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“The augmented fourth (A4) and the diminished fifth (d5) are the only augmented and diminished intervals that appear in diatonic scales”

How to differentiate between a diminished fifth and an augmented fourth interval?Are doubly augmented and doubly diminished intervals practical?Why is a major second not called a perfect second?Diminished and augmented key signatureHow to correctly invert non-compound greater-than-octave intervals?Diminished and augmented scalesWhat's significant about diatonic scales? Are there equivalents to the diatonic scales in smaller divisions of the octave (e.g. 19-EDO, 31-EDO, etc.)?Confusion about intervals in chromatic VS diatonic scalesWhich are all the musical intervals that are valid?How to properly notate scales that are not heptatonic

1

how is this true?
A4 & d5 are 2 types of tritones. and there are 1 or 2 tritones in a diatonic scale depending on the definition. but A4 and d5 are the only 2 augmented and diminished intervals in a diatonic scale? i don't think so. please correct me if i am wrong.

theory

share|improve this question

asked 1 hour ago

stupr instupr in

111

New contributor

stupr in is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.

• 
  
  
  

  
  

  
  
  
  
  
  

  
  
  "i don't think so. please correct me if i am wrong." -- maybe you should expand on this to clarify your question.
  
  – David Bowling
  1 hour ago
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  
  Source of the quote: en.wikipedia.org/wiki/Interval_(music)#Augmented_and_diminished
  
  – replete
  1 hour ago
  

  
  
  
  

add a comment | 

1

how is this true?
A4 & d5 are 2 types of tritones. and there are 1 or 2 tritones in a diatonic scale depending on the definition. but A4 and d5 are the only 2 augmented and diminished intervals in a diatonic scale? i don't think so. please correct me if i am wrong.

theory

share|improve this question

asked 1 hour ago

stupr instupr in

111

New contributor

stupr in is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.

• 
  
  
  

  
  

  
  
  
  
  
  

  
  
  "i don't think so. please correct me if i am wrong." -- maybe you should expand on this to clarify your question.
  
  – David Bowling
  1 hour ago
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  
  Source of the quote: en.wikipedia.org/wiki/Interval_(music)#Augmented_and_diminished
  
  – replete
  1 hour ago
  

  
  
  
  

add a comment | 

how is this true?
A4 & d5 are 2 types of tritones. and there are 1 or 2 tritones in a diatonic scale depending on the definition. but A4 and d5 are the only 2 augmented and diminished intervals in a diatonic scale? i don't think so. please correct me if i am wrong.

theory

share|improve this question

asked 1 hour ago

stupr instupr in

111

New contributor

stupr in is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.

share|improve this question

asked 1 hour ago

stupr instupr in

111

New contributor

stupr in is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.

share|improve this question

asked 1 hour ago

stupr instupr in

111

New contributor

stupr in is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.

asked 1 hour ago

stupr instupr in

111

New contributor

stupr in is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.

asked 1 hour ago

stupr instupr in

111

1 Answer
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2

I don't know your source, but the term "diatonic scale" typically refers to the major scale and its rotations (i.e., the modes). As such, we can test this claim just by looking at the intervals of a major scale.

• All seconds within in the scale are either minor (E–F and B–C) or major (C–D, D–E, F–G, G–A, A–B).


• All thirds are either minor (D–F, E–G, A–C, B–D) or major (C–E, F–A, G–B).


• All fourths are either perfect (C–F, D–G, E–A, G–C, A–D, B–E), or augmented (F–B). There's one augmented interval!

And conveniently, we don't have to do the rest of the work. Due to intervallic inversion, we know that seconds invert to sevenths, thirds to sixths, and fourths to fifths. Furthermore, we know that the qualities invert in particular ways, and only diminished/augmented intervals invert to each other.

As such, the only diminished/augmented intervals of a fifth, sixth, or seventh is the diminished fifth.

So yes, in fact, your source is correct: the only augmented/diminished interval that appears in the diatonic scale is the tritone.

You may be thinking of the augmented second (and its inversion, the diminished seventh) that is included in the harmonic minor scale. But this scale is not usually considered a "diatonic scale" since it requires a chromatic pitch: the raised leading tone.

share|improve this answer

answered 1 hour ago

RichardRichard

44.6k7105192

• 
  
  
  

  
  

  
  
  
  
  
  

  
  
  well there are other diminished &augmented intervals that lie on the diatonic scale. maybe what is meant by the source is that A4 & d5 are the only 2 that aren't enharmonic equivalent of any other interval. is that it?
  
  – stupr in
  1 hour ago
  

  
  
  
  


• 
  
  
  

  
  1
  

  
  
  
  
  
  

  
  
  What other diminished and augmented intervals lie on the diatonic scale?
  
  – Richard
  1 hour ago
  

  
  
  
  


• 
  
  
  

  
  1
  

  
  
  
  
  
  

  
  
  The only way you can get those intervals within a diatonic scale is through enharmonic reinterpretation. But in the act of enharmonic reinterpretation, you're no longer using the diatonic scale. Using only C D E F G A B, it's impossible to have those intervals.
  
  – Richard
  1 hour ago
  

  
  
  
  


• 
  
  
  

  
  1
  

  
  
  
  
  
  

  
  
  Are you saying E to F is a diminished fourth? And yes, for this purpose "enharmonic reinterpretation" just means "enharmonic equivalent."
  
  – Richard
  56 mins ago
  

  
  
  
  


• 
  
  
  

  
  1
  

  
  
  
  
  
  

  
  
  @stuprin E to F is just a half step. More specifically, it's a minor second. It's certainly not a fourth, since E up to F is only two note names and thus a type of second.
  
  – Richard
  41 mins ago
  

  
  
  
  

 | 
show 7 more comments

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2

I don't know your source, but the term "diatonic scale" typically refers to the major scale and its rotations (i.e., the modes). As such, we can test this claim just by looking at the intervals of a major scale.

• All seconds within in the scale are either minor (E–F and B–C) or major (C–D, D–E, F–G, G–A, A–B).


• All thirds are either minor (D–F, E–G, A–C, B–D) or major (C–E, F–A, G–B).


• All fourths are either perfect (C–F, D–G, E–A, G–C, A–D, B–E), or augmented (F–B). There's one augmented interval!

And conveniently, we don't have to do the rest of the work. Due to intervallic inversion, we know that seconds invert to sevenths, thirds to sixths, and fourths to fifths. Furthermore, we know that the qualities invert in particular ways, and only diminished/augmented intervals invert to each other.

As such, the only diminished/augmented intervals of a fifth, sixth, or seventh is the diminished fifth.

So yes, in fact, your source is correct: the only augmented/diminished interval that appears in the diatonic scale is the tritone.

You may be thinking of the augmented second (and its inversion, the diminished seventh) that is included in the harmonic minor scale. But this scale is not usually considered a "diatonic scale" since it requires a chromatic pitch: the raised leading tone.

share|improve this answer

answered 1 hour ago

RichardRichard

44.6k7105192

• 
  
  
  

  
  

  
  
  
  
  
  

  
  
  well there are other diminished &augmented intervals that lie on the diatonic scale. maybe what is meant by the source is that A4 & d5 are the only 2 that aren't enharmonic equivalent of any other interval. is that it?
  
  – stupr in
  1 hour ago
  

  
  
  
  


• 
  
  
  

  
  1
  

  
  
  
  
  
  

  
  
  What other diminished and augmented intervals lie on the diatonic scale?
  
  – Richard
  1 hour ago
  

  
  
  
  


• 
  
  
  

  
  1
  

  
  
  
  
  
  

  
  
  The only way you can get those intervals within a diatonic scale is through enharmonic reinterpretation. But in the act of enharmonic reinterpretation, you're no longer using the diatonic scale. Using only C D E F G A B, it's impossible to have those intervals.
  
  – Richard
  1 hour ago
  

  
  
  
  


• 
  
  
  

  
  1
  

  
  
  
  
  
  

  
  
  Are you saying E to F is a diminished fourth? And yes, for this purpose "enharmonic reinterpretation" just means "enharmonic equivalent."
  
  – Richard
  56 mins ago
  

  
  
  
  


• 
  
  
  

  
  1
  

  
  
  
  
  
  

  
  
  @stuprin E to F is just a half step. More specifically, it's a minor second. It's certainly not a fourth, since E up to F is only two note names and thus a type of second.
  
  – Richard
  41 mins ago
  

  
  
  
  

 | 
show 7 more comments

2

I don't know your source, but the term "diatonic scale" typically refers to the major scale and its rotations (i.e., the modes). As such, we can test this claim just by looking at the intervals of a major scale.

• All seconds within in the scale are either minor (E–F and B–C) or major (C–D, D–E, F–G, G–A, A–B).


• All thirds are either minor (D–F, E–G, A–C, B–D) or major (C–E, F–A, G–B).


• All fourths are either perfect (C–F, D–G, E–A, G–C, A–D, B–E), or augmented (F–B). There's one augmented interval!

And conveniently, we don't have to do the rest of the work. Due to intervallic inversion, we know that seconds invert to sevenths, thirds to sixths, and fourths to fifths. Furthermore, we know that the qualities invert in particular ways, and only diminished/augmented intervals invert to each other.

As such, the only diminished/augmented intervals of a fifth, sixth, or seventh is the diminished fifth.

So yes, in fact, your source is correct: the only augmented/diminished interval that appears in the diatonic scale is the tritone.

You may be thinking of the augmented second (and its inversion, the diminished seventh) that is included in the harmonic minor scale. But this scale is not usually considered a "diatonic scale" since it requires a chromatic pitch: the raised leading tone.

share|improve this answer

answered 1 hour ago

RichardRichard

44.6k7105192

• 
  
  
  

  
  

  
  
  
  
  
  

  
  
  well there are other diminished &augmented intervals that lie on the diatonic scale. maybe what is meant by the source is that A4 & d5 are the only 2 that aren't enharmonic equivalent of any other interval. is that it?
  
  – stupr in
  1 hour ago
  

  
  
  
  


• 
  
  
  

  
  1
  

  
  
  
  
  
  

  
  
  What other diminished and augmented intervals lie on the diatonic scale?
  
  – Richard
  1 hour ago
  

  
  
  
  


• 
  
  
  

  
  1
  

  
  
  
  
  
  

  
  
  The only way you can get those intervals within a diatonic scale is through enharmonic reinterpretation. But in the act of enharmonic reinterpretation, you're no longer using the diatonic scale. Using only C D E F G A B, it's impossible to have those intervals.
  
  – Richard
  1 hour ago
  

  
  
  
  


• 
  
  
  

  
  1
  

  
  
  
  
  
  

  
  
  Are you saying E to F is a diminished fourth? And yes, for this purpose "enharmonic reinterpretation" just means "enharmonic equivalent."
  
  – Richard
  56 mins ago
  

  
  
  
  


• 
  
  
  

  
  1
  

  
  
  
  
  
  

  
  
  @stuprin E to F is just a half step. More specifically, it's a minor second. It's certainly not a fourth, since E up to F is only two note names and thus a type of second.
  
  – Richard
  41 mins ago
  

  
  
  
  

 | 
show 7 more comments

I don't know your source, but the term "diatonic scale" typically refers to the major scale and its rotations (i.e., the modes). As such, we can test this claim just by looking at the intervals of a major scale.

• All seconds within in the scale are either minor (E–F and B–C) or major (C–D, D–E, F–G, G–A, A–B).


• All thirds are either minor (D–F, E–G, A–C, B–D) or major (C–E, F–A, G–B).


• All fourths are either perfect (C–F, D–G, E–A, G–C, A–D, B–E), or augmented (F–B). There's one augmented interval!

And conveniently, we don't have to do the rest of the work. Due to intervallic inversion, we know that seconds invert to sevenths, thirds to sixths, and fourths to fifths. Furthermore, we know that the qualities invert in particular ways, and only diminished/augmented intervals invert to each other.

As such, the only diminished/augmented intervals of a fifth, sixth, or seventh is the diminished fifth.

So yes, in fact, your source is correct: the only augmented/diminished interval that appears in the diatonic scale is the tritone.

You may be thinking of the augmented second (and its inversion, the diminished seventh) that is included in the harmonic minor scale. But this scale is not usually considered a "diatonic scale" since it requires a chromatic pitch: the raised leading tone.

share|improve this answer

answered 1 hour ago

RichardRichard

44.6k7105192

share|improve this answer

answered 1 hour ago

RichardRichard

44.6k7105192

answered 1 hour ago

RichardRichard

44.6k7105192

answered 1 hour ago

RichardRichard

44.6k7105192