# Retrogade melodies



## Dim7

How common they are in tonal, non-serial music? How many can really hear the connection between the "original" melody and the retrogade version on intellectual or instictual level?


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## Mahlerian

You can find examples of motifs played backwards in Beethoven, Bruckner, and Bach, which is where Schoenberg got the idea. There's always the "crab canon", which is played both forwards and backwards at the same time. Inversion is actually both more common and much easier to hear.

I think that people might sense that the melodies have a kinship to each other, but for anything longer than a short motif it would probably be difficult to hear for most. Fortunately, whether or not one knows that one is hearing a retrograde or not is really not very important to following the music.


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## Richannes Wrahms

I'd guess relatively common. All the contrapuntal masters like Bach, Brahms, Bruckner, Schoenberg (including the tonal period), etc all used it (on purpose) profusely. How can you notice it? It sounds quite literally like a reverse tape of something you previously heard sounds like, though the ideal (I think) would be not to notice the effect (as if the retrograde were actually new material, as interesting as the original). You can actually play around and use a program like Free audio editor  to reverse a recording of say Brahms Symphony No. 3 and notice the themes and their reverse 'swapping place'.


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## Dim7

Mahlerian said:


> You can find examples of motifs played backwards in Beethoven, Bruckner, and Bach, which is where Schoenberg got the idea. There's always the "crab canon", which is played both forwards and backwards at the same time. Inversion is actually both more common and much easier to hear.
> 
> I think that people might sense that the melodies have a kinship to each other, but for anything longer than a short motif it would probably be difficult to hear for most. Fortunately, whether or not one knows that one is hearing a retrograde or not is really not very important to following the music.


But Schoenberg made a pretty big deal out retrogades didn't he? To a degree that was unheard of. The point of using a retrogade form of a tone row rather than an entirerly new tone row was to maintain some kind of unity, but if the vast majority of people can only feel a vague connection at best (and even that is questionable), wouldn't it make more sense to just vary the tone row in other ways, alter the order of some of the notes. I just find it a little bit bizarre that in serialism suddenly retrogades are given so much importance.


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## Mahlerian

Dim7 said:


> But Schoenberg made a pretty big deal out retrogades didn't he? To a degree that was unheard of. The point of using a retrogade form of a tone row rather than an entirerly new tone row was to maintain some kind of unity, but if the vast majority of people can only feel a vague connection at best (and even that is questionable), wouldn't it make more sense to just vary the tone row in other ways, alter the order of some of the notes. I just find it a little bit bizarre that in serialism suddenly retrogades are given so much importance.


Why should it be bizarre?

The point is that you can create diversity out of unity. Using retrogrades and inversions helps to ensure that the material is related. The important thing is not the technique, but the result, and of course the fact that a retrograde is used is not nearly as crucial as how it functions within a given musical context.

Here's a clear example:








The tone row is stated twice in these two bars. In the first bar, it is distributed as follows:

The clarinet has a pentatonic scale motif: Df-Ef-Bf-Gf-Af
The mandolin fills in two notes (a fifth): E-B
The muted violin has the other five notes, which also are a pentatonic scale: C-D-A-F-G

The two pentatonic scales are the same thing, a half step apart.

All of the melodic lines are based on the pentatonic motif of the clarinet. Schoenberg makes use of several different tone rows, but he builds melodies out of only those first five notes of each (the rest of the notes end up in the accompaniment, usually separated as above). Whether you play those first five notes backwards or forwards, even whether you invert them or not (as in the second bar), they still end up spelling out a pentatonic scale, which forms an immediately recognizable aural signature.


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## clavichorder

Retrogrades are usually easy to recognize if they incorporate the same rhythms, no? And their use certainly precedes Bach.


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## Dim7

Mahlerian said:


> Why should it be bizarre?
> 
> The point is that you can create diversity out of unity. Using retrogrades and inversions helps to ensure that the material is related.


It helps to ensure that the material is "logically" related but I feel the relation is instinctually so weak that you might as well use a new tone row. Maybe a one that begins similarily but ends differently. You would be breaking the "rules" because the new tone row wouldn't be an inversion, retrograde nor a retrograde inversion, but you would make the connection more audible than between the original row and retrograde.

Inversion is used often in tonal music because it makes sense on a gut level. Retrograde is a lot rarer (correct me if I'm wrong, that's why I started this thread) because it doesn't, at least not nearly as well. Not that using it is exactly a bad idea either, but it might be that tonal composers used it just for the intellectual satisfaction and because it happened to sound ok. But as far as I understand they didn't make it a crucial technique in their composition.



Mahlerian said:


> Whether you play those first five notes backwards or forwards, even whether you invert them or not (as in the second bar), they still end up spelling out a pentatonic scale, which forms an immediately recognizable aural signature.


IMHO, you might as well use the same notes of the pentatonic scale in any order and you'd feel pretty much the same connection.


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## Mahlerian

Dim7 said:


> It helps to ensure that the material is "logically" related but I feel the relation is instinctually so weak that you might as well use a new tone row. Maybe a one that begins similarily but ends differently. You would be breaking the "rules" because the new tone row wouldn't be an inversion, retrograde nor a retrograde inversion, but you would make the connection more audible than between the original row and retrograde.
> 
> Inversion is used often in tonal music because it makes sense on a gut level. Retrograde is a lot rarer (correct me if I'm wrong, that's why I started this thread) because it doesn't, at least not nearly as well. Not that using it is exactly a bad idea either, but it might be that tonal composers used it just for the intellectual satisfaction and because it happened to sound ok. But as far as I understand they didn't make it a crucial technique in their composition.


The technique and the piece are not one and the same. The tone row is the material for the piece, and its derivations are material as well. The music does not consist of an arrangement of tone rows any more than a tonal piece consists of a succession of scales.

You still seem to be under the impression that the listener needs to be aware of how a piece was constructed on the level of rows? Why? Most composers emphasize particular parts of rows, either as motifs or as individual intervals. The row is not a theme that the listener needs to follow.

If it works, nothing else matters, right?



> IMHO, you might as well use the same notes of the pentatonic scale in any order and you'd feel pretty much the same connection.


You will find examples of this kind of thing being done, with the row being broken up into segments and making the succession of those segments into an analogue for the row. The reason for not doing it all the time is it loses the row's identity as a succession of intervals, but obviously the row is broken up all the time anyway.


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## EdwardBast

Dim7 said:


> How common they are in tonal, non-serial music? How many can really hear the connection between the "original" melody and the retrogade version on intellectual or instictual level?


Machaut's three-voice rondeau, _Ma fin est mon commencement_, is a retrograde canon (I think two voices are involved in the canon. Don't have the score handy.)

The clearest and most readily audible example I know in common practice music is the _Menuetto al roverso_ from Haydn's Symphony no. 47; it completely retrogrades the minuet and trio sections.

One movement of Bartok's _Music for Strings Percussion and Celeste_, the third I think(?), has a significant passage that is immediately retrograded, the transformation clearly audible.

Around the "hinge point" in the second movement of Webern's Symphony, Op. 21, the point where the first half of the movement begins to retrograde, the reversal is obvious to the ear. The second half of the row for the symphony, by the way, is the retrograde of the first.

In orchestral music retrograde passages, serial or otherwise, are readily recognized when, as in the Webern and Bartok examples, the relationship is underscored by parallel orchestration.


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## millionrainbows

A retrograde in tonality is different than a retrograde in a tone row. A tonal retrograde uses note-identities; a serial retrograde uses quantities.

For example C-E-G is a major chord, easily recognizable. The retrograde would be G-E C, which is heard as a C major chord in second inversion.

C-E-G, in serial terms, is the set (0, 4, 7), and the reverse, or retrograde is (0, -4, -7) which is C-Ab-F, or F minor.


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## Dim7

millionrainbows said:


> C-E-G, in serial terms, is the set (0, 4, 7), and the reverse, or retrograde is (0, -4, -7) which is C-Ab-F, or F minor.


Wouldn't that be an inversion and not a retrograde?


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## millionrainbows

Dim7 said:


> Wouldn't that be an inversion and not a retrograde?


C-E-G, G-E C; that's a reversal, or retrograde, in tonality. It also happens to be an inversion.

Sets in serial theory are not attached to pitch names; they are quantities. So the retrograde of (0, 4, 7) would be...(7, 4, 0). Is that better?


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## Dim7

I meant isn't C-Ab-F (f minor) the inversion of C-E-G?


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## millionrainbows

Dim7 said:


> I meant isn't C-Ab-F (f minor) the inversion of C-E-G?


Yes, serially. But in tonality, an inversion of a C major is another C major. They call them "first inversion" and "second inversion."


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## Skilmarilion

Dim7 said:


> Wouldn't that be an inversion and not a retrograde?


Sorry to ask what might be a very basic question, but what is the exact difference between the two?

Using the example of Rachmaninov's 18th variation in the _Paganini Rhapsody_, is it an inversion and not a retrograde simply because he shifts to D-flat major?


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## Dim7

Inversion: if the original melody goes up, say a third, the inverted version goes down the same interval and vice versa
If the inversion is diatonic minor third up might become a major third down, perfect fifth might become diminished etc. depending which note is in the scale. Diatonic inversion of the Paganini melody A C B A E would be A F G A D 

Retrograde: original melody backwards (paganini melody A C B A E, retrograde E A B C A)

Change of key has nothing to do with it, it's just an additional element of variation to the melody.


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## millionrainbows

So a retrograde melody is simply a backwards version of the original melody; it uses the same pitches as the original. Therefore, the interval relations remain consistent.


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## Dim7

I'm beginning to suspect that "retrograding" a tone row makes more sense than retrograding a "tonal" melody (that is not just a very short motif), though I cannot explain why.


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## Mahlerian

Dim7 said:


> I'm beginning to suspect that "retrograding" a tone row makes more sense than retrograding a "tonal" melody (that is not just a very short motif), though I cannot explain why.


A longer tonal melody is usually a closed shape with beginning, middle, and end; it proceeds logically and is self-contained.

A tone row is not usually a closed shape, and functions more as raw material for melodies/harmonies, etc. Therefore it can be more easily manipulated and broken apart while retaining the essential elements of its identity.

Once again, the point is not to perceive the manipulation though, just the results of it.


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## millionrainbows

If we consider the effects of "directionality" in intervals, a retrograde (backwards) melody will have consequences which completely change it, in terms of tonal gravity and establishing a tone center.

Refer to Schoenberg's *Structural Functions of Harmony,* in which he discusses root movement by intervals, and the relative strengths and weaknesses of each. From my blog *Root Movement:*

FURTHER THOUGHTS: To remember these root progressions & their relative strengths, it will help to think of them *simultaneously as being steps from one root note to another, traveling forward through time horizontally, and also as harmonic intervals, sounding simultaneously at once, vertically:*

1. Strong, or Ascending: (a) A fourth up, identical with a fifth down;

...this is because when we hear fourths, either as a simultaneous sounding of two notes, or as one note followed by another, *we always hear fourths with the top note as root;* in root function terms, we have moved *UP TO* this note (higher in pitch, within the upper octave above the root); this makes it *'strong' *or *'ascending'* *TO* the root on top.

A fifth down (lower in pitch below the root, in the octave below the root) is the inversion; when we hear both notes at once, *we always hear fifths with the bottom note as root,* as we do with all fifths. Every head-banger knows this. Spread out horizontally, a fifth down means the second (bottom) note is root.

(b) A third down: we hear the second note as root, or resting point. Makes sense. Listen to Cream play "Spoonful."

2. Descending: (a) A fourth down, identical with a fifth up; we hear the top of the fourth as root, still, but *we have moved away from it to a weaker note; thus, it is "descending."* If we hear a fifth, again, the bottom note is root; but we have moved a fifth up to the weaker note; thus, it is _"descending,"_ or getting weaker. By 'weak' or 'strong' we mean simply *reinforcing* a root or key center, or '*weakening'* the root or key, and moving away from it, to perhaps another key.

*(b) A third up.* We hear the bottom note as root, but we jumped up, away from it. It's getting weaker.

*3. Superstrong: (a) One step up; (b) One step down.* We hear the second note as a new root. I need to think about this one some more.


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## Dim7

Mahlerian said:


> Once again, the point is not to perceive the manipulation though, just the results of it.


Once again, I've never implied that nor have I implied that anyone has implied that.


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## Mahlerian

Dim7 said:


> Once again, I've never implied that nor have I implied that anyone has implied that.


I'm sorry if I'm misreading you, but then I fail to see the thrust of your argument.

Criticisms of serial music (eg Lehrdahl) often depend upon the supposed opacity of serial procedures and/or their distance from the experience of the listener. Many of these arguments draw parallels between themes in non-serial works and tone rows, pointing out that the latter is often not perceived by the listener in all of its transformations, unlike the former.

I really don't see the point in this comparison (nor any force in this argument), because as I said before, tone rows are generally not used as themes. Rather, themes, if present, are created using tone rows. Often, the retrograde and inversion of the row are treated as separate (if subtly related) themes, rather than as the same theme.


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## Dim7

Even if it isn't the point to consciously hear the retrogrades, the point is nevertheless to feel some kind of connection and my argument was that the connection couldn't be heard at all, that one might as well use a completely new tone row. But as I said I've sort of retracted that position and admit that in the case of tone rows retrogrades make more sense than with longer tonal melodies. Like if a segment of the tone row forms a pentatonic scale, it will also do that in the case of the retrograde, or if the tone row consists mostly of minor seconds and tritones, so will the retrograde and thus it will sound similar. So the connection isn't necessarily inaudible.

But I'd still make the point that what's so important _in particular_ with inversions and retrogrades? Couldn't you vary the tone row in other ways just as well?


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## Dim7

LOL It took me this long to realize that I kept spelling retrograde wrong in the first posts in this thread and in the title :lol:


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## Dim7

HEh.

Pachelbel's Canon Backwards

Upside and down

Backwards and upside down


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## Gaspard de la Nuit

I've never even heard of such a thing as a retrograde melody, for a second I thought this thread was about astrology.


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## millionrainbows

How about this exception: you can retrograde a melody, but you can't retrograde a scale.


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## millionrainbows

Dim7 said:


> Even if it isn't the point to consciously hear the retrogrades, the point is nevertheless to feel some kind of connection and my argument was that the connection couldn't be heard at all, that one might as well use a completely new tone row. But as I said I've sort of retracted that position and admit that in the case of tone rows retrogrades make more sense than with longer tonal melodies. *Like if a segment of the tone row forms a pentatonic scale, it will also do that in the case of the retrograde, or if the tone row consists mostly of minor seconds and tritones, so will the retrograde and thus it will sound similar. So the connection isn't necessarily inaudible.*


That's a very good observation, Dim7. When tone rows are used and combined, they are segmented into hexads or some such group. These partitions are then combined with other hexads from other rows which share the same content (but not same order). This gives the partition a 'harmonic flavor' or identity as a vertical array.

If tone rows were not partitioned into smaller units, combining them would be meaningless, because without ordering, tone rows are just the 12 notes. Harmonic identity or delineation is dependent upon what is left out. Otherwise, it's just a 12-note mud.



Dim7 said:


> But I'd still make the point that what's so important _in particular_ with inversions and retrogrades? Couldn't you vary the tone row in other ways just as well?


If you do an inversion of a hexad or other partition, the_ interval vector _is unchanged. This means the same number and frequency of intervals is still there, even though inversion changes the pitches.

Retrograding is not as important, because all that does is change the order. If the row is to be partitioned, order becomes irrelevant; only content matters.


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## millionrainbows

Mahlerian said:


> Criticisms of serial music (eg Lehrdahl) often depend upon the supposed opacity of serial procedures and/or their distance from the experience of the listener. Many of these arguments draw parallels between themes in non-serial works and tone rows, pointing out that the latter is often not perceived by the listener in all of its transformations, unlike the former.


This is a valid criticism in one sense, if we are comparing diatonic 7-note music with serial music. Diatonic tonality limits itself to 7 notes; serial music uses all 12 notes. Seven notes are easier to keep track of than twelve notes; the numbers prove this; 12 is greater than 7.



Mahlerian said:


> I really don't see the point in this comparison (nor any force in this argument), because as I said before, tone rows are generally not used as themes. Rather, themes, if present, are created using tone rows.


That's somewhat misleading.

What if we said: _scales are generally not used as themes; rather, themes, if present, are created using scales. _

This would be true, since a scale is simply an index of available notes, without regard to order, which also defines the harmonic content and the key.

But there are caveats when we say:_ tone rows are generally not used as themes. Rather, themes, if present, are created using tone rows. 
_A tone row is not a scale; it has order. Therefore, a theme derived from a tone row would reflect this order, pre-compositionally, in the order of the pitches.

A 12-tone row-derived theme would be rhythmically articulated, maybe change registers, and have dynamics, but the pitch-class order would remain the same.

The change of register, if present, would also greatly affect the intelligibility of the theme. In tonality, a melody's identity is defined by its contour. In serialism, only pitch-classes matter; a row of ordered pitches is identical to themes derived from it, in terms of pitch order, regardless of register.

(Rows are said to function as pre-compositional motives, if not themes)


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## Che2007

Million: The guy was asking about retrograding a given melody - it doesn't matter what music you are dealing with. Retrograde means play backward. It doesn't involve changing any pitches. It isn't anything to do with scale theory. It can happen in exactly the same way in tonal and atonal music.

As for retrograde melodies, you can find them in Bach Fugues  But to echo what others have said, you find them all over the place really...


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## Dim7

Dim7 said:


> It helps to ensure that the material is "logically" related but I feel the relation is instinctually so weak that you might as well use a new tone row. Maybe a one that begins similarily but ends differently. You would be breaking the "rules" because the new tone row wouldn't be an inversion, retrograde nor a retrograde inversion, but you would make the connection more audible than between the original row and retrograde.


It seems Barrasque did something like this. From Wikipedia:

"Barraqué's use of tone rows in his work is quite distinctive. Rather than using a single tone row for an entire piece, as Anton Webern did, or using a number of related rows in one work, as Alban Berg or Arnold Schoenberg sometimes did, Barraqué starts by using one row, and then subtly alters it to get a second. This second row is then used for a while before being slightly altered again to make a third. This process continues throughout the work. He called this technique "proliferating series". "


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