Minor third: Difference between revisions
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{{Interwiki | |||
| en = Minor third | |||
| zh = 小三度 | |||
}} | |||
{{Wikipedia}} | |||
A '''minor third (m3)''' is the smaller 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 minor scale, hence its name. Another diatonic interval around the same size is the '''augmented second''' ('''A2'''). More generally, an interval close to 300 cents in size can be called a minor third. | |||
== As an interval region == | |||
{{Infobox interval region | {{Infobox interval region | ||
| Name = Minor third | | Name = Minor third | ||
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| JI intervals = 6/5, 7/6 | | JI intervals = 6/5, 7/6 | ||
| MOSes = [[5L 4s]], [[4L 5s]], [[4L 3s]] | | MOSes = [[5L 4s]], [[4L 5s]], [[4L 3s]] | ||
| Complement = [[Major sixth]] | | Complement = [[Major sixth]] | ||
| Lower region = [[ | | Lower region = [[Major second]] | ||
| Higher region = [[Neutral third]] | | Higher region = [[Neutral third]] | ||
}} | }} | ||
As a concrete [[interval region]], the minor third is typically near 300{{c}} in size, distinct from the [[major third]] of roughly 400{{c}} and the [[neutral third]] of roughly 350{{c}}. A rough tuning range for the minor third is about 260 to 330{{c}} according to [[Margo Schulter]]'s theory of interval regions. ''Minor third'' in this sense refers both to the ~240–340{{c}} range as a whole, and to a specific subdivision within it (~285–340{{c}}) as opposed to subminor thirds; minor thirds flat of this are often called subminor thirds. | |||
This section covers intervals between 240 and 340{{c}}. The outer range of this might be too extreme to call minor thirds, but this is done so that one can find what they're looking for easily. | |||
This section covers intervals between 240 and 340{{c}}. The outer range of this might be too extreme to call | |||
=== In mos scales === | === In mos scales === | ||
Intervals between 267 and 343{{c}} generate the following [[mos]] scales | Intervals between 267 and 343{{c}} generate the following [[mos]] scales. 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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== As a diatonic interval category == | == As a diatonic interval category == | ||
{{Infobox|Title=Diatonic minor third|Header 1=MOS|Data 1=[[5L 2s]]|Header 2=Other names|Data 2=Minor 2-diastep|Header 3=Generator span|Data 3=-3 generators|Header 4=Tuning range|Data 4=240–343{{c}}|Header 5=Basic tuning|Data 5=300{{c}}|Header 6=Function on root|Data 6=Mediant|Header 7=Interval regions|Data 7=[[Semifourth]], | {{Infobox | ||
| Title = Diatonic minor third | |||
| Header 1 = MOS | Data 1 = [[5L 2s]] | |||
| Header 2 = Other names | Data 2= Minor 2-diastep | |||
| Header 3 = Generator span | Data 3 = -3 generators | |||
| Header 4 = Tuning range | Data 4 = 240–343{{c}} | |||
| Header 5 = Basic tuning | Data 5 = 300{{c}} | |||
| Header 6 = Function on root | Data 6 = Mediant | |||
| Header 7 = Interval regions | Data 7 = [[Semifourth]], minor third, [[neutral third]] | |||
| Header 8 = Associated just intervals | Data 8 = [[6/5]], [[32/27]] | |||
| Header 9 = Octave complement | Data 9 = [[Major sixth]] | |||
}} | |||
As a diatonic interval category, a minor third is an interval that spans two scale steps in the [[5L 2s|diatonic]] scale with the minor (narrower) quality. It is generated by stacking 3 fourths [[octave reduction|octave reduced]], and depending on the specific tuning, it ranges from 240 to 343{{c}} ([[5edo|1\5]] to [[5edo|2\7]]). | |||
In [[just intonation]], an interval may be classified as a minor third if it is reasonably mapped to two steps of the diatonic scale and three steps of the chromatic scale, or formally 2\7 and [[24edo|6\24]]. The use of 24edo's 6\24 as the mapping criteria here rather than [[12edo]]'s 3\12 better captures the characteristics of many intervals in the [[11-limit|11-]] and [[13-limit]]. | In [[just intonation]], an interval may be classified as a minor third if it is reasonably mapped to two steps of the diatonic scale and three steps of the chromatic scale, or formally 2\7 and [[24edo|6\24]]. The use of 24edo's 6\24 as the mapping criteria here rather than [[12edo]]'s 3\12 better captures the characteristics of many intervals in the [[11-limit|11-]] and [[13-limit]]. | ||
The [[ | 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 ''minor 2-diastep''. | ||
The augmented second is enharmonic with the minor third, ranging from 171 to | The augmented second is enharmonic with the minor third, ranging from 171 to 480{{c}} (1\7 to 2\5). It is generated by stacking 9 fifths octave reduced, and is as such not found in the diatonic scale. Regardless, in TAMNAMS, it may be called the ''augmented 1-diastep''. | ||
In | In just intonation, an interval may be classified as an augmented second if it is reasonably mapped to ''one'' step of the diatonic scale and three steps of the chromatic scale, or formally 1\7 and [[24edo|6\24]]. | ||
=== Scale info === | === Scale info === | ||
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Much [[odd limit|simpler]] minor thirds exist in higher [[prime limit|limits]], however, for example: | Much [[odd limit|simpler]] minor thirds exist in higher [[prime limit|limits]], however, for example: | ||
* The 5-limit | * The 5-limit classical minor third is a ratio of [[6/5]], and is about 316{{c}}. | ||
* The 7-limit | * The 7-limit (septimal) subminor third is a ratio of [[7/6]], and is about 267{{c}}. | ||
* The 13-limit | * The 13-limit neogothic minor third is a ratio of [[13/11]], and is about 290{{c}}. | ||
** Note that this is | ** Note that this is ''not'' the fifth complement to the neogothic [[major third]] (unless [[364/363]] is tempered out), which is actually a ratio of 33/28, and is about 284{{c}}. | ||
* The 13-limit | * The 13-limit (tridecimal) inframinor third is a ratio of [[15/13]], and is about 248{{c}}. | ||
** There is also a 13-limit | ** There is also a 13-limit (tridecimal) supraminor third, which is a ratio of [[63/52]], and is about 332{{c}}. | ||
* The 17-limit | * The 17-limit (septendecimal) supraminor third is a ratio of [[17/14]], and is about 336{{c}}. | ||
** The | ** The septendecimal subminor third is a ratio of [[20/17]], and is about 281{{c}}. | ||
=== By delta === | === By delta === | ||
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== In regular temperaments == | == In regular temperaments == | ||
The two simplest minor third ratios are 7/6 and 6/5. The following notable temperaments are generated by them: | The two simplest minor third ratios are 7/6 and 6/5. The following notable temperaments are generated by them: | ||
* [[Kleismic]], which stacks six 6/5s (octave reduced) to reach 3/2. | * [[Kleismic]], which stacks six 6/5s (octave reduced) to reach 3/2. | ||
* [[Orwell]], which stacks seven 7/6s (octave reduced) to reach 3/2. | * [[Orwell]], which stacks seven 7/6s (octave reduced) to reach 3/2. | ||