# Interval Names



## RubberDuckie

Hi everyone. Just want to throw this out there :

Without re-spelling the pitch names, how would you name the interval between a Cb and an F#?

It would sound like a Perfect 5th when played on a piano. But theoretically, it is a 4th and bigger than an Augmented 4th.

There are many other intervals like Cb to Dx, Cb to E#, Cx to Eb, etc. All can occur theoretically but are there names for them without re-spelling?


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## EdwardBast

It's a doubly augmented fourth. Can't think of any situation where writing it that way would make sense, which is why one doesn't often hear about doubly augmented intervals. If one wishes to name even more silly intervals one need only add prefixes like triply or quadruply.


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## RubberDuckie

Technically, it can happen in 12 Tone music ... but why bother?

Doubly? Triply? Quadruply? Really? ^^

This reminds me of cycling through the "hemidemisemi" when a new flag or tail is added in the Tree of Note Values. I.e. after hemidemisemiquaver comes the semihemidemisemiquaver ... then demisemihemidemisemiquaver ... then hemidemisemihemidemisemiquaver ...

Haha ... I find it very amusing.


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## mikeh375

also pianissississississississississ...immo, in theory anyhow......


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## RubberDuckie

By the way, Diminished Prime does not exist.


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## Bwv 1080

RubberDuckie said:


> Hi everyone. Just want to throw this out there :
> 
> Without re-spelling the pitch names, how would you name the interval between a Cb and an F#?


its a '7' (and also poor notation)


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## RubberDuckie

Bwv 1080 said:


> its a '7' (and also poor notation)


aaah there are 7 half steps. But the interval is still a 4th.

C to Db is a Minor 2nd
C to D is a Major 2nd
C to Eb is a Minor 3rd
C to E is a Major 3rd
C to F is a Perfect 4th
etc.

You are right about it being a poor notation, but it could theoretically happen in 12-Tone compositions.


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## Bwv 1080

RubberDuckie said:


> aaah there are 7 half steps. But the interval is still a 4th.
> 
> C to Db is a Minor 2nd
> C to D is a Major 2nd
> C to Eb is a Minor 3rd
> C to E is a Major 3rd
> C to F is a Perfect 4th
> etc.
> 
> You are right about it being a poor notation, but it could theoretically happen in 12-Tone compositions.


How? in 12-tone, its just 7


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## SuperTonic

RubberDuckie said:


> Technically, it can happen in 12 Tone music ... but why bother?
> 
> Doubly? Triply? Quadruply? Really? ^^
> 
> This reminds me of cycling through the "hemidemisemi" when a new flag or tail is added in the Tree of Note Values. I.e. after hemidemisemiquaver comes the semihemidemisemiquaver ... then demisemihemidemisemiquaver ... then hemidemisemihemidemisemiquaver ...
> 
> Haha ... I find it very amusing.


In 12 tone music theory, intervals are named by the number of half steps between the notes, which is in the case you provided is 7. The standard interval naming conventions have tonal implications that most 12 tone theorists prefer to avoid.


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## RubberDuckie

Bwv 1080 said:


> How? in 12-tone, its just 7


In 12-Tone compositions (Second Viennese School), these intervals can occur between two voices. For example, someone could be playing an A# while another holding an Eb below it. The interval is a 4th between E & A ... with the accidentals added, it is still a 4th, but the quality (sonority name of interval) is no longer Major or Minor or Perfect or Augmented or Diminished because it is bigger than an Augmented 4th.

E to A = Perfect 4th
E to A# = Augmented 4th
Eb to A# = bigger than Augmented 4th


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## RubberDuckie

SuperTonic said:


> In 12 tone music theory, intervals are named by the number of half steps between the notes, which is in the case you provided is 7. The standard interval naming conventions have tonal implications that most 12 tone theorists prefer to avoid.


True. You are right.

It was a bad example.

There is an interval in Chopin's Prelude in A Minor Op. 28. No. 2 ... bar 12, 3rd beat & a half ... the left hand plays Cx and C natural above it.


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## EdwardBast

RubberDuckie said:


> True. You are right.
> 
> It was a bad example. These intervals exist only theoretically then?


Not necessarily. Unable to resist a twisted harmonic problem, I managed to use that doubly augmented 4th in a sentence. It occurs as part of an altered vii4/3 in G minor:


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## RubberDuckie

EdwardBast said:


> Not necessarily. Unable to resist a twisted harmonic problem, I managed to use that doubly augmented 4th in a sentence. It occurs as part of an altered vii4/3 in G minor:
> 
> View attachment 140440


Whoa! What is this piece? And a chord with a flat 5 and a dim 7th?

F#°7-5/Cb? Dang!


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## EdwardBast

RubberDuckie said:


> Whoa! What is this piece? And a chord with a flat 5 and a dim 7th?
> 
> F#°7-5/Cb? Dang!


I just wrote a little passage in G minor to see if I could coherently use the peculiar interval in a tonal style. Just an exercise for this thread.


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## RubberDuckie

EdwardBast said:


> I just wrote a little passage in G minor to see if I could coherently use the peculiar interval in a tonal style.


Nice! An original! Copyrighted? ^^

Do check out the interval in Chopin's Prelude in A Minor Op. 28. No. 2 ... bar 12, 3rd beat & a half ... and see the doubly diminished octave.


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## millionrainbows

When I learned to recognize and name intervals, it was our ear training. I'd hear it (Cb-F#) as a fifth. So for me, I learned intervals as sounds.


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## RubberDuckie

millionrainbows said:


> When I learned to recognize and name intervals, it was our ear training. I'd hear it (Cb-F#) as a fifth. So for me, I learned intervals as sounds.


Cool! From listening, it would be a Perfect 5th for sure. But some intervals, due to voice-leading, need to be spelled in a weird way. I am trying to find as many as I can and compile a list here.


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## mikeh375

In more extended harmony and atonality I've found that sometimes it's best to consider spelling an individual part from the players perspective, rather than the correct (as perceived by the composer and his methodologies) spelling. So voice leading yes, absolutely, but a more focused and less correct approach to the part can aid practicality in a chromatic environment, especially one that does not adhere to more traditional resolutions of chord members.

As an aside, I think MR's learning of intervals is a sound way (pun intended) to initially learn and train the ear. I found that the practise of mentally singing separately say a maj.6th i.e perhaps c and then a, with a few seconds between them and then gradually reducing the time between them until they are heard as one, eventually enabled me to hear all intervals. This concept can then be extended, so that one could then mentally hear a maj.6th and then a few seconds later, imagine another note and gradually bring the two mentally together as before. In this way, one acquires important harmonic, mental hearing agility and building blocks to work with. Anyway I digress....


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## RubberDuckie

So ... as of now, I have found 2 pieces with such intervals :

1) Chopin's Prelude in A Minor Op. 28. No. 2 ... bar 12, 3rd beat & a half - a Doubly Diminished Octave
2) Liszt's Au lac de Wallenstadt from Années de pèlerinage ... bar 52 - a Compound Doubly Augmented 4th


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## RubberDuckie

mikeh375 said:


> In more extended harmony and atonality I've found that sometimes it's best to consider spelling an individual part from the players perspective, rather than the correct (as perceived by the composer and his methodologies) spelling. So voice leading yes, absolutely, but a more focused and less correct approach to the part can aid practicality in a chromatic environment, especially one that does not adhere to more traditional resolutions of chord members.
> 
> As an aside, I think MR's learning of intervals is a sound way (pun intended) to initially learn and train the ear. I found that the practise of mentally singing separately say a maj.6th i.e perhaps c and then a, with a few seconds between them and then gradually reducing the time between them until they are heard as one, eventually enabled me to hear all intervals. This concept can then be extended, so that one could then mentally hear a maj.6th and then a few seconds later, imagine another note and gradually bring the two mentally together as before. In this way, one acquires important harmonic, mental hearing building blocks to work with. Any way I digress....


Good to know. Thanks for the tip.


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## Bwv 1080

RubberDuckie said:


> Whoa! What is this piece? And a chord with a flat 5 and a dim 7th?
> 
> F#°7-5/Cb? Dang!


respelled its B D# F# A, just a dom 7 chord, so B7 if it was on a jazz chart, now it resolves to tonic Gm with the augmented^2 fourth expanding to a Major 6, which is the rationale for the odd spelling


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## millionrainbows

RubberDuckie said:


> Whoa! What is this piece? And a chord with a flat 5 and a dim 7th?
> 
> F#°7-5/Cb? Dang!


I thought all diminished seventh chords had a flat five.


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## RubberDuckie

millionrainbows said:


> I thought all diminished seventh chords had a flat five.


True true ... with its naturally flat 5, it gets flattened once more ...

so in that example :

F# - A - Cb - Eb bass Cb

How should that be correctly named in jazz chord?

(scratch head)


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## mikeh375

RubberDuckie said:


> True true ... with its naturally flat 5, it gets flattened once more ...
> 
> so in that example :
> 
> F# - A - Cb - Eb bass Cb
> 
> How should that be correctly named in jazz chord?
> 
> (scratch head)


...well as an ex jazz guitarist, I'd just play a dom.7th on B just like Bwv 1080 said and to hell with the spelling. Practicalities first, theory later, although in this case I'm not sure the theory is worth it anyway as the labelling would be unnecessarily complicated. Thank God for enharmonic thinking as Cb dom.7th would also lead to a key I wouldn't particularly want to be in...


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## Bwv 1080

RubberDuckie said:


> True true ... with its naturally flat 5, it gets flattened once more ...
> 
> so in that example :
> 
> F# - A - Cb - Eb bass Cb
> 
> How should that be correctly named in jazz chord?
> 
> (scratch head)


Eb=D#, Cb=B, so BD#F#A = B7 (or maybe Cb7)


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## Bwv 1080

mikeh375 said:


> ...well as an ex jazz guitarist, I'd just play a dom.7th on B just like Bwv 1080 said and to hell with the spelling. Practicalities first, theory later, although in this case I'm not sure the theory is worth it anyway as the labelling would be unnecessarily complicated. Thank God for enharmonic thinking as Cb dom.7th would also lead to a key I wouldn't particularly want to be in...


Most charts of Girl from Ipanema (in F) have a Cb7 as the second chord of the bridge, following the GbM7 (which is in Db)


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## mikeh375

Bwv 1080 said:


> Most charts of Girl from Ipanema (in F) have a Cb7 as the second chord of the bridge, following the GbM7 (which is in Db)


True, it's only for one bar though and it does move to an F sharp minor 9th rather than heading on down to the flat side. (..he says trying to justify his lazy musicianship..). I was really just referring to the concept of absurd chord naming, more than seriously dissing poor Cb7 (along with dissing a potential jam in F flat).

I love Jobim btw, my favourite of his to play was 'How Insensitive'. I used to love riffing over that chord sequence.


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## RubberDuckie

Hmmm... enharmonic spelling certainly takes care of the problem ... but does this mean there is no other way of theoretically naming them without re-spelling?


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## mikeh375

Cb maj. ++4/+6.....?

Why though? It has no practical use whatsoever and no jazzer will thank you for it. I can see it on a manuscript, spelt as such for voice leading, but not for chord shorthand. Always err on the side of the clearest, simplest notation possible.


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## Kyler Key

The problem you have is you would need to add all the other intervals otherwise it would not fit and would not mesh at all with the rest of the scale. It would essentially be useless and would ruin the piece you attempt to write unless you add all the others intervals.


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## Piers Hudson

If you're writing in a tuning such as 31-tone equal temperament, then you can in fact distinguish between enharmonic intervals, such as D# and Eb, which his referred to as a diesis:

https://en.wikipedia.org/wiki/Diesis

With that in mind, Cb-F# would sound one diesis flat from a perfect fifth (F# being one step lower than Gb), so it's a strange, inharmonic interval.

Paul Rapoport has a simple primer in 31-tone theory if you want to learn more:

http://www.huygens-fokker.org/docs/rap31.html


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