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

[Robert Dahm]

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. 

Scholarship is far from unanimous on the topic of when equal temperament came to be a 'standard' practice, but latest consensus seems to indicate that it was sometime during the nineteenth century. So, given that equal temperament is a comparatively recent convention, C–F# hasn't sounded the same as C–Gb for very long...

Also, while we tend to 'think' in equal temperament, it only really ends up being keyboard, percussion and harp players that use it. Stirng, wind and brass players tend to tune intervals based on function, rather than against the equal tempered scale. Note, for instance, that string players generally tune their open strings to 'pure' (as opposed to tempered) fifths.

[jochanaan]

...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#

A certain amount of frustration appears to be not merely beneficial, but necessary, in the long journey that is musical understanding. It may be merely the immediate precursor to a "light-bulb" moment--or it might even spur one on to innovation.

"It is a good thing to know the rules in order to know what is contrary to them." --Ludwig van Beethoven 0:)

[millionrainbows]

Here's the way I understand it.

"Augmented fourth" and "diminished fifth": "fourth" and "fifth" refer to scale steps.

"Augmented fourth" means "count 4 letters of the scale." 1-2-3-4, equals C-D-E-F. Now augment it.

"Diminished fifth" means "count 5 letters of the scale." 1-2-3-4-5, equals C-D-E-F-G. Now diminish it.

"Tritone" is the name for the interval, separated from function associations. It names an interval distance in whole tones: 3 tone-spaces. It is 6 semitones, and 6÷2=3, or "tri."

[arpeggio]

I remember what I was taught in college.  We were trained to treat (corrected bad typo. thanks for not jumping on it) these intervals as leading tones.  It depends on where one goes with it.

One of the most famous is "Maria" from West Side Story.  Since it resolves itself by going up one would perform it slightly sharp.  If one was going down, as it occurs later in the song, one would play the tone a little flat going toward the resolution.

Other musicians may have been taught this differently than I have.

[(poco) Sforzando]

If one was going down, as it occurs later in the song, one would play the tone a little flat going toward the resolution.

That is, if one assumes Tony was going down on Maria . . . .

[Spineur]

The upper note of the tritone interval is sqrt(2) the frequency of the base note.  It is exactly midway the octave as 2 consecutive tritones give you sqrt(2) sqrt(2)=2, i.e. one octave above