43/32 - Revision history

Overthink: obvious note

2026-01-10T22:07:16Z

obvious note

← Older revision		Revision as of 22:07, 10 January 2026
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	\| Sound = Ji-43-32-csound-foscil-220hz.mp3		\| Sound = Ji-43-32-csound-foscil-220hz.mp3
	}}		}}
	'''43/32''', the '''quadracesimotertial harmonic fourth''' or '''prime harmonic fourth''', is the [[Octave reduction\|octave-reduced]] 43rd [[harmonic]]. It is a wide fourth close to those of [[7edo]] and [[26edo]], and is the first octave-reduced harmonic that is a [[5L 2s\|diatonic]] fourth. The "prime" in the name "prime harmonic fourth" can be taken both as referring to the fact that it is a prime harmonic and to the fact that it is the simplest octave-reduced harmonic that generates [[5L 2s]], the diatonic [[mos]]. It is sharp of the [[4/3\|perfect fourth (4/3)]] by [[129/128]].		'''43/32''', the '''quadracesimotertial harmonic fourth''' or '''prime harmonic fourth''', is the [[Octave reduction\|octave-reduced]] 43rd [[harmonic]]. It is a wide fourth close to those of [[7edo]] and [[26edo]], and is the first octave-reduced harmonic that is a [[5L 2s\|diatonic]] fourth. The "prime" in the name "prime harmonic fourth" can be taken both as referring to the fact that it is a prime harmonic and to the fact that it is the simplest octave-reduced harmonic (besides [[3/2]]) that generates [[5L 2s]], the diatonic [[mos]]. It is sharp of the [[4/3\|perfect fourth (4/3)]] by [[129/128]].

	== Approximation ==		== Approximation ==

FloraC: Expand

2024-12-07T09:51:20Z

Expand

← Older revision		Revision as of 09:51, 7 December 2024
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	\| Sound = Ji-43-32-csound-foscil-220hz.mp3		\| Sound = Ji-43-32-csound-foscil-220hz.mp3
	}}		}}
			'''43/32''', the '''quadracesimotertial harmonic fourth''' or '''prime harmonic fourth''', is the [[Octave reduction\|octave-reduced]] 43rd [[harmonic]]. It is a wide fourth close to those of [[7edo]] and [[26edo]], and is the first octave-reduced harmonic that is a [[5L 2s\|diatonic]] fourth. The "prime" in the name "prime harmonic fourth" can be taken both as referring to the fact that it is a prime harmonic and to the fact that it is the simplest octave-reduced harmonic that generates [[5L 2s]], the diatonic [[mos]]. It is sharp of the [[4/3\|perfect fourth (4/3)]] by [[129/128]].
	'''43/32''', the '''quadracesimotertial harmonic fourth''' or '''prime harmonic fourth''', is the [[Octave reduction\|octave-reduced]] 43rd [[harmonic]]. It is a wide fourth close to those of [[7edo]] and [[26edo]], and is the first octave-reduced harmonic that is a [[5L 2s\|diatonic]] fourth. The "prime" in the name "prime harmonic fourth" can be taken both as referring to the fact that it is a prime harmonic and to the fact that it is the simplest octave-reduced harmonic that generates [[5L 2s]], the diatonic [[mos]].

	== Approximation ==		== Approximation ==

FloraC: Cleanup

2024-12-07T09:50:19Z

Cleanup

← Older revision		Revision as of 09:50, 7 December 2024
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	}}		}}

	'''43/32''', the '''quadracesimotertial harmonic fourth''' or '''prime harmonic fourth''', is the [[Octave reduction\|octave-reduced]] 43rd [[harmonic]]. It is a wide fourth close to those of [[7edo]] and [[26edo]], and, is the first octave-reduced harmonic that is a [[5L 2s\|diatonic]] fourth. The "prime" in the name "prime harmonic fourth" can be taken both as referring to the fact that it is a prime harmonic or to the fact that it is the simplest ~~/2<sup>n</sup> interval~~ that generates [[5L 2s]], the diatonic [[~~MOS~~]]. Due to its complexity, it is sensitive to mistuning. Nontheless, it is tuned somewhat acceptably in [[7edo]] at 2.768{{cent}} sharp, but increasingly better [[edo]] approximations are [[40edo\|17\40]], [[47edo\|20\47]], [[54edo\|23\54]] and especially [[61edo\|26\61]], where it is less than 0.05{{cent}} flat, though some reasonable less accurate tunings in yet larger edos are [[68edo\|29\68]] (<0.25{{cent}} sharp) and [[75edo\|32\75]] (<0.5{{cent}} sharp), with good approximations becoming very noticeably more frequent in edos above this size.		'''43/32''', the '''quadracesimotertial harmonic fourth''' or '''prime harmonic fourth''', is the [[Octave reduction\|octave-reduced]] 43rd [[harmonic]]. It is a wide fourth close to those of [[7edo]] and [[26edo]], and is the first octave-reduced harmonic that is a [[5L 2s\|diatonic]] fourth. The "prime" in the name "prime harmonic fourth" can be taken both as referring to the fact that it is a prime harmonic and to the fact that it is the simplest octave-reduced harmonic that generates [[5L 2s]], the diatonic [[mos]].

			== Approximation ==
			Due to its complexity, this interval is sensitive to mistuning. Nontheless, it is tuned somewhat acceptably in [[7edo]] at 2.768{{cent}} sharp, but increasingly better [[edo]] approximations are [[40edo\|17\40]], [[47edo\|20\47]], [[54edo\|23\54]] and especially [[61edo\|26\61]], where it is less than 0.05{{cent}} flat, though some reasonable less accurate tunings in yet larger edos are [[68edo\|29\68]] (< 0.25{{cent}} sharp) and [[75edo\|32\75]] (< 0.5{{cent}} sharp), with good approximations becoming very noticeably more frequent in edos above this size.

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

CompactStar: I believe there isn't a consensus on this so I am keeping both names.

2024-10-25T02:22:16Z

I believe there isn't a consensus on this so I am keeping both names.

← Older revision		Revision as of 02:22, 25 October 2024
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	{{Infobox Interval		{{Infobox Interval
	\| Name = prime harmonic fourth		\| Name = quadracesimotertial harmonic fourth, prime harmonic fourth
	\| Color name = 43o4, fotho fourth		\| Color name = 43o4, fotho fourth
	\| Sound = Ji-43-32-csound-foscil-220hz.mp3		\| Sound = Ji-43-32-csound-foscil-220hz.mp3
	}}		}}

	'''43/32''', the '''prime harmonic fourth''', is the [[Octave reduction\|octave-reduced]] 43rd [[harmonic]]. It is a wide fourth close to those of [[7edo]] and [[26edo]], and, is the first octave-reduced harmonic that is a [[5L 2s\|diatonic]] fourth. The "prime" in the name can be taken both as referring to the fact that it is a prime harmonic or to the fact that it is the simplest /2<sup>n</sup> interval that generates [[5L 2s]], the diatonic [[MOS]]. Due to its complexity, it is sensitive to mistuning. Nontheless, it is tuned somewhat acceptably in [[7edo]] at 2.768{{cent}} sharp, but increasingly better [[edo]] approximations are [[40edo\|17\40]], [[47edo\|20\47]], [[54edo\|23\54]] and especially [[61edo\|26\61]], where it is less than 0.05{{cent}} flat, though some reasonable less accurate tunings in yet larger edos are [[68edo\|29\68]] (<0.25{{cent}} sharp) and [[75edo\|32\75]] (<0.5{{cent}} sharp), with good approximations becoming very noticeably more frequent in edos above this size.		'''43/32''', the '''quadracesimotertial harmonic fourth''' or '''prime harmonic fourth''', is the [[Octave reduction\|octave-reduced]] 43rd [[harmonic]]. It is a wide fourth close to those of [[7edo]] and [[26edo]], and, is the first octave-reduced harmonic that is a [[5L 2s\|diatonic]] fourth. The "prime" in the name "prime harmonic fourth" can be taken both as referring to the fact that it is a prime harmonic or to the fact that it is the simplest /2<sup>n</sup> interval that generates [[5L 2s]], the diatonic [[MOS]]. Due to its complexity, it is sensitive to mistuning. Nontheless, it is tuned somewhat acceptably in [[7edo]] at 2.768{{cent}} sharp, but increasingly better [[edo]] approximations are [[40edo\|17\40]], [[47edo\|20\47]], [[54edo\|23\54]] and especially [[61edo\|26\61]], where it is less than 0.05{{cent}} flat, though some reasonable less accurate tunings in yet larger edos are [[68edo\|29\68]] (<0.25{{cent}} sharp) and [[75edo\|32\75]] (<0.5{{cent}} sharp), with good approximations becoming very noticeably more frequent in edos above this size.

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

Godtone at 01:35, 8 October 2024

2024-10-08T01:35:24Z

← Older revision		Revision as of 01:35, 8 October 2024
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	}}		}}

	'''43/32''', the '''prime harmonic fourth''', is [[Octave reduction\|octave-reduced]] 43rd [[harmonic]]. It is a wide fourth close to those of [[7edo]] and [[26edo]], and, is the first octave-reduced harmonic that is a [[5L 2s\|diatonic]] fourth. The "prime" in the name can be taken both as referring to the fact that it is a prime harmonic or to the fact that it is the simplest /2<sup>n</sup> interval that generates [[5L 2s]], the diatonic [[MOS]]. Due to its complexity, it is sensitive to mistuning. Nontheless, it is tuned somewhat acceptably in [[7edo]] at 2.768{{cent}} sharp, but increasingly better [[edo]] approximations are [[40edo\|17\40]], [[47edo\|20\47]], [[54edo\|23\54]] and especially [[61edo\|26\61]], where it is less than 0.05{{cent}} flat, though some reasonable less accurate tunings in yet larger edos are [[68edo\|29\68]] (<0.25{{cent}} sharp) and [[75edo\|32\75]] (<0.5{{cent}} sharp), with good approximations becoming very noticeably more frequent in edos above this size.		'''43/32''', the '''prime harmonic fourth''', is the [[Octave reduction\|octave-reduced]] 43rd [[harmonic]]. It is a wide fourth close to those of [[7edo]] and [[26edo]], and, is the first octave-reduced harmonic that is a [[5L 2s\|diatonic]] fourth. The "prime" in the name can be taken both as referring to the fact that it is a prime harmonic or to the fact that it is the simplest /2<sup>n</sup> interval that generates [[5L 2s]], the diatonic [[MOS]]. Due to its complexity, it is sensitive to mistuning. Nontheless, it is tuned somewhat acceptably in [[7edo]] at 2.768{{cent}} sharp, but increasingly better [[edo]] approximations are [[40edo\|17\40]], [[47edo\|20\47]], [[54edo\|23\54]] and especially [[61edo\|26\61]], where it is less than 0.05{{cent}} flat, though some reasonable less accurate tunings in yet larger edos are [[68edo\|29\68]] (<0.25{{cent}} sharp) and [[75edo\|32\75]] (<0.5{{cent}} sharp), with good approximations becoming very noticeably more frequent in edos above this size.

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

Godtone at 01:33, 8 October 2024

2024-10-08T01:33:12Z

← Older revision		Revision as of 01:33, 8 October 2024
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	}}		}}

	'''43/32''', the '''prime harmonic fourth''', is [[Octave reduction\|octave-reduced]] 43rd [[harmonic]]. It is a wide fourth close to those of [[7edo]] and [[26edo]], and, is the first octave-reduced harmonic that is a [[5L 2s\|diatonic]] fourth. The "prime" in the name can be taken both as referring to the fact that it is a prime harmonic or to the fact that it is the simplest /2<sup>n</sup> interval that generates [[5L 2s]], the diatonic [[MOS]]. Due to its complexity, it is sensitive to mistuning. Nontheless, it is tuned somewhat acceptably in [[7edo]] at 2.768{{cent}} sharp, but increasingly better [[edo]] approximations are [[40edo\|17\40]], [[47edo\|20\47]], [[54edo\|23\54]] and especially [[61edo\|26\61]], where it is less than 0.05{{cent}} flat~~, so arguably virtually just~~, though some reasonable less accurate tunings in yet larger edos are [[68edo\|29\68]] (<0.25{{cent}} sharp) and [[75edo\|32\75]] (<0.5{{cent}} sharp), with good approximations becoming very noticeably more frequent in edos above this size.		'''43/32''', the '''prime harmonic fourth''', is [[Octave reduction\|octave-reduced]] 43rd [[harmonic]]. It is a wide fourth close to those of [[7edo]] and [[26edo]], and, is the first octave-reduced harmonic that is a [[5L 2s\|diatonic]] fourth. The "prime" in the name can be taken both as referring to the fact that it is a prime harmonic or to the fact that it is the simplest /2<sup>n</sup> interval that generates [[5L 2s]], the diatonic [[MOS]]. Due to its complexity, it is sensitive to mistuning. Nontheless, it is tuned somewhat acceptably in [[7edo]] at 2.768{{cent}} sharp, but increasingly better [[edo]] approximations are [[40edo\|17\40]], [[47edo\|20\47]], [[54edo\|23\54]] and especially [[61edo\|26\61]], where it is less than 0.05{{cent}} flat, though some reasonable less accurate tunings in yet larger edos are [[68edo\|29\68]] (<0.25{{cent}} sharp) and [[75edo\|32\75]] (<0.5{{cent}} sharp), with good approximations becoming very noticeably more frequent in edos above this size.

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

Godtone at 01:32, 8 October 2024

2024-10-08T01:32:46Z

← Older revision		Revision as of 01:32, 8 October 2024
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	}}		}}

	'''43/32''', the '''prime harmonic fourth''', is [[Octave reduction\|octave-reduced]] 43rd [[harmonic]]. It is a wide fourth close to those of [[7edo]] and [[26edo]], and, is the first octave-reduced harmonic that is a [[5L 2s\|diatonic]] fourth. The "prime" in the name can be taken both as referring to the fact that it is a prime harmonic or to the fact that it is the simplest /2<sup>n</sup> interval that generates [[5L 2s]], the diatonic [[MOS]].		'''43/32''', the '''prime harmonic fourth''', is [[Octave reduction\|octave-reduced]] 43rd [[harmonic]]. It is a wide fourth close to those of [[7edo]] and [[26edo]], and, is the first octave-reduced harmonic that is a [[5L 2s\|diatonic]] fourth. The "prime" in the name can be taken both as referring to the fact that it is a prime harmonic or to the fact that it is the simplest /2<sup>n</sup> interval that generates [[5L 2s]], the diatonic [[MOS]]. Due to its complexity, it is sensitive to mistuning. Nontheless, it is tuned somewhat acceptably in [[7edo]] at 2.768{{cent}} sharp, but increasingly better [[edo]] approximations are [[40edo\|17\40]], [[47edo\|20\47]], [[54edo\|23\54]] and especially [[61edo\|26\61]], where it is less than 0.05{{cent}} flat, so arguably virtually just, though some reasonable less accurate tunings in yet larger edos are [[68edo\|29\68]] (<0.25{{cent}} sharp) and [[75edo\|32\75]] (<0.5{{cent}} sharp), with good approximations becoming very noticeably more frequent in edos above this size.

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

Godtone at 01:17, 8 October 2024

2024-10-08T01:17:38Z

← Older revision		Revision as of 01:17, 8 October 2024
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	{{Infobox Interval		{{Infobox Interval
	\| Name = ~~octave-reduced 43rd~~ harmonic		\| Name = prime harmonic fourth
	\| Color name = 43o4, fotho fourth		\| Color name = 43o4, fotho fourth
	\| Sound = Ji-43-32-csound-foscil-220hz.mp3		\| Sound = Ji-43-32-csound-foscil-220hz.mp3
	}}		}}

	'''43/32''', the '''~~quadracesimotertial~~ harmonic fourth''', is [[Octave reduction\|octave-reduced]] 43rd [[harmonic]]. It is a wide fourth close to those of [[7edo]] and [[26edo]], and, is the first octave-reduced harmonic that is a diatonic fourth.		'''43/32''', the '''prime harmonic fourth''', is [[Octave reduction\|octave-reduced]] 43rd [[harmonic]]. It is a wide fourth close to those of [[7edo]] and [[26edo]], and, is the first octave-reduced harmonic that is a [[5L 2s\|diatonic]] fourth. The "prime" in the name can be taken both as referring to the fact that it is a prime harmonic or to the fact that it is the simplest /2<sup>n</sup> interval that generates [[5L 2s]], the diatonic [[MOS]].

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

Aura at 08:39, 16 June 2023

2023-06-16T08:39:04Z

← Older revision		Revision as of 08:39, 16 June 2023
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	}}		}}

	'''43/32''', the '''quadracesimotertial harmonic fourth''', is [[Octave reduction\|octave-reduced]] 43rd [[harmonic]]. It is a ~~narrow~~ fourth close to those of [[7edo]] and [[26edo]], and, is the first octave-reduced harmonic that is a diatonic fourth.		'''43/32''', the '''quadracesimotertial harmonic fourth''', is [[Octave reduction\|octave-reduced]] 43rd [[harmonic]]. It is a wide fourth close to those of [[7edo]] and [[26edo]], and, is the first octave-reduced harmonic that is a diatonic fourth.

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

Aura at 08:33, 16 June 2023

2023-06-16T08:33:45Z

← Older revision		Revision as of 08:33, 16 June 2023
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	== See also ==		== See also ==
	* [[64/43]] – its [[octave complement]]		* [[64/43]] – its [[octave complement]]
			* [[Gallery of just intervals]]

	[[Category:Fourth]]		[[Category:Fourth]]