Neutral third: Difference between revisions

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{{Infobox interval region|Name=Neutral third|Cents lower=340|Cents lower wide=330|Cents upper=360|Cents upper wide=370|JI intervals=11/9, 27/22, 16/13|MOSes=[[4L 3s]], [[3L 4s]], [[7L 3s]], [[3L 7s]]|Complement=[[Neutral sixth]]|Lower region=[[Minor third]]|Higher region=[[Major third]]}}{{Wikipedia}}

{{Infobox interval region

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~~.

| Name = Neutral third

| Cents lower = 340

| Cents lower wide = 330

| Cents upper = 360

| Cents upper wide = 370

| JI intervals = 11/9, 27/22, 16/13

| MOSes = [[4L 3s]], [[3L 4s]], [[7L 3s]], [[3L 7s]]

| Complement = [[Neutral sixth]]

| Lower region = [[Minor third]]

| Higher region = [[Major third]]

}}

A '''neutral third''' ('''n3''') is an interval that spans two steps of the [[5L 2s|diatonic]] scale with a quality between major and minor. It exists in [[neutralization|neutralized]] diatonic scales as exactly one half of a [[perfect fifth]].

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.

~~In the~~ [[~~diatonic~~]] ~~scale~~, ~~a neutral~~ third ~~spans two steps~~ of ~~the~~ [[~~5L 2s|diatonic~~]] ~~scale with a quality between major~~ and ~~minor. It exists in~~ [[~~neutralization|neutralized~~]] ~~diatonic scales as exactly one half~~ of a [[~~perfect fifth~~]].

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.

Two neutral thirds stack to a perfect fifth, and as such 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.

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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~~|EDO~~]]s. For applicable ~~EDOs~~, it also lists one half of the ~~EDO~~'s perfect fifth, approximating 1\[[2edf]], 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 1\[[2edf]], which, while not a just interval, is the "canonical" neutral third tuning, as stacking two of them gives [[3/2]].

{| class="wikitable"

|-

! ~~EDO~~

! Edo

! 1\2edf

! 39/32

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== In moment-of-symmetry scales ==

Intervals between 327 and 400{{c}} generate the following [[mos~~|MOS~~]] scales:

Intervals between 327 and 400{{c}} generate the following [[mos]] scales:

These tables start from the last monolarge ~~MOS~~ generated by the interval range.

These tables start from the last monolarge mos generated by the interval range.

Scales with more than 12 notes are not included.

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|-

! Range

! colspan="4" | ~~MOS~~

! colspan="4" | Mos

|-

| 327–343{{c}}

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-{{Infobox interval region|Name=Neutral third|Cents lower=340|Cents lower wide=330|Cents upper=360|Cents upper wide=370|JI intervals=11/9, 27/22, 16/13|MOSes=[[4L 3s]], [[3L 4s]], [[7L 3s]], [[3L 7s]]|Complement=[[Neutral sixth]]|Lower region=[[Minor&nbsp;third]]|Higher region=[[Major&nbsp;third]]}}{{Wikipedia}}
+{{Infobox interval region
-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.
+| Name = Neutral third
+| Cents lower = 340
+| Cents lower wide = 330
+| Cents upper = 360
+| Cents upper wide = 370
+| JI intervals = 11/9, 27/22, 16/13
+| MOSes = [[4L 3s]], [[3L 4s]], [[7L 3s]], [[3L 7s]]
+| Complement = [[Neutral sixth]]
+| Lower region = [[Minor&nbsp;third]]
+| Higher region = [[Major&nbsp;third]]
+}}
+{{Wikipedia}}
+A '''neutral third''' ('''n3''') is an interval that spans two steps of the [[5L 2s|diatonic]] scale with a quality between major and minor. It exists in [[neutralization|neutralized]] diatonic scales as exactly one half of a [[perfect fifth]].
 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.
-In the [[diatonic]] scale, a neutral third spans two steps of the [[5L 2s|diatonic]] scale with a quality between major and minor. It exists in [[neutralization|neutralized]] diatonic scales as exactly one half of a [[perfect fifth]].
+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.
 Two neutral thirds stack to a perfect fifth, and as such 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.
@@ Line 55: / Line 67: @@
 |}
-== In EDOs ==
+== In edos ==
-The following table lists the best tuning of 39/32 and 16/13 in various significant [[edo|EDO]]s. For applicable EDOs, it also lists one half of the EDO's perfect fifth, approximating 1\[[2edf]], 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 1\[[2edf]], which, while not a just interval, is the "canonical" neutral third tuning, as stacking two of them gives [[3/2]].
 {| class="wikitable"
 |-
-! EDO
+! Edo
 ! 1\2edf
 ! 39/32
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 == In moment-of-symmetry scales ==
-Intervals between 327 and 400{{c}} generate the following [[mos|MOS]] scales:
+Intervals between 327 and 400{{c}} generate the following [[mos]] scales:
-These tables start from the last monolarge MOS generated by the interval range.
+These tables start from the last monolarge mos generated by the interval range.
 Scales with more than 12 notes are not included.
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 |-
 ! Range
-! colspan="4" | MOS
+! colspan="4" | Mos
 |-
 | 327–343{{c}}