Does It Go Up or Does It Go Down?

This is one of the most obvious things in notated music: It's a piece of cake; you can see it right away.  So what difference can it possibly make?

Well, the ear seems to care a great deal about the difference between rising and falling.  So much so that for many years falling meant sadness and rising meant joy.  Then comes a tune like Joy to the World, which goes in altogether the wrong direction.  But that's Handel--announcing this great good news by turning acoustical logic upside down.

(Actually another example, far less meaningful, but still: London Bridge is Falling --- should be up! This was one of the examples from a wonderful children's book popular about 50 years ago called The Silly Book.)

When we hear a single tone without accompanying chord it is fairer to expect it to rise than to fall.  We take the tone to be a fundamental, especially if it is centrally placed within the vocal range, G for example.  This is why the opening G of Mozart's G Minor Piano Quartet is so deeply unsettling: It goes down to D rather than up, thus establishing D as a more secure tone.  Did Mozart know this?  How could he not?  The theme is identical to that of the early G major, actually minor piano and violin sonata except that in that piece the D is a 5th above not a 4th below the G.

Just because we know where the proper sounds are located on our instruments doesn't mean we have processed them in terms of their resonance within tonal space.

That Note Again

In 1999 I published What Might It Mean? An Uncommon Glossary of Musical Terms and Concepts for the Stuck, Bored, and Curious.  Now, 15 years later I find myself using it over and over again to solve problems of the sort that make me feel stuck, bored (I admit it!), and most definitely curious.  So I turn to the entry on Ratio Rhythm.

This is a concept I made up to describe what happens in Classical sonata allegro movements, in which the principal themes are defined by ratio rhythms of 4:1, usually with one theme being 4 eighths to the half note, the other 4 sixteenths to the quarter.

But in Op. 24 of Beethoven ("Spring" Sonata) we have a special case:  On the face of it there are clearly 4 eighths in the piano Right Hand to establish the proper ratio with the violin's half note.  But there are also the sixteenth notes that relate to NO quarter notes in the bar.  The value still unaccounted for is that pesky whole note in the piano Left Hand.  Aha!

There are two ratios moving simultaneously: 4:1 and 16:1 which is totally different from a bar with a staightforward 4/4 meter.  It must infer a subcurrent of sixteenths within the half note, otherwise why would the whole measure be under one bow stroke?

Could it be that this subcurrent is what turns into the trills that come before the Recapitulation?  But no one plays them that way.  They are always played like technical exercises, unk-a-chunk-a with accented quarter-note beats.

Paper Accepted for International Conference on Music Perception and Cognition

I got word today that my proposed presentation of my work of the past 50 years on the individual's awareness of subconscious responses to sound has been accepted by the International Conference on Music Perception and Cognition, to take place in Seoul, Korea in August.

I am, of course, honored at the prospect of presenting Tonal Refraction to such an esteemed gathering.  In order to get there I must raise the air fare within this week, as they need to know by March 18 that I am coming.

I ask your help in making this important step materialize.  You may give online or contact me for other options. All of my work has been undertaken independent of academic affiliation as it does not fit any existing categories.  This makes every aspect of this recognition all the more meaningful.

Please help it take place!  And thanks.  www.tonalrefraction.com

Awakened by a Note

Not just any note: This is the all-too-familiar yet totally baffling first note on the violin of Beethoven's "Spring" Sonata, Op. 24, subject of Vol. III of Tone Perception Visualized.  Why does it wake me up?

• It is too long
• It is difficult to tune
• It doesn't really go anywhere
• Yet it eventually becomes four closely connected As in unison with the piano
• Later to turn into trills, also in unison with the piano

No wonder it wakes me up.

Is there a possibility that Beethoven is telling me something I hadn't thought of before?  I had known that this sonata is about the difference between tones that are stable and tones that move, usually by sliding rather by articulated motion.  But this is a kind of tone motion I had not yet figured out.

Visualize What Exactly?

The more I think about it, the more convinced I become that the slur is the critical marking in music, but that different kinds of slurs mean different things.

For example, a slur over two notes indicates a slide from the first to the second, usually down, but not always.  The note value of the sound produced is the sum of the two slurred notes.  So a half-note slurred to a quarter becomes a dotted half-note, or a half-note that slides onto the quarter-note pitch.  Also, it is important to note that the release of that quarter note will not coincide precisely with the beginning of the following beat, as it is weak rather than emphatic.

The three-note slur may be an indication of an ornamental slide familiar from the Baroque period when a curved line before a note indicated such a lead-in to it.  These are not actually rises to the top note, though that note may be notated with a longer value than the two leading up to it.  Rather, it is a weak pulling away from the lowest tone, which must remain the most "real."

More problematic are the slurs over several notes, of which I can cite two problematic examples:

In the case of four or more notes of like value I check whether the last note is higher, lower, or the same as the first and feel that overall direction as the point of the slur.  Hardest by far is when the notes match and I must "move" without going anywhere.  (Schumann: Einsame Blume)

When there four or more notes of unlike value the problem is more difficult..  I have in mind the opening of Beethoven's "Spring" Sonata for Piano and Violin, which opens with a half-note slurred to eight sixteenths that seem to fall.  But how can a line convincingly fall from such a sustained value through so many quick values?  I maintain that it does not fall, but rather that it is wisped away, so to speak, at the end of the upbow, permitting the true counterpoint of the melody to assert itself.  In the sense of "like goes to like," then, the half-note A goes via the wisp to the half-note C and so on.  It makes sense when you think about it but only if you imagine playing the entire bar without counting to four.

Chopin and Beethoven

I am not the first person to notice close connections between these two giants of piano composition in the early 19th century, though that connection might be hard to discern in the overly self-indulgent virtuosity that seems de riguer in the hands of certain players.

Just looking over some of the Preludes while giving Beethoven some extremely detailed study reveals similarities I never noticed before: For example

1. A fascination with multi-level meters:  what look like repeated eighth-note chords actually going against the grain of the quarter- and half-notes they accompany
2. Figures that repeat odd numbered groupings within duple meters
3. The indication to play lento or sostenuto when "nothing" seems to be happening

The last one is by far the most revealing when it comes to measuring the distance between visual and auditory response.  As a student I was a fast reader at the expense of being a good listener.  An observant and wise teacher (Hans Neumann) caught me at it and knew how to change it, for which I will always be grateful.   It seems these two activities occupy the mind in opposite direction, the one ultra fast, the other even faster though on the surface ostensibly slower.

The trouble is that most of our education relies on quick responses to visual information, in fact everything in our multi-tasked environment suggests that this is the way to go.  But listening, though it seems at first to be passive, is actually attuning one's mind to the speed of vibration, than which nothing is faster.

The ear signal requires the ability to open the mind to peripheral vibration, the parts of the sound that cannot be written down, and the parts that vary from piano to piano and from room to room.

This is definitely the hard part.

Listening for Meaning

We encounter markings in printed music that are difficult to understand, ranging from notes that are marked as if to be played staccato but with a slur over them, to peculiar tempo indications, like rubato.  I don't recall where I found out that those slurred staccato notes indicate a very specific touch on the piano.

But yesterday I was overjoyed to find them in Beethoven's "Spring" Sonata, which I am exploring with Gregor Kitzis, violin.  Four repeated unisons, in both instruments, once marked crescendo, at other times with no crescendo indicated.  If played correctly there will be no pedal used, but rather a touch that permits the hammers to restrike the strings without the dampers reducing the vibrations in between hammer strokes.  The result is a very specific overtone ring that can be attained only in this fashion.

Gregor had to move so that he could savor the result and savor he did.

I think this is the reason why these sonatas are for piano and violin, not the other way around: their acoustical world is generated by the sympathetic vibration of the piano strings.