Neutral third: Difference between revisions
The concept started as an interval in the diatonic scale, and is still used this way. The interval region is a later association. You can't just make it the main definition Tag: Undo |
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{{Interwiki | |||
| en = Neutral third | |||
| zh = 中三度 | |||
}} | |||
{{Infobox interval region | |||
| Name = Neutral third | |||
| Cents lower = 340 | |||
| Cents lower wide = 330 | |||
| Cents upper = 360 | |||
| Cents upper wide = 370 | |||
| JI intervals = 11/9, 16/13 | |||
| MOSes = [[4L 3s]], [[3L 4s]], [[7L 3s]], [[3L 7s]] | |||
| Complement = [[Neutral sixth]] | |||
| Lower region = [[Minor Third]] | |||
| Higher region = [[Major third]] | |||
}} | |||
{{Wikipedia}} | {{Wikipedia}} | ||
A '''neutral third (n3 | 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 [[just intonation]], an interval may be classified as a neutral third if it is reasonably mapped to | 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. | ||
As a concrete [[interval region]], it is typically near 350 [[cents]] in size, distinct from the | 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, 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 | * 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 | * 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 | * 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 | |||
=== 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 | 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 | ||