate your effort to explain rare music theory concepts for us

[tanyapri]

that was actually insightful and understandable, thank you!
such a work you have done, impressive

[RaptorTV]

О мой Бог! Музыкальный анализ Капустина 🤩🥺😍

[burtcolk]

This was an interesting take! Thanks for putting it together.

I think even when speaking English it would make sense to pronounce the "Ton-" in Tonnetz as "Tone."

[nathanielmarks]

Really interesting and very easy to understand! Thanks for this video!

[intevolver]

It seems to me that the Tonnetz should be front and center in teaching music, and introduced early. Many of the concepts you present are beyond my theory but become immediately intuitive when cast on the net visually. What seems arbitrary on the page becomes obvious on the lattice. Thank you.

[andrewsantopietro]

I think there’s some interesting stuff to be said about how chord changes can subvert this idea you present about lum7, specifically in the case you bring up around 19:40 where that flip happens on some, but it kind of leaves a “ghost note” resolution to the other notes. That assumes of course that subconsciously you expect all the notes to follow the same flip, but they don’t. In this case, they are just left out.

[john]

This is cool! I've never heard of the Tonnetz before

[RaptorTV]

There is a video with a live Nikolai Kapustin, in which he talks about his concept of tonal arrangement in his cycle ‘24 Preludes and Fugues’
<<
The native minor of each major is set off from it by a major third downwards.
The distance between these twos is a minor third.
>>
For example, C major and A-flat minor, then F major and C-sharp minor, then B-flat major and G minor, and so on....
Notice that the major tonalities are exactly a fourth apart. So it is also a circle of fifths, in essence!

I understand that Nikolai Kapustin is NOT talking about relative tonalities here, but about something else. About some ‘native’ tonalities.
But, it has to be said, it sounds very beautiful!

And one more interesting observation.
Here is how the principle of tonalities arrangement looks like in the cycle ‘24 Preludes and Fugues’ by N. G. Kapustin

maj | min
0# |
| 5#
1b |
| 4#
2b |
| 3#
3b |
| 2#
4b |
| 1#
5b |
| 0#
6b = 6#
| 1b
5# |
| 2b
4# |
| 3b
3# |
| 4b
2# |
| 5b
1# |
| 6b

I found this in the comments under the video ‘Nikolai Kapustin - 24 Preludes and Fugues, Op 82’.

And to summarise what you said in your video.
There is another principle of arranging tonalities in twos, but the distance between these twos will not be a minor third, but a major third. That is, it's the other way round.
Here's an example:
1) Let's just take a pair of relative tonalities - E major and C-sharp minor. The distance between them = minor third, since they are relative tonalities.
2) Then we step the major third down - we get A major and F-sharp minor relative to it.
And then by analogy - D major and B minor, G major and E minor, and so on....

And you know what the 2 main features of this arrangement are?
1) Major tonalities are a circle of fifths.
E, A, D, G, C, F....
2) The lower/left (depending on how one represents the circle) one moves, the darker the tonality becomes. Correspondingly, the higher/right you move, the lighter it becomes.
The brightest tonalities are B major, E major, A major.
The darkest tonalities are B-flat minor, E-flat minor, A-flat minor.

[MrVarsityphysics]

It’s weird as an engineer to see someone brilliant approach music with an engineer-like imagination.

[vocalchords]

I want to let you know that you have a rare gift - forensic mind and a wonderfully engaging way of sharing what your forensic explorations have discovered, arranged - in order to illuminate some of the underlying patterns embedded within western tonal music. As a professional composer and performing musician - I salute you and thank you for this excellent illustration of our art.

[RaptorTV]

Everything you told is very similar to matrices and their linear transformations (hi, 1blue3brown), especially when it came to ‘Lum7’.
It turns out that Lum1 and Lum7 are nothing but basis vectors in 2D space.

[liamp.]

is harmonic "luminosity" as described here another word for pitch? seems in the examples you give a brighter sound is always higher, a darker sound is always lower

[RLITY_SUX]

What software do you use for the Circle of Fifths?

[philosemith]

It looks a lot like the DNA of music, the fundamental blueprint of music, the sefirot tree of life applied to music… it should be 3-dimensional

[NationDixon]

What do you mean C maj is darker than G maj? 4:23 they both have the exact same intervals, so unless you have perfect pitch you wouldn’t be able to tell which one is which. Do you mean that when playing a song in C maj and switching keys would make G maj sound brighter?

[Typical.Anomaly]

1:40 Sounds like a little bit of an "Iron Man" motif in there in a few spots, at least to my uncultured ears lol