25/16 - Revision history

FloraC: Text replacement - " {{Interval_Edo_Approximation | " to "{{Interval edo approximation|"

2025-11-03T13:07:46Z

Text replacement - " {{Interval_Edo_Approximation | " to "{{Interval edo approximation|"

← Older revision		Revision as of 13:07, 3 November 2025
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	While this interval has been referred to as the ''classic augmented fifth'' or ''classical augmented fifth'' for some time, the term ''diptolemaic'' [https://discord.com/channels/332357996569034752/516067802864549890/912167264789364736 was coined on Discord] by [[Flora Canou]] while discussing a proposal for a consistent naming scheme for different 5-limit intervals with [[Aura]]. Specifically, since "diptolemaic" intervals have two instances of prime 5 in their factorization, this interval is also referred to as the '''diptolemaic augmented fifth'''.		While this interval has been referred to as the ''classic augmented fifth'' or ''classical augmented fifth'' for some time, the term ''diptolemaic'' [https://discord.com/channels/332357996569034752/516067802864549890/912167264789364736 was coined on Discord] by [[Flora Canou]] while discussing a proposal for a consistent naming scheme for different 5-limit intervals with [[Aura]]. Specifically, since "diptolemaic" intervals have two instances of prime 5 in their factorization, this interval is also referred to as the '''diptolemaic augmented fifth'''.
	== Approximation ==		== Approximation ==
	{{~~Interval_Edo_Approximation~~ \| 25/16}}		{{Interval edo approximation\|25/16}}
	== See also ==		== See also ==
	* [[32/25]] – its [[octave complement]]		* [[32/25]] – its [[octave complement]]

Pailiaq at 07:35, 3 November 2025

2025-11-03T07:35:36Z

← Older revision		Revision as of 07:35, 3 November 2025
Line 8:		Line 8:

	While this interval has been referred to as the ''classic augmented fifth'' or ''classical augmented fifth'' for some time, the term ''diptolemaic'' [https://discord.com/channels/332357996569034752/516067802864549890/912167264789364736 was coined on Discord] by [[Flora Canou]] while discussing a proposal for a consistent naming scheme for different 5-limit intervals with [[Aura]]. Specifically, since "diptolemaic" intervals have two instances of prime 5 in their factorization, this interval is also referred to as the '''diptolemaic augmented fifth'''.		While this interval has been referred to as the ''classic augmented fifth'' or ''classical augmented fifth'' for some time, the term ''diptolemaic'' [https://discord.com/channels/332357996569034752/516067802864549890/912167264789364736 was coined on Discord] by [[Flora Canou]] while discussing a proposal for a consistent naming scheme for different 5-limit intervals with [[Aura]]. Specifically, since "diptolemaic" intervals have two instances of prime 5 in their factorization, this interval is also referred to as the '''diptolemaic augmented fifth'''.
			== Approximation ==
			{{Interval_Edo_Approximation \| 25/16}}
	== See also ==		== See also ==
	* [[32/25]] – its [[octave complement]]		* [[32/25]] – its [[octave complement]]

FloraC: - ptolemisma related contents (see talk)

2025-09-28T15:53:44Z

- ptolemisma related contents (see talk)

← Older revision		Revision as of 15:53, 28 September 2025
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	}}		}}

	'''25/16''', the '''classic(al) augmented fifth''' is the interval obtained by stacking two [[5/4]] major thirds, however, it gains additional [[isoharmonic chord\|isoharmonic]] identity from its position between [[11/8]] and [[7/4]], so it can frequently be used in conjunction with those, even in chords~~. It is [[100/99]] sharp of [[99/64]], and tempering out 100/99 makes 1-5/4-25/16 into a [[ptolemismic chords\|ptolemismic chord]]~~.		'''25/16''', the '''classic(al) augmented fifth''' is the interval obtained by stacking two [[5/4]] major thirds, however, it gains additional [[isoharmonic chord\|isoharmonic]] identity from its position between [[11/8]] and [[7/4]], so it can frequently be used in conjunction with those, even in chords.

	While this interval has been referred to as the ''classic augmented fifth'' or ''classical augmented fifth'' for some time, the term ''diptolemaic'' [https://discord.com/channels/332357996569034752/516067802864549890/912167264789364736 was coined on Discord] by [[Flora Canou]] while discussing a proposal for a consistent naming scheme for different 5-limit intervals with [[Aura]]. Specifically, since "diptolemaic" intervals have two instances of prime 5 in their factorization, this interval is also referred to as the '''diptolemaic augmented fifth'''.		While this interval has been referred to as the ''classic augmented fifth'' or ''classical augmented fifth'' for some time, the term ''diptolemaic'' [https://discord.com/channels/332357996569034752/516067802864549890/912167264789364736 was coined on Discord] by [[Flora Canou]] while discussing a proposal for a consistent naming scheme for different 5-limit intervals with [[Aura]]. Specifically, since "diptolemaic" intervals have two instances of prime 5 in their factorization, this interval is also referred to as the '''diptolemaic augmented fifth'''.

	== See also ==		== See also ==

BudjarnLambeth: Change/remove expand/stub in accordance with XW:IntTodo

2025-01-03T07:34:39Z

Change/remove expand/stub in accordance with XW:IntTodo

← Older revision		Revision as of 07:34, 3 January 2025
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	[[Category:Fifth]]		[[Category:Fifth]]
	[[Category:Augmented fifth]]		[[Category:Augmented fifth]]
	~~[[Category:todo:expand]]~~

BudjarnLambeth: User:Aura —> Aura

2024-10-14T03:22:01Z

User:Aura —> Aura

← Older revision		Revision as of 03:22, 14 October 2024
Line 7:		Line 7:
	'''25/16''', the '''classic(al) augmented fifth''' is the interval obtained by stacking two [[5/4]] major thirds, however, it gains additional [[isoharmonic chord\|isoharmonic]] identity from its position between [[11/8]] and [[7/4]], so it can frequently be used in conjunction with those, even in chords. It is [[100/99]] sharp of [[99/64]], and tempering out 100/99 makes 1-5/4-25/16 into a [[ptolemismic chords\|ptolemismic chord]].		'''25/16''', the '''classic(al) augmented fifth''' is the interval obtained by stacking two [[5/4]] major thirds, however, it gains additional [[isoharmonic chord\|isoharmonic]] identity from its position between [[11/8]] and [[7/4]], so it can frequently be used in conjunction with those, even in chords. It is [[100/99]] sharp of [[99/64]], and tempering out 100/99 makes 1-5/4-25/16 into a [[ptolemismic chords\|ptolemismic chord]].

	While this interval has been referred to as the ''classic augmented fifth'' or ''classical augmented fifth'' for some time, the term ''diptolemaic'' [https://discord.com/channels/332357996569034752/516067802864549890/912167264789364736 was coined on Discord] by [[Flora Canou]] while discussing a proposal for a consistent naming scheme for different 5-limit intervals with [[~~User:Aura\|~~Aura]]. Specifically, since "diptolemaic" intervals have two instances of prime 5 in their factorization, this interval is also referred to as the '''diptolemaic augmented fifth'''.		While this interval has been referred to as the ''classic augmented fifth'' or ''classical augmented fifth'' for some time, the term ''diptolemaic'' [https://discord.com/channels/332357996569034752/516067802864549890/912167264789364736 was coined on Discord] by [[Flora Canou]] while discussing a proposal for a consistent naming scheme for different 5-limit intervals with [[Aura]]. Specifically, since "diptolemaic" intervals have two instances of prime 5 in their factorization, this interval is also referred to as the '''diptolemaic augmented fifth'''.

	== See also ==		== See also ==

Aura at 20:21, 28 January 2023

2023-01-28T20:21:12Z

← Older revision		Revision as of 20:21, 28 January 2023
Line 5:		Line 5:
	}}		}}

	'''25/16''', the '''classic(al) augmented fifth''' is the interval obtained by stacking two [[5/4]] major thirds, however, it gains additional [[isoharmonic chord\|isoharmonic]] identity from its position between [[11/8]] and [[7/4]], so it can frequently be used in conjunction with those, even in chords. It is [[100/99]] sharp of [[99/64]], and tempering out 100/99 makes 1-5/4-25/16 into ~~the~~ [[ptolemismic chords\|ptolemismic ~~augmented triad~~]].		'''25/16''', the '''classic(al) augmented fifth''' is the interval obtained by stacking two [[5/4]] major thirds, however, it gains additional [[isoharmonic chord\|isoharmonic]] identity from its position between [[11/8]] and [[7/4]], so it can frequently be used in conjunction with those, even in chords. It is [[100/99]] sharp of [[99/64]], and tempering out 100/99 makes 1-5/4-25/16 into a [[ptolemismic chords\|ptolemismic chord]].

	While this interval has been referred to as the ''classic augmented fifth'' or ''classical augmented fifth'' for some time, the term ''diptolemaic'' [https://discord.com/channels/332357996569034752/516067802864549890/912167264789364736 was coined on Discord] by [[Flora Canou]] while discussing a proposal for a consistent naming scheme for different 5-limit intervals with [[User:Aura\|Aura]]. Specifically, since "diptolemaic" intervals have two instances of prime 5 in their factorization, this interval is also referred to as the '''diptolemaic augmented fifth'''.		While this interval has been referred to as the ''classic augmented fifth'' or ''classical augmented fifth'' for some time, the term ''diptolemaic'' [https://discord.com/channels/332357996569034752/516067802864549890/912167264789364736 was coined on Discord] by [[Flora Canou]] while discussing a proposal for a consistent naming scheme for different 5-limit intervals with [[User:Aura\|Aura]]. Specifically, since "diptolemaic" intervals have two instances of prime 5 in their factorization, this interval is also referred to as the '''diptolemaic augmented fifth'''.

Aura at 20:19, 28 January 2023

2023-01-28T20:19:26Z

← Older revision		Revision as of 20:19, 28 January 2023
Line 7:		Line 7:
	'''25/16''', the '''classic(al) augmented fifth''' is the interval obtained by stacking two [[5/4]] major thirds, however, it gains additional [[isoharmonic chord\|isoharmonic]] identity from its position between [[11/8]] and [[7/4]], so it can frequently be used in conjunction with those, even in chords. It is [[100/99]] sharp of [[99/64]], and tempering out 100/99 makes 1-5/4-25/16 into the [[ptolemismic chords\|ptolemismic augmented triad]].		'''25/16''', the '''classic(al) augmented fifth''' is the interval obtained by stacking two [[5/4]] major thirds, however, it gains additional [[isoharmonic chord\|isoharmonic]] identity from its position between [[11/8]] and [[7/4]], so it can frequently be used in conjunction with those, even in chords. It is [[100/99]] sharp of [[99/64]], and tempering out 100/99 makes 1-5/4-25/16 into the [[ptolemismic chords\|ptolemismic augmented triad]].

	While this interval has been referred to as the ''classic'' or ''classical'' ~~augmented fifth~~ for some time, the term ''diptolemaic'' [https://discord.com/channels/332357996569034752/516067802864549890/912167264789364736 was coined on Discord] by [[Flora Canou]] while discussing a proposal for a consistent naming scheme for different 5-limit intervals with [[User:Aura\|Aura]]. Specifically, since "diptolemaic" intervals have two instances of prime 5 in their factorization, this interval is also referred to as the '''diptolemaic augmented fifth'''.		While this interval has been referred to as the ''classic augmented fifth'' or ''classical augmented fifth'' for some time, the term ''diptolemaic'' [https://discord.com/channels/332357996569034752/516067802864549890/912167264789364736 was coined on Discord] by [[Flora Canou]] while discussing a proposal for a consistent naming scheme for different 5-limit intervals with [[User:Aura\|Aura]]. Specifically, since "diptolemaic" intervals have two instances of prime 5 in their factorization, this interval is also referred to as the '''diptolemaic augmented fifth'''.

	== See also ==		== See also ==

Aura: Simplified and fixed the previous intended addition

2023-01-28T20:18:57Z

Simplified and fixed the previous intended addition

← Older revision		Revision as of 20:18, 28 January 2023
Line 5:		Line 5:
	}}		}}

	'''25/16''', the '''classic(al) ~~augmented fifth''' or '''diptolemaic~~ augmented fifth''' is the interval obtained by stacking two [[5/4]] major thirds, however, it gains additional [[isoharmonic chord\|isoharmonic]] identity from its position between [[11/8]] and [[7/4]], so it can frequently be used in conjunction with those, even in chords. It is [[100/99]] sharp of [[99/64]], and tempering out 100/99 makes 1-5/4-25/16 into the [[ptolemismic chords\|ptolemismic augmented triad]].		'''25/16''', the '''classic(al) augmented fifth''' is the interval obtained by stacking two [[5/4]] major thirds, however, it gains additional [[isoharmonic chord\|isoharmonic]] identity from its position between [[11/8]] and [[7/4]], so it can frequently be used in conjunction with those, even in chords. It is [[100/99]] sharp of [[99/64]], and tempering out 100/99 makes 1-5/4-25/16 into the [[ptolemismic chords\|ptolemismic augmented triad]].

			While this interval has been referred to as the ''classic'' or ''classical'' augmented fifth for some time, the term ''diptolemaic'' [https://discord.com/channels/332357996569034752/516067802864549890/912167264789364736 was coined on Discord] by [[Flora Canou]] while discussing a proposal for a consistent naming scheme for different 5-limit intervals with [[User:Aura\|Aura]]. Specifically, since "diptolemaic" intervals have two instances of prime 5 in their factorization, this interval is also referred to as the '''diptolemaic augmented fifth'''.

	== See also ==		== See also ==

Aura at 20:05, 28 January 2023

2023-01-28T20:05:01Z

← Older revision		Revision as of 20:05, 28 January 2023
Line 6:		Line 6:

	'''25/16''', the '''classic(al) augmented fifth''' or '''diptolemaic augmented fifth''' is the interval obtained by stacking two [[5/4]] major thirds, however, it gains additional [[isoharmonic chord\|isoharmonic]] identity from its position between [[11/8]] and [[7/4]], so it can frequently be used in conjunction with those, even in chords. It is [[100/99]] sharp of [[99/64]], and tempering out 100/99 makes 1-5/4-25/16 into the [[ptolemismic chords\|ptolemismic augmented triad]].		'''25/16''', the '''classic(al) augmented fifth''' or '''diptolemaic augmented fifth''' is the interval obtained by stacking two [[5/4]] major thirds, however, it gains additional [[isoharmonic chord\|isoharmonic]] identity from its position between [[11/8]] and [[7/4]], so it can frequently be used in conjunction with those, even in chords. It is [[100/99]] sharp of [[99/64]], and tempering out 100/99 makes 1-5/4-25/16 into the [[ptolemismic chords\|ptolemismic augmented triad]].

	~~== Names ==~~
	While this interval has been referred to as the ''classic'' or ''classical'' augmented fifth for some time, the term "diptolemaic" [https://discord.com/channels/332357996569034752/516067802864549890/912167264789364736 was coined on Discord] by [[Flora Canou]] while discussing a proposal for a consistent naming scheme for different 5-limit intervals with [[User:Aura\|Aura]]. The concept of "diptolemaic" intervals builds on the concept of "ptolemaic"<ref>[https://marsbat.space/pdfs/JI.pdf ''Fundamental Principles of Just Intonation and Microtonal Composition''] by Thomas Nicholson and Marc Sabat —"'Ptolemaic' refers to intervals combining only the primes 2, 3, and 5."</ref> intervals, with "diptolemaic" intervals being those that have two factors of 5 in their [[monzo]] and differ from their Pythagorean counterparts by two instances of [[81/80]] in the direction of ratio simplicity— for instance, 25/16 differing from [[6561/4096]]—, while 5-limit intervals that differ from their Pythagorean counterparts by a single instance of 81/80 in the same direction are simply called "ptolemaic" intervals.

	== See also ==		== See also ==
	* [[32/25]] – its [[octave complement]]		* [[32/25]] – its [[octave complement]]

	~~== References ==~~
	~~<references/>~~

	[[Category:Fifth]]		[[Category:Fifth]]
	[[Category:Augmented fifth]]		[[Category:Augmented fifth]]
	[[Category:todo:expand]]		[[Category:todo:expand]]

Aura at 20:03, 28 January 2023

2023-01-28T20:03:23Z

← Older revision		Revision as of 20:03, 28 January 2023
Line 6:		Line 6:

	'''25/16''', the '''classic(al) augmented fifth''' or '''diptolemaic augmented fifth''' is the interval obtained by stacking two [[5/4]] major thirds, however, it gains additional [[isoharmonic chord\|isoharmonic]] identity from its position between [[11/8]] and [[7/4]], so it can frequently be used in conjunction with those, even in chords. It is [[100/99]] sharp of [[99/64]], and tempering out 100/99 makes 1-5/4-25/16 into the [[ptolemismic chords\|ptolemismic augmented triad]].		'''25/16''', the '''classic(al) augmented fifth''' or '''diptolemaic augmented fifth''' is the interval obtained by stacking two [[5/4]] major thirds, however, it gains additional [[isoharmonic chord\|isoharmonic]] identity from its position between [[11/8]] and [[7/4]], so it can frequently be used in conjunction with those, even in chords. It is [[100/99]] sharp of [[99/64]], and tempering out 100/99 makes 1-5/4-25/16 into the [[ptolemismic chords\|ptolemismic augmented triad]].

			== Names ==
			While this interval has been referred to as the ''classic'' or ''classical'' augmented fifth for some time, the term "diptolemaic" [https://discord.com/channels/332357996569034752/516067802864549890/912167264789364736 was coined on Discord] by [[Flora Canou]] while discussing a proposal for a consistent naming scheme for different 5-limit intervals with [[User:Aura\|Aura]]. The concept of "diptolemaic" intervals builds on the concept of "ptolemaic"<ref>[https://marsbat.space/pdfs/JI.pdf ''Fundamental Principles of Just Intonation and Microtonal Composition''] by Thomas Nicholson and Marc Sabat —"'Ptolemaic' refers to intervals combining only the primes 2, 3, and 5."</ref> intervals, with "diptolemaic" intervals being those that have two factors of 5 in their [[monzo]] and differ from their Pythagorean counterparts by two instances of [[81/80]] in the direction of ratio simplicity— for instance, 25/16 differing from [[6561/4096]]—, while 5-limit intervals that differ from their Pythagorean counterparts by a single instance of 81/80 in the same direction are simply called "ptolemaic" intervals.

	== See also ==		== See also ==
	* [[32/25]] – its [[octave complement]]		* [[32/25]] – its [[octave complement]]

			== References ==
			<references/>

	[[Category:Fifth]]		[[Category:Fifth]]
	[[Category:Augmented fifth]]		[[Category:Augmented fifth]]
	[[Category:todo:expand]]		[[Category:todo:expand]]