Neutral third - Revision history

FloraC: + interwiki

2026-03-30T14:43:44Z

+ interwiki

← Older revision		Revision as of 14:43, 30 March 2026
Line 1:		Line 1:
			{{Interwiki
			\| en = Neutral third
			\| zh = 中三度
			}}
	{{Infobox interval region		{{Infobox interval region
	\| Name = Neutral third		\| Name = Neutral third

FloraC: - abuse of bold

2026-03-30T13:45:39Z

- abuse of bold

← Older revision		Revision as of 13:45, 30 March 2026
Line 23:		Line 23:
	=== By prime limit ===		=== By prime limit ===
	The [[3-limit]] and 5-limit do not have simple neutral thirds (though hemipythagorean has an irrational [[sqrt(3/2)]] interval that might be considered the "canonical" neutral third), so we start with the 7-limit:		The [[3-limit]] and 5-limit do not have simple neutral thirds (though hemipythagorean has an irrational [[sqrt(3/2)]] interval that might be considered the "canonical" neutral third), so we start with the 7-limit:
			* The 7-limit artoneutral and tendoneutral thirds are the ratios of [[60/49]] and [[49/40]] respectively, and they are slightly flat of and slightly sharp of 351{{c}} respectively.
	* The 7-limit ~~'''~~artoneutral~~'''~~ and ~~'''~~tendoneutral thirds~~'''~~ are the ratios of [[60/49]] and [[49/40]] respectively, and they are slightly flat of and slightly sharp of 351{{c}} respectively.		* The 11-limit alpharabian artoneutral and tendoneutral thirds are the ratios of [[11/9]] and [[27/22]] respectively, and they are about 347 and 355{{c}} respectively.
	* The 11-limit ~~'''~~alpharabian artoneutral~~'''~~ and ~~'''~~tendoneutral thirds~~'''~~ are the ratios of [[11/9]] and [[27/22]] respectively, and they are about 347 and 355{{c}} respectively.		* The 13-limit artoneutral and tendoneutral thirds are the ratios of [[39/32]] and [[16/13]] respectively, and they are about 342 and 359{{c}} respectively.
	* The 13-limit ~~'''~~artoneutral~~'''~~ and ~~'''~~tendoneutral thirds~~'''~~ are the ratios of [[39/32]] and [[16/13]] respectively, and they are about 342 and 359{{c}} respectively.		* The 17-limit supraminor and submajor thirds are the ratios of [[17/14]] and [[21/17]] respectively, and they are about 336 and 366{{c}} respectively.
	* The 17-limit ~~'''~~supraminor~~'''~~ and ~~'''~~submajor thirds~~'''~~ are the ratios of [[17/14]] and [[21/17]] respectively, and they are about 336 and 366{{c}} respectively.

	=== By delta ===		=== By delta ===
Line 68:		Line 67:

	== In edos ==		== In edos ==
	The following table lists the best tuning of 39/32 and 16/13 in various significant [[edo]]s. For applicable edos, it also lists one half of the edo's perfect fifth, approximating [[√(3/2)]], which, while not a just interval, is the "canonical" neutral third tuning, as stacking two of them gives [[3/2]].		The following table lists the best tuning of 39/32 and 16/13 in various significant [[edo]]s. For applicable edos, it also lists one half of the edo's perfect fifth, approximating [[sqrt(3/2)]], which, while not a just interval, is the "canonical" neutral third tuning, as stacking two of them gives [[3/2]].

	{\| class="wikitable"		{\| class="wikitable"
Line 127:		Line 126:
	\|-		\|-
	\| 60/49, 49/40		\| 60/49, 49/40
	\| [[Breed (temperament)\|Breed]]*		\| [[Breed (temperament)\|Breed]] retraction*
	\|-		\|-
	\| 11/9, 27/22		\| 11/9, 27/22

FloraC: Rework intro to hopefully better explain this concept (it doesn't rely on a split octave)

2026-03-30T13:43:21Z

Rework intro to hopefully better explain this concept (it doesn't rely on a split octave)

← Older revision		Revision as of 13:43, 30 March 2026
Line 8:		Line 8:
	\| MOSes = [[4L 3s]], [[3L 4s]], [[7L 3s]], [[3L 7s]]		\| MOSes = [[4L 3s]], [[3L 4s]], [[7L 3s]], [[3L 7s]]
	\| Complement = [[Neutral sixth]]		\| Complement = [[Neutral sixth]]
	\| Lower region = [[~~Minor_third_(interval_region)\|~~Minor Third]]		\| Lower region = [[Minor Third]]
	\| Higher region = [[~~Major_third_(interval region)\|~~Major third]]		\| Higher region = [[Major third]]
	}}		}}
	{{Wikipedia}}		{{Wikipedia}}
	A '''neutral third''' ('''n3''')~~, as~~ a ~~concrete~~ [[~~interval region~~]]~~, is typically near 350~~ [[~~cents~~]] ~~in size, distinct from~~ the [[~~minor~~ third]] ~~of roughly 300 [[cent]]s~~ and ~~the~~ [[~~major~~ third]] ~~of roughly 400{{c}}. A rough tuning range for the neutral~~ third ~~is 330 to 370{{c}} according to [[Margo Schulter]]'s theory of interval regions; intervals~~ in ~~this range may be also called '''Zalzalian thirds'''~~.		A '''neutral third''' ('''n3''') is an interval that generates a variant of [[5L 2s\|diatonic]] with its original [[perfect fifth\|perfect-fifth]] generator halved. Like the [[major third]] and [[minor third]], it is considered a third, so it spans two steps in diatonic-based notation, but has a quality between major and minor.

	In ~~a diatonic functional context, neutral thirds appear as part of the~~ [[~~10L 4s\|variant of diatonic with generators halved~~]], ~~where the~~ neutral third is the ~~generator~~ and the ~~600-cent [[tritone]] is the period~~.		In [[just intonation]], an interval may be classified as a neutral third if it is reasonably mapped to two steps of the diatonic scale and three and a half steps of the chromatic scale.

	The neutral third range is generally divided at roughly 350{{c}} into ~~'''~~artoneutral~~'''~~ (flatter) and ~~'''~~tendoneutral~~'''~~ (sharper) thirds. As such, neutral thirds tend to exist in pairs.		As a concrete [[interval region]], it is typically near 350 [[cents]] in size, distinct from the minor third of roughly 300 [[cent]]s and the major third of roughly 400{{c}}. A rough tuning range for the neutral third is 330 to 370{{c}} according to [[Margo Schulter]]'s theory of interval regions; intervals in this range may be also called ''Zalzalian thirds''.

			The neutral third range is generally divided at roughly 350{{c}} into [[neutral (interval quality)\|artoneutral]] (flatter) and [[neutral (interval quality)\|tendoneutral]] (sharper) thirds. As such, neutral thirds tend to exist in pairs.

	== In just intonation ==		== In just intonation ==

Overthink: /* By delta */ hyphens

2026-03-23T00:38:48Z

By delta: hyphens

← Older revision		Revision as of 00:38, 23 March 2026
Line 32:		Line 32:
	{\| class="wikitable"		{\| class="wikitable"
	\|-		\|-
	! colspan="2" \| Delta 2		! colspan="2" \| Delta-2
	! colspan="2" \| Delta 3		! colspan="2" \| Delta-3
	! colspan="2" \| Delta 4		! colspan="2" \| Delta-4
	! colspan="2" \| Delta 5		! colspan="2" \| Delta-5
	\|-		\|-
	\| [[11/9]]		\| [[11/9]]

Jdood: link, links, and more links

2025-12-03T18:15:38Z

link, links, and more links

← Older revision		Revision as of 18:15, 3 December 2025
Line 9:		Line 9:
	\| Complement = [[Neutral sixth]]		\| Complement = [[Neutral sixth]]
	\| Lower region = [[Minor_third_(interval_region)\|Minor Third]]		\| Lower region = [[Minor_third_(interval_region)\|Minor Third]]
	\| Higher region = [[Major third]]		\| Higher region = [[Major_third_(interval region)\|Major third]]
	}}		}}
	{{Wikipedia}}		{{Wikipedia}}

Jdood: weird links again

2025-12-03T18:12:43Z

weird links again

← Older revision		Revision as of 18:12, 3 December 2025
Line 8:		Line 8:
	\| MOSes = [[4L 3s]], [[3L 4s]], [[7L 3s]], [[3L 7s]]		\| MOSes = [[4L 3s]], [[3L 4s]], [[7L 3s]], [[3L 7s]]
	\| Complement = [[Neutral sixth]]		\| Complement = [[Neutral sixth]]
	\| Lower region = [[Minor ~~third~~]]		\| Lower region = [[Minor_third_(interval_region)\|Minor Third]]
	\| Higher region = [[Major third]]		\| Higher region = [[Major third]]
	}}		}}

VectorGraphics at 06:57, 18 June 2025

2025-06-18T06:57:28Z

← Older revision		Revision as of 06:57, 18 June 2025
Line 12:		Line 12:
	}}		}}
	{{Wikipedia}}		{{Wikipedia}}
	A '''neutral third''' ('''n3'''), as a concrete [[interval region]], is typically near 350 [[cents]] in size, distinct from the [[minor third]] of roughly 300 [[cent]]s and the [[major third]] of roughly 400{{c}}. A rough tuning range for the neutral third is 330 to 370{{c}} according to [[Margo Schulter]]'s theory of interval regions.		A '''neutral third''' ('''n3'''), as a concrete [[interval region]], is typically near 350 [[cents]] in size, distinct from the [[minor third]] of roughly 300 [[cent]]s and the [[major third]] of roughly 400{{c}}. A rough tuning range for the neutral third is 330 to 370{{c}} according to [[Margo Schulter]]'s theory of interval regions; intervals in this range may be also called '''Zalzalian thirds'''.

	In a diatonic functional context, neutral thirds appear as part of the [[10L 4s\|variant of diatonic with generators halved]], where the neutral third is the generator and the 600-cent [[tritone]] is the period.		In a diatonic functional context, neutral thirds appear as part of the [[10L 4s\|variant of diatonic with generators halved]], where the neutral third is the generator and the 600-cent [[tritone]] is the period.

TallKite: TallKite moved page Neutral third (interval region) to Neutral third

2025-05-13T04:54:19Z

TallKite moved page Neutral third (interval region) to Neutral third

← Older revision	Revision as of 04:54, 13 May 2025
(No difference)

VectorGraphics at 08:58, 7 May 2025

2025-05-07T08:58:19Z

← Older revision		Revision as of 08:58, 7 May 2025
Line 14:		Line 14:
	A '''neutral third''' ('''n3'''), as a concrete [[interval region]], is typically near 350 [[cents]] in size, distinct from the [[minor third]] of roughly 300 [[cent]]s and the [[major third]] of roughly 400{{c}}. A rough tuning range for the neutral third is 330 to 370{{c}} according to [[Margo Schulter]]'s theory of interval regions.		A '''neutral third''' ('''n3'''), as a concrete [[interval region]], is typically near 350 [[cents]] in size, distinct from the [[minor third]] of roughly 300 [[cent]]s and the [[major third]] of roughly 400{{c}}. A rough tuning range for the neutral third is 330 to 370{{c}} according to [[Margo Schulter]]'s theory of interval regions.

	In a diatonic functional context, neutral thirds appear as part of the variant of diatonic with generators halved, where the neutral third is the generator and the 600-cent [[tritone]] is the period.		In a diatonic functional context, neutral thirds appear as part of the [[10L 4s\|variant of diatonic with generators halved]], where the neutral third is the generator and the 600-cent [[tritone]] is the period.

	The neutral third range is generally divided at roughly 350{{c}} into '''artoneutral''' (flatter) and '''tendoneutral''' (sharper) thirds. As such, neutral thirds tend to exist in pairs.		The neutral third range is generally divided at roughly 350{{c}} into '''artoneutral''' (flatter) and '''tendoneutral''' (sharper) thirds. As such, neutral thirds tend to exist in pairs.

VectorGraphics at 05:13, 6 May 2025

2025-05-06T05:13:50Z

← Older revision		Revision as of 05:13, 6 May 2025
Line 14:		Line 14:
	A '''neutral third''' ('''n3'''), as a concrete [[interval region]], is typically near 350 [[cents]] in size, distinct from the [[minor third]] of roughly 300 [[cent]]s and the [[major third]] of roughly 400{{c}}. A rough tuning range for the neutral third is 330 to 370{{c}} according to [[Margo Schulter]]'s theory of interval regions.		A '''neutral third''' ('''n3'''), as a concrete [[interval region]], is typically near 350 [[cents]] in size, distinct from the [[minor third]] of roughly 300 [[cent]]s and the [[major third]] of roughly 400{{c}}. A rough tuning range for the neutral third is 330 to 370{{c}} according to [[Margo Schulter]]'s theory of interval regions.

	~~Diatonically~~, neutral thirds appear as part of the variant of diatonic with generators halved, where the neutral third is the generator and the 600-cent [[tritone]] is the period.		In a diatonic functional context, neutral thirds appear as part of the variant of diatonic with generators halved, where the neutral third is the generator and the 600-cent [[tritone]] is the period.

	The neutral third range is generally divided at roughly 350{{c}} into '''artoneutral''' (flatter) and '''tendoneutral''' (sharper) thirds. As such, neutral thirds tend to exist in pairs.		The neutral third range is generally divided at roughly 350{{c}} into '''artoneutral''' (flatter) and '''tendoneutral''' (sharper) thirds. As such, neutral thirds tend to exist in pairs.