Caspar Johannes Walter: EDO-53 Supercembalo chord progressions
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- Опубликовано: 8 фев 2025
- Chord Progressions similar to the Tonality Fluxes of Harry Partch.
Played on the "Supercembalo" (31-key Clacemusicum on top of a 24-key Cimbalo Cromatico), tuned in a Just Intonation tuning similar to EDO 53.
The syntonic comma-like step is about 23 cents, the diesis twice as large.
Johannes Keller and Eva-Maria Hamberger, supercembalo.
Recording Caspar Johannes Walter (March 2017).
Amazing otherworldly sounds.
Wonderful, worthwhile explication of harmony in the 53rd dimension 👂
Lovely progressions, thanks for making this resource!
Lovely sound!
These are lovely, and it's great to see there's a working instrument out there actually ready for 53EDO or 53-tone extended just intonation!
One thing I'd like to say is the notation used here, while probably correct in historical practice, is rather hard to decipher, and requires a broken chain of fifths (or potential wolf fifth written as a regular perfect fifth), so a combined traditional sharp/flat and comma accidental pair might be more helpful, the former from Pythagorean (single chain of perfect fifths), the latter as alterations to get classic 5-prime intervals. In 53EDO, a sharp raises the note by 5 commas, and a double sharp brings you up 10 commas, which can also be notated as a major second raised by 1 comma.
So, in the first progression, assuming C=0 commas, a perfect fifth of 31 commas and an octave of 53 commas, we have:
10 "Ebb" -> D/ resolves to 12 "D#" -> Eb\
49 "Cb" -> B 48 "B" -> Cb
32 "Abb" -> G/ 34 "G#" -> Ab\
Then one also sees ascending pitches on the page for the top and bottom voices, and a smaller adjustment for the middle voice written as a pythagorean enharmonic.
For your second example, you have
13 "D#" -> Eb resolving to 13 "D#" -> Eb
3 "C#" -> Db\ 1 "C" -> C/
39 "A" -> Bbb 40 "A" -> A
25 "F#" -> Gb\ 23 "F" -> F/
Especially since the top pitch (13 commas) acts as a stable seventh in the second chord, rather than as an augmented sixth, in my view. The voice leading looks different, so if you like your original voice leading I can provide another alternative spelling that preserves those interval class relationships.
Dear Cam,
thanks for the good comments!
Notation is not yet well under control. It makes no sense to follow the notation by Partch (ratios), because this doesn't communicate with other intonation systems. And one of my idea was to show, that things like the Partch Tonality fluxes are a very general thing, that occurs in various systems.
The notation I used follows the concept of Tanaka. It is a pythagorean tuning hidden behind a limit-5 Just Intonation nomenclature. the e of the third c-e is in fact a pythagorean f flat. So all thirds are one schisma smaller than the 5:4 third. This system has a good approach towards tonal music.
look at another video in the Studio31 channel: 53 tone diminished chords....
at second 5 you see the limit-5 grid that we used to define and to tune the pitches of the harpsichords.
Your concrete comments:
first progression
First chord is at the edge of the system, both of your meanings are possible. Second chord is more in the center, my notation makes sense. I chose for the first chord the double-flat version, because it expresses nicely the tonal tension of the minor thirds placed in the middle of a major third, that you find in the very extreme enharmonic meantone music (Vicentino).
Second progression. Important is the augmented sixth of the second chord f- d sharp. This sounds similar to a Just Intonation natural seventh 7:4. Due to that the d sharp of the first chord should better be called an e flat (in the first chord all intervals are reversed.). I stayed with d sharp because that e flat (13) is off the system and for the musicians d sharp was easier to read..
But, as you see, it is not yet finally clear, how to notate.
Best, Johannes
Thanks for your reply. Interesting to see schismatic in use again! (schismatic is the name of the temperament where 8 perfect fifths down gives a just major third, hence the schisma disappearing)
If you want to keep the sharp and flat spelling, then these are the comma accidentals I would add to your notation to make it more general, in that it expresses its 5-limit intervals directly, and makes a distinction between pythagorean and classic (5-limit) thirds, which I think is important in a system like this. If I read your current notation without any comma numbers for help, I would play the first example as either a pythagorean or 5-limit major chord starting on regular old Abb (30) resolving to either a pythagorean or 5-limit minor chord on regular old G# (36). Not very helpful as a stand-alone.
The comma accidentals also show how many prime 5 "rungs" away on the lattice these notes are, which I think is helpful in terms of harmonic distance.
Ebb// resolving to D#\\
Cb/ B\
Abb// G#\\
In either case when the comma accidentals are there, now you no longer need (53)EDO numbers to precisely define notes, all 5-limit relationships are visible in the notation, and the pitches are distinct from the above and below comma steps.
If you need an extended meantone notation, just remove all comma accidentals and there you go.
Here is the second example with comma accidentals added (left spelt as a 128:225 augmented sixth). Hope I didn't make any mistakes. But now the progressions are readable, analysable and playable without any reference, in any tuning that supports 5-limit thirds (e.g. 12, 19, 22, 31, 37, 34, 41, 43, 46, 53, 55EDOs, just intonation)
D#\ to D#\
C#\\ C/
A\ A
F#\\ F/
Yes, the slash/backslashs of the first progression are correct!
In this context it absolutely makes sense, although I would discuss maybe to change slash and backslash (to make it more similar to Helmholtz/Tanaka: they used underlines to indicate a lowered comma and overline for a raising comma). Oettingen uses it the opposite way, but his whole system is quite confusing.
But for other contexts this good working limit-5 notation comes very fast to its limits. E.g. look at the small video "Quartertone Accordion in Just Intonation Music" (same channel). Quartertones cannot be caught well by the syntonic comma notation. And the septimal ratios of the electronic sounds too. Nevertheless this small examples are absolutely tonal and consonant. For this I used a typical contemporary music-notation with modified accidentals (indication 1/12-tones). This is not sufficient to understand all, a kind of harmonic analysis must be added. So my proposition would be, to use notation a bit flexible..
To your 5-limit thirds:
I think, (12), 19,31,43,50 and 55 are truly meantone. (They avoid syntonic commas)
22, 34 and 53 have a different DNA, they express a difference between 2 different sized full tones, so they have a tendency towards limit-5 Just Intonation.
37 and 41 I have never analysed.
We obviously disagree on notation, but I think for music showing off the 5-prime limit with (syntonic) commas as a structural element they should be visible from the notation. / points up, \ points down, so those are the direction of the commas. If I wanted to emulate Tanaka's notation I might use ' for up and , for down, or simply + and -, but it's just an ASCII symbol.
I am not prescribing 5-limit comma notation for music that is tuned using higher primes, or that uses smaller divisions. However what I was saying listing those EDOs is that 5-limit music written using a similar notation would translate just fine through all of those systems and more. For the meantones, indeed 12, 19, 31, 43, 50, 55, we could ignore the comma symbols and still have the correct note, as the syntonic comma vanishes entirely. That means that even writing the symbol wouldn't change the pitch. 22, 34, 41, 46, 53 all do a good job at interpreting the syntonic comma notation, as a syntonic comma is one step in each, and ratios of 5 are tuned fairly well. 37 is an oddball, as it has a particularly large fifth, but a very good 5/4 small major third, so vertically it sounds quite a bit like JI, but melodically a bit different. Still, the notation holds. 41-equal is a lot like pythagorean, with the one step comma a bit larger, meaning slightly flat 5/4 and slightly sharp 6/5, but in general, better than 22 equal, and with fifths very close to just 3/2.
It's interesting how much the cues we pickup in music come from expectations based on what we've heard before. Because this just reminds me of learning how to tune a guitar 😅
Cthulhu loved to play on instruments like this one. 👾
oh man, that last one though 🤤
cool stuff
The 7th simultaneously makes it more complex and more "edible", interesting.
At the beginning, it seems like an out of tune child's piano....by the end, it sounds like it's always been that way, EDO-12 sounds like a plastic toy, and there are no longer enough frets on my guitar...
One question: What exactly is a clavemusicum? Does it just mean keyboard instrument?
The "clavemusicum omnitonum" is a harpsichord built by Vito Trasuntino in 1606. It has 31 keys per octave and was used as a model to build the instrument that you can see in the video (the top one).
Is Archicembalo a Clavemusicum omnitonum?
Good to hear and see an actual harpsichord built for microtonal music and sounding good. I know they were made back in the very early Baroque, but as far as I know only 1 example survives, in a museum. From the RUclips sidebar it looks like somebody else has also made one that is different from this one -- ruclips.net/video/bEmfg5oa59Y/видео.html although that one has only 19 keys per octave, on 1 manual (but sounds like the Ghost of Arnold Schoenberg got his hands on it). I must say, though -- this one (like the original Arcicembalo, but even more so) looks extremely hard to play, needing 4 hands. This (and the extra expense of construction) may have limited adoption back in the day . . . . Here's another 19-tone instrument used to play a composition by Froberg: ruclips.net/video/S0rbrNqDCew/видео.html
Can you tell me where I can but this instrument? And for how much?
www.krebs-cembalobau.ch/Instrumente/Clavemusicum-Omnitonum/ Sorry it's in another language.
THEY JUST PLACED IT ON TOP OF THE 34 KEY, IDK why i'm laughing so hard about it
The more unimpressive an art is the more impressive the theory needs to sound with impressive looking words - "syntonic comma", "diesis", "tonality flux", "cubic flux". Give me a break. Sounds like shit, unless used as special effect noises that are supposed to sound kind of weird, but you will never make a great melody with this tuning, not even a catchy one, nor will you make great chord progressions. The reason for this is that most of the effect in art comes from the big movements or big forms, microtones are little details -says so right in the name - and will only sound good as embellishments or small adjustments of twelve tone motions.
ok and
Lmao. Syntonic comma, diesis, etc... Those are just labels given to intervals of a certain size (in this case very small intervals). No different from differentiating whole tone from semi tone. "You will never make a great melody with this tuning" Your statement cannot be more wrong and ignorant. This tuning can both make sounds that are more dissonant AND more consonant than 12-tet. It depends on how you use it. You can literally play a song made in 12-tet AND MAKE IT SOUND BETTER. "most of the effect in art comes from the big movements" Again, wrong. V to I works because the leading tone moves up to the tonic which is A SEMI TONE, THE SMALLEST INTERVAL IN 12TET. This also uses something called Voice Leading which is using the least amount of movement per "voice" (per note) which makes a much smoother transition between chords. Microtonal music potentially allows for even smoother voice leading because you have smaller intervals. In the end it's a matter of what you're accustomed to and opinion. And your opinion sucks, in my opinion. :) Open up your mind and ears, and have a good one. Oh and check this out ruclips.net/video/sLHKmbXkoco/видео.html and this cuz why not. ruclips.net/video/Try25EAlZgw/видео.html Also check out Sevish. He's cool.
Sure, nobody needs to know these terms or is expected to appreciate such exploratory examples on an artistic level. These little videos are not showing pieces of art, they document a kind of a laboratory situation, where people explore very specific things. Whether they are or will be relevant for "actual art" depends whether composers and music producers chose to use these specific things or not.
@@Studio31plus Anything that can be heard by the ears, or sensed by the other sense organs, has artistic potential, but some things have very high artistic potential, while others have extremely low potential. And every time someone practices anything musical they're doing an experiment, whether they know it or not. The labels are secondary to the experience - in this case of sounds -and are useful only to recall these experiences and to organize them so that they're easier to explore, and the labels become valuable only if the sound itself is impressive.
The thing with aesthetics is that we can only distinguish, and make intelligible, between a small number of things within a certain gamut or palette. This is why the big movements are most important, and why the first principle of design is simplification. We can compare by analogy the available range of notes with shapes. It's easy to imagine a triangle or a rectangle, but once you get above a dodecagon everything pretty much looks like a circle. The standard 12 tones, which technically are microtonal, are like a dodecagon, where additional tones just sound like variations of those other twelve. This can be interesting, but only after someone has a strong grasp of the basic shapes of music and knows how to limit their palette.
@@armando9740 While I totally agree with your generic statements, I disagree with your conclusion. I like all kinds of analogies, and while I understand your analogy to the dodecagon geometrically, it doesn't work to assess the complexity of musical structures. The eye and the ear are too different to make this analogy be productive. I'm not arguing that "big movements" are not important, but in my personal perception and experience, tiny details can make a remarkable difference and shape a piece. As a musician I change between large scale opera productions and microtonal chamber music very often (and many things in between), and I witness how my sensitivity and perception scales to the musical environment. Therefore I can't share your dismissal of small intervals.