Difference between Diminished and Augmented Intervals??????

[c#minor]

Okay i know the standard definitions and such.

Diminished is one half step lower than it's corresponding m or P interval.

Augmented is one half step higher than it's corresponding M or P interval.



So then how why is the tritone distinguished as a augmented 4th and it is not a diminished 5th???


If i am looking at Eb and F# and the key signiture is CM, why is this a diminished 3rd and not an augmented 2nd? or even a m3?


Please theory buffs help me out!

[(poco) Sforzando]

Okay i know the standard definitions and such.

Diminished is one half step lower than it's corresponding m or P interval.

Augmented is one half step higher than it's corresponding M or P interval.



So then how why is the tritone distinguished as a augmented 4th and it is not a diminished 5th???


If i am looking at Eb and F# and the key signiture is CM, why is this a diminished 3rd and not an augmented 2nd? or even a m3?


Please theory buffs help me out!

Being midway between the two pitches of a perfect octave, a tritone is either an augmented 4th or a diminished 5th depending on spelling: Eb and the A above are an augmented fourth, Eb and Bbb (double-flat) a diminished 5th, E and Bb also a diminished fifth, but E and A# an augmented fourth (again reading from low note to high). But E and the A# below or Eb and the A below are a diminished fifth. (It is always acceptable to speak of a tritone if this sounds too fussy.)

Eb and Fb are a minor second, Eb and F are a major second, therefore Eb and F# are (yes) an augmented second. Eb and G would be a major third, Eb and Gb a minor third, and Eb and Gbb a diminished third (regardless of the key). It's all a matter of the spelling of the intervals.

[PerfectWagnerite]

So then how why is the tritone distinguished as a augmented 4th and it is not a diminished 5th???

I think Sforzando pretty much answered this one. Where did you get the idea that the tritone is distinguised as an augmented 4th and not a diminished 5th? Both interval names are used for the tritone. It is actually two minor thirds piled on top of one another if you look at it. Has a kind of nice symmetry to it don't you think?

If i am looking at Eb and F# and the key signiture is CM, why is this a diminished 3rd and not an augmented 2nd? or even a m3?

Since nether note is part of the C-major scale the key signature the key is pretty much irrelevant in this case. Since it is "written" as an E-flat and F# and NOT E-flat and G-flat it has to be some kind of second and not third.

[(poco) Sforzando]

tritone. It is actually two minor thirds piled on top of one another if you look at it. Has a kind of nice symmetry to it don't you think?

Or you can also figure it as the interval caused by the distance of three major seconds. Thus tritone.

[c#minor]

okay on the tritone thing i will quote my theory book. "Because the +4 consists of three whole tones (C-D-E-F#), it is often called a tritone (a term which is sometimes also used, inaccurately, to refer to the diminished 5)." Harmony in Context p.11

I don't get it. Whatever, Mr. Roig-Francoli apparently thinks a tritone cannot be a diminished 5. I honestly do not care, i really think a lot of the "intricacies" of music theory are bullshit. All made by a bunch of people who would rather do a Shanker reduction on a piece of music rather than play it.

(Sorry, just venting)

And aside from that thank you both. I wish that is how augmented and diminished was explained to me the first time. That makes much more sense.  

Thanks,
c#

[Ephemerid]

C# Minor, that's what you get for messin' with The Devil in Music!   

[(poco) Sforzando]

okay on the tritone thing i will quote my theory book. "Because the +4 consists of three whole tones (C-D-E-F#), it is often called a tritone (a term which is sometimes also used, inaccurately, to refer to the diminished 5)." Harmony in Context p.11

I don't get it. Whatever, Mr. Roig-Francoli apparently thinks a tritone cannot be a diminished 5. I honestly do not care, i really think a lot of the "intricacies" of music theory are bullshit. All made by a bunch of people who would rather do a Shanker reduction on a piece of music rather than play it.

(Sorry, just venting)

And aside from that thank you both. I wish that is how augmented and diminished was explained to me the first time. That makes much more sense.  

Thanks,
c#

Mr. Roig-Francoli is probably not a moron, and he may be thinking that C-D-E-Gb doesn't constitute a tritone because E-Gb is a diminished third rather than a major second (or whole tone). Strictly speaking true, but in common parlance I think you're safe using the word tritone to apply to this interval no matter how spelled. Of course it is one of the easiest intervals to hear; its sound is unmistakable.

And I wouldn't be so dismissive of theory and Schenker analysis if I were you. It can be extremely useful stuff, and no one ever claimed theory was a substitute for listening or performance.

[PerfectWagnerite]

Or you can also figure it as the interval caused by the distance of three major seconds. Thus tritone.

Of course, there are many ways to skin the same cat.

okay on the tritone thing i will quote my theory book. "Because the +4 consists of three whole tones (C-D-E-F#), it is often called a tritone (a term which is sometimes also used, inaccurately, to refer to the diminished 5)." Harmony in Context p.11

I don't get it. Whatever, Mr. Roig-Francoli apparently thinks a tritone cannot be a diminished 5. I honestly do not care, i really think a lot of the "intricacies" of music theory are bullshit. All made by a bunch of people who would rather do a Shanker reduction on a piece of music rather than play it.

(Sorry, just venting)

And aside from that thank you both. I wish that is how augmented and diminished was explained to me the first time. That makes much more sense.  

Thanks,
c#

Hmmm, I think in some instances the tritone actually makes more sense if you think of it as a fifth and not a fourth. FOr example in the C-F# example you gave the C wants to resolve up to D-flat and the F# wants to resolve downwards into a F-natural to form D-flat - F, which are the first two notes of the D-flat major triad. Since the resolution D-flat - F is an interval of a third, C-F# occupies two more notes and is therefore some kind of 5th.

[(poco) Sforzando]

Of course, there are many ways to skin the same cat.

Hmmm, I think in some instances the tritone actually makes more sense if you think of it as a fifth and not a fourth. FOr example in the C-F# example you gave the C wants to resolve up to D-flat and the F# wants to resolve downwards into a F-natural to form D-flat - F, which are the first two notes of the D-flat major triad. Since the resolution D-flat - F is an interval of a third, C-F# occupies two more notes and is therefore some kind of 5th.

And what if C-F# wants to resolve outwards to the minor sixth B-G? Fourth or fifth? It all depends really on the interval between the notes and their direction. C-F upwards is a perfect fourth; C-F downwards a perfect fifth. Thus with C and the F# above, it is an augmented fourth regardless of resolution. C and the F# below would be a diminished fifth, that could resolve outwards to the minor sixth F and Db, or inwards to the major third G and B.

[Actually: let me correct myself. With a resolution to F-Db, C and the Gb (an augmented fourth) below would be the more likely spelling. It would be spelled C and F# if resolving to G and B.]

[c#minor]

Mr. Roig-Francoli is probably not a moron, and he may be thinking that C-D-E-Gb doesn't constitute a tritone because E-Gb is a diminished third rather than a major second (or whole tone). Strictly speaking true, but in common parlance I think you're safe using the word tritone to apply to this interval no matter how spelled. Of course it is one of the easiest intervals to hear; its sound is unmistakable.

And I wouldn't be so dismissive of theory and Schenker analysis if I were you. It can be extremely useful stuff, and no one ever claimed theory was a substitute for listening or performance.

Mr. Roig-Francoli is definitely not a moron, i do know that. Esteemed professor at Cincinnati Conservatory. And i know Schenker analysis has it's place and its helpful for performers, studying composers, and so on. I really was just in a total state of frustration when i wrote that response. After some food and time away from the books i am back on planet earth.  Now back to the books and once again i am sure i will inevitably get frustrated. 

c#

[(poco) Sforzando]

Mr. Roig-Francoli is definitely not a moron, i do know that. Esteemed professor at Cincinnati Conservatory.

I'll have to take your word for it, 'cause I'm not buying his book which costs over $100 at Amazon!

Now back to the books and once again i am sure i will inevitably get frustrated. 

That's what it's all about.

[Mark G. Simon]

Hmmm, I think in some instances the tritone actually makes more sense if you think of it as a fifth and not a fourth. FOr example in the C-F# example you gave the C wants to resolve up to D-flat and the F# wants to resolve downwards into a F-natural to form D-flat - F, which are the first two notes of the D-flat major triad. Since the resolution D-flat - F is an interval of a third, C-F# occupies two more notes and is therefore some kind of 5th.

The factor that determines what an interval is called is the way it's notated. You count lines and spaces up from the bottom note. C up to F will always be some kind of fourth. C up to G will always be some kind of fifth. C-F# will always be an augemtented fourth. If you want to think of it as a diminished fifth you will have to rewrite it as C-Gb.

Or B#-F# for that matter.

[Robert Dahm]

The term 'tritone' applies only to the augmented 4th, thus the interval C–F# is a tritone, while C–Gb is not.

This is precisely because of its derivation from three whole tones (which, I believe, originate from the series of three whole tones in any given scale [F–B in C major, for instance]). The diminished fifth does not find representation 'within the scale', as it were (ie: you'd need to go outside the notes expressed by a scale within a single octave) unless it is as a chromatic alteration. I wouldn't be surprised to discover that old-timey music theorists viewed the diminished fifth as simply an inversion of the tritone.

[(poco) Sforzando]

The diminished fifth does not find representation 'within the scale', as it were.

B (leading tone) in C major to the F a diminished fifth above?

(edited to clean up html)

[Robert Dahm]

The diminished fifth does not find representation 'within the scale', as it were.

B (leading tone) in C major to the F a diminished fifth above?

Sorry, I didn't express myself clearly.

What I meant was that in a given octave of the C major scale (ie: from c to the c above it), there is no naturally occurring diminished fifth. You need to step outside of the octave to find the notes for it (in this case, either the b below or the f above), which might be interpreted as a registral substitution.

[karlhenning]

The term 'tritone' applies only to the augmented 4th, thus the interval C–F# is a tritone, while C–Gb is not.

This is precisely because of its derivation from three whole tones (which, I believe, originate from the series of three whole tones in any given scale [F–B in C major, for instance]). The diminished fifth does not find representation 'within the scale', as it were (ie: you'd need to go outside the notes expressed by a scale within a single octave) unless it is as a chromatic alteration. I wouldn't be surprised to discover that old-timey music theorists viewed the diminished fifth as simply an inversion of the tritone.

That is, entirely correctly, the source of the term, but it has routinely been equally applied to other enharmonically equivalent intervals, which are not actually spelled as a augmented fourth.

[MahlerSnob]

Although the term tritone only technically refers to +4's, it is commonly used with dim. 5's as well. For example, when you're doing a harmonic dictation of two note intervals, you can only know that a augmented 4/dim. 5 is a tritone. In order to know if it was a fourth or fifth you would need to know how it is notated.
On the other hand, there is a slight practical difference between an aug 4 and dim 5 when it comes to tuning. If it is resolving out most performers (of non-keyboard instruments) will make the higher note slightly higher, as they would with a leading tone resolving up. If the interval resolves in, they would make the higher note a bit low (as with a P4 resolving to a 3rd).

[johnQpublic]

Correct me if missed something by skimming but I don't believe anyone mentioned the important factor of inversion in this process.

Inverting the A4 of C up to F# which is called appropriately a "tritone" sounds identical to the dimished fifth (F# up to C). So unless one is physically looking at the pitches then aurally it sounds the same as
G-flat up to C which of course is a tritone too.

The Devil's tone indeed. 

[PerfectWagnerite]

Correct me if missed something by skimming but I don't believe anyone mentioned the important factor of inversion in this process.

Inverting the A4 of C up to F# which is called appropriately a "tritone" sounds identical to the dimished fifth (F# up to C). So unless one is physically looking at the pitches then aurally it sounds the same as
G-flat up to C which of course is a tritone too.

The Devil's tone indeed. 

Well sometimes the Devil can make beautiful dissonances. The Prelude to Tristan and Isolde is brimming with tritones. The so-called Tristan chord, which is a half-diminished 7th chord contains a tritone. This chord appears three times in the first dozen bars or so. The answer, in the oboes and then in the clarinets and flutes also spell out a tritone. But you don't associate this with dissonace music though. It feels quite soothing and nice.

[karlhenning]

Although the term tritone only technically refers to +4's . . .

Plus fours?