I'm John C. Baez. I'm an emeritus professor at the math department of the University of California, Riverside, but during the autumn of 2022 and 2023 I gave a series of math lectures at the University of Edinburgh, where I had a Leverhulme Visiting Professorship. In May-June 2024 I will return to Edinburgh to work on software for agent-based models with some epidemiologists and computer scientists at the International Centre for Mathematical Sciences.

I like quantum field theory, general relativity, n-categories, and other things that seem scary at first but turn out to be simple and beautiful when you understand them. Since I enjoy these things so much, I can't help but feel that everyone else will too. So, I like to explain stuff on my website. In 2003, I added a diary, where I can be a bit more random and diverse. In August 2006, I joined David Corfield and Urs Schreiber on a group blog: the n-Category Café.

In 2010 I went to the Centre for Quantum Technology in Singapore for 2 years and began developing a general theory of networks, aimed at getting mathematicians interested in applying their brilliance to the global ecological crisis. To help do this I started another blog, called Azimuth. Since 2021, I have been applying this theory of networks to software for epidemiological modeling.

If you want to know what I'm thinking about these days, try my articles on the n-Category Café, my blog Azimuth, and my diary.

Just intonation

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Some modified versions of a chart on the article on just intonation.

Simplified version of original chart

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factor 19 13 1 3 9
5 D A E B F note
10:9 5:3 5:4 15:8 45:32 ratio
1 B F C G D note
16:9 4:3 1:1 3:2 9:8 ratio
15 G D A E B note
64:45 16:15 8:5 6:5 9:5 ratio

Version with fractions instead of ratios

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factor 19 13 1 3 9
5 D A E B F note
109 53 54 158 4532 ratio
1 B F C G D note
169 43 1 32 98 ratio
15 G D A E B note
6445 1615 85 65 95 ratio


Ptolemy's intense diatonic scale

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factor 19 13 1 3 9
5 D- A E B F note
109 53 54 158 4532 ratio
1 B- F C G D note
169 43 1 32 98 ratio
15 G- D A E B note
6445 1615 85 65 95 ratio

Versions omitting powers of 2 required to keep the numbers between 1 and 2

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factor 19 13 1 3 9
5 D A E B F note
59 53 5 15 45 ratio
1 B F C G D note
19 13 1 3 9 ratio
15 G D A E B note
145 115 15 35 95 ratio


Versions just showing powers of 2 and 3

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factor 3-2 3-1 1 31 32
5 D A E B F note
3-2·5 3-1·5 5 31·5 32·5 ratio
1 B F C G D note
3-2 3-1 1 31 32 ratio
15 G D A E B note
3-2·5-1 3-1·5-1 5-1 31·5-1 32·5-1 ratio