




































DNA Decipher Journal | July 2020 | Volume 10 | Issue 1 | pp 14-25 

Smith, S. P.,  Pitch Inverted Songs as Affirmation of Panpsychism Based on a Theoretical Mirror Universe 

 

ISSN: 2159-046X DNA Decipher Journal 
Published by QuantumDream, Inc. 

www.dnadecipher.com 

 

14 

Article 

Pitch Inverted Songs as Affirmation of Panpsychism  

Based on a Theoretical Mirror Universe 
 

Stephen P. Smith
*  

 

Abstract 

Every song that carries a melody can be pitch inverted to uncover a dual song that is different to 

the original song and where the pitch-inverted melody also relates to our emotions. This is 

creating music for the minor cost of pitch inversion, and without a lot of creativity beyond 

technical skills. The principle is demonstrated on 50 songs, with 100% success. As a general 

principle this implicates a reflective property that is necessarily part of human psychology. 

Moreover, this discovery affirms the belief in panpsychism where the reflexive property is active 

as part of a broader mirror universe. 
 

Keywords: Song, pitch inversion, panpsychism, mirror universe, reflective property. 

 

 

1. Introduction 
 

Panpsychism is a philosophical theory of consciousness that is gaining acceptance today 

(Skrbina 2017). This theory stipulates that consciousness is a fundamental property of matter. 

Because matter cannot be disconnected from the entire universe, panpsychism also asserts that 

consciousness is a fundamental property of the universe. 

 

Smith (2018, 2019) described a panpsychism that relates to a fundamental symmetry described 

by physics, the charge-parity-time symmetry (or CPT symmetry), and also connects it to a mirror 

universe theory described as a two-sided CPT inversion. As a logical necessity for a 

comprehensible universe, it must be that the universe holds a reflective properly that permits 

comprehension, otherwise the world would not be comprehendible (Langan 2017). This logical 

necessity resembles photographic prints that are made from negative film, where the negative 

film equates to the reflective property in the universe as an analogy. Moreover, while the 

negative film is found necessary, there remains an undeclared middle-term that takes the 

negatives and does the work of making the prints, agreeing with Trinitarian philosophy (Smith 

2008). Therefore, evidence that supports the belief in such a mirror universe comes in the form 

of discovering the negative film, or reflections, that are found after looking for them. 

 

This paper entertains the theoretical possibility that songs also carry a negative, or dual song, and 

these songs are represented by pitch-inversion. To the extent that every song that has ever been 

composed comes with such a dual song, that is also recognized to carry a distinct melody that 

evokes an emotional response to some degree, then this would constitute evidence of a mirror 

universe that encapsulates the emotive source. The theory predicts a 100% success rate in finding 

                                                
Correspondence: Stephen P. Smith, Ph.D., Independent Researcher.  E-mail: hucklebird@aol.com 
 



DNA Decipher Journal | July 2020 | Volume 10 | Issue 1 | pp 14-25 

Smith, S. P.,  Pitch Inverted Songs as Affirmation of Panpsychism Based on a Theoretical Mirror Universe 

 

ISSN: 2159-046X DNA Decipher Journal 
Published by QuantumDream, Inc. 

www.dnadecipher.com 

 

15 

a dual song that carries a melody, not that all such melodies will be found pleasing. This is a 

testable prediction that is reported in this paper on 50 different attempts to create dual songs. 

 

Section 2 describes pitch inversion in music, and how to pitch-invert songs. Appendix A provides 

more details on how to pitch-invert sheet music by hand. These instructions were used to pitch 

invert 50 popular songs, using a music note editor (Cresceno, made by NCH Software). Section 3 

describes the information content in songs, and how songs carry a relativity that makes them 

invariant to transposition. Section 4 explains how the relative information contained in a song 

pertains to panpsychism and the mirror universe. Section 5 summarizes the results for 50 songs, 

including links to YouTube videos where the songs can be heard. All 50 attempts were found 

successful in generating a distinct melody, most being very different from the initial song, and 

these findings support the belief in the mirror universe. Concluding remarks are presented in 

Section 6. 

 

 

2. Pitch Inversion 
 

The pitch inversion of musical notes have been studied in musical set theory (Forte 1977). Pitch 

inversion is defined as the flipping, or reflecting, of a note around a second note that represents 

the center note. The center note is selected once
1
 but can be selected anywhere, but various keys 

have natural center notes that do not complicate the notation. For example, using the note D as 

the center note returns notation in C major given that the original song is in C major, where the 

pitch-inverted notes will have accidentals only when the original notes have accidentals.  

 

Like the transposition of notes, pitch inversion maps a song into a class without changing the 

tempo while making a second song. In the case of transposition, which is the raising or lowering 

of notes a specified number of chromatic steps, the same melody is returned. That is, melody is 

found invariant to transposition, even as the tone changes. Pitch inversion changes the melody, 

but not necessarily to an extreme extent even as extreme changes are found in particular 

examples. Therefore, the pitch-inverted song represents a dual song that shadows the original 

melody, and only when the melody and its dual are defined equivalent is a broader equivalence 

or invariance (representing a class) meaningful. 

 

When working with an audio file, it is possible to use software (e.g., Patrick Feaster‟s software 

described on griffonagedotcom.wordpress.com) to pitch-invert a song around a selected pitch (if 

not a note). The evolution of sound from notes played by a musical instrument are impacted by 

time creating a waveform signature that‟s asymmetrical in its presentation (changes in 

amplitude), and in any regard, pitch-inverting sound is not as pristine as pitch-inverting notes 

before they are played. The bigger challenge is that the chromatic scale is exponentially spaced, 

where frequency must be log transformed to make a linear scale for direct pitch inversion of 

sound. Its more straightforward to invert notes before they are turned into sound, using the 

natural exponential chromatic spacing. C++ Software (Craig Stuart‟s MIDI file parsing library, 

part of GitHub) is available for pitch-inverting a midi file around a center note. If not careful, 

however, reflecting midi files can lock the process into making all notes on the bass clef high 

                                                

1. When inverting notes in one staff. 



DNA Decipher Journal | July 2020 | Volume 10 | Issue 1 | pp 14-25 

Smith, S. P.,  Pitch Inverted Songs as Affirmation of Panpsychism Based on a Theoretical Mirror Universe 

 

ISSN: 2159-046X DNA Decipher Journal 
Published by QuantumDream, Inc. 

www.dnadecipher.com 

 

16 

notes and while making all notes on the treble clef low notes, and this creates an inflexible 

method that is not desirable. It is preferable to break a song into multiple staffs (which is 

tantamount to making multiple midi files), pitch-invert each staff individually using a center note 

that‟s natural for the key but in the middle of the staff (more or less), then transpose each staff up 

or down one octave to present the most desired arrangement for all the staffs together. Therefore, 

pitch-inversion of a song does not necessarily lock the process into a single center note. The 

added flexibility is actually preferred with a process that is otherwise highly automatic, and the 

process can now be done by hand using a good music note editor (See Appendix A). The 

disadvantage of doing the inversion by hand with a note editor is that the operation can introduce 

errors. 

 

3. Information Contained in a Song and Relativity 

 

The exponential spacing (given by the factor 
12

√2) that typifies the chromatic scale is 

remarkable. The implication is that the human ear not only can distinguish among these notes, 

but actually prefers this arrangement when notes are set to music. Because the normal scale with 

seven notes represent a subsequence of the 12 chromatic notes, the same preference given to 

exponentially spaced notes is again realized. Its unclear how this preference can be explained in 

mathematical terms, but there is a vague hint that this preference connects to the probabilistic 

concept of entropy, or to the scale invariant prior and utility function of Bayesian statistics, all of 

which incriminate multiplicative transitions. The fact that this preference connects to 

consciousness makes the spacing very mysterious. Nevertheless, pitch inversion will be taken to 

pertain to this unusual spacing, which is not linear in pitch, it is multiplicative. 

 

The fact that a transposition of notes in a song leaves the melody intact while changing the tone, 

implies that the information that is recognized as a melody is contained in the relative changes of 

notes as time unfolds according to the tempo. Only the tempo and transitions between notes 

define the melody, not the absolute frequency that defines any particular note. This represents a 

type of relativity given by the representation of melody as the transitions given in the exponential 

scale. This is not saying that the melody is relative, only the representation of melody is relative. 

The representation does not stand in isolation to its reception in mind, i.e., something must 

receive the representation, and something must hold the representation to its reception. The strict 

application of relativity only applies to the song‟s representation, and perhaps the song‟s 

reception, but not to the undeclared middle-term that holds the representation to its reception. 

Imposing relativity on the middle-term is to imply that everything is relative, which is to confuse 

the thing-in-itself with appearance and is a mistake that Kant recognized in the Critique of Pure 

Reason.       

 

The observation that representation is relative, as is the representation‟s reception, is presumably 

a condition of consciousness. Information showing the middle-term gets left out of appearance 

by necessity, and must be apprehended by something other than simple appearance. We cannot 

see the middle-term for the same reason that our eyes cannot see the back of our head without the 

aid of a mirror; i.e., the blind spot is caused by self-referral. A mirror, or frame of reference, must 

always be provided in order to detect something closer to the middle-term. Likewise, a popular 

science turned folk philosophy might leap to the false conclusion that everything is relative 

(radical relativism) based on the findings of special and general relativity (if not postmodernism), 



DNA Decipher Journal | July 2020 | Volume 10 | Issue 1 | pp 14-25 

Smith, S. P.,  Pitch Inverted Songs as Affirmation of Panpsychism Based on a Theoretical Mirror Universe 

 

ISSN: 2159-046X DNA Decipher Journal 
Published by QuantumDream, Inc. 

www.dnadecipher.com 

 

17 

but clear thinking shows that something fundamental and non-relative may go unnoticed in the 

possible eather that never finds experimental detection. It is not accidental that Einstein‟s 

theories postulated a frame of reference as a first step in his thought experiments. However, a 

frame of reference (even those described in physics) implies a self-referral that carries its own 

blind spots. 

 

 

4. Panpsychism and the Mirror Universe 
 

Information of any kind presupposes the existence of consciousness. Or if consciousness is to be 

taken for granted, attempts to turn information into a one-sided measure (such as Shannon‟s 

information given the thermodynamic quantity called entropy) pushes consciousness out of the 

window of appearance and into a metaphysics that may get completely ignored. In the worst case 

this is to confuse appearance with the thing-in-itself again, as Kant warned. Nevertheless, the 

push of consciousness out of the one-sided appearance leaves it fully in reality as the other side 

of appearance, consciousness carries the appearance that is reflected off the other side, and 

carries an undeclared middle-term again. Consciousness becomes a fundamental substance in 

reality, something that is not a derivative of one-sided causation, and even if it is not admitted by 

those confused by appearances. This view of consciousness that connects to a fundamental is the 

definition of panpsychism, and because this view also carries a realty that is two-sided with an 

undeclared middle-term this view indicates a rediscovery of the Logos that makes a particular 

type of panpsychism and implies a mirror universe. 

 

The Logos that represents the absolute mover
2
 of the universe acts now as a strange attactor, and 

forms a fractal pattern in evolution by leaving behind a reflection of itself on all levels. The 

mirror universe leaves behind lesser mirrors that may serve as evidence for the theory of the 

mirror universe.      

 

Information that represents a melody, given as tempo and the relative spacing of notes, must 

somehow meet the representation‟s reception (the reflection). The hypothesis of this paper is that 

the organic reception, or the song‟s reflection, is none other than the pitch inversion of the 

melody. This is not to say that there are not deeper reflections, perhaps going all the way to CPT-

inversion that‟s described in physics. However, its very ambitious to dig this deep, and a deeper 

reflection may be unintelligible to the human mind. The deeper search is unnecessary, however, 

as the proof in the mirror universe is the finding of lesser mirrors that are all necessary; we are 

permitted to make incremental discoveries.  

 

So finding ourselves sitting at a piano we may also find our self-looking into a near-by mirror. 

Playing the piano while looking into the mirror we discover that the right hand is playing on the 

low-pitched keys while the left hand is playing on the high-pitched keys, the complete reverse of 

what normally happens, but matching perfectly the operation of pitch-inversion using the 

chromatic scale with its exponential spacing. The pitch-inverted song matches perfectly the 

mirror reflection of ourselves playing the piano that‟s unified through the unspecified middle-

term. Could this be the organic mirror we are looking for, a lesser mirror that‟s found necessary? 

                                                
2. As in motivation and the source of all that is emotive. 



DNA Decipher Journal | July 2020 | Volume 10 | Issue 1 | pp 14-25 

Smith, S. P.,  Pitch Inverted Songs as Affirmation of Panpsychism Based on a Theoretical Mirror Universe 

 

ISSN: 2159-046X DNA Decipher Journal 
Published by QuantumDream, Inc. 

www.dnadecipher.com 

 

18 

Songs carry a remarkable connection to emotion, and less so to intellect. A possible panpsychism 

is better described as a vitalism because its emotion that we look for, not so much consciousness. 

To seek is to be motivated, and that‟s an emotional requirement. To seek is futile if there was no 

awareness of fulfilment, and so consciousness in some degree is also required and therefore goes 

hand in hand with emotion. A song is like a language that connects with emotion and takes us 

somewhere with a motivated direction. The mirror image of the song should also take us 

somewhere as it necessarily does if the original song is faithful to a direction representing the 

melody. Therefore, all pitch-inverted songs should carry a hidden melody, the dual song, 

provided pitch-inversion is the actual organic mirror, a lesser mirror, that is necessary for the 

mirror universe where the middle-term represents the source of all that is emotive. This is a 

testable prediction, 100% of the inverted songs should carry a melody if the hypothesis is true. 

Finding one song that is little more than random noise would indicated that the organic mirror is 

not yet discovered.  

 

 

5. Fifty Pitch-Inverted Songs 
 

All the songs were pitch-inverted following the method in Appendix A, for the present 

investigation, and are identified in Table 1. The 50 remade songs are presented in a YouTube 

play-list and are found with this internet link: 

 
https://www.youtube.com/playlist?list=PLdHv1duZhJ8-NhMv2wxEVVUHPi-56Bp5q 

 

Simply match the video named in Table 1 to the video in the play-list. 

 

 

Table 1. List of pitch-inverted songs. 

Video Original Song Composers 

1. Beautiful Dreamer Beautiful Dreamer Stephen Foster 

2. Southern Swamps Bonnie Blue Flag  Harry McCarthy 

3. Swan Lake and its Echo Swan Lake Peter Ilyich Tchaikovsky 

4. Abducted by the Mirror Man in the Mirror Glen Ballard and Siedah Garrett 

5. Wanderlust America Paul Simon 

6. Broken Ties Castles in the Air Don McLean 

7. Once Upon a Time in the 

Mirror 

Once Upon a Time in the West Ennio Morricone 

8.Brothers in Repose Brothers in Arms Mark Knopfler 

9. The Big Mirror The Big Country Jerome Moross 

10. Polished Corn Popcorn Gershon Kingsley 

11. The Magnificent Mimic The Magnificent Seven Elmer Bernstein 

12. Do You Know the Way? Do You Know the Way to San 
Jose 

Burt Bacharach 



DNA Decipher Journal | July 2020 | Volume 10 | Issue 1 | pp 14-25 

Smith, S. P.,  Pitch Inverted Songs as Affirmation of Panpsychism Based on a Theoretical Mirror Universe 

 

ISSN: 2159-046X DNA Decipher Journal 
Published by QuantumDream, Inc. 

www.dnadecipher.com 

 

19 

13. The Reflection of Love The Look of Love Burt Bacharach 

14. Don‟t Wake in a Dream Don‟t Sleep in the Subway Tony Hatch and Jackie Trent 

15. Burning Daylight The Hustle Van McCoy 

16. Hot Death Valley Hot Hot Hot Alphonsus Cassell 

17. Ride the Train Locomotive Breath Ian Anderson 

18. Ode to Joy and its Echo Ode to Joy Ludwig Van Beethoven 

19. Ipanema The Girl from Ipanema Antonio Garlos Jobim 

20. Gun Fighters The Man Who Shot Liberty 

Valance 

Burt Bacharach 

21. Sailor‟s Dream Daydream Believer John Stewart 

22. Painted Desert This Guy‟s in Love with You Burt Bacharach 

23. Internet Killed the Shopping 

Mall 

Video Killed the Radio Star Bruce Woolley, Trevor Horn and 

Geoff Downes 

24. Cover of Darkness The Sun Ain‟t Gonna Shine 
Anymore 

Bob Crewe and Bob Gaudio 

25. Saturday‟s Travel Come Saturday Morning Fred Karlin 

26. Everybody‟s Leavin‟ Town Good Time Charlie‟s Got the 
Blues 

Danny O‟Keefe 

27. New Beginnings Goodbye John Lennon and Paul McCartney 

28. Empty Places Brandy Elliot Lurie 

29. Dancing in the Garden Dancin‟ in the Moonlight Sherman Kelly 

30. Baja California Come Monday Jimmy Buffett 

31. God‟s Will be Done God Only Knows Brian Wilson and Tony Asher 

32. Empty Streets Downtown Tony Hatch 

33. Sweeter Song than the Birds My Girl William “Smokey” Robinson and 
Ronald White 

34. Wabash Cannonball and its 

Echo 

Wabash Cannonball A.P. Carter 

35. Armidale by Afternoon Amarillo by Morning Terry Stafford and Paul Frasier 

36. The Master‟s Tapestry Coat of Many Colors Dolly Parton 

37. God‟s Sanctuary Amazing Grace John Newton 

38. Where Have They Gone Abraham, Martin and John Richard Holler 

39. On Straight and Narrow The Only Daddy that Will Walk 

the Line 

Ivy J. Bryant 

40. The Fast Track Lost Highway Leon Payne 

41. Is Anybody Goin‟ to 

Shangrila 

Is Anybody Goin‟ to San Antone Dave Kirby and Glenn Martin 



DNA Decipher Journal | July 2020 | Volume 10 | Issue 1 | pp 14-25 

Smith, S. P.,  Pitch Inverted Songs as Affirmation of Panpsychism Based on a Theoretical Mirror Universe 

 

ISSN: 2159-046X DNA Decipher Journal 
Published by QuantumDream, Inc. 

www.dnadecipher.com 

 

20 

42. How „Bout them Memories How „Bout them Cowgirls Casey Beathard and Ed Hill 

43. Time Reversal Time Passages Al Stewart and Peter White 

44. Waiting for a Sign Waiting on a Friend Mick Jagger and Keith Richards 

45. My Front Pages My Back Pages Bob Dylan 

46. Ghost Returning from other 

Side 

Wuthering Heights Kate Bush 

47. Megaliths and Geoglyphs No One to Depend On Gregg Rolie, Michael Carabello 
and Thomas Escovedo 

48. Music from the Other Side Both Sides Now Joni Mitchell 

40. Pyroclastic Flow Landslide Stevie Nicks 

50. From Flower to Seed From Hank to Hendrix Neil Young 

 

All 50 remakes produced melodies, supporting the belief that pitch-inversion is more than just an 

interesting generation of musical notes. By comparison, playing notes backward can create 

interesting sounds sometimes, but these are unlikely to generate interesting melodies; playing 

notes backward may only generate uninteresting sounds. What has been demonstrated here is 

more of a general principle, a demonstration that all songs that have a defined melody also carry 

a hidden song by necessity, a dual song that can be recovered by pitch-inversion. This is not to 

say that the pitch-inverted songs are necessarily beautiful, or as beautiful as the originating song. 

Its only that an emotion connecting melody is guaranteed by the principle that‟s now found 

validating the hypothesis of a mirror universe, as described. 

 

Some of the pitch-inverted songs are quite beautiful, however. The author finds the songs (5, 21, 

25, 27, 30, 41, 42, 48 and 50) very beautiful, and quite striking. Other songs (4, 5, 8, 10, 15, 16, 

20, 38, 39 and 46) are very interesting, and beautiful in an unconventional way. Most of the 

pitch-inverted melodies bear little resemblance to the originals, but there are dual songs (9, 10, 

12, 15, 19, 28, 30, 34, 46 and 47) that hold some minor similarities with the original song. These 

appraisals are likely to show subjective variation. 

 

When first investigating pitch-inversion, very simple songs were considered, limited to one staff 

showing mostly single notes, with few or no chords. But to avoid the selection bias of only 

showing interesting examples, these few simple songs (Videos 1 and 2) have a listing in Table 1. 

Video 1 plays the original song followed by the pitch inversion, followed again by an 

improvisation that has little to do with pitch-inversion. Video 2 also plays the original melody 

followed by the pitch inversion, but it also experiments with overlaying a two melodies which 

actually worked for that particular song. Overlaying the song with its pitch-inversion, however, 

was in general found to generate dissonant sounding notes and was abandoned in the later 

productions. Videos 3 and 34 also plays the original song and its pitch inversion. The remaining 

videos only play the pitch-inverted songs, but versions of the original melodies can easily be 

found on YouTube if a comparison is needed. 

 

It was found that the method of Appendix A was very robust, and worked best for more 

complicated songs that had several staffs. The staffs for a more complicated song can all be 



DNA Decipher Journal | July 2020 | Volume 10 | Issue 1 | pp 14-25 

Smith, S. P.,  Pitch Inverted Songs as Affirmation of Panpsychism Based on a Theoretical Mirror Universe 

 

ISSN: 2159-046X DNA Decipher Journal 
Published by QuantumDream, Inc. 

www.dnadecipher.com 

 

21 

inverted independently, then transposed up or down to make a harmonious synthesis of all the 

inverted staffs. Most of the 50 songs listed in Table 1 came with four staffs: for a guitar; the 

chords, and the piano‟s bass and treble clef. These staffs were then borrowed by different musical 

instruments (by the computer synthesizer) to create more interesting productions. 

 

Something must be strangely said about the very unusual experience of hearing a pitch-inverted 

song for the very first time. In some cases the music comes out as not sounding right, confusing, 

and more like a failure showing less than the expected 100% success rate now reported. Some of 

this is due to small errors that end up getting corrected, and doing the inversion by hand can 

introduce errors. However, this can‟t be the only reason for the initial confusion. Its like looking 

at the Figure 1 below, and getting confused about seeing a vase or two opposing faces. 

 

 
 

 
Figure 1. Optical Illusion. 

 

Having recognized the melody for the very first time, then the confusion goes away like magic! 

The melody becomes a rote that‟s first learned, but this is where the experience becomes 

inexplicable because I doubt that any of my YouTube viewers find an initial confusion while 

listening to these 50 songs! The implication is that the learned rote becomes part of the collective 

memory, a sort of Mandela effect that rewrites history, or a type of morphic resonance that 

becomes available to the collective. Extraordinary claims demand extraordinary evidence, and no 

one should adopt this speculation as certain. Something unusual happened when listening to 

some (not all, but including 8, 13, 31, 40, 43, 45 and 46) of the pitch-inverted songs for the first 

time, that‟s all that is being claimed. Fortunately, the experience can be repeated if its real. If any 

investigator wants to pitch invert different songs in the future, be looking for this experience. 

There is no shortage of songs that can be inverted, and so its possible to bring clarity to this 

issue.  

 

 



DNA Decipher Journal | July 2020 | Volume 10 | Issue 1 | pp 14-25 

Smith, S. P.,  Pitch Inverted Songs as Affirmation of Panpsychism Based on a Theoretical Mirror Universe 

 

ISSN: 2159-046X DNA Decipher Journal 
Published by QuantumDream, Inc. 

www.dnadecipher.com 

 

22 

 

 

6. Conclusion 
 

The attempts to make melodies by pitch inverting 50 songs was 100% successful. Interesting 

songs of all types were generated using the robust method presented in  Appendix A, and most of 

the remade songs showed little resemblance to the originating song even when the tempo was 

maintained. This strongly implies the validity of a general principle, that all songs that carry an 

identifiable melody can be pitch inverted to make new melodies with 100% success. This 

conclusion is firm because the results are highly reproducible. Doubters will find the identical 

melodies reported here following independent attempts at pitch inversion with any of the same 

50 songs. Moreover, new songs can be inverted to further test the general principle, but it is now 

doubtful that the conclusion will change. 

 

The only possible controversy is with what these findings mean, including the general principle 

that‟s now uncovered. As argued in this paper, these results affirm the belief that we live in a 

mirror universe that is a necessary adjunct of panpsychism of a sort that endorses Trinitarian 

philosophy. The proof of the mirror universe is in the lesser mirrors that are discovered, and one 

such lesser mirror is the pitch-inverted song that equally brings the listener on an emotion laden 

journey like all songs. Moreover, the middle-term that holds the song to its reflection is the 

emotive source that connects to the absolute mover or motivator for the entire universe. Such a 

system act as a strange attractor that generates the lesser mirrors out of necessity and on all levels 

of a fractal pattern, and so finding these mirrors constitutes evidence that affirms this 

speculation. Yes, this last paragraph is speculation, but it now falls into testable science because 

there are many kinds of mirrors beyond music that can be gathered as evidence.  

 

 
Appendix: Robust Method to Pitch Invert Songs with Multiple Staffs 

 

A.1 General Protocol 

 

1. Rewrite the sheet music using C major notation.  
 

An attempt might be made to pitch invert a song directly in the key its written in (sheet music notation) 

by following the instructions given under Section A.3. But this will lead to unwanted complexity for those 

notes that come with accidentals. Therefore, its better to rewrite the sheet music into the key of C major 
(or A minor). Music note editors may provide this operation as part of software, and a transposition of 

notes is also needed to minimize the creation of accidentals when going into C major. Those required 

transpositions are presented in Section A.2. 
 

2. Identify and separate out all the staffs, and transpose all the notes down making bass clefs. 

 

Songs come with multiple staffs, and these will all have to be treated separately. In addition to the staffs 
that are explicitly represented with the sheet music, it is sometimes recommended to break a staff into 

sub-staffs when notes are found running over a few octave levels. These sub-staffs can all be inverted 

separately (jumping ahead to Step 3), and brought back together after inversion by resetting them on 
preferred octave levels (jumping ahead to Step 4) and this need not mimic pitch inversion of the 

originating staff and had the staff not been broken up. This lets the composer stir the process better based 



DNA Decipher Journal | July 2020 | Volume 10 | Issue 1 | pp 14-25 

Smith, S. P.,  Pitch Inverted Songs as Affirmation of Panpsychism Based on a Theoretical Mirror Universe 

 

ISSN: 2159-046X DNA Decipher Journal 
Published by QuantumDream, Inc. 

www.dnadecipher.com 

 

23 

on preference rather than being locked into an automatic protocol.  

 
More generally, all the notes and staffs (and possible sub-staffs) will be in the key C major, where the note 

D is the reflective center as found in Section A.3. The note D is right in the center of the bass clef, 

running longitudinally down the middle, making an ideal platform to pitch invert by hand. Therefore, its 

preferable to transpose all staffs down by octave steps and express them as bass clefs. 
 

3.  Pitch invert all the staffs around the note D that‟s in the middle of each bass clef.  

 
The precise instructions for pitch inversion are given in Section A.3, with reference to music in the key of 

C major notation. However, it is now very easy to see pitch inversion in Figure 2. 

 

 
 

Figure 2. Showing two staffs in C major notation, where the top staff is the pitch inversion of 

the bottom staff, and visa versa. The note D that serves as the center note, is indicated by the red 

line that runs through the middle of each staff. The notes are flipped around the red line making 
the pitch inversion. Sharps are turned into flats, and flats into sharps, and the natural accidental 

is carried without adjustment. 

 
4. Transpose up and re-express the preferred key. 

 

Transpose all the pitch-inverted staffs up by octave steps to reestablish treble clefs, perhaps leaving only 
one bass clef for the piano. By following Section A.2, its also possible to change the music key (for all the 

staffs) into something other than C major, noting the further transpositions in Table 2 that may be 

preferred. 

 
One uses preference to determine the octave levels for each staff, and the overall key for all staffs, and 

this is different than using a single center note across all staffs where a literal pitch inversion is found 

unnecessarily restricted. The recommended inversion described here provides for multiple center notes
3
 

that permit a harmonious union over all the staffs.  

 

 

A.2 Instructions for Changing Sheet Music Notation 
 

Rewrite the notation into the new notation; either C Major or one of the other keys if starting from C 

Major. This may introduce many accidentals. Then transpose the notes up or down the prescribed steps as 
given by Table 2. The transposition will remove all of the newly introduced accidentals. 

                                                
3. That‟s suitable for the key. As an example, the note D can be found in several places and is suitable for the key of 

C major. 



DNA Decipher Journal | July 2020 | Volume 10 | Issue 1 | pp 14-25 

Smith, S. P.,  Pitch Inverted Songs as Affirmation of Panpsychism Based on a Theoretical Mirror Universe 

 

ISSN: 2159-046X DNA Decipher Journal 
Published by QuantumDream, Inc. 

www.dnadecipher.com 

 

24 

 

Table 2. Transposition steps needed to change sheet music notation from a given key into C Major (or A 
Minor), or from C Major into the key. 

 Transposition Steps  

 #‟s → C Major ♭‟s → C Major  

Key in Sharps C Major → ♭‟s  C Major → #‟s  Key in Flats 

# -7 or +5 +7 or -5 ♭ 

# # -2 or +10 +2 or -10 ♭♭ 

# # # -9 or +3 +9 or -3 ♭♭♭ 

# # # # -4 or +8 +4 or -8 ♭♭♭♭ 

# # # # # -11 or +1 +11 or -1 ♭♭♭♭♭ 

# # # # # # -6 or +6 +6 or -6 ♭♭♭♭♭♭ 

# # # # # # # -1 or +11 +1 or -11 ♭♭♭♭♭♭♭ 

 

 

A.3 Instructions for Manual Pitch Reflection of Musical Notes 

 

Identify the key that the music is written in, thus finding the note representing the reflective center in 
Table 3. Locate one note position on the staff corresponding to the reflective center, selecting from 

suitable choices merely by preference. Reflect all the notes in a measure around the reflective center, as if 

this center note represents a mirror going down the length of the measure. Notes that happen to equal the 
reflective center are left unreflected.  

 

Special treatment is given to notes that may rarely come with accidentals. First observe that if sharps (#) 

always increased the impacted note by one semitone, and if flats (♭) always decreased the impacted note 

by one semitone, and if the natural accidental (♮) always reset the impacted note to the default for the 

selected key, then pitch reflection would be an easy extension. However, these conditions are only 

satisfied for C major (or A minor) notation. These conditions are not stickily enforced for the other keys, a 

fact that is sometimes missing off introductory accounts of sheet music notation pertaining to accidentals.  

 
Fortunately, Table 2 permits a transformation of music into C major that‟s followed by the specified 

transposition to minimize accidentals, and this transformation can be made for music written in any of the 

keys. Its in C major that pitch inversion is made following these straightforward instructions: first, it is 
recommended simplifying the notation by removing multiple expressions of enharmonic equivalence, so 

that each note inside one measure is represented only by one of the variants that come as the natural 

accidental (♮), sharp (#), flat (♭), or an adjacent scale note, making sure any ties are correctly indicated; 

accidentals are reflected like regular notes, but in the reflection show a flat if starting from a sharp, or 

show a sharp if starting from a flat, or show a natural accidental if starting from a natural accidental; ties 

are transferred automatically. This pitch reflection is made around a central note D that is well positioned 
in the staff. Once this is completed for all the measures, the entire staff can be transposed up or down one 

octave to improve appearance. Table 2 is also used to return the reflected notes back into the originating 

notation or key. 
 

Table 3. Center note that permits pitch reflection while maintaining the notation (without the need of accidentals) 



DNA Decipher Journal | July 2020 | Volume 10 | Issue 1 | pp 14-25 

Smith, S. P.,  Pitch Inverted Songs as Affirmation of Panpsychism Based on a Theoretical Mirror Universe 

 

ISSN: 2159-046X DNA Decipher Journal 
Published by QuantumDream, Inc. 

www.dnadecipher.com 

 

25 

within a key. 

Key Sheet Music Notation Reflective Center 

C Major or A Minor Default D 

G Major or E Minor # A 

D Major or B Minor 2 #‟s  E 

A Major or F# Minor 3 #‟s B 

E Major or C# Minor 4 #‟s F 

B Major of G# Minor 5 #‟s C 

F# Major or D# Minor 6 #‟s G 

C# Major or A# Minor 7 #‟s C 

F Major or D Minor b G 

Bb Major or G Minor 2 b‟s C 

Eb Major or C Minor 3 b‟s F 

Ab Major or F Minor 4 b‟s B 

Db Major or Bb Minor 5 b‟s E 

Gb Major or Eb Minor 6 b‟s A 

Cb Major or Ab Minor 7 b‟s E 

 

 

 

References 
 
Forte, A., 1977, The Structure of Atonal Music, Yale University Press. 

 

Langan, C., 2017, An Introduction to Mathematical Metaphysics, Cosmos and History: The Journal of 
Natural and Social Philosophy, 13 (2), 313-330. 

 

Skrbina, D., 2017, Panpsychism in the West, 2
nd

 Edition, The MIT Press. 

 
Smith, S.P., 2008, Trinity: The Scientific Basis of Vitalism and Transcendentalism, i-Universe, Inc. 

 

Smith, S.P., 2018, Time, Life & the Emotive Source, Journal of Consciousness Exploration & Research, 9 
(8), 707-721. 

 

Smith, S.P., 2019, A Possible Holarchy Representing Morphic Resonance as One Side of the Poised 
Realm, Journal of Consciousness Exploration & Research, 10 (5), 371-379. 

 


