Neutral third: Difference between revisions

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 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 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.

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 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 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.

! colspan="2" | Delta-2

! colspan="2" | Delta-3

! colspan="2" | Delta-4

! colspan="2" | Delta-5

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]].

| [[Breed (temperament)|Breed]] retraction*

| [[Neutral (temperament)|Neutral]]

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

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

Scales with more than 12 notes are not included.

! colspan="4" | Mos

| colspan="1" rowspan="3" | [[1L 2s]]

| colspan="1" rowspan="3" | [[3L 1s]]

| rowspan="1" | [[4L 3s]]

| [[7L 4s]]

| rowspan="2" | [[3L 4s]]

| [[7L 3s]]

| [[3L 7s]]