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Reproducible Example

import pandas as pd

# These work:
print(pd.Period(year=2014, quarter=3, freq=pd.offsets.QuarterEnd(startingMonth=12))) # -> 2014Q3
print(pd.Period(year=2014, quarter=3, freq=pd.offsets.QuarterEnd(startingMonth=2))) # -> 2014Q3

print(pd.Period(year=2014, quarter=3, freq=pd.offsets.QuarterEnd(startingMonth=12)).freqstr) # -> Q-DEC
print(pd.Period(year=2014, quarter=3, freq=pd.offsets.QuarterEnd(startingMonth=2)).freqstr) # -> Q-FEB

# this works
print(pd.PeriodIndex(year=[2014], quarter=[3], freq=pd.offsets.QuarterEnd(startingMonth=12))) # -> PeriodIndex(['2014Q3'], dtype='period[Q-DEC]')

# this does not work:
pd.PeriodIndex(year=[2014], quarter=[3], freq=pd.offsets.QuarterEnd(startingMonth=2))

Issue Description

I am able to create Periods with a freq of pd.offsets.QuarterEnd(startingMonth=2) but not a PeriodIndex:

AssertionError                            Traceback (most recent call last)
Cell In[9], line 12
      9 print(pd.PeriodIndex(year=[2014], quarter=[3], freq=pd.offsets.QuarterEnd(startingMonth=12))) # -> PeriodIndex(['2014Q3'], dtype='period[Q-DEC]')
     11 # this does not work:
---> 12 pd.PeriodIndex(year=[2014], quarter=[3], freq=pd.offsets.QuarterEnd(startingMonth=2))

File ~/.pyenv/versions/3.12.0/envs/scratch/lib/python3.12/site-packages/pandas/core/indexes/period.py:244, in PeriodIndex.__new__(cls, data, ordinal, freq, dtype, copy, name, **fields)
    240 if not fields:
    241     # test_pickle_compat_construction
    242     cls._raise_scalar_data_error(None)
--> 244 data, freq2 = PeriodArray._generate_range(None, None, None, freq, fields)
    245 # PeriodArray._generate range does validation that fields is
    246 # empty when really using the range-based constructor.
    247 freq = freq2

File ~/.pyenv/versions/3.12.0/envs/scratch/lib/python3.12/site-packages/pandas/core/arrays/period.py:341, in PeriodArray._generate_range(cls, start, end, periods, freq, fields)
    339     subarr, freq = _get_ordinal_range(start, end, periods, freq)
    340 elif field_count > 0:
--> 341     subarr, freq = _range_from_fields(freq=freq, **fields)
    342 else:
    343     raise ValueError("Not enough parameters to construct Period range")

File ~/.pyenv/versions/3.12.0/envs/scratch/lib/python3.12/site-packages/pandas/core/arrays/period.py:1249, in _range_from_fields(year, month, quarter, day, hour, minute, second, freq)
   1247     base = libperiod.freq_to_dtype_code(freq)
   1248     if base != FreqGroup.FR_QTR.value:
-> 1249         raise AssertionError("base must equal FR_QTR")
   1251 freqstr = freq.freqstr
   1252 year, quarter = _make_field_arrays(year, quarter)

AssertionError: base must equal FR_QTR

Expected Behavior

This is printed:

PeriodIndex(['2014Q3'], dtype='period[Q-FEB]')

Installed Versions

INSTALLED VERSIONS ------------------ commit : a60ad39b4a9febdea9a59d602dad44b1538b0ea5 python : 3.12.0.final.0 python-bits : 64 OS : Darwin OS-release : 22.1.0 Version : Darwin Kernel Version 22.1.0: Sun Oct 9 20:19:12 PDT 2022; root:xnu-8792.41.9~3/RELEASE_ARM64_T6020 machine : arm64 processor : arm byteorder : little LC_ALL : None LANG : en_US.UTF-8 LOCALE : en_US.UTF-8 pandas : 2.1.2 numpy : 1.26.1 pytz : 2023.3.post1 dateutil : 2.8.2 setuptools : 68.2.2 pip : 23.3.1 Cython : None pytest : None hypothesis : None sphinx : None blosc : None feather : None xlsxwriter : None lxml.etree : None html5lib : None pymysql : None psycopg2 : None jinja2 : 3.1.2 IPython : 8.17.2 pandas_datareader : None bs4 : 4.12.2 bottleneck : None dataframe-api-compat: None fastparquet : None fsspec : None gcsfs : None matplotlib : 3.8.0 numba : None numexpr : None odfpy : None openpyxl : None pandas_gbq : None pyarrow : None pyreadstat : None pyxlsb : None s3fs : None scipy : 1.11.3 sqlalchemy : None tables : None tabulate : None xarray : None xlrd : None zstandard : None tzdata : 2023.3 qtpy : None pyqt5 : None