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".  

 

 

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

Scales with more than 12 notes are not included.

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.

In [[TAMNAMS]], this interval is called the '''major 2-diastep'''.

The diminished fourth is enharmonic with the major third, ranging from 240 to 514{{c}} (2\5 to 3\7). It is generated by stacking 8 fourths octave reduced, and is as such not found in the diatonic scale. Regardless, in TAMNAMS, it may be called the '''diminished 3-diastep'''.

In [[just intonation]], an interval may be classified as a diminished fourth if it is reasonably mapped to '''three''' steps of the diatonic scale and four steps of the chromatic scale, or formally 3\7 and [[24edo|8\24]].

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}}

 

* The 5-limit '''classical major third''' is a ratio of [[5/4]], and is about 386{{c}}.

* The 7-limit '''(septimal) supermajor third''' is a ratio of [[9/7]], and is almost exactly 435{{c}}.

* The 11-limit '''neogothic major third''' is a ratio of [[14/11]], and is about 418{{c}}. (Note that this is often considered an imperfect or diminished fourth.)

* The 13-limit '''(tridecimal) ultramajor third''' is a ratio of [[13/10]], and is about 454{{c}}.

** There is also a 13-limit '''(tridecimal) submajor third''', which is a ratio of [[26/21]], and is about 370{{c}}.

* The 17-limit '''(septendecimal) submajor third''' is a ratio of [[21/17]], and is about 366{{c}}.

* The 23-limit '''vicesimoterial supermajor''' third is a ratio of [[23/18]], and is about 424{{c}}.