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{{Interwiki
| en = Neutral third
| zh = 中三度
}}
{{Infobox interval region
{{Infobox interval region
| Name = Neutral third
| Name = Neutral third
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| 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]]
| 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 ==
=== 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 ===
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{| 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]]
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== 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"
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|-
|-
| 60/49, 49/40
| 60/49, 49/40
| [[Breed (temperament)|Breed]]*
| [[Breed (temperament)|Breed]] retraction*
|-
|-
| 11/9, 27/22
| 11/9, 27/22
Retrieved from "https://en.xen.wiki/w/Neutral_third"