Major third: Difference between revisions
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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 === | ||