Major third: Difference between revisions

A '''major third (M3)''' in the [[5L 2s|diatonic scale]] is an interval that spans two scale steps with the major (wider) quality. It is generated by stacking 4 fifths [[octave reduction|octave reduced]], and depending on the specific tuning, it ranges from 343 to 480 [[cent]]s ([[7edo|2\7]] to [[5edo|2\5]]).  

In [[just intonation]], an interval may be classified as a major third if it is reasonably mapped to 2\7 and [[24edo|8\24]] (precisely two steps of the diatonic scale and four steps of the chromatic scale). The use of 24edo's 8\24 as the mapping criteria here rather than [[12edo]]'s 4\12 better captures the characteristics of many intervals in the [[11-limit|11-]] and [[13-limit]].  

As a concrete [[interval region]], it is typically near 400 [[cents]] in size, distinct from the [[minor third]] of roughly 300 cents and the [[neutral third]] of roughly 350 cents. A rough tuning range for the major third is about 370 to 440 cents according to [[Margo Schulter]]'s theory of interval regions. ''Major third'' in this sense refers both to the ~350-450 cent range as a whole, and to a specific subdivision within it (~370–415 cents) as opposed to supermajor thirds; major thirds sharp of this are often called "supermajor thirds".  

3-limit intervals in the range of major thirds include the '''Pythagorean major third''' of [[81/64]], about 408 cents in size, which corresponds to the mos-based interval category of the diatonic major third and is generated by [[stacking]] four just perfect fifths of [[3/2]], and the '''Pythagorean diminished fourth''' of [[8192/6561]], which is flat of 81/64 by one Pythagorean comma, and is about 384 cents in size.

Much [[odd limit|simpler]] major thirds exist in higher [[prime limit|limits]], however, for example:

== In edos ==

The following table lists the best tuning of 5/4 and 9/7, as well as other major thirds if present, in various significant [[edos]].