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sebastianrosenzweig committed Mar 7, 2025
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---
title: 'Gala: A Python package for galactic dynamics'
title: '`pytch`: A Real-Time Pitch Analysis Tool For Polyphonic Music'
tags:
- Python
- astronomy
- dynamics
- galactic dynamics
- milky way
- Audio Processing
- Music Information Retrieval
- Singing Voice Analysis
- GUI
authors:
- name: Adrian M. Price-Whelan
orcid: 0000-0000-0000-0000
equal-contrib: true
affiliation: "1, 2" # (Multiple affiliations must be quoted)
- name: Author Without ORCID
equal-contrib: true # (This is how you can denote equal contributions between multiple authors)
affiliation: 2
- name: Author with no affiliation
corresponding: true # (This is how to denote the corresponding author)
affiliation: 3
- given-names: Ludwig
dropping-particle: van
surname: Beethoven
- name: Sebastian Rosenzweig
orcid: 0000-0003-4964-9217
corresponding: true
affiliation: 1
- name: Marius Kriegerowski
orcid:
corresponding: false
affiliation: 3
- name: Lukas Dietz
orcid:
corresponding: false
affiliation: 5
- name: Peter Meier
orcid: 0000-0002-3094-1931
corresponding: false
affiliation: 2
- name: Sebastian Strahl
orcid: 0009-0007-9654-7762
corresponding: false
affiliation: 2
- name: Frank Scherbaum
orcid: 0000-0002-5050-7331
corresponding: false
affiliation: 2
- name: Meinard Müller
orcid: 0000-0001-6062-7524
corresponding: false
affiliation: 2


affiliations:
- name: Lyman Spitzer, Jr. Fellow, Princeton University, United States
- name: Audoo Ltd., London, UK
index: 1
ror: 00hx57361
- name: Institution Name, Country
- name: International Audio Laboratories Erlangen, Germany
index: 2
- name: Independent Researcher, Country
- name: University of Potsdam, Germany
index: 3
date: 13 August 2017
- name: Independent Researcher, Berlin, Germany
index: 4
- name: Tantive GmbH, Nürnberg Germany
index: 5
date: 7 March 2025
bibliography: paper.bib

# Optional fields if submitting to a AAS journal too, see this blog post:
# https://blog.joss.theoj.org/2018/12/a-new-collaboration-with-aas-publishing
aas-doi: 10.3847/xxxxx <- update this with the DOI from AAS once you know it.
aas-journal: Astrophysical Journal <- The name of the AAS journal.
---

# Summary

The forces on stars, galaxies, and dark matter under external gravitational
fields lead to the dynamical evolution of structures in the universe. The orbits
of these bodies are therefore key to understanding the formation, history, and
future state of galaxies. The field of "galactic dynamics," which aims to model
the gravitating components of galaxies to study their structure and evolution,
is now well-established, commonly taught, and frequently used in astronomy.
Aside from toy problems and demonstrations, the majority of problems require
efficient numerical tools, many of which require the same base code (e.g., for
performing numerical orbit integration).

# Statement of need
# Graphical User Interface (GUI)
![`pytch` GUI.\label{fig:GUI}](pictures/screenshot.png){ width=90% }

`Gala` is an Astropy-affiliated Python package for galactic dynamics. Python
enables wrapping low-level languages (e.g., C) for speed without losing
flexibility or ease-of-use in the user-interface. The API for `Gala` was
designed to provide a class-based and user-friendly interface to fast (C or
Cython-optimized) implementations of common operations such as gravitational
potential and force evaluation, orbit integration, dynamical transformations,
and chaos indicators for nonlinear dynamics. `Gala` also relies heavily on and
interfaces well with the implementations of physical units and astronomical
coordinate systems in the `Astropy` package [@astropy] (`astropy.units` and
`astropy.coordinates`).
A screenshot of the main GUI is shown in Figure \autoref{fig:GUI}.

`Gala` was designed to be used by both astronomical researchers and by
students in courses on gravitational dynamics or astronomy. It has already been
used in a number of scientific publications [@Pearson:2017] and has also been
used in graduate courses on Galactic dynamics to, e.g., provide interactive
visualizations of textbook material [@Binney:2008]. The combination of speed,
design, and support for Astropy functionality in `Gala` will enable exciting
scientific explorations of forthcoming data releases from the *Gaia* mission
[@gaia] by students and experts alike.
# Audio Processing

# Mathematics
# Statement of Need

Single dollars ($) are required for inline mathematics e.g. $f(x) = e^{\pi/x}$

Double dollars make self-standing equations:

$$\Theta(x) = \left\{\begin{array}{l}
0\textrm{ if } x < 0\cr
1\textrm{ else}
\end{array}\right.$$

You can also use plain \LaTeX for equations
\begin{equation}\label{eq:fourier}
\hat f(\omega) = \int_{-\infty}^{\infty} f(x) e^{i\omega x} dx
\end{equation}
and refer to \autoref{eq:fourier} from text.

# Citations

Citations to entries in paper.bib should be in
[rMarkdown](http://rmarkdown.rstudio.com/authoring_bibliographies_and_citations.html)
format.

If you want to cite a software repository URL (e.g. something on GitHub without a preferred
citation) then you can do it with the example BibTeX entry below for @fidgit.

For a quick reference, the following citation commands can be used:
- `@author:2001` -> "Author et al. (2001)"
- `[@author:2001]` -> "(Author et al., 2001)"
- `[@author1:2001; @author2:2001]` -> "(Author1 et al., 2001; Author2 et al., 2002)"

# Figures

Figures can be included like this:
![Caption for example figure.\label{fig:example}](figure.png)
and referenced from text using \autoref{fig:example}.

Figure sizes can be customized by adding an optional second parameter:
![Caption for example figure.](figure.png){ width=20% }

# Acknowledgements

We acknowledge contributions from Brigitta Sipocz, Syrtis Major, and Semyeong
Oh, and support from Kathryn Johnston during the genesis of this project.
We would like to thank all singers that helped developing this tool. The International Audio Laboratories Erlangen are a joint institution of the Friedrich-Alexander-Universität Erlangen-Nürnberg (FAU) and Fraunhofer Institute for Integrated Circuits IIS.

# References

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