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{{Interwiki
| en = Major third
| zh = 大三度
}}
{{Wikipedia}}
{{Wikipedia}}
A '''major third (M3)''' in the [[5L 2s|diatonic scale]] is an interval that spans two scale steps with the major (wider) quality. It is generated by stacking 4 fifths [[octave reduction|octave reduced]], and depending on the specific tuning, it ranges from 343 to 480{{cent}} ([[7edo|2\7]] to [[5edo|2\5]]).  
A '''major third''' ('''M3''') is the larger 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 major scale, hence its name. Another diatonic interval around the same size is the '''diminished fourth''' ('''d4'''). More generally, an interval close to 400 cents in size can be called a major third.  


In [[just intonation]], an interval may be classified as a major third if it is reasonably mapped to 2\7 and [[24edo|8\24]] (precisely two steps of the diatonic scale and four steps of the chromatic scale). The use of 24edo's 8\24 as the mapping criteria here rather than [[12edo]]'s 4\12 better captures the characteristics of many intervals in the [[11-limit|11-]] and [[13-limit]].  
Many JI intervals are called major thirds, but the term usually refers to one of these three intervals:
* [[5/4]], the classical major third of about 386 cents.
* [[9/7]], the septimal major third of about 435 cents.  
* [[81/64]], the Pythagorean major third of about 408 cents.  


As a concrete [[interval region]], it is typically near 400{{c}} in size, distinct from the [[minor third]] of roughly 300{{c}} and the [[neutral third]] of roughly 350{{c}}. A rough tuning range for the major third is about 370 to 440{{c}} according to [[Margo Schulter]]'s theory of interval regions. ''Major third'' in this sense refers both to the ~350–450{{c}} range as a whole, and to a specific subdivision within it (~370–415{{c}}) as opposed to supermajor thirds; major thirds sharp of this are often called "supermajor thirds".  
== As an interval region ==
{{Infobox interval region
| Name = Major third
| Cents lower = 372
| Cents lower wide = 343
| Cents upper = 440
| Cents upper wide = 480
| MOSes = [[3L 4s]], [[7L 3s]], [[3L 7s]], [[3L 5s]], [[5L 3s]]
| JI intervals = 5/4, 9/7
| Lower region = [[Neutral third]]
| Higher region = [[Perfect fourth]]
| Complement = [[Minor sixth]]
| Subregions = [[Submajor third]] <br> [[Supermajor third]] <br> [[Ultramajor third]]
}}
As an [[interval region]], a major third is typically near 400{{c}} in size. A rough tuning range for the major third is about 370 to 440{{c}} according to [[Margo Schulter]]'s theory of interval regions. ''Major third'' in this sense refers both to the ~350–450{{c}} range as a whole, and to a specific subdivision within it (~370–415{{c}}) as opposed to supermajor thirds; major thirds sharp of this are often called supermajor thirds.  


This article covers intervals between 360 and 460{{c}}. The outer range of this might be too extreme to call "major thirds", but this is done so that one can find what they're looking for easily.   
This section covers intervals between 360 and 460{{c}}. The outer range of this might be too extreme to call major thirds, but this is done so that one can find what they're looking for easily.   
 
=== In mos scales ===
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.
 
{| class="wikitable"
|-
! Range
! colspan="5" | Mos
|-
| 360–400{{c}}
| [[1L 2s]]
| [[3L 1s]]
| [[3L 4s]]
| colspan="2" | [[3L 7s]]
|-
| 400–436{{c}}
| rowspan="3" | [[1L 1s]]
| rowspan="3" | [[2L 1s]]
| rowspan="3" | [[3L 2s]]
| rowspan="2" | [[3L 5s]]
| [[3L 8s]]
|-
| 436–450{{c}}
| [[8L 3s]]
|-
| 450–480{{c}}
| colspan="2" | [[5L 3s]]
|}
 
== As a diatonic interval category ==
{{Infobox
| Title = Diatonic major third
| Header 1 = MOS | Data 1 = [[5L&nbsp;2s]]
| Header 2 = Other names | Data 2 = Major 2-diastep
| Header 3 = Generator span | Data 3 = +4 generators
| Header 4 = Tuning range | Data 4 = 343–480{{c}}
| Header 5 = Basic tuning | Data 5 = 400{{c}}
| Header 6 = Function on root | Data 6 = Mediant
| Header 7 = Interval regions | Data 7 = [[Neutral third]], major third, ([[naiadic]])
| Header 8 = Associated just intervals | Data 8 = [[5/4]], [[81/64]]
| Header 9 = Octave complement | Data 9 = [[Minor sixth]]
}}
As a diatonic interval category, a major third is an interval that spans two scale steps in the [[5L 2s|diatonic]] scale with the major (wider) quality. It is generated by stacking 4 fifths [[octave reduction|octave reduced]], and depending on the specific tuning, it ranges from 343 to 480{{cent}} ([[7edo|2\7]] to [[5edo|2\5]]).
 
In [[just intonation]], an interval may be classified as a major third if it is reasonably mapped to two steps of the diatonic scale and four steps of the chromatic scale, or formally 2\7 and [[24edo|8\24]]. The use of 24edo's 8\24 as the mapping criteria here rather than [[12edo]]'s 4\12 better captures the characteristics of many intervals in the [[11-limit|11-]] and [[13-limit]].
 
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 ''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 ''diminished 3-diastep''.
 
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 ===
The diatonic scale contains three major thirds. In the Ionian mode, major thirds are found on the first, fourth, and fifth degrees of the scale; the other four degrees have minor thirds. This roughly equal distribution leads to diatonic tonality being largely based on the distinction between major and minor thirds and triads.
 
=== 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. This is similar for the diminished fourth.
 
The tuning range of the diatonic major third ranges from 342.8 to 480{{c}}. The generator for a given tuning in cents, ''n'', for the diatonic major third can be found by {{nowrap| (''n'' + 2400)/4 }}. For example, the third 384{{c}} gives us {{nowrap| (384 + 2400)/4 {{=}} 2784/4 {{=}} 696{{c}} }}, corresponding to 50edo.
 
The tuning range of the diatonic diminished fourth ranges from 240 to 514{{c}}. The generator for a given tuning in cents, n, for the diminished fourth can be found by {{nowrap| (''n'' + 3600)/8 }}. For example, the diminished fourth 384{{c}} gives us {{nowrap| (384 + 3600)/8 {{=}} 3984/8 {{=}} 498{{c}} }}, corresponding to 200edo.
 
Several example tunings are provided below:
{| class="wikitable center-all left-1"
|+Tunings of the major third and diminished fourth
! Tuning
! Step ratio
! Edo
! Major third
! Diminished fourth
|-
| Equalized
| 1:1
| 7
| 343{{c}}
| 514{{c}}
|-
| Supersoft
| 4:3
| 26
| 369{{c}}
| 462{{c}}
|-
| Soft
| 3:2
| 19
| 379{{c}}
| 442{{c}}
|-
| Semisoft
| 5:3
| 31
| 387{{c}}
| 426{{c}}
|-
| Basic
| 2:1
| 12
| 400{{c}}
| 400{{c}}
|-
| Semihard
| 5:2
| 29
| 414{{c}}
| 372{{c}}
|-
| Hard
| 3:1
| 17
| 424{{c}}
| 353{{c}}
|-
| Superhard
| 4:1
| 22
| 436{{c}}
| 327{{c}}
|-
| Collapsed
| 1:0
| 5
| 480{{c}}
| 240{{c}}
|}


== In just intonation ==
== In just intonation ==
=== By prime limit ===
=== By prime limit ===
3-limit intervals in the range of major thirds include the '''Pythagorean major third''' of [[81/64]], 407.8{{c}} in size, which corresponds to the MOS-based interval category of the diatonic major third and is generated by [[stacking]] four just perfect fifths of [[3/2]], and the '''Pythagorean diminished fourth''' of [[8192/6561]], which is flat of 81/64 by one Pythagorean comma, and is about 384{{c}} in size.
The simplest 3-limit major third is the Pythagorean major third of [[81/64]], 408{{c}} in size, which is generated by [[stacking]] four just perfect fifths of [[3/2]]. There is also a Pythagorean diminished fourth of about 384{{c}}.


Much [[odd limit|simpler]] major thirds 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 classical major third is a ratio of [[5/4]], and is about 386{{c}}.
* The 5-limit '''classical major third''' is a ratio of [[5/4]], and is about 386{{c}}.
* The 7-limit (septimal) supermajor third is a ratio of [[9/7]], and is almost exactly 435{{c}}.
* The 7-limit '''(septimal) supermajor third''' is a ratio of [[9/7]], and is almost exactly 435{{c}}.
* 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 11-limit '''neogothic major third''' is a ratio of [[14/11]], and is almost exactly 417.5{{c}}.
* The 13-limit (tridecimal) ultramajor third is a ratio of [[13/10]], and is about 454{{c}}.
* The 13-limit '''(tridecimal) ultramajor third''' is a ratio of [[13/10]], and is about 454{{c}}.
** There is also a 13-limit (tridecimal) submajor third, which is a ratio of [[26/21]], and is about 370{{c}}.
** There is also a 13-limit '''(tridecimal) submajor third''', which is a ratio of [[26/21]], and is about 370{{c}}.
* The 17-limit (septendecimal) submajor third is a ratio of [[21/17]], and is about 366{{c}}.
* The 17-limit '''(septendecimal) submajor third''' is a ratio of [[21/17]], and is about 366{{c}}.
* The 23-limit vicesimoterial supermajor third is a ratio of [[23/18]], and is about 424{{c}}.


=== By delta ===
=== By delta ===
Line 77: Line 225:
|}
|}


== In EDOs ==
== In edos ==
The following table lists the best tuning of 5/4 and 9/7, as well as other major thirds if present, in various significant [[edos|EDOs]].
The following table lists the best tuning of 5/4 and 9/7, alongside the diatonic major third in various significant [[edo]]s.


{| class="wikitable"
{| class="wikitable"
|-
|-
! EDO
! Edo
! 5/4
! 5/4
! 9/7
! 9/7
! Other major thirds
! Diatonic major third
|-
|-
| 12
| 12
| colspan="2" | 400{{c}}
| colspan="3" | 400{{c}}
|
|-
|-
| 15
| 15
| 400{{c}}
| 400{{c}}
| *
| colspan="2" | *
|
|-
|-
| 16
| 16
| 375{{c}}
| 375{{c}}
| 450{{c}}
| 450{{c}}
|  
| *
|-
|-
| 17
| 17
| **
| *
| 424{{c}}
| colspan="2" | 424{{c}}
|
|-
|-
| 19
| 19
| 379{{c}}
| 379{{c}}
| 442{{c}}
| 442{{c}}
|  
| 379{{c}}
|-
|-
| 22
| 22
| 382{{c}}
| 382{{c}}
| 436{{c}}
| 436{{c}}
|  
| 436{{c}}
|-
|-
| 24
| 24
| 400{{c}}
| 400{{c}}
| 450{{c}}
| 450{{c}}
|  
| 400{{c}}
|-
|-
| 25
| 25
| 384{{c}}
| 384{{c}}
| 432{{c}}
| 432{{c}}
|  
| *
|-
|-
| 26
| 26
| 369{{c}}
| 369{{c}}
| 415{{c}}
| 415{{c}}
|  
| 369{{c}}
|-
|-
| 27
| 27
| 400{{c}}
| 400{{c}}
| 444{{c}}
| 444{{c}}
|  
| 444{{c}}
|-
|-
| 29
| 29
Line 142: Line 287:
|-
|-
| 31
| 31
| 388{{c}}
| 387{{c}}
| 426{{c}}
| 426{{c}}
|  
| 387{{c}}
|-
|-
| 34
| 34
| 388{{c}}
| 388{{c}}
| 424{{c}}
| colspan="2" | 424{{c}}
| {{nowrap|459{{c}} ≈ 13/10}}
|-
|-
| 41
| 41
Line 159: Line 303:
| 385{{c}}
| 385{{c}}
| 430{{c}}
| 430{{c}}
| {{nowrap|362{{c}} ≈ 21/17|408{{c}} ≈ 81/64|452{{c}} ≈ 13/10}}
| 408{{c}} ≈ 81/64
|}
|}
<nowiki />* These edos have an approximation to 9/7, but it's sharper than 460{{c}}, not really a major third.
<nowiki>*</nowiki> There is a valid interval in this edo, but it is well outside the range of a major third.
 
<nowiki />** These edos have an approximation to 5/4, but it's flatter than 360{{c}}, not really a major third.


== In regular temperaments ==
== In regular temperaments ==
The two simplest major 3rd ratios are 5/4 and 9/7. The following notable temperaments are generated by them:
The two simplest major third ratios are 5/4 and 9/7. The following notable temperaments are generated by them:


=== Temperaments that use 5/4 as a generator ===
=== Temperaments that use 5/4 as a generator ===
Line 173: Line 315:
* [[Dicot]], an exotemperament which generates 3/2 by stacking two 5/4's so that the mapping dictates that 5/4 and [[6/5]] are equated.
* [[Dicot]], an exotemperament which generates 3/2 by stacking two 5/4's so that the mapping dictates that 5/4 and [[6/5]] are equated.
* [[Father]], an exotemperament which equates [[4/3]] and 5/4 as a single "fourth-third" interval, from which it derives its name.
* [[Father]], an exotemperament which equates [[4/3]] and 5/4 as a single "fourth-third" interval, from which it derives its name.
* [[Augmented (temperament)|Augmented]], which splits the octave into three equal parts, each representing [[5/4]].
** The 5-limit [[Circular temperament|circular temperaments]] in general


=== Temperaments that use 9/7 as a generator ===
=== Temperaments that use 9/7 as a generator ===
* [[Sensi]], generated by sharp supermajor thirds representing [[9/7]] and [[13/10]], such that a stack of two gives a major sixth approximating [[5/3]].
* [[Sensi]], generated by sharp supermajor thirds representing [[9/7]] and [[13/10]], such that a stack of two gives a major sixth approximating [[5/3]], and a stack of seven gives [[6/1]].
* [[Squares]], generated by flat supermajor thirds representing [[9/7]] and [[14/11]], such that a stack of four gives [[8/3]].
* [[Squares]], generated by flat supermajor thirds representing [[9/7]] and [[14/11]], such that a stack of four gives [[8/3]].
== In moment-of-symmetry scales ==
Intervals between 360 and 480 cents generate the following [[MOS]] scales:
These tables start from the last monolarge [[MOS]] generated by the interval range.
MOSes with more than 12 notes are not included.
{| class="wikitable"
|-
! Range
! colspan="5" | MOS
|-
| 360–400{{c}}
| [[1L&nbsp;2s]]
| [[3L&nbsp;1s]]
| [[3L&nbsp;4s]]
| colspan="2" | [[3L&nbsp;7s]]
|-
| 400–436{{c}}
| rowspan="3" | [[1L&nbsp;1s]]
| rowspan="3" | [[2L&nbsp;1s]]
| rowspan="3" | [[3L&nbsp;2s]]
| rowspan="2" | [[3L&nbsp;5s]]
| [[3L&nbsp;8s]]
|-
| 436–450{{c}}
| [[8L&nbsp;3s]]
|-
| 450–480{{c}}
| colspan="2" | [[5L&nbsp;3s]]
|}


{{Navbox intervals}}
{{Navbox intervals}}

Latest revision as of 14:42, 30 March 2026

English Wikipedia has an article on:

A major third (M3) is the larger 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 major scale, hence its name. Another diatonic interval around the same size is the diminished fourth (d4). More generally, an interval close to 400 cents in size can be called a major third.

Many JI intervals are called major thirds, but the term usually refers to one of these three intervals:

  • 5/4, the classical major third of about 386 cents.
  • 9/7, the septimal major third of about 435 cents.
  • 81/64, the Pythagorean major third of about 408 cents.

As an interval region

← Neutral third Major third Perfect fourth →
Name Major third
Lower bound 343¢ – 372¢
Upper bound 440¢ – 480¢
Generated MOSes 3L 4s, 7L 3s, 3L 7s, 3L 5s, 5L 3s
Example JI intervals
Intervals 5/4 (386.3¢)
9/7 (435.1¢)
Related regions
Complement Minor sixth
Subregions Submajor third
Supermajor third
Ultramajor third

As an interval region, a major third is typically near 400 ¢ in size. A rough tuning range for the major third is about 370 to 440 ¢ according to Margo Schulter's theory of interval regions. Major third in this sense refers both to the ~350–450 ¢ range as a whole, and to a specific subdivision within it (~370–415 ¢) as opposed to supermajor thirds; major thirds sharp of this are often called supermajor thirds.

This section covers intervals between 360 and 460 ¢. The outer range of this might be too extreme to call major thirds, but this is done so that one can find what they're looking for easily.

In mos scales

Intervals between 360 and 480 cents 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.

Range Mos
360–400 ¢ 1L 2s 3L 1s 3L 4s 3L 7s
400–436 ¢ 1L 1s 2L 1s 3L 2s 3L 5s 3L 8s
436–450 ¢ 8L 3s
450–480 ¢ 5L 3s

As a diatonic interval category

Diatonic major third
MOS 5L 2s
Other names Major 2-diastep
Generator span +4 generators
Tuning range 343–480 ¢
Basic tuning 400 ¢
Function on root Mediant
Interval regions Neutral third, major third, (naiadic)
Associated just intervals 5/4, 81/64
Octave complement Minor sixth

As a diatonic interval category, a major third is an interval that spans two scale steps in the diatonic scale with the major (wider) quality. It is generated by stacking 4 fifths octave reduced, and depending on the specific tuning, it ranges from 343 to 480 ¢ (2\7 to 2\5).

In just intonation, an interval may be classified as a major third if it is reasonably mapped to two steps of the diatonic scale and four steps of the chromatic scale, or formally 2\7 and 8\24. The use of 24edo's 8\24 as the mapping criteria here rather than 12edo's 4\12 better captures the characteristics of many intervals in the 11- and 13-limit.

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 major 2-diastep.

The diminished fourth is enharmonic with the major third, ranging from 240 to 514 ¢ (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 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 8\24.

Scale info

The diatonic scale contains three major thirds. In the Ionian mode, major thirds are found on the first, fourth, and fifth degrees of the scale; the other four degrees have minor thirds. This roughly equal distribution leads to diatonic tonality being largely based on the distinction between major and minor thirds and triads.

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. This is similar for the diminished fourth.

The tuning range of the diatonic major third ranges from 342.8 to 480 ¢. The generator for a given tuning in cents, n, for the diatonic major third can be found by (n + 2400)/4. For example, the third 384 ¢ gives us (384 + 2400)/4 = 2784/4 = 696 ¢, corresponding to 50edo.

The tuning range of the diatonic diminished fourth ranges from 240 to 514 ¢. The generator for a given tuning in cents, n, for the diminished fourth can be found by (n + 3600)/8. For example, the diminished fourth 384 ¢ gives us (384 + 3600)/8 = 3984/8 = 498 ¢, corresponding to 200edo.

Several example tunings are provided below:

Tunings of the major third and diminished fourth
Tuning Step ratio Edo Major third Diminished fourth
Equalized 1:1 7 343 ¢ 514 ¢
Supersoft 4:3 26 369 ¢ 462 ¢
Soft 3:2 19 379 ¢ 442 ¢
Semisoft 5:3 31 387 ¢ 426 ¢
Basic 2:1 12 400 ¢ 400 ¢
Semihard 5:2 29 414 ¢ 372 ¢
Hard 3:1 17 424 ¢ 353 ¢
Superhard 4:1 22 436 ¢ 327 ¢
Collapsed 1:0 5 480 ¢ 240 ¢

In just intonation

By prime limit

The simplest 3-limit major third is the Pythagorean major third of 81/64, 408 ¢ in size, which is generated by stacking four just perfect fifths of 3/2. There is also a Pythagorean diminished fourth of about 384 ¢.

Much simpler major thirds and diminished fourths exist in higher limits, however, for example:

  • The 5-limit classical major third is a ratio of 5/4, and is about 386 ¢.
  • The 7-limit (septimal) supermajor third is a ratio of 9/7, and is almost exactly 435 ¢.
  • The 11-limit neogothic major third is a ratio of 14/11, and is about 418 ¢. (Note that this is often considered an imperfect or diminished fourth.)
  • The 13-limit (tridecimal) ultramajor third is a ratio of 13/10, and is about 454 ¢.
    • There is also a 13-limit (tridecimal) submajor third, which is a ratio of 26/21, and is about 370 ¢.
  • The 17-limit (septendecimal) submajor third is a ratio of 21/17, and is about 366 ¢.
  • The 23-limit vicesimoterial supermajor third is a ratio of 23/18, and is about 424 ¢.

By delta

See Delta-N ratio.

Delta 1 Delta 2 Delta 3 Delta 4 Delta 5
5/4 386 ¢ 9/7 435 ¢ 13/10 454 ¢ 19/15 409 ¢ 22/17 446 ¢
14/11 418 ¢ 21/17 366 ¢ 23/18 424 ¢
24/19 404 ¢
26/21 370 ¢

In edos

The following table lists the best tuning of 5/4 and 9/7, alongside the diatonic major third in various significant edos.

Edo 5/4 9/7 Diatonic major third
12 400 ¢
15 400 ¢ *
16 375 ¢ 450 ¢ *
17 * 424 ¢
19 379 ¢ 442 ¢ 379 ¢
22 382 ¢ 436 ¢ 436 ¢
24 400 ¢ 450 ¢ 400 ¢
25 384 ¢ 432 ¢ *
26 369 ¢ 415 ¢ 369 ¢
27 400 ¢ 444 ¢ 444 ¢
29 372 ¢ 455 ¢ 414 ¢ ≈ 81/64, 14/11
31 387 ¢ 426 ¢ 387 ¢
34 388 ¢ 424 ¢
41 381 ¢ 439 ¢ 410 ¢ ≈ 81/64
53 385 ¢ 430 ¢ 408 ¢ ≈ 81/64

* There is a valid interval in this edo, but it is well outside the range of a major third.

In regular temperaments

The two simplest major third ratios are 5/4 and 9/7. The following notable temperaments are generated by them:

Temperaments that use 5/4 as a generator

  • Würschmidt, which generates 6/1 by stacking eight 5/4's, so that 128/125 flat of 5/4 represents a neutral third.
  • Magic, which generates 3/1 by stacking five 5/4's.
  • Dicot, an exotemperament which generates 3/2 by stacking two 5/4's so that the mapping dictates that 5/4 and 6/5 are equated.
  • Father, an exotemperament which equates 4/3 and 5/4 as a single "fourth-third" interval, from which it derives its name.

Temperaments that use 9/7 as a generator

  • Sensi, generated by sharp supermajor thirds representing 9/7 and 13/10, such that a stack of two gives a major sixth approximating 5/3, and a stack of seven gives 6/1.
  • Squares, generated by flat supermajor thirds representing 9/7 and 14/11, such that a stack of four gives 8/3.


View • Talk • EditInterval classification
Interval regions
Unison and octave Unison • Comma and diesis • Octave
Seconds Minor second • Neutral second • Major second
Thirds Minor third • Neutral third • Major third
Fourths and fifths Perfect fourth • Superfourth • Tritone • Subfifth • Perfect fifth
Sixths Minor sixth • Neutral sixth • Major sixth
Sevenths Minor seventh • Neutral seventh • Major seventh
Interseptimal intervals Interseptimal 2nd-3rd • Interseptimal 3rd-4th • Interseptimal 5th-6th • Interseptimal 6th-7th
Interval qualities
Diatonic qualities Diminished • Minor • Perfect • Major • Augmented
Tuning ranges Neutral (interval quality) • Submajor and supraminor • Pental major and minor • Novamajor and novaminor • Neogothic major and minor • Supermajor and subminor • Ultramajor and inframinor
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