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User:John Baez

I'm John C. Baez. I'm an emeritus professor at the [http://math.ucr.edu/ math department of the University of California, Riverside], but during the autumn of 2022 and 2023 I gave a [https://math.ucr.edu/home/baez/twf/ series of math lectures] at the University of Edinburgh, where I had a [https://www.leverhulme.ac.uk/visiting-professorships Leverhulme Visiting Professorship]. In May-June 2024 I will return to Edinburgh to work on [https://johncarlosbaez.wordpress.com/2023/08/17/agent-based-models-part-2/ software for agent-based models] with some epidemiologists and computer scientists at the [https://www.icms.org.uk/ 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 [http://math.ucr.edu/home/baez/FUN.html website]. In [http://math.ucr.edu/home/baez/diary/2003.html 2003], I added a [http://math.ucr.edu/home/baez/diary/ diary], where I can be a bit more random and diverse. In [http://golem.ph.utexas.edu/category/2006/08/index.shtml August 2006], I joined David Corfield and Urs Schreiber on a group blog: [http://golem.ph.utexas.edu/category the n-Category Café].

In 2010 I went to the Centre for Quantum Technology in Singapore for 2 years and began developing a [http://math.ucr.edu/home/baez/networks/ 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 [http://johncarlosbaez.wordpress.com/ Azimuth]. Since 2021, I have been applying this theory of networks to [https://math.ucr.edu/home/baez/epidemiology_african/ software for epidemiological modeling].

If you want to know what I'm thinking about these days, try [https://golem.ph.utexas.edu/category/john.html my articles on the n-Category Café], my blog [http://johncarlosbaez.wordpress.com/ Azimuth], and my [http://math.ucr.edu/home/baez/diary/index.html#now diary].

Just intonation

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

= Simplified version of original chart =

class="wikitable" style="text-align: center"
factor

! style="width: 4em" | {{fraction|1|9}}

! style="width: 4em" | {{fraction|1|3}}

! style="width: 4em" | 1

! style="width: 4em" | 3

! style="width: 4em" | 9

!

rowspan="2" | 5

| style="background:coral;" | D

| A

| E

| B

| style="background:springgreen;" | F{{music|sharp}}

! note

style="background:coral;" | 10:9

| 5:3

| 5:4

| 15:8

| style="background:springgreen;" | 45:32

! ratio

rowspan="2" | 1

| style="background:gold;" | B{{music|b}}

| F

| C

| G

| style="background:coral;" | D

! note

style="background:gold;" | 16:9

| 4:3

| 1:1

| 3:2

| style="background:coral;" | 9:8

! ratio

rowspan="2" | {{fraction|1|5}}

| style="background:springgreen;" | G{{music|flat}}

| D{{music|flat}}

| A{{music|flat}}

| E{{music|flat}}

| style="background:gold;" | B{{music|flat}}

! note

style="background:springgreen;" | 64:45

| 16:15

| 8:5

| 6:5

| style="background:gold;" | 9:5

! ratio

= Version with fractions instead of ratios =

class="wikitable" style="text-align: center"
factor

! style="width: 4em" | {{fraction|1|9}}

! style="width: 4em" | {{fraction|1|3}}

! style="width: 4em" | 1

! style="width: 4em" | 3

! style="width: 4em" | 9

!

rowspan="2" | 5

| style="background:coral;" | D

| A

| E

| B

| style="background:springgreen;" | F{{music|sharp}}

! note

style="background:coral;" | {{fraction|10|9}}

| {{fraction|5|3}}

| {{fraction|5|4}}

| {{fraction|15|8}}

| style="background:springgreen;" | {{fraction|45|32}}

! ratio

rowspan="2" | 1

| style="background:gold;" | B{{music|b}}

| F

| C

| G

| style="background:coral;" | D

! note

style="background:gold;" | {{fraction|16|9}}

| {{fraction|4|3}}

| 1

| {{fraction|3|2}}

| style="background:coral;" | {{fraction|9|8}}

! ratio

rowspan="2" | {{fraction|1|5}}

| style="background:springgreen;" | G{{music|flat}}

| D{{music|flat}}

| A{{music|flat}}

| E{{music|flat}}

| style="background:gold;" | B{{music|flat}}

! note

style="background:springgreen;" | {{fraction|64|45}}

| {{fraction|16|15}}

| {{fraction|8|5}}

| {{fraction|6|5}}

| style="background:gold;" | {{fraction|9|5}}

! ratio

= Ptolemy's intense diatonic scale =

class="wikitable" style="text-align: center"
factor

! style="width: 4em" | {{fraction|1|9}}

! style="width: 4em" | {{fraction|1|3}}

! style="width: 4em" | 1

! style="width: 4em" | 3

! style="width: 4em" | 9

!

rowspan="2" | 5

| style="background:darkred;" | D-

| style="background:lightcyan;" | A

| style="background:lightcyan;" | E

| style="background:lightcyan;" | B

| style="background:cadetblue;" | F{{music|sharp}}

! note

style="background:darkred;" | {{fraction|10|9}}

| style="background:lightcyan;" | {{fraction|5|3}}

| style="background:lightcyan;" | {{fraction|5|4}}

| style="background:lightcyan;" | {{fraction|15|8}}

| style="background:cadetblue;" | {{fraction|45|32}}

! ratio

rowspan="2" | 1

| style="background:paleturquoise;" | B{{music|b}}-

| style="background:lightcyan;" | F

| style="background:lightcyan;" | C

| style="background:lightcyan;" | G

| style="background:lightcyan;" | D

! note

style="background:paleturquoise;" | {{fraction|16|9}}

| style="background:lightcyan;" |{{fraction|4|3}}

| style="background:lightcyan;" |1

| style="background:lightcyan;" | {{fraction|3|2}}

| style="background:lightcyan;" | {{fraction|9|8}}

! ratio

rowspan="2" | {{fraction|1|5}}

| style="background:cadetblue;" | G{{music|flat}}-

| style="background:paleturquoise;" | D{{music|flat}}

| style="background:paleturquoise;" | A{{music|flat}}

| style="background:paleturquoise;" | E{{music|flat}}

| style="background:darkred;" | B{{music|flat}}

! note

style="background:cadetblue;" | {{fraction|64|45}}

| style="background:paleturquoise;" | {{fraction|16|15}}

| style="background:paleturquoise;" | {{fraction|8|5}}

| style="background:paleturquoise;" | {{fraction|6|5}}

| style="background:darkred;" | {{fraction|9|5}}

! ratio

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

class="wikitable" style="text-align: center"
factor

! style="width: 4em" | {{fraction|1|9}}

! style="width: 4em" | {{fraction|1|3}}

! style="width: 4em" | 1

! style="width: 4em" | 3

! style="width: 4em" | 9

!

rowspan="2" | 5

| style="background:coral;" | D

| A

| E

| B

| style="background:springgreen;" | F{{music|sharp}}

! note

style="background:coral;" | {{fraction|5|9}}

| {{fraction|5|3}}

| 5

| 15

| style="background:springgreen;" | 45

! ratio

rowspan="2" | 1

| style="background:gold;" | B{{music|b}}

| F

| C

| G

| style="background:coral;" | D

! note

style="background:gold;" | {{fraction|1|9}}

| {{fraction|1|3}}

| 1

| 3

| style="background:coral;" | 9

! ratio

rowspan="2" | {{fraction|1|5}}

| style="background:springgreen;" | G{{music|flat}}

| D{{music|flat}}

| A{{music|flat}}

| E{{music|flat}}

| style="background:gold;" | B{{music|flat}}

! note

style="background:springgreen;" | {{fraction|1|45}}

| {{fraction|1|15}}

| {{fraction|1|5}}

| {{fraction|3|5}}

| style="background:gold;" | {{fraction|9|5}}

! ratio

= Versions just showing powers of 2 and 3 =

class="wikitable" style="text-align: center"
factor

! style="width: 4em" | 3{{sup

2}}

! style="width: 4em" | 3{{sup

1}}

! style="width: 4em" | 1

! style="width: 4em" | 3{{sup|1}}

! style="width: 4em" | 3{{sup|2}}

!

rowspan="2" | 5

| style="background:coral;" | D

| A

| E

| B

| style="background:springgreen;" | F{{music|sharp}}

! note

style="background:coral;" | 3{{sup
2}}·5

| 3{{sup

1}}·5

| 5

| 3{{sup|1}}·5

| style="background:springgreen;" | 3{{sup|2}}·5

! ratio

rowspan="2" | 1

| style="background:gold;" | B{{music|b}}

| F

| C

| G

| style="background:coral;" | D

! note

style="background:gold;" | 3{{sup
2}}

| 3{{sup

1}}

| 1

| 3{{sup|1}}

| style="background:coral;" | 3{{sup|2}}

! ratio

rowspan="2" | {{fraction|1|5}}

| style="background:springgreen;" | G{{music|flat}}

| D{{music|flat}}

| A{{music|flat}}

| E{{music|flat}}

| style="background:gold;" | B{{music|flat}}

! note

style="background:springgreen;" | 3{{sup
2}}·5{{sup
1}}

| 3{{sup

1}}·5{{sup
1}}

| 5{{sup

1}}

| 3{{sup|1}}·5{{sup

1}}

| style="background:gold;" | 3{{sup|2}}·5{{sup

1}}

! ratio