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Note 7 - Real Estate (Details Textual) - USD ($) | 12 Months Ended |
--- | --- | ---
Dec. 31, 2019 | Dec. 31, 2018 | Dec. 31, 2017
Real Estate Held-for-sale, Period Increase (Decrease) | $ 12,068,730 | $ 3,984,605 |
Real Estate Held-for-sale | 48,270,000 | 36,201,270 | $ 33,016,665
Port Jefferson Professional Park [Member] |  |  |
Real Estate Held-for-sale, Period Increase (Decrease) |  | $ (800,000) |
Real Estate Held-for-sale | $ 48,270,000 |  |

X
- Definition Amount of increase (decrease) before accumulated depreciation of investments in land and buildings held for sale, excluding real estate considered to be inventory of the entity. + References No definition available. + Details
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Namespace Prefix: | gyro_
Data Type: | xbrli:monetaryItemType
Balance Type: | credit
Period Type: | duration

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- Definition Carrying amount as of the balance sheet date of investments in land and buildings held for sale, excluding real estate considered to be inventory of the entity. + References Reference 1: http://fasb.org/us-gaap/role/ref/legacyRef -Publisher FASB -Name Accounting Standards Codification -Topic 944 -SubTopic 210 -Section S99 -Paragraph 1 -Subparagraph (SX 210.7-03.1(f)) -URI http://asc.fasb.org/extlink&oid=119400593&loc=d3e572229-122910 + Details
Name: | us-gaap_RealEstateHeldforsale
Namespace Prefix: | us-gaap_
Data Type: | xbrli:monetaryItemType
Balance Type: | debit
Period Type: | instant

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- Details
Name: | us-gaap_LongLivedAssetsHeldForSaleByAssetTypeAxis=gyro_PortJeffersonProfessionalParkMember
Namespace Prefix: |
Data Type: | na
Balance Type: |
Period Type: |