Major third: Difference between revisions
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{{Interwiki | |||
| en = Major third | |||
| zh = 大三度 | |||
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{{Wikipedia}} | {{Wikipedia}} | ||
A '''major third''' ('''M3''') is the larger of the two thirds – intervals spanning 3 degrees or 2 scale steps in the diatonic scale. It is found between the 1st and 3rd notes of the major scale, hence its name. Another diatonic interval around the same size is the '''diminished fourth''' ('''d4'''). More generally, an interval close to 400 cents in size can be called a major third. | A '''major third''' ('''M3''') is the larger of the two thirds – intervals spanning 3 degrees or 2 scale steps in the diatonic scale. It is found between the 1st and 3rd notes of the major scale, hence its name. Another diatonic interval around the same size is the '''diminished fourth''' ('''d4'''). More generally, an interval close to 400 cents in size can be called a major third. | ||
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=== In mos scales === | === In mos scales === | ||
Intervals between 360 and 480 cents generate the following [[mos scale]]s | Intervals between 360 and 480 cents generate the following [[mos scale]]s. These tables start from the last monolarge mos generated by the interval range. Scales with more than 12 notes are not included. | ||
These tables start from the last monolarge mos generated by the interval range. | |||
Scales with more than 12 notes are not included. | |||
{| class="wikitable" | {| class="wikitable" | ||
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The major third can be stacked with a [[minor third]] to form a perfect fifth, and as such is often involved in chord structures in diatonic harmony. | The major third can be stacked with a [[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 | 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 | 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 | 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]]. | ||
=== Scale info === | === Scale info === | ||
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Much [[odd limit|simpler]] major thirds and diminished fourths exist in higher [[prime limit|limits]], however, for example: | Much [[odd limit|simpler]] major thirds and diminished fourths exist in higher [[prime limit|limits]], however, for example: | ||
* The 5-limit | * The 5-limit classical major third is a ratio of [[5/4]], and is about 386{{c}}. | ||
* The 7-limit | * The 7-limit (septimal) supermajor third is a ratio of [[9/7]], and is almost exactly 435{{c}}. | ||
* The 11-limit | * 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 | * The 13-limit (tridecimal) ultramajor third is a ratio of [[13/10]], and is about 454{{c}}. | ||
** There is also a 13-limit | ** There is also a 13-limit (tridecimal) submajor third, which is a ratio of [[26/21]], and is about 370{{c}}. | ||
* The 17-limit | * The 17-limit (septendecimal) submajor third is a ratio of [[21/17]], and is about 366{{c}}. | ||
* The 23-limit | * The 23-limit vicesimoterial supermajor third is a ratio of [[23/18]], and is about 424{{c}}. | ||
=== By delta === | === By delta === | ||