difference between diminished fifth and augmented fourth

[40Hz]

Yeah, it's the same pitch--but we did have a lengthy discussion on another thread about whether or how much it mattered how it was notated. I'm in the camp that holds the notation should follow function, in general.

For instance, if you had a maj7#11 chord (think of it as a B minor triad stacked on a C major triad), it would have an F#. But a C dim7 chord would have a Gb. If you arpeggiate those chords on your bass, the difference in tone color is noticeable, and you can easily imagine how they would function differently in chord progressions.

But that's more a matter of chord voicing than it is the actual F#/Gb note itself isn't it?

When you start a progression, your brain processes and anticipates the next notes in the sequence. If you go outside what's anticipated at a certain point in the stack or sequence, that's what constitutes the perceived unique character of a chord's voicing AFAIK. The F#/Gb is still the same note. But it's positional relationship to the other notes in the chord or sequence can (and does) vary.

With music it's often far less about frequency and duration and more about perception (as it relates to neuropsychology) than most people realize. Because sounds are just sounds. It's we who decide if they constitute music or noise. And if they're what we call music, whether they "make sense" and are "correct" or not.

 

[dreamadream99]

... the notation should follow function, in general....

Yes, there are many reasons for notating it differently: Key, chord progression, resolution direction...
but the original post questioned the difference between a raised 4 and flatted 5, and that is solely a notational distinction.

 

[40Hz]

Yes, there are many reasons for notating it differently: Key, chord progression, resolution direction...
but the original post questioned the difference between a raised 4 and flatted 5, and that is solely a notational distinction.

This.

 

[dreamadream99]

For instance, if I'm reading a C up to an F#, then that's an augmented fourth.
Now Invert it.
If I'm reading an F# up to a C, that's a diminished fifth. They are both tritone intervals.

 

[monsterthompson]

Because reasons.

 

[stringtapper]

Yes, there are many reasons for notating it differently: Key, chord progression, resolution direction...
but the original post questioned the difference between a raised 4 and flatted 5, and that is solely a notational distinction.

But it's not solely notational. For instance it could be verbal. Function is the ultimate reason for choice in spelling whether it's being notated or being spoken aloud between two musicians.

If someone at a jam session says "Play a Gmin7♭5 here. It's spelled 'G-B♭-C♯-F,'" then they're spelling the chord incorrectly and no notation was involved. There's a right way to say it and there's a right way to notate it.

Where it wouldn't matter is if someone was merely playing the notes of the chord so another musician could just learn it by rote and no chord tone names ever got mentioned at all.

 

[Ewo]

Yes, there are many reasons for notating it differently: Key, chord progression, resolution direction...
but the original post questioned the difference between a raised 4 and flatted 5, and that is solely a notational distinction.

In equal temperament, yeah. But they wouldn't be in Just temperament, for instance. (Granted, this is getting down to fine points: our beloved electric basses are fretted in equal temperament, and F# = Gb. But there's one guy, a Warwick endorsee whose name I can't remember, who had a bass built that could play in Just temperament. That's something I don't need, myself...)

[Invalid or Expired Link Removed]

Note this passage:

You will note that the most "pleasing" musical intervals above are those which have a frequency ratio of relatively small integers. Some authors have slightly different ratios for some of these intervals, and the Just scale actually defines more notes than we usually use. For example, the "augmented fourth" and "diminished fifth," which are assumed to be the same in the table, are actually not the same.

 

[lsabina]

This is a good thread so far. I don't think there has been a single incorrect answer!

 

[Imaginary Pony]

Because reasons.

Because reasons and other stuff!

 

[Bob_Ross]

Function is the ultimate reason for choice in spelling whether it's being notated or being spoken aloud between two musicians.

Well... I would argue that in both situations the "ultimate" reason for choice in spelling should be conveying the necessary information to the musician who has to perform it.
(E.g., there may be times where it makes sense to notate a passage with intervals misspelled (sic) from a functional standpoint, simply because it's easier for the performer to sight-read the line.)
A subsequent priority should be conveying the necessary information to the musician who has to understand it...and then function is indeed the ultimate arbiter. But generally we want to audiate music before we analyze it, so getting it performed should be the first priority.

 

[stringtapper]

Well... I would argue that in both situations the "ultimate" reason for choice in spelling should be conveying the necessary information to the musician who has to perform it.
(E.g., there may be times where it makes sense to notate a passage with intervals misspelled (sic) from a functional standpoint, simply because it's easier for the performer to sight-read the line.)
A subsequent priority should be conveying the necessary information to the musician who has to understand it...and then function is indeed the ultimate arbiter. But generally we want to audiate music before we analyze it, so getting it performed should be the first priority.

Well I don't disagree with most of that, but to put it a better way, what I'm saying is that the reason the distinction exists in the first place is because of the system of keys and how note name spellings function within that system.

 

[wrench45us]

In some book somewhere I recall reading when bebop commonly started using the flat 5 that 'theoretically' it was really the sharped 4, but because so much bebop was chord oriented and the 5 is integral to chords, the bias was to call this note a flat 5 when 'theoretically' it may have been more accurate to call it a sharp 4.

 

[Bob_Ross]

In some book somewhere I recall reading when bebop commonly started using the flat 5 that 'theoretically' it was really the sharped 4, but because so much bebop was chord oriented and the 5 is integral to chords, the bias was to call this note a flat 5 when 'theoretically' it may have been more accurate to call it a sharp 4.

In many (most?) cases that's not true; technically a #11 chord (raised 4th) can also contain the perfect 5th...whereas a b5 chord by definition cannot.

(fwiw most of the b5 chords I encounter in bebop are used to elicit a whole-tone sound object, which to my ear are very different from the Lydian or Lydian Flat 7 sound that #11 chords ellicit.)

 

[Thuddy Waters]

I think this topic has been explained very well. Do we dare delve into the difference between a b3 and a #9?

 

[Imaginary Pony]

I think this topic has been explained very well. Do we dare delve into the difference between a b3 and a #9?

How about a 6 chord and a 13 chord?

 

[Whousedtoplay]

I think this topic has been explained very well.

Maybe you could explain in simple words this:
"In Invalid Link Removed have slightly different pitches. In 5-limit intonation, it is the case that
the interval (frequency ratio) between a higher F and a lower B is a diminished fifth ( 610 cents)
and
the interval between a higher B and a lower F is an augmented fourth (590 cents). This difference in pitch can be achieved by continuous pitch instruments, e.g. non-fretted strings and especially voice; so they're different because they (can) sound different."

Five-limit tuning - Wikipedia, the free encyclopedia

http://m_kimber.tripod.com/12-tone_intonation.pdf

On the Sensations of Tone as a Physiological Basis for the Theory of Music - Hermann von Helmholtz, Alexander John Ellis - Google Books

More about the 5-limit intervals:
Invalid Link Removed

HARMONIC EXPLORER - Ancient Musicology by Limiting Numbers

 

[Thuddy Waters]

Maybe you could explain in simple words this:
"In Invalid Link Removed have slightly different pitches. In 5-limit intonation, it is the case that
the interval (frequency ratio) between a higher F and a lower B is a diminished fifth ( 610 cents)
and
the interval between a higher B and a lower F is an augmented fourth (590 cents). This difference in pitch can be achieved by continuous pitch instruments, e.g. non-fretted strings and especially voice; so they're different because they (can) sound different."
View attachment 689373
Five-limit tuning - Wikipedia, the free encyclopedia

View attachment 689374
http://m_kimber.tripod.com/12-tone_intonation.pdf

View attachment 689376
On the Sensations of Tone as a Physiological Basis for the Theory of Music - Hermann von Helmholtz, Alexander John Ellis - Google Books

View attachment 689378
More about the 5-limit intervals:
Invalid Link Removed

HARMONIC EXPLORER - Ancient Musicology by Limiting Numbers

Yeah. That clears it up.

 

[Mushroo]

What about the other 30 bricks?

 

[Matthew_84]

so basically in a lydian mode of E, the augmented fourth will be A# and the diminished fifth will be a Bb ... Correct ?

No, in the Lydian mode there is only an Augmented 4th. The 5th is a Perfect 5th.

In the Locrian mode there is only a Perfect 4th and a diminished 5th.

Count the notes of the scale. Two scale degrees of the same scale can never be the same note/pitch/frequency.

 

[Thuddy Waters]

What about the other 30 bricks?

All in all you're just another 30 bricks in the wall.