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The SOABI does not make any difference between GNU libc and musl libc.
Using official docker images:
# debian build with GNU libc
$ docker run --rm python:slim python -c 'import sysconfig;print(sysconfig.get_config_var("SOABI"))'
cpython-39-x86_64-linux-gnu
# alpine build with musl libc
$ docker run --rm python:alpine python -c 'import sysconfig;print(sysconfig.get_config_var("SOABI"))'
cpython-39-x86_64-linux-gnu
Both ends with `-gnu`, while it would be expected that with musl it would end with `-musl`
This affects the extension suffix:
$ docker run --rm python:slim python-config --extension-suffix
.cpython-39-x86_64-linux-gnu.so
$ docker run --rm python:alpine python-config --extension-suffix
.cpython-39-x86_64-linux-gnu.so
Which again affects the pre-compiled binary wheels, and binary modules built with musl libc gets mixed up with the GNU libc modules due to the -gnu.so suffix.
The source of the problem is that the `configure.ac` file assumes that all defined(__linux__) is -gnu when detecting the PLATFORM_TRIPLET.
```
...
#if defined(__ANDROID__)
 # Android is not a multiarch system.
#elif defined(__linux__)
# if defined(__x86_64__) && defined(__LP64__)
 x86_64-linux-gnu
# elif defined(__x86_64__) && defined(__ILP32__)
 x86_64-linux-gnux32
# elif defined(__i386__)
...
```
So when building python with musl libc the PLATFORM_TRIPLET always sets `*-linux-gnu`.
output from configure run on musl system:
```
...
checking for a sed that does not truncate output... /bin/sed 
checking for --with-cxx-main=<compiler>... no 
checking for the platform triplet based on compiler characteristics... x86_64-linux-gnu 
...
```
A first step in fixing this would be to make sure that we only set -gnu when __GLIBC__ is defined:
```diff
diff --git a/configure.ac b/configure.ac
index 1f5a008388..1b4690c90f 100644
--- a/configure.ac
+++ b/configure.ac
@@ -726,7 +726,7 @@ cat >> conftest.c <<EOF
 #undef unix
 #if defined(__ANDROID__)
 # Android is not a multiarch system.
-#elif defined(__linux__)
+#elif defined(__linux__) && defined (__GLIBC__)
 # if defined(__x86_64__) && defined(__LP64__)
 x86_64-linux-gnu
```
But that would make build with musl fail with "unknown platform triplet".
Not sure what the proper fix would be, but one way to extract the suffix from `$CPP -dumpmachine`

The suffix "-gnu" does not stand for "glibc".
The triplet defines the calling convention. For example x86_64-linux-gnu means x86_64 / AMD64 CPU architecture, Linux, with standard GNU / GCC calling convention. Other calling conventions are "x86_64-linux-gnux32" for X32 on AMD64 and "arm-linux-gnueabihf" for 32bit ARM with extended ABI and hardware float support.
The triplets are standardized beyond Python. Debian's multiarch page lists and explains a large amount of triplets, https://wiki.debian.org/Multiarch/Tuples 

Does this mean that the SOABI should be the same for python built with musl libc and GNU libc?
They are not really ABI compatible.

SOABI basically contains the CPU architecture and Kernel ABI. The libc ABI is yet another dimension that is not encoded in the shared library ABI. 
The libc ABI is more complex than just glibc or musl. You need to include the ABI version of all core components. For example manylinux2014 defines the ABI for glibc as GLIBC_2.17, CXXABI_1.3.7, CXXABI_TM_1, GLIBCXX_3.4.19, GCC_4.8.0.
As a rule of thumb, a SOABI like ".cpython-39-x86_64-linux-gnu.so" only works the current host. You cannot safely move the file to another host or bump the SO version of any library, unless you ensure that the ABIs of all libraries are compatible.

The referenced https://wiki.debian.org/Multiarch/Tuples doc says:
> we require unique identifiers for each architecture that identifies an incompatible set of libraries that we want to be co-installed.
Since GNU libc and musl libc are not ABI compatible they can not share same unique identifier. I think replacing -gnu with -musl makes sense.

Do you have glibc and musl installed side by side?

> Do you have glibc and musl installed side by side?
No. But there is nothing preventing me to have the libc runtimes installed in parallel with glibc.
/lib/libc.so.6
/lib/libc.musl-x86_64.so.1
And it is not common that people copy libc.so.6 (with friends) to their alpine docker images to run both in same container. If that is a good idea is other discussion.
I do understand that full ABI compatibility also may involve libc ABI version, but I think that is a slightly different problem. Newer versions of glibc and musl libc are backwards compatible. You can expect a binary built with old libc version to run with new libc. But you cannot expect a binary built with musl libc to run with gnu libc.
gcc recognizes -linux-musl as a valid platform tuple different that differs from -linux-gnu:
https://github.com/gcc-mirror/gcc/blob/master/gcc/config/t-musl
The standard autotools' config.guess[1] also recognizes -musl as different platform. 
 $ ./config.guess 
 x86_64-pc-linux-musl
[1]: https://github.com/python/cpython/blob/12d0a7642fc552fa17b1608fe135306cddec5f4e/config.guess#L158
So I think it makes sense to treat *-linux-musl as a different platform than *-linux-gnu.
If you still insist that this is only about calling convention and not platform, then I think you should at least clarify that in the configure.ac script to avoid confusion:
 sed -i -e 's/PLATFORM_TRIPLET/CALLING_CONVENTION_TRIPLET/g' -e 's/platform triplet/calling convention triplet/g' configure.ac

I stand corrected. The last element in the platform triplet does seem to indicate libc.
Is there any formal definition of the platform triplet or is it defined by GCC's reference implementation? A quick search didn't reveal any decisive results.
The next steps here would be:
- document the platform triplet in regards of musl libc (and potentially other libcs like uclibc and embedded newlibc)
- buildbot with Alpine musl
Let's continue this on https://discuss.python.org/t/wheels-for-musl-alpine/7084 

This mentions some examples for musl triplets/tuples:
https://wiki.musl-libc.org/getting-started.html
It points to https://github.com/richfelker/musl-cross-make/blob/master/README.md#supported-targets which I think is the best documentation. (Rich Felker is the author and lead developer or musl libc).
I'm not sure its worth spend time on uClibc which does not seem to have any commits at all since 2015. https://git.uclibc.org/uClibc/log/
We will work on our side on buildbot with Alpine linux.
Thank you for being understanding.

While original uClibc is not maintained, its fork called uClibc-ng is supposedly binary-compatible with uClibc and is still somehow maintained:
https://uclibc-ng.org/
https://repo.or.cz/w/uclibc-ng.git
https://www.uclibc.org/news.html also says:
"While uClibc releases are on hold, you may use uClibc-ng"
libc part of platform tuple on uClibc-ng systems is expected to be "uclibc".

I created a PR for this https://github.com/python/cpython/pull/24502 

If this is deemed a bugfix, the PR should be backported.

Can anyone problem examples that it’s not an option to continue using the "technically incorrect" `-gnu` suffix on 3.9 and 3.10? From what I understand, te suffix technically works (as in the module will load correctly), it just fails to distinguish the ABI in the name.
If that’s correct, I feel "being able to distinguish between modules built against musl and glibc" should be a feature request and only implemented for 3.11+, while versions 3.10 and prior continue to use `-gnu`. This will also provide a simpler way out of the wheel compatibility problem; projects can distribute different wheels for 3.10 (or lower) and 3.11 (or higher), while the former wheel continues to contain `-gnu`-suffixed modules, and only contain `-musl`-suffixed ones in the latter.

We had a call and have a potential path forward. Quick summary:
* Add a patch on top of the current patch to make CPython look for `-gnu` on top of `-musl` for Alpine 3.15 and 3.14. Reverting the patch would break every Alpine wheel previously locally compiled (like NumPy) and would require rebuilding all shipped packages that depend on Python.
* Revert the patch for CPython 3.10 in Alpine 3.16, due mid next year.
* Take the existing patch (PR 24502) targeting upstream CPython 3.11 and change search to include `abi3-gnu` on musl after looking for `abi3-musl`. The ability to install both binaries into a single folder would be a new "feature" of CPython 3.11.
* Optionally this could be checked and normalized by auditwheel (like changing `-musl` to `-gnu` on 3.9) if desired. ABI3 wheels targeting <3.11 could be normalized to `-gnu`.
How does that sound?

I noticed that 9 test suites are failing on Alpine 3.15, see bpo-46390. Should we require a stable buildbot before we proclaim official support for Alpine?

New changeset 1f036ede59e2c4befc07714cf76603c591d5c972 by Natanael Copa in branch 'main':
bpo-43112: detect musl as a separate SOABI (GH-24502)
https://github.com/python/cpython/commit/1f036ede59e2c4befc07714cf76603c591d5c972