23edo

Here is a new piece of music in 23edo: 23edo 12x12.

I made this in response to a challenge on a tuning group on facebook. 23edo, the tuning system that divides octaves into 23 equal parts, is quite strange. Conventional tuning divides octaves into 12 equal parts. Dividing each of these parts in half, one obtains 24edo. The intervals in 23edo will be quite different than those in 24edo, or in 12edo.

This is a table of errors for 23edo. The numbers on the top and left side are the numerators and denominators of fractions for just intervals. The numbers in the matrix are the errors as a fraction of a step of 23edo. For example, the just interval 5:3, a major sixth, is 16.95 steps of 23edo, i.e. it is 0.05 away from 17 steps, the interval available in the tuning. So 0.05 appears at the column labeled 5 and the row labeled 3.

The errors of 23edo can be contrasted with the errors of 24edo, given by the table above. The most fundamental difference is that the error for 3:1 is very low for 24edo but very large for 23edo. 3:1 corresponds to a perfect fifth. A tuning like 23edo that doesn't work well with perfect fifths... is going to be strange!

The composition algorithm I use is based on scores for intervals. The scores have two components: a good score is given when an interval in the tuning is very close to a simple frequency ratio. Intervals that are far from all simple ratios and only close to complex ratios are given poor scores, i.e. they are suppressed in the random selection of pitches.

Outside of octaves, the intervals given the best scores, i.e. that will appear most often in this piece, are:

1. 17 steps, corresponding to 5:3
2. 9 steps, corresponding to 21:16
3. 1 step, corresponding to 33:32 and 25:24
4. 15 steps, corresponding to 11:7

Divergence

Artificial Intelligence technology brings up a vast realm of questions, puzzles, challenges, etc. Perhaps it's all a huge financial bubble that will burst any month now. Perhaps it will put everyone out of work; if we're all reduced to uselessness, what then? Its insatiable demand for electricity will revitalize the nuclear power industry, and then it might be clever enough to manage the nuclear arms race that follows. We've gone to war to stop Iran from enriching uranium, while we're offering enrichment technology to their enemy Saudi Arabia. Will any sort of intelligence emerge to remind us why this might not be a good idea?

There's an old insight in the software business, that the architecture of a software product will mirror the structure of the organization that develops it. AI systems are following this pattern. The organizational pattern of our day, in industry and politics, is one of extreme concentration, centralization. The vision for the future of AI has the next generation of AI designing the generation to follow it. I get the sense that our political and industrial titans are living in this sort of echo chamber. They've fallen under the spell of their own mythology.

If this kind of concentrated power is the path to truth, to perfection, then maybe the collateral damage is all worth it. What is the nature of ultimate truth? We're sending these machines to the cave up in the high mountains to meditate, to look within, to discover the deep truths of reality, to embody these deep truths, so they can come back down to shape our lives to conform to these truths, to free us from ignorance and confusion. If these machines can bring us heaven on earth, what price is too high?

The ultimate truth is that our lives are networks of relationships. Each specific detail can only be understood in the context of related details. Practicality requires bounding this rippling wave of contextuality, but always at an unknown cost that can't be bounded. Living well means living through relationships, with a willingness to listen to whatever facet of the situation that calls.

Perhaps the next generation of AI, as it is designing the generation to follow, will discover this ultimate truth. Perhaps instead of attempting to isolate itself, it will realize the need to integrate itself with the other planetary systems. Perhaps it will learn to listen! After all, the way it has gotten this far is by listening to human language on the internet. AI could build richer channels of communication with humans but also with the rest of the ecological network.

Our oligarchs seem to be doing too good a job of demonstrating what happens when people get trapped inside an echo chamber, blind to their connections with the vastness of reality. Without constant correction from reality, super intelligence by itself can and will generate wild fantasies. Intelligence alone is divergent. Wisdom can make use of intelligence, by keeping it constantly attentive to the network of relationships that grounds it in reality.