Thursday, February 26, 2015

Assigning numerical values

Despite setting a person record in walking yesterday evening (5.24km, 6.84 km/h, 435 calories), I didn't sleep very well last night. One might think that the exercise tires me out which would enable me to sleep better, but I believe that the fact that I walked so fast and that I didn't sleep well are connected to a third factor - my mind was working overtime. This helps when I'm walking as I can ignore certain physical aspects and so walk faster, but it doesn't help when I'm trying to relax.

Over the past few days, I have begun to receive questionnaires back from the company where the pilot study is taking place. These questionnaires are very useful as I can see a few problems which still have to be addressed. Aside from that, I have also been working on the program to store each recipient's answers in a form suitable for future analysis. Once I completed that task, I started on another task which I have purposely ignored until now: assigning numerical values to the various sections.

For some sections (e.g. age, department, gender), this is trivial. Similarly, for the sections which are built on Likert scales (I strongly disagree/I disagree/I neither agree nor disagree/I agree/I strongly agree), calculating a value is simple. The section on Priority and spreadsheet usage is critical but I think that I can manage this, by assigning weights to questions (that is, one question may be important that another so I assign it a higher weight). I have already changed the order of one question's options in order to improve the calculation and I may have to change the option order in other questions as well. Otherwise I will have to assign weights to the various options which seems (at the moment) like overkill.

There may or may not be a problem with the section on spreadsheet competency. My original conception was that six questions would be presented; each question has five options, of which one is correct, three are incorrect and one is "I don't know". The competency score would simply be the number of correct answers. Whilst this still stands, I wondered whether I should differentiate between supplying a wrong answer and admitting that one doesn't know. I tried finding some information about this via Google Scholar last night but got nowhere. I have asked my advisor about this point.

At the moment, I need to spend a few concentrated hours going over the questionnaire. Hopefully I will find that time on Saturday.

[SO: 3846; 3,15,36]

Saturday, February 21, 2015

Musicology and harmony

I happened to tune the television yesterday onto a discussion between someone who is probably a professor of music or composition, and Aviv Geffen, Israeli musician (and son of). The programme was billed as "analysing modern Israeli music from a classical viewpoint". I suspect that the programme had begun some time before I started to watch, but quickly they moved to a discussion of the harmonies behind the song "Ata po haser li". This was a song that was introduced to the world at approximately the same time as my son, 22 and a half years ago.

The professor was in turn praising and patronising; the discussion reminded me of a hypothetical discussion between a music professor and John Lennon (incidentally, one of Geffen's idols) which might have taken place fifty years ago. Lennon and McCartney were famous for inventing new chord progressions, sounds which seemingly had never been heard before but probably resulted no small amount from their composing on guitar (as opposed to piano). Lennon's laziness probably contributed as well, by preferring to move his fingers as little as possible.

The trouble started with the second chord of the song. Whilst the professor said that the progression from the first to the second chord sounded good, it would also get Geffen an F in any composition class. There are parallel fifths here, the professor declared, then contradicted himself by saying that Geffen had introduced a tritone. I'll explain in a moment.

Assuming that the song is in the key A minor (the version above is in Bb minor), the first chord is A minor - the three notes A, C and E. This is easily played on the piano - three white keys. The second chord is somewhat more interesting: move the hand one key to the right, staying on the white keys. The resulting notes should be B, D and F. This chord has various names, but for the time being, I'll call it B diminished. When the professor said that there were parallel fifths and a tritone, he meant that E is the fifth of A and that F (or more accurately, F#) is the fifth of B. But F is a diminished fifth, so there aren't really parallel fifths. The interval between B and F is indeed a tritone (three whole tones), once known as the devil's interval and banned from music until about the 18th century due to the dissonance that it introduces.

The third chord might be Am but it might be C - obtained by moving the fingers one more key to the right. The fourth chord is definitely Dm, again obtained by moving the fingers yet another key to the right. Viewed on the piano, what we have here is what can be called a chord stream: the bass moves in steps A-B-C-D, the inner voice moves C-D-E-F and the the top note E-F-G-A: all notes in the key of A minor, or from what was once called the Aeolian mode. Lennon would have loved this progression although I don't think that he ever used it.

This is definitely a lazy pianist's progression: It's hard to play this well on the guitar. Three note diminished chords don't really exist on the guitar; the form in which the second chord would normally be played has the second fret on the  fifth string (B), the third fret on the fourth string (F - the tritone), the second fret on the third string (A) and the third fret on the second string (D). The resulting chord (in root inversion) is BDFA, which can be called Bm7b5 or Dm6; the first name makes the bass movement clearer in the sequence (A-B) whereas the second name shows that the chord is a type of subdominant, like the fourth chord in the sequence (Dm). This chord is technically known as the half diminished seventh.

The second chord change which caught the professor's ear was the movement in the second line of the song: Am - Am6 - Gm - Gm7. Again, Am6 (A-C-E-F#) can be viewed as a half diminished seventh (F#m7b5). The move to Gm is a stroke of brilliance and really sounds strange, probably because of the Bb which is introduced. The fourth chord (Gm7) is really only colouration.

But the chord movement which really took the professor's breath away and amazed him was the beginning of the chorus. The first chord can be spelled as F-Ab-B-D and would thus be called F diminished seventh; this is the true fully diminished chord and there are only three of them as each interval is three semitones (so the bass note can either be F, F# or G; one more step brings one to G# or Ab, which is the same as the first chord). As the professor noted, this is a wonderful chord for introducing a modulation as there are several ways of resolving it. He suggested that Bach would probably have resolved the chord by moving the bass note down a semitone, thus playing the notes E-Ab/G# - B - D, aka E7, which is the dominant seventh chord in the key of A minor and which would naturally resolve in turn to A minor.

But Geffen makes a softer - and more exciting transition: he lowers the bottom two notes of the chord, thus playing E-G-B-D, aka E minor 7; again, this chord change sounds unusual. The resolution is still to A minor, but Em7-Am sounds weaker than E7-Am.

I doubt how many people watching the show would have known what the professor was talking about when he mentioned the diminished seventh (I only understood it properly when watching the show a second time). "Of course, the people at home know what I'm talking about", he declared pompously. But what really took my breath away for pretentiousness came a bit later when he started talking about the intervals E-F-G-A - again, I really only understood what he said when I rewatched the show again.

He mentioned that Geffen was using music from the 16th century then went on to mention (without real explanation) the Phrygian mode. I'm sure that Geffen - and the home audience - had no idea what he was talking about. Going back to my second paragraph, I am reminded of the famous (at least, to me) case of the Beatles' song "Not a second time" - as Ian Macdonald writes in "Revolution in the head" - Struck by the song's self-taught unorthodoxies, the classical critic of The Times drew attention to its author's use of Aeolian cadences. "To this day", Lennon admitted to Playboy in 1980, "I have no idea what they are. They sounded like exotic birds."

I don't know whether this Professor ever listens to modern music, but diminished chords are hardly news and no one cares about modes anymore. Never mind how unorthodox the harmony is (at least, in terms of classical music), the question is how it sounds to modern ears.  The Phrygian mode pops up all over the place, although strict adherence to the mode (for an entire song) is rare.

I know about this material but I don't understand its relevance (if there is any) to popular song. What matters is that the song sounds good; the minor 6th chords (or half diminished, if you prefer) in my ears is the saddest of all chords, and I'm always on the lookout for a good chord sequence: the transition from Fdim7 to Em7 is something from another plane of existence. I highly recommend this song.