Symmetry is a well-known phenomenon, both in nature, whose existence does not depend on persons, and in culture, the person- and people-made part of reality. It is found in the physical world of atoms and molecules, in the geometrical world of ellipses and spheres and in the biological world of plants and animals, including human bodies (at least as far as their outward appearance is concerned). It is found in the domestic world of chairs and tables, in the architectural world of buildings and towns and in the artistic world of paintings and jewelry. We find symmetry everywhere, in nature because of some principle of conservation or maximum entropy, and in culture because of the sense of beauty it evokes or, perhaps, for some other reason.

A sober person who values truth, and hopefully also relevance, is bound to rejoin that asymmetry too is found everywhere, and not only because every so-called 'symmetry' is probably in practice merely an approximation of it. 'E is certainly correct, and with only truth or truth and relevance as values this would, indeed, finish off this debate. And yet, there is something which places symmetry above asymmetry, other things being equal, that is. (The 'ceteris paribus' is necessary for the discussion, as anyone can think of a series of things or events whose being asymmetrical would be better than its being symmetrical.) In the DNI, the doctrine of neutral-inclusivity, as introduced in the Model of Neutral-Inclusivity, symmetry is considered better than or '(normatively) superior' to asymmetry. It is not that symmetry is a fundamental value in the DNI; the fundamental value (besides truth and relevance or inclusiveness) is neutrality. Symmetry is superior as a form of catenical neutrality, that is a predicate (attribute or relation) which limits negativity on the one hand and positivity on the other. It is from this neutrality (if applicable, together with relevance) that a variety of other, subordinate values derive, such as rest and stability, harmony and equilibrium, equality and nondiscrimination.

The sober person who values truth and relevance is advised to value neutralness as well. When 'e does so, a world will emerge in which the balanced and the lopsided do not exist side by side as mere facts anymore. A world will emerge, then, in which symmetry as a value is related to other values, perhaps, to all values. When symmetry is not looked upon in isolation but associated with equilibrium and equality, or even inclusivity, it is going to strike a special note. And those who recognize symmetry as a value, albeit a derivative one, will, then, notice it everywhere. "Everywhere ...", with the possible exception of music.

What is symmetry in music supposed to mean? Simply put, it means that an aural composition can be divided into two parts, the one being the reverse of the other. Here reverse replaces the term mirror image when speaking about symmetry in the visual domain. Aural symmetry is not something totally new. It is found in palindromes when the way in which they are spelled (the visual palindrome) corresponds with the way in which they are pronounced (the aural palindrome) as in mum (|MAM|) and dad (|DAED|). While a visual verbal palindrome reads the same backward and forward with characters as elements, an aural verbal palindrome sounds the same backward and forward with phonemes as elements. Unfortunately, the two seldom coincide in the present language. Thus, the word eve is an example of a visual palindrome which does not work in the aural domain, as the reverse of |EEV| is |VEE|, and not |EEV| again. The phrase nice sign is an example of an aural palindrome, even tho it is not a palindrome in spelling: |NAIS SAIN| reversed is the same and therefore symmetrical. (Note that |AI| represents one phoneme only, so that its reverse is not |IA|, which would represent two phonemes.) Obviously, these 'symmetries' will not be complete anymore on the level of parts of characters (the way individual characters are written) and on the phonetic level. When the elements of the palindrome are notes, rather than characters or speech sounds, the symmetry holds only on the level of notes, unless the tone throughout each note is also symmetrical, or even constant, with equal attack and decay. Especially with percussion instruments, such as pianos and drums, this is (almost) impossible and for symmetrical music in general it is not a requirement. Palindromic music may be symmetrical on the level of tones only, music which consists of two parts which are each other's reverse will also reverse attacks and decays, regardless of their being the same or not. While a palindromic tune is a simple example of symmetry in music, symmetrical music encompasses much more than this. It is only because more complex symmetrical music requires the technology to play compositions backwards that it has taken such a long time to come into existence.

With modern technology we can now create perfectly symmetrical compositions by adding the reverse of an original piece of music at the back of it, by starting with the reverse and adding the original or by mixing the two. A music editor will immediately provide us with a graphical representation of the new composition and in such a picture the left part of a piece of symmetrical music will, indeed, be the mirror image of the right part. The three symmetrical compositions which can be made in this way from one original are not only different, they are not even one another's reverse. Reversing a perfectly symmetrical piece of music will not have any effect! It is the choice between mixing or not mixing, and if not mixing the order between 'prime' (the original) and 'retrograde' (the reverse) which makes all the difference, especially when the original does not have a palindromic structure.

There is one type of symmetrical music to which the idea of two parts being each other's mirror image does not seem to apply. It is when in a stereo arrangement an original nonsymmetrical composition is assigned one channel (let's say the left ear) and its reverse the other (the right ear). However, there is no essential difference between such stereo music and a composition which uses one channel only in which the original and the reverse parts are mixed together (with the length of the composition unchanged rather than doubled). Undoubtedly, to make the symmetry more tranparent and convincing the two channels should each have a piece of music which is symmetrical on its own. If only one original is used for making a real stereo composition this can be done by playing first the original and then the reverse on the one channel, and first the reverse and then the original on the other.

A song without instrumental accompaniment is one the simplest forms of music, and we will now briefly discuss the symmetrization of two such songs here. The first one is the neutralistic chant which is part of the Model song called "Include the Neutral Name". This chant is in itself already a fair approximation of symmetrical noninstrumental music, especially with primary stress in the middle of an odd number of syllables: nan, (nanan,) nananan, (nanananan,) nananananan, and so on. Since all the n's and all the a's are in principle pronounced the same (as |N| and |AH| respectively), the chant proper is both a visual and an aural palindrome. On the level of characters and phonemes it is a clear example of neutralistic symbolism, but, of course, when just sung it will not be symmetrical on the phonetic level by any manner of means. However, it is made completely symmetrical by adding the reverse to the original at the end. And after doing so, it may be decided to add an echo. Adding an echo is, strictly speaking, an act of 'desymmetrization' (for the echo has a forward effect only), but the total structure remains basically the same, that is, symmetrical nonetheless, provided that the echo is not too strong. With the original followed by the reverse on the one channel and the reverse followed by the original on the other a stereo composition can now be created. This is done in the sound file NchcN1ES.mp3 (849 kB).

The second song to be discussed here is a 'real' song, that is, one entirely asymmetrical in itself. It is The Wheel That Turns, the fourth of the Wheel poems. What would be more appropriate than turning a cyclic song about a wheel that turns into a symmetrical object itself, one which can be repeated again and again? To do this we start with making a reverse copy of the original. This reverse may not be as acceptable as the reverse of the neutralistic chant, because the chant is fairly symmetrical in itself, whereas The Wheel That Turns is not. Moreover, the lyrics of this song were never written with a possible reversal in mind. The reverse of |MEENZ| (means), for instance, is |ZMEEN|, which may sound alright, but the reverse of |MEEning| (meaning) is |nginEEM| or, perhaps, |ngiNEEM|, whose beginning may not sound alright at all. (Note again that |ng| stands for one phoneme only.) Yet, the alliteration of |MEENZ| and |MEEning| in the original becomes the rime of |ZNEEM| and |ngiNEEM| in the reverse, and this rime sounds at least as good as in any 'regular' song. Whether one likes the reverse or not, this song certainly gives us a fine example of what symmetrical music encompasses. With the retrograde which may or may not sound acceptable on its own two mono arrangements can be made in reverse order. These two mono compositions are already pieces of symmetrical music in their own right, but they can still be combined in a new stereo composition which is symmetrical as well. Especially for songs without accompaniment adding an echo may enhance the pleasure of listening to them. It is done in the sound file WhlhW4SE.mp3 (1.83 MB), even tho it entails a slight desymmetrization.

Reversing forward-played music and combining the forward and the backward parts does not yield 'music' by definition. What is music is, of course, not an issue which we will try to solve here (if ever). Suffice it to admit that good music played forward may sound horrible when played backward. What lies at the basis of symmetrical music is the discovery that music played backward may nonetheless in certain cases under certain conditions sound 'not too bad' or even 'good'. And, more importantly, that music played backward which does not deserve the epithet of music anymore after reversing it, can be made to sound better or even good after deleting parts and reorganizing other parts of it. For symmetrical music this is a two-edged sword tho, as it may mean that some euphonious parts in the original will have to be rearranged or even deleted too. It stands to reason that for a suitable retrograde the first requirement is a suitable prime.

With modern technology we have all facilities for making symmetrical music. Whether we should make it is a question not different from the question whether we should make the design of a lamp or a house symmetrical or not. On the surface it may not be a matter of principle but merely of beauty. Yet, beauty is not only in the eye of the beholder, it is also in the ear of the listener. Few people like any type of music, even when played forward only. And if the genre is acceptable for them, the one may love a piece of symmetrical music in that genre, whereas the other may hate it, especially the backward played part or parts. Needless to say, no-one should be forced to like or dislike symmetrical music, or to be ashamed of 'er personal taste, so long as 'e is unbiased.

However, there is more to symmetry in the fine arts than personal like or dislike. In the social field symmetry represents the neutrality which stands for equality, nondiscrimination and, indirectly, beneficence or the absence of maleficence, where situational goodness is concerned. From a neutralistic perspective a person must not aim at unneutrality or asymmetry, one of its manifestations, per se. An asymmetrical design may be a good design (particularly when it is part of a larger, balanced whole) but not because of its (own) asymmetry. On the other hand, a symmetrical design is good in at least one respect: that of its symmetry. Nonetheless, symmetry is not an ultimate value (and neutrality not the sole ultimate value), and a symmetrical design may therefore be bad for other reasons, but not because of its being symmetrical. This applies to visual or physical designs and this applies to music as well. On the neutralistic view there is a suprapersonal significance in symmetrical music which transcends personal taste or distaste, even if merely symbolically. It is a form of art which provides people with a new medium for opening their minds to what is good under the neutral norm, if not in music itself, then in the other things of life that keep on touching the listener.

59.NLY

¹ symmetrical music (sy-MME-tri.c.al MU.s.ic, |si-ME-tri.k.al MJOO.z.ik|) is an alliterative term which can be found in the Vocabulary of Alliteration by MVVM. This dictionary is concerned with the sound of the language, rather than with its appearance on paper or screens. The transcription of speech sounds in this article is the one used in the Vocabulary. It is called "the double-case phonemic transcription". In this transcription stressed (|STREST|) phonemes are represented by capitals.