Major second: Difference between revisions
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| Complement = [[Minor seventh]] | | Complement = [[Minor seventh]] | ||
| Lower region = [[Neutral second]] | | Lower region = [[Neutral second]] | ||
| Higher region = [[Minor | | Higher region = [[Minor third]] | ||
}} | }} | ||
As a concrete [[interval region]], a major second is typically near 200{{c}} in size, distinct from the [[Semitone (interval region)|semitone]] of roughly 100{{c}} and the [[neutral second]] of roughly 150{{c}}. A rough tuning range for the major second is about 180 to 240{{c}} according to [[Margo Schulter]]'s theory of interval regions. | As a concrete [[interval region]], a major second is typically near 200{{c}} in size, distinct from the [[Semitone (interval region)|semitone]] of roughly 100{{c}} and the [[neutral second]] of roughly 150{{c}}. A rough tuning range for the major second is about 180 to 240{{c}} according to [[Margo Schulter]]'s theory of interval regions. | ||
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This article covers intervals between 160 and 260{{c}}. The outer range of this might be too extreme to call "major seconds", but this is done so that one can find what they are looking for easily. | This article covers intervals between 160 and 260{{c}}. The outer range of this might be too extreme to call "major seconds", but this is done so that one can find what they are looking for easily. | ||
=== In | === In mos scales === | ||
Being a small interval, major seconds generate a number of monosmall and monolarge [[mos scale]]s. | Being a small interval, major seconds generate a number of monosmall and monolarge [[mos scale]]s. | ||
These tables start from the last monolarge | These tables start from the last monolarge mos generated by the interval range. Scales with more than 12 notes are not included. | ||
Scales with more than 12 notes are not included. | |||
{| class="wikitable" | {| class="wikitable" | ||
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In [[just intonation]], an interval may be classified as a major second if it is reasonably mapped to 2 steps of the chromatic scale - formally, this is 4\24, which is used as opposed to [[12edo]]'s 2\12 to better capture the characteristics of many intervals in the [[11-limit|11-]] and [[13-limit]] – and 1 step of the diatonic scale. Diminished thirds are mapped to 2 steps of the chromatic scale and 2 steps of the diatonic scale. | In [[just intonation]], an interval may be classified as a major second if it is reasonably mapped to 2 steps of the chromatic scale - formally, this is 4\24, which is used as opposed to [[12edo]]'s 2\12 to better capture the characteristics of many intervals in the [[11-limit|11-]] and [[13-limit]] – and 1 step of the diatonic scale. Diminished thirds are mapped to 2 steps of the chromatic scale and 2 steps of the diatonic scale. | ||
In TAMNAMS, the major second is called the | In TAMNAMS, the major second is called the ''major 1-diastep''. | ||
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. | 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. | ||
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Other major seconds exist in higher [[prime limit|limits]], however, for example: | Other major seconds exist in higher [[prime limit|limits]], however, for example: | ||
* The 5-limit | * The 5-limit ptolemaic major second is a ratio of [[10/9]], however in 5-limit harmony it is used alongside 9/8. It is about 182{{c}}. | ||
* The 7-limit | * The 7-limit (septimal) supermajor second is a ratio of [[8/7]], and is about 231{{c}}. | ||
* The 11-limit | * The 11-limit (undecimal) submajor second is a ratio of [[11/10]], and is about 165{{c}}, though it can also be analyzed as a [[neutral second]]. Despite that, it is also here for completeness. | ||
* The 13-limit | * The 13-limit (tridecimal) ultramajor second is a ratio of [[15/13]], and is about 248{{c}}, though it can also be analyzed as an [[minor third|inframinor third]]. Despite that, it is also here for completeness. | ||
=== By delta === | === By delta === | ||
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Due to the [[9/8]] major second being closely related to the perfect fifth, it is often useful to detune the fifth to approach other intervals with the diatonic major second. If the diatonic perfect fifth is treated as [[3/2]], approximating various intervals with the diatonic major second leads to the following temperaments: | Due to the [[9/8]] major second being closely related to the perfect fifth, it is often useful to detune the fifth to approach other intervals with the diatonic major second. 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 center-2 center-5" | {| class="wikitable center-2 center-5" | ||
|+ | |+ | ||
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| 21/19 | | 21/19 | ||
| 173{{c}} | | 173{{c}} | ||
| [[ | | [[Surprise]] | ||
| [[57/56]] | | [[57/56]] | ||
| 687{{c}} | | 687{{c}} | ||
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| 19/17 | | 19/17 | ||
| 193{{c}} | | 193{{c}} | ||
| Little ganassi | | [[Little ganassi]] | ||
| [[153/152]] | | [[153/152]] | ||
| 696{{c}} | | 696{{c}} | ||
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| 17/15 | | 17/15 | ||
| 217{{c}} | | 217{{c}} | ||
| Fiventeen | | [[Fiventeen]] | ||
| [[136/135]] | | [[136/135]] | ||
| 708{{c}} | | 708{{c}} | ||