I have tried with the melody from "love will tear us apart" and I think it's beautiful.
In general (as already noted), yes. Not always. Other transformations have been used. Besides playing backwards, a melody may be "inverted" about an axis. The simplest is the axis around the first note; each interval is inverted from the first note so that C-E-G would become C-Ab-F (real inversion; intervals are exact) or even C-A-F (going down in both cases) which is called tonal inversion (intervals are the same but no accidentals are introduced; minor and major quality may be exchanged.)
Similarly, the melody could be inverted around D above the C yielding: E-C-A (I think).
Reversing the melody can be combined with inversion. Bach's "Art of the Fugue" has lots of stuff like this.
Even more weirdly, Obrecht (I think) tried sorting a melody by note length; all whole notes then half notes then quarter then eighths, etc., (tied and dotted notes are long; I don't know about staccato) . Or one can sort by smaller to larger (which doesn't give a reversal).
I suppose (and would guess) that someone has tried combining lots of these ideas.
Reversing a melody (not keeping the same note lengths though) is, I have found by trial, a nice way to make a second theme. It's different but still related.
One can (this is more common) reverse motifs (or riffs) or invert them. These are all ways of "varying" a theme. They don't work as well in some pop styles I have found as the pieces are not long enough to allow the various transformations to be heard. (This in one difference between long pieces commonly found in art music and short one found in pop or jazz or latin or country.)
It's impossible to generalize on such a topic, but I would venture that yes, in some cases, in certain portions, some of the aesthetic value of a melody will somehow remain if the melody is reversed.
In certain cases, melodies are also deliberately written as retrograde or palindrome, see e.g.
And finally, sorry, but I cannot resist linking this:
Yes, and no! There are times in melodies where certain note sequences are what make the melody what it is. Reversing it will change that effect. Take for example the penultimate bar of a tune, the last note being the leading note, moving to the tonic above it in the last bar.
Playing that backwards completely changes the effect. Mainly with reference to that leading note. Originally, it was at the weakest point in a bar, now it's emphasised, straught after the first note, the tonic.
Not saying it's a good or bad thing, because it may have a beauty of its own, but abiding by the wording in the question, it can't retain that same beauty it may have possessed previously.
This is basically one of the four tenents of contrapuntal harmony. Prime, Inversion, Retrograde and Retrograde-Inversion as it is made perfect in the Well-Tempered Clavier and in the Art of Fugue..
Prime being the original motif. Inversion is the same intervals going the other direction (Bach side down). Retrograde which is the prime played backwards (Bach-wards) and the Retrograde-Inversion is Bach-side-down, played Bach-wards.
If you want to see Bach interpretation of Megadeth then look no further, and yes using the tenents of counterpoint on metal music is the easiest and most efficient way to summon the great lord Beelsebub himself...
Something to consider in addition to things like inversion is that there are (at least) two kinds of time reversion:
The more conventional choice is to reverse the notation, which is equivalent to reversing the note durations: moving backwards along the score, each note enters when it ended in the original.
This is logical for instruments with a long sustain, like the voice, but it makes less sense for a percussion instrument like the snare drum, where the notated duration means nothing and the beat onset time is what matters.
Therefore, another option is to reverse the note attacks. To do this, you need to pick a discrete time unit; in this example I chose the eighth note, which is the smallest subdivision used. Then, we proceed in eighth-note steps from the end of the bar and let each note enter when it would have been struck in the original. For example, the whole note was on beat 1, which is the 1st of 8 eighth notes in the measure. Under note-attack reversal, it begins on beat 4+, the 8th of 8 eighth notes. This changes the harmonies because if one voice had a held note while another was moving, the held note will change to the next held note in the static voice.
Note-attack reversal is far less common, but it can create interesting syncopations and help the composer break from rhythmic cliches. And as a commenter noted, there's no need to start the reversed melody on a certain beat; to preserve the downbeat feel of the original, you could delay the above example of attack reversal by one eighth note.
It depends on what you mean by "beauty." Can a retrograde version of a melody still be beautiful? Yes, but unless the melody is rather symmetrical to begin with, the "beauty" of the retrograde version is likely to be found in different places or different effects. Music is a temporal artform, meant to be listened to as it develops in order. You can't just run it backwards and expect to have the same thing. That said, good melodies with a nice shape and few weird leaps etc. will still often continue to have a nice shape and no problems going backwards. They'll generally still be quite different, though.
To be clear, short motives are frequently reversed to generate thematic variation. The melody (or just the contour), the rhythm, or both can often be turned around to provide a motivic variant.
But reversing an entire melody can encounter other issues. Part of it is style-dependent. Some genres of music are more flexible when it comes to ordering of things like harmonic progressions than others. Traditional classical style (and styles derived from it) is normally built on so-called "functional tonality." That means that chord progressions tend to have an ordering: it's normal to proceed I-IV-V-I, but much less common to do the reverse I-V-IV-I. Some other answers bring up use of these sorts of transformations in early music, often transforming a chant melody in a renaissance mass. Those chant melodies predate functional tonality, making reversals easier to accomplish convincingly.
Melodies are frequently composed with some connection to the underlying harmony, so a straight retrograde can create problems for a coherent harmonic progression. On a related note, as Tim's answer points out, certain melodic motions tend to be highly directional: leading tones resolve upward, other tendency tones (like sevenths) resolve downward. To reharmonize these melodies in reverse, some creativity and flexibility may be needed -- not just playing the entire texture backwards. (Partly for that reason, I think a historical survey of tonal retrograde attempts would probably show that composers more frequently employed retrograde inversions than simple strict retrogrades.)
Rhythm also has built-in directionality as well. We tend to feel emphasis on longer notes, for example, something known as an "agogic accent." Therefore, in many styles, it's more common to have shorter duration notes on weaker beats, arriving on longer notes for strong beats. Changing this can end up creating a much different rhythmic effect, giving a backbeat or syncopated feel. Depending on how the rhythm is reversed with the melody, you might end up with something that feels very different in which notes are emphasized.
And then there are often dramatic elements of melodies, which frequently have a temporal direction built in. For example, a melody might not just have a leading tone, but it might dwell on a leading tone for a while to create tension before a final resolution. Try doing that backwards, and now you have this weird leading tone hanging in the air at the beginning of a melody -- which makes less sense. In such a case, perhaps a less strict retrograde that allows some alteration to a few intervals or durations might be more advisable. Or think of the dramatic arcs created by melodic shape: rises and falls and arches. "Somewhere Over the Rainbow" begins with an enormous octave leap, which is gradually filled in, with several other dramatic upward leaps, meandering its way back down to the first note again. Reverse this pattern, and the melody becomes completely different -- gradually building upwards (with several unusual downward leaps) only to take a final nosedive.
Can such a reversal create a workable melody? Perhaps, with the proper modifications to harmony, and maybe some flexibility with a few melodic notes or rhythms here and there. But the key point is that a melody will often not maintain its original beauty in retrograde, but could perhaps develop a different type of beauty in its new form with proper treatment.
My general understanding has been retrograde music will change character.
I think it's easy to generalize about why the characteristics change.
Like many other things, it depends on musical style.
First, just one quote: Piston, Counterpoint. Chapter on Motive Structure
..."Retrograde forms are rarely employed since it is very difficult for the ear to recognize a motive [as the retrograde of another motif] played in this fashion."
The general reason is simple. Music is a temporal art. It's perceived as time moves forward. More specifically, functional tonal harmony works along a forward direction. So,
I V6 with melody
DO RE is an opening gesture, while the retrograde
V6 I with melody
RE DO is a closing! A similar reversal can happen rhythically. Something like an anacrusis figure on a weak beat, become a strong beat when reversed.
The Wikipedia article on retrograde as nice summary reference:
However, as Edmund Rubbra (1960, p. 35) points out, “This is, of course, a purely mental concept, as music can never do anything but go forwards, even if the given tune is reversed. The different relationships set up by reversing the direction of a theme make it completely unrecognizable; and when a composer indulges in this device the disclosure of it makes not the slightest difference to our apprehension of the music, which must be listened to as going parallel with the time-processes of our existence.”
Having said that if the music isn't tonal - like atonal 12-tone music, quartal harmony, some kind of static modal harmony, etc. - retrograde probably won't present this problem of reversed syntax.
Will it be beautiful?
That's a different question.
If you modify some artwork, and the output has a very different character, there is no reason to expect by necessity it won't be beautiful. It could be beautiful, it could be garbage.
If you are asking specifically about backmasking - reversing a recording - that's a very different matter. The_attack envelope_ will be reversed and will sound totally different. It most examples I've heard it sounds bizarre.
You will find plenty of examples about retrograde in counterpoint.
But you are asking about the character and beauty of a retrograde. You are asking more about aesthetics than technical matters.
When Bach used retrograde and other devices like that it was an intellectual display of his masterful control of composition. Importantly, the retrograde would be combined seamlessly with the other material. In that sense the retrograde would not contrast with the main character of the whole work. The unstudied listener isn't necessarily aware of this kind of retrograde.
So, while this is true about Bach, I don't think it has much bearing on your particular question.
(I would have preferred to leave a comment but I don't have the rep)
As said by MMazzon above,it's impossible to generalize this as it really just depends on the context and your perceptions on melody and beauty for that matter.