↬ Twenty-one – 03

I’m a little further down the Partch rabbit hole, although not as much as I’d hoped. (More on why later.) Curious as to how one navigates a scale with 43 degrees, I started to look into how Partch constructed it. At its core lies a tonality diamond – a two-dimensional set of ratios in which one dimension mirrors the other. A 5-limit tonality diamond, for example, looks like this:

5⁄4 6⁄5
1⁄1 1⁄1 1⁄1
8⁄5 5⁄3

Tonality diamonds display symmetry both in terms of the upper and lower part of the diamond (which could also be thought of in terms of a harmonic and sub-harmonic series – an overtone (otonality/major) and undertone (utonality/minor) scale), as well as the distances between the notes – when measured in cents a scale constructed using them is symmetrical whether ascending or descending.

Given that each odd number represents a new note in the harmonic series and may thus be considered an ‘identity’, a 5-limit scale contains only 3 identities. Partch takes an 11-limit tonality diamond, or up to the 11th harmonic of the overtone series, as the core of his scale, which thus has 6 distinct identities. In-depth explanations can be found on Wikipedia.

Partch constructed his Diamond Marimba on the basis of this tonality diamond – as can be seen in this documentary (which also covers many of his other instruments) in which Partch demonstrates how it is easy to play triads or full chords with a single stroke of a mallet.

However, as the Wikipedia article explains:

There are two reasons why the 11-limit ratios by themselves would not make a good scale. First, the scale only contains a complete set of chords based on one tonic pitch. Second, it contains large gaps, between the tonic and the two pitches to either side, as well as several other places.

Partch attempted to remedy this through the addition of 14 extra ratios (obtained from the product or quotient of other intervals within the 11 limit) to the 29 of the 11-limit diamond. This makes it possible to modulate to many degrees of the scale (though not all) and play justly tuned harmonies based on those new tonics.

I was wondering if using colours to distinguish the notes of the diamond might be useful as an addition to my Partch overlay for the Sensel Morph, and began experimenting with various possibilities, when it occurred to me that Partch had himself added colours to the keys of his Chromolodeons. After spending some time zooming in on the photographs in the Wikipedia article I simply transferred his colours to my overlay. Interestingly he has a full rainbow of colours (one for each identity) to distinguish the root and split colours on the 4/3 and 3/4.

  • Red = 2, 4, 8, 16
  • Orange = 3, 6, (9), 12
  • Yellow = 5, 10, 20
  • Green = 7, 14
  • Blue = (3), 9 (9 is not a prime number, neither is it a new ratio, since it can be arrived at from two fifths), 18 
  • Purple = 11
  • Grey = additional ratios derived as products or quotients of the ratios in the diamond, but exceeding the 11 limit.

Giving each number of the ratios (each identity) a colour, rather than the ratio as a whole, as I had initially tried, works surprisingly well.

I’ve found the addition of the colours a great help in navigating the scale when playing it with the Morph – it certainly makes its symmetries clear. I’ll hopefully get round to making a video demonstrating it soon. It’s also interesting to experience the layout and how one can modulate to different keys within it in relation to the sounding results.

And for an extra tidbit on the topic of balance and symmetry in scales and rhythms – see this video demonstration with a bicycle wheel.

* * *

If all of the above sounds extremely nerdy and removed from everyday life, Sune Anderberg pointed out (after the previous newsletter) that super-talented multi-award-winning Jacob Collier was an example of someone in the popular sphere sharing his enthusiasm for just intonation with his fans on social media.

Here he is explaining his harmonisation of The Bleak Midwinter.

My first listen to Djesse 3, his latest album, got me thinking of Prince’s lesser known album The Rainbow Children from 20 years ago.

The overtone/undertone, major/minor mirrors of Partch’s constructions play an important role in Collier’s approach to harmony. Executed with an incredible finesse (the kids these days!) and made possible with the layering that can be achieved with a DAW and a laptop. All three parts of the interview linked to above are well worth working through.

* * *

Something that has consumed far more of my attention that I would have liked during the past few weeks has been NFTs. Non Fungible Tokens, which are basically a way of creating a digital something (in most cases metadata attached to a token stored in a blockchain) that cannot be altered or duplicated and which the art world has jumped on as a way of, once again, making very large sums of money.

They popped onto my radar in earnest when some of the people I admire began ‘minting’ them – which is all very interesting as a development, a tool in one’s arsenal as an artist that might be explored – until one becomes aware of the horrific environmental costs they bring with them – and that at a time in which the world is facing a serious environmental crisis.

Everest Pipkin has written an article that I find perhaps best sums up the reasons not to jump in on the NFT frenzy.

As fate would have it, none other than our above-mentioned friend Mr. Collier announced that he would be auctioning some screenshots from his Grammy nominated Djesse 3 sessions as NFTs using the Zora platform/protocol. As with many exploring the NFT realm a disclaimer concerning the environmental issues was built into the announcement itself: Jacob stated that given the environmental costs, he would be donating proceeds from the auction towards research into how the technology might me more sustainably implemented in the future.

Jacob’s twitter feed exploded with push-back from his fans. Perhaps 98% of the replies expressed disappointment, imploring him not to go ahead with it, explaining that most artists were against it, and pointing-out the absurdity of “fucking-up the environment” in order to try and throw money at fixing it. On the day of the auction nothing appeared on Zora at the appointed time, and eight hours later Collier announced that he wouldn’t be going through with it, having decided “to postpone it to a time where the methods are more sustainable and ecologically sound.”

I truly believe that NFTs will be able to radically change and decentralise the creative industry as we know it, once the tech is proven to be more sustainable. I am all for it – but, in the midst of a climate crisis, there are other things that feel more important at this time. —JC

The sense of needing to place a moratorium on NFTs for art projects until the environmental issues have been resolved is well laid out in Joanie Lemercier‘s The problem of CryptoArt. Everest Pipkin, in the article mentioned above, argues however that there is no sustainable version – that crypto currencies are irrevocably tied to energy consumption and that the move from their being based on PoW (Proof of Work) models to a PoS (Proof of Stake – essentially a kind of lottery) system brings other problems with it.

PoS currencies operate within the same conceptual framework as PoW currencies, and despite a number of PoS coins that do function, a pretty standard use case for PoS has been for PoW to point at and say “we’ll be there soon”.

Proof of stake is, and always has been, valuable as a bait and switch, but there are other, obvious problems with PoS (and various other proofs), which are that to more or less degrees they don’t address any of the problems with access to cryptocurrency relying on existing wealth.

And reminds us that climate and social justice are inextricably tied together. They also argue against artificially creating digital scarcity, that duplication is the one thing digital art has going for it:

Digital artists have media that can proliferate over a network and be held by many people at once without cheapening or breaking the aura of a first-hand experience. It is the one true benefit to working in digital space.

I’m horrified to see this willingly traded for an opportunity to reproduce the worst parts of the existing physical art market, where “the original” is useful foremost as a rare thing- a unique thing- that, in its scarcity, is an asset.

So given all those problems, what is it about NFTs that are proving so irresistible to so many? Johnny Miller (@unequalscenes), is a photographer known for his work in highlighting social inequality through drone photography that I’ve been following for a number of years. When he recently announced on Twitter that he had created his first NFT, stating that he was “aware of the hype and the costs associated with doing it”, I took the opportunity offered by his #askmeanything hashtag to ask him about his motivations, To which he replied:

Few reasons, 1: I think crypto is important and want to support it, 2: artists/businesses need to seek new markets/tech, 3: I dont think the eco footprint is fully clear yet, 4: the tradeoff for “trying” the tech is worth the hype for me.

Also (this might sound weird) the emotional calculations don’t become fully apparent to me unless I actually participate in something. So I guess I also wanted to try it out. 🤷

I appreciated his answer, and in the subsequent discussion he did acknowledge the devastating environmental cost. As someone interested in social justice he pointed to the need, especially in African countries for example, for alternative currencies that could be used for payments, rather than as assets.

That hope for Crypto as a way to stick it to the man, as an alternative to established systems is echoed in the Zora (the platform/protocol Collier was to have used for his NFT) “Manifesto”:


The platforms that hold our audiences and content hostage. The labels that lock down our rights. The galleries that hold our art ransom. The big brands that think exposure is cash. They have a monopoly on ownership, a monopoly on creativity and they have been robbing us of the value we create for as long as there’s been a creative industry.

So why not simply pay for a few carbon offset’s and enjoy the benefits of this new technology? To @unequalscenes “the blockchain (assigning contracts and verifying them) is valuable, because it provides me a way to verify ownership… Payment/network is a separate question.”

But, as Everest points out, they aren’t separate questions – the two are inextricably intertwined. And the costs of minting NFTs are not to be sneezed at. Besides Zora’s punk posturing, the system is one that builds riches for the few on the backs of the many. And is the offset lifestyle one we want to be a part of at this climate crucial time? Is it worth tying our creations to something inherently destructive?

I’ll close off this section with that quote from Quinn Norton’s wonderful A Ledger and a Network. Bitcoin, Money, and Datalove, Part Two – written all the way back in 2014, and a good starting point if one would like to get an idea of how the backbone of all this works.

The people involved in the Bitcoin economy are participating in a massive act of desire, a passionate creation of a truth through time, true even for those who feel nothing but greed, or nothing at all.

The community around Bitcoin calls the blockchain money, and their willingness to treat it like money is what makes it money. The more important people believe Bitcoin to be, the more impervious its record of the memory becomes. The desire to make Bitcoin money concentrates people and their processing power on fixing memory, and fixed it is.

* * *

Robin Sloan is the only example I’ve come across of someone approaching NFTs with a refreshing dose of playfulness. He created a little series of poems, “amulets”, the value of which is tied to the characteristics of the hash numbers that are the cornerstone of creating NFTs. He provides a little scratchpad in which one can try out various (poetic) inputs and see the hashes that are generated from them. It’s a wonderful way to get a sense of one of the basic building blocks of this technology. It would be especially wonderful if the amulets existed in a realm that didn’t require the consumption of huge amounts of electricity. Unfortunately they do – at least Robin has made buying offsets for each NFT a requirement baked into his system.

In what other way could NFTs be “cool”? One example that Robin covers in his article is the CryptoPunks that appeared as the first NFT on the Ethereum blockchain a few years ago – Ethereum being the currency/network that has cultivated a very different aesthetic from the more hardcore Bitcoin universe. The first to embrace using their blockchain for more artistic endeavours.

Dylan Field (@zoink) is the CEO of Figma – an exceptionally fine piece of browser-based software especially suited to collaboration. He was the proud owner of CryptoPunk #2890 until he recently sold it for a very healthy sum. Being the rightful owner he could use that CryptoPunk as his Twitter avatar (although anyone could in principle also use that combination of coloured pixels – though that in turn wouldn’t be cool), until the point at which he sold it. A lengthy Clubhouse conversation around that particular NFT and others has been uploaded to YouTube and it offers some insight into this world. There’s some sense of the joy of collecting for its own sake, and all that comes with owning and selling, not just investing. But all of that is predicated on it all being “pure bits” without the huge energy requirements that this technology involves. It baffles me how that elephant in the room continues to be ignored. “Insane” was the word going through my head as I listened to the Clubhouse conversation above – and indeed in this and many other conversations there seems to be some kind almost religious rapture and without any sense of how it all remains rooted within the physical world.


If you still have the stomach for more:

* * *

To close off, here’s Sam Prekop’s Spelling which has provided some wonderfully soothing, well-sounding ambience to my working hours during the past few weeks.

All the best

Leave a comment

Available formatting commands

Use Markdown commands or their HTML equivalents to add simple formatting to your comment:

Text markup
*italic*, **bold**, ~~strikethrough~~, `code` and <mark>marked text</mark>.
- Unordered item 1
- Unordered list item 2
1. Ordered list item 1
2. Ordered list item 2
> Quoted text
Code blocks
// A simple code block
// Some PHP code
[Link text](https://example.com)
Full URLs are automatically converted into links.

Hi, I’m <a rel="me" class="p-name u-url" href="https://rudigermeyer.com">Rudiger Meyer</a>, a composer interested in the play between music, sound, and&nbsp;media.