|
|
| (11 intermediate revisions by 3 users not shown) |
| Line 1: |
Line 1: |
| {{Infobox|Title=Diatonic major third|Data 5=400c|Data 8=1, 4, 5|Header 9=Interval regions|Header 8=Positions in major scale|Data 7=Mediant|Data 6=[[Diatonic minor third]]|Header 7=Function on root|Header 6=Chromatically adjacent interval|Data 4=343c - 480c|Header 1=MOS|Data 3=+4 generators|Data 2=Major 2-diastep|Header 5=Basic tuning|Header 4=Tuning range|Header 3=Generator span|Header 2=Other names|Data 1=[[5L 2s]]|Data 9=[[Neutral third]], [[Major third (interval region)|Major third]], [[Perfect fourth]]|Header 10=Associated just intervals|Data 10=[[5/4]], [[81/64]]}}''This article is about the diatonic interval category. For the interval region, see [[Major third (interval region)]].''
| | #REDIRECT [[Major third (interval region)]] |
| | | [[Category:Diatonic interval categories]] |
| A '''major third (M3)''', in the diatonic scale, 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]]). 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]].
| |
| | |
| The major third can be stacked with a [[Minor third (diatonic interval)|diatonic 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'''.
| |
| | |
| == Scale info ==
| |
| The diatonic scale contains three major thirds. In the Ionian mode, major thirds are found on the first, fourth, and fifth degrees of the scale; the other four degrees have minor thirds. This roughly equal distribution leads to diatonic tonality being largely based on the distinction between major and minor thirds and triads.
| |
| | |
| == Tunings ==
| |
| Being an abstract MOS degree, and not a specific interval, the diatonic major third doesn't have a fixed tuning, but instead has a range of ways it can be tuned, based on the tuning of the generator used in making the scale.
| |
| | |
| The tuning range of the diatonic major third ranges from 342.8 cents to 480 cents. The generator for a given tuning in cents, n, for the diatonic major third can be found by (n+2400)/4. For example, the third 384c gives us (384+2400)/4 = 2784/4 = 696c, corresponding to 50edo.
| |
| | |
| Several example tunings are provided below:
| |
| {| class="wikitable"
| |
| |+Tunings of the major third
| |
| !Tuning
| |
| !Step ratio
| |
| !Edo
| |
| !Cents
| |
| |-
| |
| |Equalized
| |
| |1:1
| |
| |7
| |
| |343c
| |
| |-
| |
| |Supersoft
| |
| |4:3
| |
| |26
| |
| |369c
| |
| |-
| |
| |Soft
| |
| |3:2
| |
| |19
| |
| |379c
| |
| |-
| |
| |Semisoft
| |
| |5:3
| |
| |31
| |
| |387c
| |
| |-
| |
| |Basic
| |
| |2:1
| |
| |12
| |
| |400c
| |
| |-
| |
| |Semihard
| |
| |5:2
| |
| |29
| |
| |414c
| |
| |-
| |
| |Hard
| |
| |3:1
| |
| |17
| |
| |424c
| |
| |-
| |
| |Superhard
| |
| |4:1
| |
| |22
| |
| |436c
| |
| |-
| |
| |Collapsed
| |
| |1:0
| |
| |5
| |
| |480c
| |
| |}
| |
| | |
| == In regular temperaments ==
| |
| | |
| === P5 = 3/2 ===
| |
| If the diatonic perfect fifth is treated as [[3/2]], approximating various intervals with the diatonic major third leads to the following temperaments:
| |
| {| class="wikitable"
| |
| |+
| |
| !Just interval
| |
| !Cents
| |
| !Temperament
| |
| !Tempered comma
| |
| !Generator (eigenmonzo tuning)
| |
| |-
| |
| |[[27/22]]
| |
| |355c
| |
| |[[Io]]
| |
| |[[33/32]]
| |
| |Perfect fifth ≈ 689c
| |
| |-
| |
| |[[16/13]]
| |
| |359c
| |
| |[[Superflat]]
| |
| |[[1053/1024]]
| |
| |Perfect fifth ≈ 690c
| |
| |-
| |
| |[[21/17]]
| |
| |366c
| |
| |Temperament of 459/448
| |
| |459/448
| |
| |Perfect fifth ≈ 692c
| |
| |-
| |
| |[[5/4]]
| |
| |386c
| |
| |[[Meantone]]
| |
| |[[81/80]]
| |
| |Perfect fifth ≈ 697c
| |
| |-
| |
| |[[81/64]]
| |
| |408c
| |
| |[[Pythagorean tuning|Pythagorean]]
| |
| |[[1/1]]
| |
| |Perfect fifth ≈ 702c
| |
| |-
| |
| |[[14/11]]
| |
| |418c
| |
| |[[Parapyth]]/[[Pentacircle]]
| |
| |[[896/891]]
| |
| |Perfect fifth ≈ 705c
| |
| |-
| |
| |[[9/7]]
| |
| |435c
| |
| |[[Superpyth|Archy/Superpyth]]
| |
| |[[64/63]]
| |
| |Perfect fifth ≈ 709c
| |
| |-
| |
| |[[13/10]]
| |
| |454c
| |
| |[[Oceanfront]]/Temperament of 416/405
| |
| |[[416/405]]
| |
| |Perfect fifth ≈ 714c
| |
| |}
| |
| | |
| == In just notation systems ==
| |
| Due to the way the primes 7 and 11 are notated, in many systems of notation for just intonation, the interval [[14/11]] is not considered to be a major third, but instead belongs to the [[enharmonic]] category of diminished fourth.
| |