Sunday 14 October 2018

Accidental similarity

This is one of the most important articles in this blog...

A recurring situation in the music plagiarism cases that lay people jury members have to decide whether or not two melodic samples are substantially similar. Their inputs are the testimonies, the comparative sheets, sometimes also audio samples (original or prepared, mash-up). The jurors are instructed how to consider these inputs, but they lack the necessary reference to judge what is usual/unusual level of melodic similarity. The plaintiff party experts tend to magnify the point of similarities while the opposite party are trying to diminish them. The comparative sheets prepared by the complaining party experts are marking the allegedly similar points. It is tipically full of arrows, circles or red colored notes influencing the jurors more effectively than a verbal counter arguments by the defending party. An example: the plaintiff may find a sequence of five consecutive pitches in both songs. An effective testimony backed up with visual elements may make jurors think it's something extraordinary. The defendant will say it's a commonplace detail. The judgement of the jurors will depend much on how effectively the opposite arguments influence jurors. 

Proposal: 
In order to obtain a more reasonable judgement jurors could be briefly taught what extent of similarity is usual and what not. The jurors' sense of similarity could be properly "adjusted" this way. Note: this is not a step that necessarily supports the defendant party. It may easily show that the similarity is extraordinary (or substantial) indeed. The result of the test is visual and easy to interpret for lay people as well. 

Explanation: 
Investigating the usual level of similarity we can follow (at least) two approaches: 
Type A) 
Comparing the melodic material of two randomly chosen songs. Possible more songs to obtain a representative base. If the similarity of the compared songs returns a set of coincidences that is qualitatively and quantitatively in the range of what is usual for type-A results, then the melodic similarity is usual. This does not mean the non existence of any type of similarity, because an expert will be able to find points of similarity between very different melodic samples as well.

Type B)
Comparing a randomly chosen song and find the possibly closest melodic sample from another (prior) song. Considering recent pop hits and the similarity test introduced on this blog, most of pop songs can be found a song with a similar melody resulting around 6.0 on my proposed similarity test. Test is "positive", if we find a third party song (preferably prior to both complaining and defendant song) with a melodic sample that is more similar (higher P-index) than the songs of the case. If the third party song example is prior to only the defendant song, then it may indicate that the motif is moved meanwhile (since the release of the complaining song) to the public domain. If we can find a third party song with a melodic pattern that is more similar to either the complaining or the defendant song, than it again shows that the two songs are not substantially similar or this similarity is not protectible. If the found pattern is prior to 1) the defendants song 2) or the complaining song as well.

Type A tests.
 Hereby I present a series of comparative tests on randomly chosen songs taking the first three US No1 songs in 2018. The test was investigating how long melodic sequences appear simultainously in two randomly chosen songs. These three songs were Havana, Perfect and God's Plan, three rather different songs. Havana is in minor mode, while both Perfect and God's Plan are in major. A major and a minor melody can be compared two ways. First way is to use the dergrees of the homekeys. Second is the enharmonic view: minor key degrees can be transposed to the enharmonic (relative) major key. This is similar to solmization view, where the 1st degree of the minor mode is "la" that is equivalent to the 6th degree in a major key.
 In the tests we will omit sequences that are shorter than three notes. For the rhythmically also matching finding I used a limit of minimal two notes. For this test the music was transcribed to numerical degrees. Most of the transcriptions don't cover the entire song, only the key lead melodies. Errors in the transcriptions may occure, but these are not expected to impact the final conclusions. In the charts I may have not found all the identic sequences. The sequences with differently repeated pitches are marked with dashed line. The rhythmically also identic fragments are marked with colored numbers.

Havana vs. Perfect - homekey degrees 
Havana vs. Perfect - solmization degrees 
Havana vs God's Plan - homekey degrees 
Havana vs God's Plan - solmization degrees 
Perfect vs God's Plan 

Tests related to recent cases 

Stairway To Heaven vs Taurus 
Taurus vs Havana 
Blurred Lines vs Got To Give It Up 
Got To Give It Up vs God's Plan 
Let's Get It On vs Thinking Out Loud Thinking Out Lod vs God's Plan

Test results:
Havana vs. Perfect - homekey degrees 
- three notes long sequences: 5 
- four notes long sequences: 1 
- five notes long sequences: 2
- six notes long sequences: 1
- length of sequence with the same rhythmic placement: 4 in different meter tough. 

Havana vs. Perfect - solmization degrees 
- three notes long sequences: 3 
- four notes long sequences: 2 
- five notes long sequences: 2
- six notes long sequence: 1 
- length of sequence with the same rhythmic placement: 2 

Havana vs God's Plan - homekey degrees 
- three notes long sequences: 5 
- four notes long sequences: 5 
- five notes long sequences: 0 
- length of sequences with the same rhythmic placement: 2, 2 and 2. 

Havana vs God's Plan - solmization degrees 
- three notes long sequences: 2
- four notes long sequences: 3 
- five notes long sequences: 1 
- length of sequences with the same rhythmic placement: 4 and 3 

A similar melodic motif: 
 1 . 2 . 3 . 4 . 1 : beats 
 66 63 3 4 3 2 3   : Havana 
 6 6 5 5 4 3 2 3 3 : God's Plan

 The melodic part of the similarity test for these samples is 4,8 that occured accidentally. 

Perfect vs God's Plan - three notes long sequences: 5 
- four notes long sequences: 2 
- five notes long sequences: 1 
- length of sequence with the same rhythmic placement: 2 

Stairway To Heaven vs Taurus (instrumental/harpischord parts) The complaint argues that there exist melodic similarities between the harpischord parts in Taurus and vocal melodies of Stairway thus the transcription is fragmentary. 
- three notes long sequences: 3 - four notes long sequences: 0 
- five notes long sequences: 1 
- length of sequence with the same rhythmic placement: 3 This 3-2-1 motif is also occuring in Havana (both view), Perfect (dozens of times) and in God's Plan. 

Taurus vs Havana 
- three notes long sequences: 5 
- four notes long sequences: 2 
- five notes long sequences: 0 
- length of sequences with the same rhythmic placement: 2 and 2 

Blurred Lines vs. Got To Give It Up (deposited melodies) 
- three notes long sequences: 6 
- four notes long sequences: 3 
- five notes long sequences: 0 
- length of sequences with the same rhythmic placement: 2 and 3. Interestingly this latter one (a 2-2-2 sequence) accidentally occures in God's Plan as well with the same rhythmic placements. Note that the these findings were not (found?) pointed out by the complaining party. Most reports (including mine) were pointing out the lack of even two consecutively matching notes. As you see it's not quite correct. For the comparison I just considered only the first page of the three pages of the original deposite sheet plus two of the hook motifs. Transcribing all three pages (including the non-repetitive melodies in Got To Give It Up) would result more findings for both Blurred Lines and God's Plan (see below). 

Got To Give It Up vs God's Plan 
- three notes long sequences: 6 
- four notes long sequences: 1 
- five notes long sequences: 1 
- length of sequences with the same rhythmic placement: 3, 3 and 2

Let's Get It On vs Thinking Out Loud 
- three notes long sequences: 2 
- four notes long sequences: 0 
- five notes long sequences: 2 
- length of sequence with the same rhythmic placement: 

Thinking Out Loud vs God's Plan 
- three notes long sequences: 3 
- four notes long sequences: 3 
- eight (!) notes long sequences: 1 
- length of sequences with the same rhythmic placement: 3, 3, 2 and 2 

Average results: 
- three notes long sequences: 5,1 
- four notes long sequences: 2,3 
- five or more notes long sequences: 1,1 
- max length of sequences with the same rhythmic placement: 2,9 

Maximal results:
- three notes long sequences: 6
- four notes long sequences: 4
- five or more notes long sequences: 2
- max length of identic sequences of degrees: 8
- max length of sequences with the same rhythmic placement: 4
- max number of different sequences with the same rhythmic placement: 4


In more recent cases the plaintiff experts pointed out as evidences identic pitch sequences in different rhythmic placements, or melodic fragments of notes where the rhythmic placements are also identic. The defendant experts were claiming these were just commonplaces. The jurors were helpless to decide who is right unless the plaintiff expert is not forced to agree with the defending expert. Charts like this are badly needed for jurors to get a reference to obtain a more reasonable judgement. This result makes one conclude that a sequence of pitches without rhythmical similarity worths almost nothing. Wide leaps between the pitches may have certain evidental weight, but scalar sequences (around five notes) without rhythmical similarity are weightless. Up-hold-down similarities mean an even lower bar with even less proving strength. Out of nine comparisons we had an accidental matching of four consecutively identic notes (both pitch and placement), and a sequence of eight degrees without (strong) rhythmical similarity. These were not occuring in any complaint. If we would do the same test series for hundred songs we would find higher results. I skip estimating these this time.

Another point is the way how the mutually appering pitch sequences cover the big part of the other track. It looks very clear on the charts and surely could mislead lay people. It makes no sense to interpret this as a high ratio of one song copying the other song. Similarly as it makes no sense to consider the high ratio of weakly similar motifs covering the defendant song, and concluding that the complaining song is copyed for the same high ratio.
Note, that the amount of melodic content of the compared song affects the amount of melodic matchings found.

Type B test results.
Note that it usually a question of time to find a high-scoring songs, preferably a prior art one. It also depends on the skill of the experts. Below findings are mine except Runaway. This test remains an important point of argument for defendant parties.

Blurred Lines - You Can Leave Your Hat On : six consecutive melodic degrees with an octave shift in the middle that is a difference.
Got To Give It Up - Runaway: six consecutive notes found.
Thinking Out Loud - Forget You: 4-7 consecutive notes.
Let's get It On - the four note signature title phrase is a common fanfare motif.
Let's Get It On - It's Not Unusual: six note sequence (that's a lower bar).