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
Some modified versions of a chart on the article on just intonation.
Simplified version of original chart
| factor | 1⁄9 | 1⁄3 | 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 | |
| 1⁄5 | G♭ | D♭ | A♭ | E♭ | B♭ | note |
| 64:45 | 16:15 | 8:5 | 6:5 | 9:5 | ratio |
Version with fractions instead of ratios
| factor | 1⁄9 | 1⁄3 | 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 | 3⁄2 | 9⁄8 | ratio | |
| 1⁄5 | G♭ | D♭ | A♭ | E♭ | B♭ | note |
| 64⁄45 | 16⁄15 | 8⁄5 | 6⁄5 | 9⁄5 | ratio |
Ptolemy's intense diatonic scale
| factor | 1⁄9 | 1⁄3 | 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 | 3⁄2 | 9⁄8 | ratio | |
| 1⁄5 | G♭- | D♭ | A♭ | E♭ | B♭ | note |
| 64⁄45 | 16⁄15 | 8⁄5 | 6⁄5 | 9⁄5 | ratio |
Versions omitting powers of 2 required to keep the numbers between 1 and 2
| factor | 1⁄9 | 1⁄3 | 1 | 3 | 9 | |
|---|---|---|---|---|---|---|
| 5 | D | A | E | B | F♯ | note |
| 5⁄9 | 5⁄3 | 5 | 15 | 45 | ratio | |
| 1 | B♭ | F | C | G | D | note |
| 1⁄9 | 1⁄3 | 1 | 3 | 9 | ratio | |
| 1⁄5 | G♭ | D♭ | A♭ | E♭ | B♭ | note |
| 1⁄45 | 1⁄15 | 1⁄5 | 3⁄5 | 9⁄5 | ratio |
Versions just showing powers of 2 and 3
| 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 | |
| 1⁄5 | G♭ | D♭ | A♭ | E♭ | B♭ | note |
| 3-2·5-1 | 3-1·5-1 | 5-1 | 31·5-1 | 32·5-1 | ratio |
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
Some modified versions of a chart on the article on just intonation.
Simplified version of original chart
| factor | 1⁄9 | 1⁄3 | 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 | |
| 1⁄5 | G♭ | D♭ | A♭ | E♭ | B♭ | note |
| 64:45 | 16:15 | 8:5 | 6:5 | 9:5 | ratio |
Version with fractions instead of ratios
| factor | 1⁄9 | 1⁄3 | 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 | 3⁄2 | 9⁄8 | ratio | |
| 1⁄5 | G♭ | D♭ | A♭ | E♭ | B♭ | note |
| 64⁄45 | 16⁄15 | 8⁄5 | 6⁄5 | 9⁄5 | ratio |
Ptolemy's intense diatonic scale
| factor | 1⁄9 | 1⁄3 | 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 | 3⁄2 | 9⁄8 | ratio | |
| 1⁄5 | G♭- | D♭ | A♭ | E♭ | B♭ | note |
| 64⁄45 | 16⁄15 | 8⁄5 | 6⁄5 | 9⁄5 | ratio |
Versions omitting powers of 2 required to keep the numbers between 1 and 2
| factor | 1⁄9 | 1⁄3 | 1 | 3 | 9 | |
|---|---|---|---|---|---|---|
| 5 | D | A | E | B | F♯ | note |
| 5⁄9 | 5⁄3 | 5 | 15 | 45 | ratio | |
| 1 | B♭ | F | C | G | D | note |
| 1⁄9 | 1⁄3 | 1 | 3 | 9 | ratio | |
| 1⁄5 | G♭ | D♭ | A♭ | E♭ | B♭ | note |
| 1⁄45 | 1⁄15 | 1⁄5 | 3⁄5 | 9⁄5 | ratio |
Versions just showing powers of 2 and 3
| 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 | |
| 1⁄5 | G♭ | D♭ | A♭ | E♭ | B♭ | note |
| 3-2·5-1 | 3-1·5-1 | 5-1 | 31·5-1 | 32·5-1 | ratio |