125/81 - Revision history

CompactStar at 05:01, 24 October 2026

2026-10-24T05:01:41Z

← Older revision		Revision as of 05:01, 24 October 2026
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	== Approximation ==		== Approximation ==
	This interval can be closely approximated by [[17/11]] and by 5 steps of [[8edo]].		This interval can be closely approximated by [[17/11]] and by 5 steps of [[8edo]]. The fractional-octave [[microtemperament]] [[octoid]] equates this interval to 5 steps of 8edo.

	{{Interval edo approximation\|17/11}}		{{Interval edo approximation\|17/11}}

FloraC: Correct math notation; move approximation info to the relevant section

2026-10-23T11:14:09Z

Correct math notation; move approximation info to the relevant section

← Older revision		Revision as of 11:14, 23 October 2026
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	\| Color name = triyo 5th, y<sup>3</sup>5		\| Color name = triyo 5th, y<sup>3</sup>5
	}}		}}
			'''125/81''', the '''triptolemaic augmented fifth''' or '''Trithagorean ultrafifth''', is a [[5-limit]] just interval equal to the Pythagorean augmented fifth [[6561/4096]] lowered by three syntonic commas (([[81/80]])<sup>3</sup>). It is also equal to [[25/16]] lowered by [[81/80]] and to [[128/81]] lowered by [[128/125]]. It also appears as a notable interval in the [[Trithagorean]] scale / [[3.5 subgroup]], being the [[3/1\|tritave]]-reduction of ([[5/3]])<sup>3</sup>.

	The '''triptolemaic augmented fifth''' or '''Trithagorean ultrafifth''', '''125/81''', is a [[5-limit]] just interval equal to the Pythagorean augmented fifth [[6561/4096]] lowered by 3 syntonic commas ([[81/80]]<sup>3</sup>). It is also equal to [[25/16]] lowered by [[81/80]] and to [[128/81]] lowered by [[128/125]]. It also appears as a notable interval in the [[Trithagorean]] scale/[[3.5 subgroup]], being the [[3/1\|tritave]]-reduction of [[5/3]]<sup>3</sup>. It can be closely approximated by [[17/11]] and by 5 steps of [[8edo]].
	== Approximation ==		== Approximation ==
			This interval can be closely approximated by [[17/11]] and by 5 steps of [[8edo]].

	{{Interval edo approximation\|17/11}}		{{Interval edo approximation\|17/11}}

CompactStar at 09:42, 23 October 2026

2026-10-23T09:42:52Z

← Older revision		Revision as of 09:42, 23 October 2026
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	}}		}}

	The '''triptolemaic augmented fifth''' or '''Trithagorean ultrafifth''', '''125/81''', is a [[5-limit]] just interval equal to the Pythagorean augmented fifth [[6561/4096]] lowered by 3 syntonic commas ([[81/8p]]<~~sub~~>3</sup>). It is also equal to [[25/16]] lowered by [[81/80]] and to [[128/81]] lowered by [[128/125]]. It also appears as a notable interval in the [[Trithagorean]] scale/[[3.5 subgroup]], being the [[3/1\|tritave]]-reduction of [[5/3]]<sup>3</sup>. It can be closely approximated by [[17/11]] and by 5 steps of [[8edo]].		The '''triptolemaic augmented fifth''' or '''Trithagorean ultrafifth''', '''125/81''', is a [[5-limit]] just interval equal to the Pythagorean augmented fifth [[6561/4096]] lowered by 3 syntonic commas ([[81/80]]<sup>3</sup>). It is also equal to [[25/16]] lowered by [[81/80]] and to [[128/81]] lowered by [[128/125]]. It also appears as a notable interval in the [[Trithagorean]] scale/[[3.5 subgroup]], being the [[3/1\|tritave]]-reduction of [[5/3]]<sup>3</sup>. It can be closely approximated by [[17/11]] and by 5 steps of [[8edo]].
	== Approximation ==		== Approximation ==
	{{Interval edo approximation\|17/11}}		{{Interval edo approximation\|17/11}}

CompactStar at 09:42, 23 October 2026

2026-10-23T09:42:45Z

← Older revision		Revision as of 09:42, 23 October 2026
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	}}		}}

	The '''triptolemaic augmented fifth''' or '''Trithagorean ultrafifth''', '''125/81''', is a [[5-limit]] just interval equal to the Pythagorean augmented fifth [[6561/4096]] lowered by 3 syntonic commas ([[81/80]]<sub>3</~~sub~~>)0. It is also equal [[25/16]] lowered by [[81/80]] and to [[128/81]] lowered by [[128/125]]. It also appears as a notable interval in the [[Trithagorean]] scale/[[3.5 subgroup]], being the [[3/1\|tritave]]-reduction of [[5/3]]<sup>3</sup>. It can be closely approximated by [[17/11]] and by 5 steps of [[8edo]].		The '''triptolemaic augmented fifth''' or '''Trithagorean ultrafifth''', '''125/81''', is a [[5-limit]] just interval equal to the Pythagorean augmented fifth [[6561/4096]] lowered by 3 syntonic commas ([[81/8p]]<sub>3</sup>). It is also equal to [[25/16]] lowered by [[81/80]] and to [[128/81]] lowered by [[128/125]]. It also appears as a notable interval in the [[Trithagorean]] scale/[[3.5 subgroup]], being the [[3/1\|tritave]]-reduction of [[5/3]]<sup>3</sup>. It can be closely approximated by [[17/11]] and by 5 steps of [[8edo]].
	== Approximation ==		== Approximation ==
	{{Interval edo approximation\|17/11}}		{{Interval edo approximation\|17/11}}

CompactStar at 09:42, 23 October 2026

2026-10-23T09:42:34Z

← Older revision		Revision as of 09:42, 23 October 2026
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	}}		}}

	The '''triptolemaic augmented fifth''' or '''Trithagorean ultrafifth''', '''125/81''', is a [[5-limit]] just interval equal to [[25/16]] lowered by [[81/80]]~~, or alternatively the Pythagorean minor sixth~~ [[128/81]] lowered by [[128/125]]. It also appears as a notable interval in the [[Trithagorean]] scale/[[3.5 subgroup]], being the [[3/1\|tritave]]-reduction of [[5/3]]<sup>3</sup>. It can be closely approximated by [[17/11]] and by 5 steps of [[8edo]].		The '''triptolemaic augmented fifth''' or '''Trithagorean ultrafifth''', '''125/81''', is a [[5-limit]] just interval equal to the Pythagorean augmented fifth [[6561/4096]] lowered by 3 syntonic commas ([[81/80]]<sub>3</sub>)0. It is also equal [[25/16]] lowered by [[81/80]] and to [[128/81]] lowered by [[128/125]]. It also appears as a notable interval in the [[Trithagorean]] scale/[[3.5 subgroup]], being the [[3/1\|tritave]]-reduction of [[5/3]]<sup>3</sup>. It can be closely approximated by [[17/11]] and by 5 steps of [[8edo]].
	== Approximation ==		== Approximation ==
	{{Interval edo approximation\|17/11}}		{{Interval edo approximation\|17/11}}

CompactStar at 09:39, 23 October 2026

2026-10-23T09:39:25Z

← Older revision		Revision as of 09:39, 23 October 2026
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	}}		}}

	The '''triptolemaic augmented fifth''' or '''Trithagorean ultrafifth''', '''125/81''', is a [[5-limit]] ~~interva of~~ equal to [[25/16]] lowered by [[81/80]], or alternatively the Pythagorean minor sixth [[128/81]] lowered by [[128/125]]. It also appears as a notable interval in the [[Trithagorean]] scale/[[3.5 subgroup]], being the [[3/1\|tritave]]-reduction of [[5/3]]<sup>3</sup>. It can be closely approximated by [[17/11]] and by 5 steps of [[8edo]].		The '''triptolemaic augmented fifth''' or '''Trithagorean ultrafifth''', '''125/81''', is a [[5-limit]] just interval equal to [[25/16]] lowered by [[81/80]], or alternatively the Pythagorean minor sixth [[128/81]] lowered by [[128/125]]. It also appears as a notable interval in the [[Trithagorean]] scale/[[3.5 subgroup]], being the [[3/1\|tritave]]-reduction of [[5/3]]<sup>3</sup>. It can be closely approximated by [[17/11]] and by 5 steps of [[8edo]].
	== Approximation ==		== Approximation ==
	{{Interval edo approximation\|17/11}}		{{Interval edo approximation\|17/11}}

CompactStar at 09:38, 23 October 2026

2026-10-23T09:38:43Z

← Older revision		Revision as of 09:38, 23 October 2026
Line 4:		Line 4:
	}}		}}

	The '''triptolemaic augmented fifth''' or '''Trithagorean ultrafifth''', '''125/81''', is a [[5-limit]] interva of equal to [[25/16]] lowered by [[81/80]], or alternatively the Pythagorean minor sixth [[128/81]] lowered by [[128/125]]. It also appears as a notable interval in the [[Trithagorean]] scale/[[3.5 subgroup]], being the [[3/1\|tritave]]-reduction of [[5/3]]<sup>3</sup>. It can be closely approximated by [[17/11]].		The '''triptolemaic augmented fifth''' or '''Trithagorean ultrafifth''', '''125/81''', is a [[5-limit]] interva of equal to [[25/16]] lowered by [[81/80]], or alternatively the Pythagorean minor sixth [[128/81]] lowered by [[128/125]]. It also appears as a notable interval in the [[Trithagorean]] scale/[[3.5 subgroup]], being the [[3/1\|tritave]]-reduction of [[5/3]]<sup>3</sup>. It can be closely approximated by [[17/11]] and by 5 steps of [[8edo]].
	== Approximation ==		== Approximation ==
	{{Interval edo approximation\|17/11}}		{{Interval edo approximation\|17/11}}

CompactStar at 09:38, 23 October 2026

2026-10-23T09:38:26Z

← Older revision		Revision as of 09:38, 23 October 2026
Line 4:		Line 4:
	}}		}}

	The '''triptolemaic augmented fifth''' or '''Trithagorean ultrafifth''', '''125/81''', is a [[5-limit]] interva of equal to [[25/16]] lowered by [[81/80]], or alternatively the Pythagorean minor sixth [[128/81]] lowered by [[128/125]]. It also appears as a notable interval in the [[Trithagorean]] scale/[[3.5 subgroup]], being the [[3/1\|tritave]]-reduction of 5<sup>3</sup>. It can be closely approximated by [[17/11]].		The '''triptolemaic augmented fifth''' or '''Trithagorean ultrafifth''', '''125/81''', is a [[5-limit]] interva of equal to [[25/16]] lowered by [[81/80]], or alternatively the Pythagorean minor sixth [[128/81]] lowered by [[128/125]]. It also appears as a notable interval in the [[Trithagorean]] scale/[[3.5 subgroup]], being the [[3/1\|tritave]]-reduction of [[5/3]]<sup>3</sup>. It can be closely approximated by [[17/11]].
	== Approximation ==		== Approximation ==
	{{Interval edo approximation\|17/11}}		{{Interval edo approximation\|17/11}}

CompactStar at 09:38, 23 October 2026

2026-10-23T09:38:22Z

← Older revision		Revision as of 09:38, 23 October 2026
Line 4:		Line 4:
	}}		}}

	The '''triptolemaic augmented fifth''' or '''Trithagorean ultrafifth''', '''125/81''', is a [[5-limit]] interva of equal to [[25/16]] lowered by [[81/80]], or alternatively the Pythagorean minor sixth [[128/81]] lowered by [[128/125]]. It also appears as a notable interval in the [[Trithagorean]] scale/[[3.5 subgroup]], being the [[3/1\|tritave]]-reduction of (5~~/3)~~<~~sub~~>3</~~sub~~>. It can be closely approximated by [[17/11]].		The '''triptolemaic augmented fifth''' or '''Trithagorean ultrafifth''', '''125/81''', is a [[5-limit]] interva of equal to [[25/16]] lowered by [[81/80]], or alternatively the Pythagorean minor sixth [[128/81]] lowered by [[128/125]]. It also appears as a notable interval in the [[Trithagorean]] scale/[[3.5 subgroup]], being the [[3/1\|tritave]]-reduction of 5<sup>3</sup>. It can be closely approximated by [[17/11]].
	== Approximation ==		== Approximation ==
	{{Interval edo approximation\|17/11}}		{{Interval edo approximation\|17/11}}

CompactStar at 09:38, 23 October 2026

2026-10-23T09:38:14Z

← Older revision		Revision as of 09:38, 23 October 2026
Line 4:		Line 4:
	}}		}}

	The '''triptolemaic augmented fifth''' or '''Trithagorean ultrafifth''', '''125/81''', is equal to [[25/16]] lowered by [[81/80]], or alternatively the Pythagorean minor sixth [[128/81]] lowered by [[128/125]]. It also appears as a notable interval in the [[Trithagorean]] scale/[[3.5 subgroup]], being the [[3/1\|tritave]]-reduction of (5/3)<sub>3</sub>. It can be closely approximated by [[17/11]].		The '''triptolemaic augmented fifth''' or '''Trithagorean ultrafifth''', '''125/81''', is a [[5-limit]] interva of equal to [[25/16]] lowered by [[81/80]], or alternatively the Pythagorean minor sixth [[128/81]] lowered by [[128/125]]. It also appears as a notable interval in the [[Trithagorean]] scale/[[3.5 subgroup]], being the [[3/1\|tritave]]-reduction of (5/3)<sub>3</sub>. It can be closely approximated by [[17/11]].
	== Approximation ==		== Approximation ==
	{{Interval edo approximation\|17/11}}		{{Interval edo approximation\|17/11}}