Major second (diatonic interval category): Difference between revisions
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{{Infobox | {{Infobox | ||
| Title = Diatonic major second | | Title = Diatonic major second | ||
| Line 7: | Line 6: | ||
| Header 4 = Tuning range | Data 4 = 171–240{{c}} | | Header 4 = Tuning range | Data 4 = 171–240{{c}} | ||
| Header 5 = Basic tuning | Data 5 = 200{{c}} | | Header 5 = Basic tuning | Data 5 = 200{{c}} | ||
| Header 6 | | Header 6 = Function on root | Data 6 = Supertonic | ||
| Header 7 = Interval regions | Data 7 = [[Major second (interval region)|Major second]] | |||
| Header | | Header 8 = Associated just intervals | Data 8 = [[10/9]], [[9/8]] | ||
| Header 9 = Octave complement | Data 9 = [[Minor seventh (diatonic interval category)|Minor seventh]] | |||
| Header | }} | ||
}}In [[just intonation]], an interval may be classified as a major second if it is reasonably mapped to one step of the diatonic scale and two steps of the chromatic scale. | A '''major second''' ('''M2'''), also called a '''whole tone''' or simply '''tone''', is an interval that spans one scale step in the [[5L 2s|diatonic]] scale with the major (wider) quality. It is generated by stacking 2 fifths [[octave reduction|octave reduced]], and depending on the specific tuning, it ranges from 171 to 240{{cent}} ([[7edo|1\7]] to [[5edo|1\5]]). It can be considered the large step of the diatonic scale. In [[just intonation]], an interval may be classified as a major second if it is reasonably mapped to one step of the diatonic scale and two steps of the chromatic scale. | ||
Given its role as the large step, it can be used to construct other diatonic intervals, along with the [[Minor second (diatonic interval category)|minor second]]: two major seconds make a [[ | Given its role as the large step, it can be used to construct other diatonic intervals, along with the [[Minor second (diatonic interval category)|minor second]]: two major seconds make a [[major third (diatonic interval category)|major third]], a major second and a minor second make a [[Minor third (diatonic interval category)|minor third]], and three major seconds result in an [[augmented fourth]], also called a tritone for that reason. | ||
In [[TAMNAMS]], this interval is called the '''major 1-diastep'''. | In [[TAMNAMS]], this interval is called the '''major 1-diastep'''. | ||
==Scale info== | == Scale info == | ||
The diatonic scale contains five major seconds. In the Ionian mode, major seconds are found on the 1st, 2nd, 4th, 5th, and 6th degrees of the scale; the other two degrees have minor seconds. The large number of major seconds compared to minor seconds ensures that thirds that include minor seconds (that is, minor thirds) are roughly evenly distributed with major thirds; in a scale with three small steps and four large steps, for example, six out of the seven thirds are [[Minor third|minor]]. | The diatonic scale contains five major seconds. In the Ionian mode, major seconds are found on the 1st, 2nd, 4th, 5th, and 6th degrees of the scale; the other two degrees have minor seconds. The large number of major seconds compared to minor seconds ensures that thirds that include minor seconds (that is, minor thirds) are roughly evenly distributed with major thirds; in a scale with three small steps and four large steps, for example, six out of the seven thirds are [[Minor third|minor]]. | ||
==Tunings== | == Tunings == | ||
Being an abstract mos degree, and not a specific interval, the diatonic major third does not 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 does not 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. | ||
| Line 29: | Line 28: | ||
{| class="wikitable" | {| class="wikitable" | ||
|- | |- | ||
!Tuning | ! Tuning | ||
!Step ratio | ! Step ratio | ||
!Edo | ! Edo | ||
!Cents | ! Cents | ||
|- | |- | ||
|Equalized | | Equalized | ||
|1:1 | | 1:1 | ||
|7 | | 7 | ||
| | | 171{{c}} | ||
|- | |- | ||
|Supersoft | | Supersoft | ||
|4:3 | | 4:3 | ||
|26 | | 26 | ||
| | | 184{{c}} | ||
|- | |- | ||
|Soft | | Soft | ||
|3:2 | | 3:2 | ||
|19 | | 19 | ||
| | | 189{{c}} | ||
|- | |- | ||
|Semisoft | | Semisoft | ||
|5:3 | | 5:3 | ||
|31 | | 31 | ||
| | | 194{{c}} | ||
|- | |- | ||
|Basic | | Basic | ||
|2:1 | | 2:1 | ||
|12 | | 12 | ||
| | | 200{{c}} | ||
|- | |- | ||
|Semihard | | Semihard | ||
|5:2 | | 5:2 | ||
|29 | | 29 | ||
| | | 207{{c}} | ||
|- | |- | ||
|Hard | | Hard | ||
|3:1 | | 3:1 | ||
|17 | | 17 | ||
| | | 212{{c}} | ||
|- | |- | ||
|Superhard | | Superhard | ||
|4:1 | | 4:1 | ||
|22 | | 22 | ||
| | | 218{{c}} | ||
|- | |- | ||
|Collapsed | | Collapsed | ||
|1:0 | | 1:0 | ||
|5 | | 5 | ||
| | | 240{{c}} | ||
|} | |} | ||
==In regular temperaments== | |||
===P5 = 3/2=== | == In regular temperaments == | ||
=== P5 = 3/2 === | |||
If the diatonic perfect fifth is treated as [[3/2]], approximating various intervals with the diatonic major second leads to the following temperaments: | If the diatonic perfect fifth is treated as [[3/2]], approximating various intervals with the diatonic major second leads to the following temperaments: | ||
{| class="wikitable" | {| class="wikitable" | ||
|+ | |+ | ||
!Just interval | ! Just interval | ||
!Cents | ! Cents | ||
!Temperament | ! Temperament | ||
!Tempered comma | ! Tempered comma | ||
!Generator (eigenmonzo tuning) | ! Generator (eigenmonzo tuning) | ||
|- | |- | ||
| | | 21/19 | ||
| | | 173{{c}} | ||
| | | [[Hendrix #Surprise|Surprise]] | ||
|[[ | | [[57/56]] | ||
| | | 687{{c}} | ||
|- | |- | ||
| | | 10/9 | ||
| | | 182{{c}} | ||
|[[ | | [[Meantone]] | ||
|[[ | | [[81/80]] | ||
| | | 691{{c}} | ||
|- | |- | ||
| | | 19/17 | ||
| | | 193{{c}} | ||
| | | Little ganassi | ||
|[[ | | [[153/152]] | ||
| | | 696{{c}} | ||
|- | |- | ||
| | | 9/8 | ||
| | | 204{{c}} | ||
| | | [[Pythagorean]] | ||
|[[ | | [[1/1]] | ||
| | | 702{{c}} | ||
|- | |- | ||
| | | 17/15 | ||
| | | 217{{c}} | ||
| | | Fiventeen | ||
|[[ | | [[136/135]] | ||
| | | 708{{c}} | ||
|- | |- | ||
| 8/7 | |||
| 231{{c}} | |||
| [[Archy]] | |||
| [[64/63]] | |||
| 716{{c}} | |||
|8/7 | |||
| | |||
|[[Archy]] | |||
|[[64/63]] | |||
| | |||
|} | |} | ||
== See also == | == See also == | ||
* [[Major second]] (disambiguation page) | * [[Major second]] (disambiguation page) | ||
[[Category:Diatonic interval categories]] | [[Category:Diatonic interval categories]] | ||
Revision as of 12:35, 17 April 2025
| MOS | 5L 2s |
| Other names | Major 1-diastep |
| Generator span | +2 generators |
| Tuning range | 171–240 ¢ |
| Basic tuning | 200 ¢ |
| Function on root | Supertonic |
| Interval regions | Major second |
| Associated just intervals | 10/9, 9/8 |
| Octave complement | Minor seventh |
A major second (M2), also called a whole tone or simply tone, is an interval that spans one scale step in the diatonic scale with the major (wider) quality. It is generated by stacking 2 fifths octave reduced, and depending on the specific tuning, it ranges from 171 to 240 ¢ (1\7 to 1\5). It can be considered the large step of the diatonic scale. In just intonation, an interval may be classified as a major second if it is reasonably mapped to one step of the diatonic scale and two steps of the chromatic scale.
Given its role as the large step, it can be used to construct other diatonic intervals, along with the minor second: two major seconds make a major third, a major second and a minor second make a minor third, and three major seconds result in an augmented fourth, also called a tritone for that reason.
In TAMNAMS, this interval is called the major 1-diastep.
Scale info
The diatonic scale contains five major seconds. In the Ionian mode, major seconds are found on the 1st, 2nd, 4th, 5th, and 6th degrees of the scale; the other two degrees have minor seconds. The large number of major seconds compared to minor seconds ensures that thirds that include minor seconds (that is, minor thirds) are roughly evenly distributed with major thirds; in a scale with three small steps and four large steps, for example, six out of the seven thirds are minor.
Tunings
Being an abstract mos degree, and not a specific interval, the diatonic major third does not 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 second ranges from 342.8 to 480 ¢. The generator for a given tuning in cents, n, for the diatonic major second can be found by n + 1200/2. For example, the third 192 ¢ gives us 192 + 1200/2 = 1392/2 = 696 ¢, corresponding to 50edo.
Several example tunings are provided below:
| Tuning | Step ratio | Edo | Cents |
|---|---|---|---|
| Equalized | 1:1 | 7 | 171 ¢ |
| Supersoft | 4:3 | 26 | 184 ¢ |
| Soft | 3:2 | 19 | 189 ¢ |
| Semisoft | 5:3 | 31 | 194 ¢ |
| Basic | 2:1 | 12 | 200 ¢ |
| Semihard | 5:2 | 29 | 207 ¢ |
| Hard | 3:1 | 17 | 212 ¢ |
| Superhard | 4:1 | 22 | 218 ¢ |
| Collapsed | 1:0 | 5 | 240 ¢ |
In regular temperaments
P5 = 3/2
If the diatonic perfect fifth is treated as 3/2, approximating various intervals with the diatonic major second leads to the following temperaments:
| Just interval | Cents | Temperament | Tempered comma | Generator (eigenmonzo tuning) |
|---|---|---|---|---|
| 21/19 | 173 ¢ | Surprise | 57/56 | 687 ¢ |
| 10/9 | 182 ¢ | Meantone | 81/80 | 691 ¢ |
| 19/17 | 193 ¢ | Little ganassi | 153/152 | 696 ¢ |
| 9/8 | 204 ¢ | Pythagorean | 1/1 | 702 ¢ |
| 17/15 | 217 ¢ | Fiventeen | 136/135 | 708 ¢ |
| 8/7 | 231 ¢ | Archy | 64/63 | 716 ¢ |
See also
- Major second (disambiguation page)