Major second - Revision history

FloraC: - abuse of bold and misc. fixes

2026-03-31T12:56:54Z

- abuse of bold and misc. fixes

← Older revision		Revision as of 12:56, 31 March 2026
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	\| Complement = [[Minor seventh]]		\| Complement = [[Minor seventh]]
	\| Lower region = [[Neutral second]]		\| Lower region = [[Neutral second]]
	\| Higher region = [[Minor ~~Third~~]]		\| 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 ~~MOS~~ scales ===		=== 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 ~~MOS~~ generated by the interval range.		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 '''major 1-diastep'''.		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 ~~'''~~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 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 ~~'''~~(septimal) supermajor second~~'''~~ is a ratio of [[8/7]], and is about 231{{c}}.		* The 7-limit (septimal) supermajor second is a ratio of [[8/7]], and is about 231{{c}}.
	* 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 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 ~~'''~~(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.		* 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}}
	\| [[~~Hendrix #Surprise\|~~Surprise]]		\| [[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}}

FloraC: Page merge followup

2026-03-30T11:55:02Z

Page merge followup

Show changes

FloraC: FloraC moved page Major second (interval region) to Major second: One page

2026-03-30T11:47:03Z

FloraC moved page Major second (interval region) to Major second: One page

← Older revision	Revision as of 11:47, 30 March 2026
(No difference)

Jdood: Fixed links

2025-12-03T18:05:34Z

Fixed links

← Older revision		Revision as of 18:05, 3 December 2025
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	\| Complement = [[Minor seventh]]		\| Complement = [[Minor seventh]]
	\| Lower region = [[Neutral second]]		\| Lower region = [[Neutral second]]
	\| Higher region = [[Minor~~ third~~]]		\| Higher region = [[Minor_third_(interval_region)\|Minor Third]]
	}}		}}
	A '''major second''' ('''M2''') is the larger of two "seconds" - intervals spanning 2 degrees or 1 scale step in the diatonic scale. It is found on the 1st note of the major scale, hence its name. Because it is one step, it is also called a "whole tone". Another diatonic interval [[Enharmonic\|around the same size]] is the '''diminished third'''.		A '''major second''' ('''M2''') is the larger of two "seconds" - intervals spanning 2 degrees or 1 scale step in the diatonic scale. It is found on the 1st note of the major scale, hence its name. Because it is one step, it is also called a "whole tone". Another diatonic interval [[Enharmonic\|around the same size]] is the '''diminished third'''.

Jerdle: /* Tunings */ Fixed multiple minor errors

2025-10-21T09:22:24Z

Tunings: Fixed multiple minor errors

← Older revision		Revision as of 09:22, 21 October 2025
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	=== 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 second 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~~{{c}}. The generator for a given tuning in cents, ''n''<nowiki>, for the diatonic major second can be found by {{nowrap\| (</nowiki>''n'' + 1200)/2. For example, the ~~third~~ 192{{c}} gives us {{nowrap\|(192 + 1200)/2 {{=}} 1392/2 {{=}} 696{{c}}}}, corresponding to 50edo.		The tuning range of the diatonic major second ranges from 171.4 to 240{{c}}. The generator for a given tuning in cents, ''n''<nowiki>, for the diatonic major second can be found by {{nowrap\| (</nowiki>''n'' + 1200)/2. For example, the second 192{{c}} gives us {{nowrap\|(192 + 1200)/2 {{=}} 1392/2 {{=}} 696{{c}}}}, corresponding to 50edo.

	Several example tunings are provided below:		Several example tunings are provided below:

VectorGraphics at 06:36, 18 June 2025

2025-06-18T06:36:56Z

@@ Line 14: / Line 14: @@
 More generally, an interval close to 200 cents can be called a major second.
 == As an interval region ==
@@ Line 55: / Line 57: @@
 == As a diatonic interval category ==
-As a diatonic interval category, a major second 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]]).
+{{Infobox|Title=Diatonic major second|Header 1=MOS|Data 1=[[5L&nbsp;2s]]|Header 2=Other names|Data 2=Major 1-diastep|Header 3=Generator span|Data 3=+2 generators|Header 4=Tuning range|Data 4=171–240{{c}}|Header 5=Basic tuning|Data 5=200{{c}}|Header 6=Function on root|Data 6=Supertonic|Header 7=Interval regions|Data 7=[[Major second (interval region)|Major second]]|Header 8=Associated just intervals|Data 8=[[10/9]], [[9/8]]|Header 9=Octave complement|Data 9=[[Minor seventh (diatonic interval category)|Minor seventh]]}}As a diatonic interval category, a major second 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 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 '''major 1-diastep'''.
 === Scale info ===
-In the Ionian (major) mode of the diatonic scale, the five major seconds can be found on the 1st, 2nd, 4th, 5th, and 6th degrees.
+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]].
 == In just intonation ==
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 {{Todo|complete list|inline=1}}
 {{Navbox intervals}}

VectorGraphics at 22:26, 19 May 2025

2025-05-19T22:26:39Z

@@ Line 11: / Line 11: @@
 | Higher region = [[Minor&nbsp;third]]
 }}
-A '''major second''' ('''M2'''), as a concrete [[interval region]], is typically near 200{{c}} in size, distinct from the [[Semitone (interval region)|semitone]] of roughly 100 ¢ 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.
+A '''major second''' ('''M2''') is the larger of two "seconds" - intervals spanning 2 degrees or 1 scale step in the diatonic scale. It is found on the 1st note of the major scale, hence its name. Because it is one step, it is also called a "whole tone". Another diatonic interval [[Enharmonic|around the same size]] is the '''diminished third'''.
 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 just intonation ==
@@ Line 189: / Line 238: @@
 |}
-== In mos scales ==
+== In regular temperaments ==
 The three simplest major second ratios are 10/9, 9/8, and 8/7, and these along with other more complex interpretations serve as [[generator]]s for a variety of [[regular temperament]]s.

ArrowHead294: /* In edos */

2025-05-05T15:29:28Z

In edos

← Older revision		Revision as of 15:29, 5 May 2025
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	The following table lists the best tuning of 10/9, 9/8, and 8/7, as well as other major seconds if present, in various significant [[edo]]s.		The following table lists the best tuning of 10/9, 9/8, and 8/7, as well as other major seconds if present, in various significant [[edo]]s.

	{\| class="wikitable"		{\| class="wikitable" style="text-align: center;"
	\|-		\|-
	! Edo		! Edo

VectorGraphics at 05:50, 16 March 2025

2025-03-16T05:50:59Z

← Older revision		Revision as of 05:50, 16 March 2025
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	\| Higher region = [[Minor third]]		\| Higher region = [[Minor third]]
	}}		}}
	A '''major second''' ('''M2''') 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.~~		A '''major second''' ('''M2'''), as a concrete [[interval region]], is typically near 200{{c}} in size, distinct from the [[Semitone (interval region)\|semitone]] of roughly 100 ¢ 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.

	~~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.~~

	As a concrete [[interval region]], it is typically near 200{{c}} in size, distinct from the [[Semitone (interval region)\|semitone]] of roughly 100 ¢ 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.

	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.

VectorGraphics: VectorGraphics moved page Major second to Major second (interval region): Diatonic category will get its own page

2025-03-16T05:49:41Z

VectorGraphics moved page Major second to Major second (interval region): Diatonic category will get its own page

← Older revision	Revision as of 05:49, 16 March 2025
(No difference)