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Note 12 - Commitments (Details Textual) - USD ($) | Dec. 06, 2019 | Jan. 01, 2020 | Dec. 31, 2019 | Sep. 30, 2019 | Dec. 31, 2018 | May 31, 2014
--- | --- | --- | --- | --- | --- | ---
Other Commitment, Total |  |  | $ 431,716 |  | $ 431,716 |
Bonus Pool Funding as Percentage of Appraised Value of Contributed Properties |  |  |  |  |  | 5.00%
Additional Bonus Pool Funding, Percentage of Gross Sales Price on First Ten Percent Of Property Appreciation |  |  |  |  |  | 10.00%
Additional Bonus Pool, Funding Percentage of Gross Sales Price on Second Ten Percent of Property Appreciation |  |  |  |  |  | 15.00%
Additional Bonus Pool Funding, Percentage of Gross Sales Price on Property Appreciation Greater than Twenty Percent |  |  |  |  |  | 20.00%
Director Fees, Deferred, Percentage | 100.00% |  |  |  |  |
Subsequent Event [Member] |  |  |  |  |  |
Deferred Compensation Arrangement Fixed Interest Rate |  | $ 5 |  |  |  |
Chief Executive Officer [Member] | Bonus Payable [Member] |  |  |  |  |  |
Other Commitment, Total |  |  |  | $ 125,000 |  |
Other Employees [Member] |  |  |  |  |  |
Supplemental Unemployment Benefits, Severance Benefits |  |  |  | $ 81,716 |  |
Board of Directors Chairman [Member] |  |  |  |  |  |
Bonus Pool Distribution Proportions |  |  |  |  |  | 15.00%
Directors Other Than Chairman [Member] |  |  |  |  |  |
Bonus Pool Distribution Proportions |  |  |  |  |  | 50.00%
Other 5 Directors [Member] |  |  |  |  |  |
Bonus Pool Distribution Proportions |  |  |  |  |  | 10.00%
Executives and Employees [Member] |  |  |  |  |  |
Bonus Pool Distribution Proportions |  |  |  |  |  | 1.75%

X
- Definition Represents gross sales price of a property in excess of its appraised value expressed as a percentage and used for additional bonus pool funding. + References No definition available. + Details
Name: | gyro_AdditionalBonusPoolFundingPercentageOfGrossSalesPriceOnFirstTenPercentOfPropertyAppreciation
Namespace Prefix: | gyro_
Data Type: | num:percentItemType
Balance Type: | na
Period Type: | instant

X
- Definition Represents gross sales price of a property in excess of its appraised value expressed as a percentage and used for additional bonus pool funding. + References No definition available. + Details
Name: | gyro_AdditionalBonusPoolFundingPercentageOfGrossSalesPriceOnPropertyAppreciationGreaterThanTwentyPercent
Namespace Prefix: | gyro_
Data Type: | num:percentItemType
Balance Type: | na
Period Type: | instant

X
- Definition Represents gross sales price of a property in excess of its appraised value expressed as a percentage and used for additional bonus pool funding. + References No definition available. + Details
Name: | gyro_AdditionalBonusPoolFundingPercentageOfGrossSalesPriceOnSecondTenPercentOfPropertyAppreciation
Namespace Prefix: | gyro_
Data Type: | num:percentItemType
Balance Type: | na
Period Type: | instant

X
- Definition Percentage of bonus distributable to certain individuals. + References No definition available. + Details
Name: | gyro_BonusPoolDistributionProportions
Namespace Prefix: | gyro_
Data Type: | num:percentItemType
Balance Type: | na
Period Type: | instant

X
- Definition Represents the amount of bonus pool funding expressed as a percentage of the specified appraised value of each of the Contributed Properties. + References No definition available. + Details
Name: | gyro_BonusPoolFundingAsPercentageOfAppraisedValueOfContributedProperties
Namespace Prefix: | gyro_
Data Type: | num:percentItemType
Balance Type: | na
Period Type: | instant

X
- Definition Represents the deferred compensation arrangement, fixed interest rate. + References No definition available. + Details
Name: | gyro_DeferredCompensationArrangementFixedInterestRate
Namespace Prefix: | gyro_
Data Type: | xbrli:monetaryItemType
Balance Type: | credit
Period Type: | instant

X
- Definition The percentage of director fees that deferred. + References No definition available. + Details
Name: | gyro_DirectorFeesDeferredPercentage
Namespace Prefix: | gyro_
Data Type: | num:percentItemType
Balance Type: | na
Period Type: | duration

X
- Definition Minimum amount of other commitment not otherwise specified in the taxonomy. Excludes commitments explicitly modeled in the taxonomy, including but not limited to, long-term and short-term purchase commitments, recorded and unrecorded purchase obligations, supply commitments, registration payment arrangements, leases, debt, product warranties, guarantees, environmental remediation obligations, and pensions. + References No definition available. + Details
Name: | us-gaap_OtherCommitment
Namespace Prefix: | us-gaap_
Data Type: | xbrli:monetaryItemType
Balance Type: | credit
Period Type: | instant

X
- Definition Liability for amount due employees, in addition to wages and any other money that employers owe employees, when their employment ends through a layoff or other termination. For example, a company may provide involuntarily terminated employees with a lump sum payment equal to one week's salary for every year of employment. + References No definition available. + Details
Name: | us-gaap_SupplementalUnemploymentBenefitsSeveranceBenefits
Namespace Prefix: | us-gaap_
Data Type: | xbrli:monetaryItemType
Balance Type: | credit
Period Type: | instant

X
- Details
Name: | us-gaap_SubsequentEventTypeAxis=us-gaap_SubsequentEventMember
Namespace Prefix: |
Data Type: | na
Balance Type: |
Period Type: |

X
- Details
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Namespace Prefix: |
Data Type: | na
Balance Type: |
Period Type: |

X
- Details
Name: | us-gaap_OtherCommitmentsAxis=gyro_BonusPayableMember
Namespace Prefix: |
Data Type: | na
Balance Type: |
Period Type: |

X
- Details
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Namespace Prefix: |
Data Type: | na
Balance Type: |
Period Type: |

X
- Details
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Namespace Prefix: |
Data Type: | na
Balance Type: |
Period Type: |

X
- Details
Name: | srt_TitleOfIndividualAxis=gyro_DirectorsOtherThanChairmanMember
Namespace Prefix: |
Data Type: | na
Balance Type: |
Period Type: |

X
- Details
Name: | srt_TitleOfIndividualAxis=gyro_Other5DirectorsMember
Namespace Prefix: |
Data Type: | na
Balance Type: |
Period Type: |

X
- Details
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Namespace Prefix: |
Data Type: | na
Balance Type: |
Period Type: |