Major third: Difference between revisions

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

This section covers intervals between 360 and 460{{c}}. The outer range of this might be too extreme to call "major thirds", but this is done so that one can find what they're looking for easily.   

=== In MOS scales ===

Intervals between 360 and 480 cents generate the following [[mos]] scales:

As a diatonic interval category, a major third is an interval that spans two scale steps in the [[5L 2s|diatonic]] scale 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}} ([[7edo|2\7]] to [[5edo|2\5]]).{{Infobox|Title=Diatonic major third|Header 1=MOS|Data 1=[[5L 2s]]|Header 2=Other names|Data 2=Major 2-diastep|Header 3=Generator span|Data 3=+4 generators|Header 4=Tuning range|Data 4=343–480{{c}}|Header 5=Basic tuning|Data 5=400{{c}}|Header 6=Function on root|Data 6=Mediant|Header 7=Interval regions|Data 7=[[Neutral third (interval region)|Neutral third]], [[major third (interval region)|major third]], ([[naiadic]])|Header 8=Associated just intervals|Data 8=[[5/4]], [[81/64]]|Header 9=Octave complement|Data 9=[[Minor sixth (diatonic interval category)|Minor sixth]]}}In [[just intonation]], an interval may be classified as a major third if it is reasonably mapped to two steps of the diatonic scale and four steps of the chromatic scale, or formally 2\7 and [[24edo|8\24]]. 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]].

The major third can be stacked with a [[Minor third (diatonic interval category)|minor third]] to form a perfect fifth, and as such is often involved in chord structures in diatonic harmony.

The tuning range of the diatonic major third ranges from 342.8 to 480{{c}}. The generator for a given tuning in cents, ''n'', for the diatonic major third can be found by {{nowrap|(''n'' + 2400)/4}}. For example, the third 384{{c}} gives us {{nowrap|(384 + 2400)/4 {{=}} 2784/4 {{=}} 696{{c}}}}, corresponding to 50edo.

The tuning range of the diatonic diminished fourth ranges from 240 to 514{{c}}. The generator for a given tuning in cents, n, for the diminished fourth can be found by (n + 3600)/8. For example, the diminished fourth 384{{c}} gives us (384 + 3600)/8 = 3984/8 = 498{{c}}, corresponding to 200edo.  

!Tuning

!Step ratio

!Edo

!Major third

!Diminished fourth

|Equalized

|1:1

|7

|343{{c}}

|514{{c}}

|Supersoft

|4:3

|26

|369{{c}}

|462{{c}}

|Soft

|3:2

|19

|379{{c}}

|442{{c}}

|Semisoft

|5:3

|31

|387{{c}}

|426{{c}}

|Basic

|2:1

|12

|400{{c}}

|400{{c}}

|Semihard

|5:2

|29

|414{{c}}

|372{{c}}

|Hard

|3:1

|17

|424{{c}}

|353{{c}}

|Superhard

|4:1

|22

|436{{c}}

|327{{c}}

|Collapsed

|1:0

|5

|480{{c}}

|240{{c}}