Debt - Historical Transactions (Narrative) (Details)						12 Months Ended
	Sep. 17, 2024 USD ($) Rate	Jun. 30, 2024	Jun. 29, 2024	Jan. 24, 2024 USD ($) Rate	Jan. 27, 2023	Sep. 30, 2025 USD ($) Rate	Sep. 30, 2024 USD ($)	Sep. 30, 2023 USD ($)	Feb. 05, 2025 Rate	Sep. 20, 2024 USD ($)	Nov. 30, 2023 USD ($)	Nov. 29, 2023 USD ($)
Debt Instrument [Line Items]
Weighted-average interest rate of total debt						4.10%	4.30%	4.10%
January 2024 Senior Term Loan Credit Agreement
Debt Instrument [Line Items]
Proceeds from issuance of secured note						$ 42,000,000
Repayments of secured debt						42,000,000
September 2024 Senior Term Loan Credit Agreement
Debt Instrument [Line Items]
Proceeds from issuance of secured note						62,000,000
Repayments of secured debt						62,000,000
Mortgage Term Loan due 2033
Debt Instrument [Line Items]
Proceeds from issuance of secured note						0	$ 0	$ 19,000,000
Repayments of secured debt						$ 1,000,000	0	$ 1,000,000
Third-Parties
Debt Instrument [Line Items]
Debt fees	$ 2,000,000			$ 3,000,000
Creditors
Debt Instrument [Line Items]
Debt fees				$ 2,000,000
Acquisition Corp.
Debt Instrument [Line Items]
Debt instrument, basis spread on variable rate (as a percent) | Rate	1.75%			2.00%
Acquisition Corp. | Fed Funds Effective Rate Overnight Index Swap Rate
Debt Instrument [Line Items]
Debt instrument, basis spread on variable rate (as a percent) | Rate	0.50%			0.50%
Acquisition Corp. | Fed Funds Effective Rate Overnight Index Swap Rate | Senior Term Loan Facility -Tranche G
Debt Instrument [Line Items]
Debt instrument, basis spread on variable rate (as a percent)						0.50%
Acquisition Corp. | Secured Overnight Financing Rate (SOFR)
Debt Instrument [Line Items]
Debt instrument, basis spread on variable rate (as a percent) | Rate	1.00%			1.00%
Acquisition Corp. | Secured Overnight Financing Rate (SOFR) | Senior Term Loan Facility -Tranche G
Debt Instrument [Line Items]
Debt instrument, basis spread on variable rate (as a percent)						1.75%
Acquisition Corp. | Secured Overnight Financing Rate (SOFR) | Mortgage Term Loan due 2033
Debt Instrument [Line Items]
Debt instrument, basis spread on variable rate (as a percent)					1.40%
Acquisition Corp. | Base Rate
Debt Instrument [Line Items]
Debt instrument, basis spread on variable rate (as a percent)	1.00%			1.00%
Acquisition Corp. | Base Rate | Senior Term Loan Facility -Tranche G
Debt Instrument [Line Items]
Debt instrument, basis spread on variable rate (as a percent)						1.00%
Term loan borrower alternate base rate election rate						1.00%
Additional interest rate on other overdue amounts						2.00%
Tempo | Tempo Asset-Based Notes due 2050
Debt Instrument [Line Items]
Debt instrument, basis spread on variable rate (as a percent) | Rate						5.00%
Weighted-average interest rate of total debt | Rate									4.62%
Tempo | Asset-Based Class A Notes
Debt Instrument [Line Items]
Debt instrument, basis spread on variable rate (as a percent) | Rate						3.53%
Tempo | Asset-Based Class B Notes
Debt Instrument [Line Items]
Debt instrument, basis spread on variable rate (as a percent) | Rate						4.28%
Revolving Credit Facility | Beethoven Credit Agreement
Debt Instrument [Line Items]
Debt instrument, basis spread on variable rate (as a percent)						1.00%
Term loan borrower alternate base rate election rate						1.00%
Revolving Credit Facility | Fed Funds Effective Rate Overnight Index Swap Rate | Beethoven Credit Agreement
Debt Instrument [Line Items]
Debt instrument, basis spread on variable rate (as a percent)						0.50%
Revolving Credit Facility | Secured Overnight Financing Rate (SOFR) | Beethoven Credit Agreement
Debt Instrument [Line Items]
Debt instrument, basis spread on variable rate (as a percent)						2.00%
Revolving Credit Facility | Eurodollar Applicable Margin Rate | 2020 Revolving Loans
Debt Instrument [Line Items]
Debt instrument, basis spread on variable rate (as a percent)		1.375%	1.875%
Revolving Credit Facility | ABR Applicable Margin Rate | 2020 Revolving Loans
Debt Instrument [Line Items]
Debt instrument, basis spread on variable rate (as a percent)		0.375%	0.875%
Revolving Credit Facility | Acquisition Corp.
Debt Instrument [Line Items]
Line of credit facility, current borrowing capacity						$ 350,000,000	$ 350,000,000				$ 350,000,000	$ 300,000,000
Increase in secured indebtedness to EBITDA											140,000,000	$ 105,000,000
Secured indebtedness of EBITDA										$ 750,000,000	$ 250,000,000
Debt instrument, covenant, total indebtedness to EBITDA ratio											3.60
Term loan borrower alternate base rate election rate						1.00%
Additional interest on overdue principal						2.00%
Revolving Credit Facility | Acquisition Corp. | Initial Revolving Loans
Debt Instrument [Line Items]
Debt instrument, basis spread on variable rate (as a percent)						0.75%
Revolving Credit Facility | Acquisition Corp. | 2020 Revolving Loans
Debt Instrument [Line Items]
Debt instrument, basis spread on variable rate (as a percent)						0.875%
Senior secured indebtedness to EBITDA ratio						2.02
Revolving Credit Facility | Acquisition Corp. | Fed Funds Effective Rate Overnight Index Swap Rate
Debt Instrument [Line Items]
Debt instrument, basis spread on variable rate (as a percent)						0.50%
Revolving Credit Facility | Acquisition Corp. | Secured Overnight Financing Rate (SOFR) | Initial Revolving Loans
Debt Instrument [Line Items]
Debt instrument, basis spread on variable rate (as a percent)						1.75%
Revolving Credit Facility | Acquisition Corp. | Secured Overnight Financing Rate (SOFR) | 2020 Revolving Loans
Debt Instrument [Line Items]
Debt instrument, basis spread on variable rate (as a percent)						1.875%