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Note 15 - Fair Value of Financial Instruments - Change in Real Estate Assets Value (Details)	9 Months Ended
	Sep. 30, 2016 USD ($)
Real estate assets at December 31, 2015	$ 46,950,000
Real estate sold during the nine-months ended September 30, 2016	(18,261,000)
Change in value of real estate assets	221,000	[1]
Real estate assets at September 30, 2016	$ 28,910,000
[1] The net increase in value of $221,000 is attributable to an increase in value from the sale of the Fairfax Medical Center at $15,000 in excess of the estimated value and the sale of two buildings in the Port Jefferson Professional Park at $206,000 in excess of the estimated value at December 31, 2015. The combined net increase of $221,000 represents the net increase in value of the real estate compared to that which was reported in the Statement of Net Assets at December 31, 2015.

X

- Definition

Amount of change in real estate to reflect the change in value under liquidation basis.

+ References

No definition available.

+ Details

Name:	gyro_LiquidationBasisOfAccountingChangeInLiquidationValueOfRealEstate
Namespace Prefix:	gyro_
Data Type:	xbrli:monetaryItemType
Balance Type:	credit
Period Type:	duration

X

- 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://www.xbrl.org/2003/role/presentationRef
-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=6879938&loc=d3e572229-122910

+ Details

Name:	us-gaap_RealEstateHeldforsale
Namespace Prefix:	us-gaap_
Data Type:	xbrli:monetaryItemType
Balance Type:	debit
Period Type:	instant

X

- Definition

Revenue from the sale of commercial, industrial, or residential property during the period. This element is more likely than not relevant to an entity for which real estate operations are a principal activity. If real estate operations are not a principal activity, the reporting entity would likely use a gain (loss) on sale of property, plant, or equipment type element.

+ References

Reference 1: http://www.xbrl.org/2003/role/presentationRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 225
-SubTopic 10
-Section S99
-Paragraph 2
-Subparagraph (SX 210.5-03.1(e))
-URI http://asc.fasb.org/extlink&oid=63488584&loc=d3e20235-122688

+ Details

Name:	us-gaap_SalesOfRealEstate
Namespace Prefix:	us-gaap_
Data Type:	xbrli:monetaryItemType
Balance Type:	credit
Period Type:	duration