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I want to keep the typical numbering system for different parts and chapters but add interlude in between with its own numbering.

Similar to what this tread does except instead of "Software Break" I want it to be "Interlude". Hopefully all that in Org-mode.

Current setup

#+OPTIONS: tags:nil toc:nil
#+LATEX_CLASS: memoir
#+TAGS: noexport sample
#+STARTUP: indent
#+LATEX_HEADER: \usepackage{chngcntr} \counterwithin*{chapter}{part}

* Interlude
** Interlude1
* A Title
** A SubTitle
** Another SubTitle
* Interlude
** Interlude2
* Another Title
** Yet another subtitle
** Yet another another subtitle
* Interlude
** Interlude3

Exporting that as pdf using C-c C-e l o produces what you'd expect, but I want it to something like this

Expectation

                        Interlude
1. First Interlude
    ...

                          Part I
                         A Title
Chapter 1
A SubTitle
    ...
Chapter 2
Another SubTitle
    ...

                        Interlude
2. Second Interlude
    ...

                          Part 2
                      Another Title
Chapter 1
Yet another subtitle
    ...
Chapter 2
Yet another another subtitle
    ...
                        Interlude
3. Third Interlude
    ...

In short

  1. Interlude subsection's (First Interlude, Second Interlude, etc) numbering is consistent across the book but Chapter's numbering resets after every Part.
  2. Interlude as the top-most header doesn't have a Part above it. It replaced Part.
#+LATEX_HEADER: \usepackage{chngcntr} \counterwithin*{chapter}{part}

resets numbering of

chapter (corresponds to ** headers)

after every

part (corresponds to * headers)

which I want interlude to completely ignore.

So my question is, is that possible in Org-mode?

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