User:VectorGraphics/Diatonic major third: Difference between revisions
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{{Infobox|Title=Diatonic major third|Data 5=400c|Data 8=[[ | {{Infobox|Title=Diatonic major third|Data 5=400c|Data 8=[[Pentic diminished third]]|Header 9=Daughter intervals|Header 8=Parent interval|Data 7=[[Antidiatonic minor third]], [[oneirotonic minor fifth]]|Data 6=[[Diatonic minor third]]|Header 7=Adjacent tunings|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=[[M-chromatic minor fifth]], [[P-chromatic major fifth]]|Header 10=Associated just intervals|Data 10=[[5/4]], [[81/64]]}} | ||
In the diatonic scale, the '''major third''' is the major variant of the 2-diastep, or ''third.'' It is generated by stacking 4 [[Diatonic perfect fifth|diatonic perfect fifths]] and octave-reducing. It can be stacked with a [[diatonic minor third]] to form a perfect fifth, and as such is often involved in chord structures in diatonic harmony. | In the diatonic scale, the '''major third''' is the major variant of the 2-diastep, or ''third.'' It is generated by stacking 4 [[Diatonic perfect fifth|diatonic perfect fifths]] and octave-reducing. It can be stacked with a [[diatonic minor third]] to form a perfect fifth, and as such is often involved in chord structures in diatonic harmony. | ||
| Line 9: | Line 9: | ||
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. | 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. Sharp of this, it becomes | The tuning range of the diatonic major third ranges from 342.8 cents to 480 cents. Sharp of this, it becomes an [[oneirotonic minor fifth]], and flat of this, it becomes an [[antidiatonic minor third]]. | ||
The diatonic major third is itself a type of [[diminished | The diatonic major third is itself a type of [[pentic diminished third]], and contains the categories of [[m-chromatic minor fifth]] and [[p-chromatic major fifth]], corresponding to the flat-of-basic and sharp-of-basic tunings of the major third respectively. | ||
{| class="wikitable" | {| class="wikitable" | ||
|+Tunings of the major 2-diastep | |+Tunings of the major 2-diastep | ||
| Line 79: | Line 79: | ||
|[[Io]] | |[[Io]] | ||
|[[33/32]] | |[[33/32]] | ||
|Perfect | |Perfect fifth ≈ 689c | ||
|- | |- | ||
|[[16/13]] | |[[16/13]] | ||
| Line 85: | Line 85: | ||
|[[Superflat]] | |[[Superflat]] | ||
|[[1053/1024]] | |[[1053/1024]] | ||
|Perfect | |Perfect fifth ≈ 690c | ||
|- | |- | ||
|[[21/17]] | |[[21/17]] | ||
| Line 91: | Line 91: | ||
|Temperament of 459/448 | |Temperament of 459/448 | ||
|459/448 | |459/448 | ||
|Perfect | |Perfect fifth ≈ 692c | ||
|- | |- | ||
|[[5/4]] | |[[5/4]] | ||
| Line 97: | Line 97: | ||
|[[Meantone]] | |[[Meantone]] | ||
|[[81/80]] | |[[81/80]] | ||
|Perfect | |Perfect fifth ≈ 697c | ||
|- | |- | ||
|[[81/64]] | |[[81/64]] | ||
| Line 103: | Line 103: | ||
|[[Pythagorean tuning|Pythagorean]] | |[[Pythagorean tuning|Pythagorean]] | ||
|[[1/1]] | |[[1/1]] | ||
|Perfect | |Perfect fifth ≈ 702c | ||
|- | |- | ||
|[[14/11]] | |[[14/11]] | ||
| Line 109: | Line 109: | ||
|[[Parapyth]]/[[Pentacircle]] | |[[Parapyth]]/[[Pentacircle]] | ||
|[[896/891]] | |[[896/891]] | ||
|Perfect | |Perfect fifth ≈ 705c | ||
|- | |- | ||
|[[9/7]] | |[[9/7]] | ||
| Line 115: | Line 115: | ||
|[[Superpyth|Archy/Superpyth]] | |[[Superpyth|Archy/Superpyth]] | ||
|[[64/63]] | |[[64/63]] | ||
|Perfect | |Perfect fifth ≈ 709c | ||
|- | |- | ||
|[[13/10]] | |[[13/10]] | ||
| Line 121: | Line 121: | ||
|[[Oceanfront]]/Temperament of 416/405 | |[[Oceanfront]]/Temperament of 416/405 | ||
|[[416/405]] | |[[416/405]] | ||
|Perfect | |Perfect fifth ≈ 714c | ||
|} | |} | ||
Latest revision as of 22:23, 25 February 2025
| MOS | 5L 2s |
| Other names | Major 2-diastep |
| Generator span | +4 generators |
| Tuning range | 343c - 480c |
| Basic tuning | 400c |
| Chromatically adjacent interval | Diatonic minor third |
| Adjacent tunings | Antidiatonic minor third, oneirotonic minor fifth |
| Parent interval | Pentic diminished third |
| Daughter intervals | M-chromatic minor fifth, P-chromatic major fifth |
| Associated just intervals | 5/4, 81/64 |
In the diatonic scale, the major third is the major variant of the 2-diastep, or third. It is generated by stacking 4 diatonic perfect fifths and octave-reducing. It can be stacked with a diatonic minor third to form a perfect fifth, and as such is often involved in chord structures in diatonic harmony.
Name
In TAMNAMS, this interval is called the major 2-diastep. However, because the diatonic scale is the standard scale of Western theory, it is more commonly called a major third, such as in standard Western notation, chain-of-fifths notation and quasi-diatonic MOS notation.
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. Sharp of this, it becomes an oneirotonic minor fifth, and flat of this, it becomes an antidiatonic minor third.
The diatonic major third is itself a type of pentic diminished third, and contains the categories of m-chromatic minor fifth and p-chromatic major fifth, corresponding to the flat-of-basic and sharp-of-basic tunings of the major third respectively.
| 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
If the diatonic perfect fifth is treated as 3/2, approximating various intervals with the diatonic major third leads to the following temperaments:
| 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 | 1/1 | Perfect fifth ≈ 702c |
| 14/11 | 418c | Parapyth/Pentacircle | 896/891 | Perfect fifth ≈ 705c |
| 9/7 | 435c | Archy/Superpyth | 64/63 | Perfect fifth ≈ 709c |
| 13/10 | 454c | Oceanfront/Temperament of 416/405 | 416/405 | Perfect fifth ≈ 714c |