On Keys, Do Re Mi
by
Claudia Schaer
or, nq,
No Jdxr, Cn Qd Lh
ax Bkztchz Rbgzdq
or, nq,
No Jdxr, Cn Qd Lh
ax Bkztchz Rbgzdq
For
A = 440Hz, G# (at a just ratio of 15:16) = 412.5, and at an
equal-tempered ratio of 12√2
(
≈1.059463)
≈ 415.3
Current
standard “Historical Performance” pitch is A=415.
Therefore, A = G#.
???
... by this standard, poor Clara, most famously immortalized in Robert Schumann's music with her theme, C-B-A-G#-A – would become B-A#-G#-Fx-G# ...
(And, Happy Daylight Savings Time! Since the clocks move ahead ... Ibqqz Ebzmjhiu Tbwjoht Ujnf!)
... by this standard, poor Clara, most famously immortalized in Robert Schumann's music with her theme, C-B-A-G#-A – would become B-A#-G#-Fx-G# ...
(And, Happy Daylight Savings Time! Since the clocks move ahead ... Ibqqz Ebzmjhiu Tbwjoht Ujnf!)
Imagine,
if the word “Clara” were written in a really strange font, maybe
some kind of wingding, in which each letter looks like the following
letter in a more regular font, say Garamond. If you can read the new
font, you'll see “Clara,” but if you read it in Garamond, you
will read “Bkzqz.” My name would appear as “Bkztchz Rbgzdq.”
(Perhaps it's akin to “seeing” 3D stereograms: the physical
position of pigment on the page is one thing, and the way we make the
connections between them is another.)
With an ability to recognize exact frequencies – that is, having developed one's sense of “absolute pitch” (aka “perfect pitch”), one can hear the difference between 415 Hz and 440 Hz and tell you which is which and sing either at any given time. In my case, it is very strong: 440 sings “A” to me, and 415 “G#” (or “Ab,” depending on the context). I've been honing this skill subconsciously since age three, for which my family members deserve some credit: after my piano teacher figured out that I could recognize the pitches, they took delight in playing various piano keys to quiz me.
With an ability to recognize exact frequencies – that is, having developed one's sense of “absolute pitch” (aka “perfect pitch”), one can hear the difference between 415 Hz and 440 Hz and tell you which is which and sing either at any given time. In my case, it is very strong: 440 sings “A” to me, and 415 “G#” (or “Ab,” depending on the context). I've been honing this skill subconsciously since age three, for which my family members deserve some credit: after my piano teacher figured out that I could recognize the pitches, they took delight in playing various piano keys to quiz me.
Being
strongly steeped in one definition of A, suddenly renaming all of the
frequencies feels like a translation – like a geography exercise in
which each city takes the name of the one just eastward, so while the
proportionate distances between cities stay the same, the names
change: eg. Calgary becomes “Vancouver”, Saskatoon becomes
“Calgary”, Winnipeg becomes “Saskatoon” and so forth. For
those with a less developed absolute pitch and a greater sense of
relative pitch, the shift is an unproblematic one-step process
(rotate the globe a little, change the font a little, shift the Hz up
or down a little). For people like me, it becomes a complicated
two-step transposition: “Now named 'A', is the pitch formerly known
as 'G#'.”
How shall those of my ilk deal with wandering definitions of “A”?
After playing the Bach solo Sonatas and Partias countless times in concert on modern violin, I was enthralled the first time I played a little of them on a baroque violin, tuned to my normal A, at the Geigenbauschule in Brienz, Switzerland. The soft quick responsiveness of the instrument lent itself to delicate, nuanced, intimate expression, and invited quicker tempi (with less power necessary for tone generation) – which keeps the harmonic rhythm moving and is thus how I've always heard the works in my head. The experience influenced my recording of those complete works, on modern violin, at A = 439.
The “A” we choose to play Bach's solo violin works is somewhat arbitrary. Heinrich Hertz, after whom the Hertz (Hz) “cycles per second” unit of measurement is named, would be born more than two hundred years after Bach; during Bach's time, measuring pitch was an inexact and comparative business (just like measuring a units of length such as feet), and A's varied from valley to valley, along with the length of organ pipes expanding and contracting in heat and cold. There was no absolute way to measure how many times per second a membrane vibrates. (Here is an excellent video explaining this in more detail.)
The current trend standardizing A=415 for Baroque playing is only minimally based in history, but is practical in some ways: players performing with various ensembles know what to expect wherever they go, instruments can settle in at one pitch, and harpsichords and organs can be tuned at the agreed-upon frequency. In a pinch, a player can even take a modern instrument tuned at 440 and transpose down a half-step to get the same effect. (More info here.)
And so, when I decided to revisit my baroque-violin experience and interest in New York City just recently, it was no surprise that the baroque violin I picked up was tuned to A=415. I tried play some solo Bach. I have rarely felt so inept in my life – stupid, incompetent, frustrated, tangled up: I could hardly play half a measure without mistakes. I could play no more than two measures in a row.
Actually, I do remember when I last felt so gibberished: when I was ten years old, I played as part of the Calgary Fiddlers in the Calgary Stampede Parade. Our hay-wagon blasted our recently-released recording, we fiddled along with it. The stereo was playing the cassette tape (!) too quickly, and everything was a half-tone too high. All the other fiddlers re-tuned their violins up and played their normal fingerings, just fine. I was hopelessly lost, and embarrassed that the crowds lining the street were surely thinking that I, the youngest player there, couldn't really play.
(By contrast, I once had a dream of playing Paganini's first Caprice, the one with the arpeggiated ricochet bowing, with a butter knife instead a bow – and that was perfectly successful.)
Using sheet music, playing at A=415 is not so difficult for me – seeing the notes, I can transpose down a half a step quickly enough that, after a little practice, and writing in 0's for open-strings over pitches sounding to me as Eb's, for example, I can manage the task. But the Sonatas and Partias, which I can sing with letter-names in my sleep, became a laborious exercise. Yes, we have to agree on something to play in ensembles; playing violin solo, however, theoretically gives me the freedom to agree with no-one, so why bother with this difficult task? Well, it became a matter of pride to be able to – at least, for more than two measures - am I really hearing music so differently from everyone else that I cannot perform a task that is easy for almost everyone??
How shall those of my ilk deal with wandering definitions of “A”?
After playing the Bach solo Sonatas and Partias countless times in concert on modern violin, I was enthralled the first time I played a little of them on a baroque violin, tuned to my normal A, at the Geigenbauschule in Brienz, Switzerland. The soft quick responsiveness of the instrument lent itself to delicate, nuanced, intimate expression, and invited quicker tempi (with less power necessary for tone generation) – which keeps the harmonic rhythm moving and is thus how I've always heard the works in my head. The experience influenced my recording of those complete works, on modern violin, at A = 439.
The “A” we choose to play Bach's solo violin works is somewhat arbitrary. Heinrich Hertz, after whom the Hertz (Hz) “cycles per second” unit of measurement is named, would be born more than two hundred years after Bach; during Bach's time, measuring pitch was an inexact and comparative business (just like measuring a units of length such as feet), and A's varied from valley to valley, along with the length of organ pipes expanding and contracting in heat and cold. There was no absolute way to measure how many times per second a membrane vibrates. (Here is an excellent video explaining this in more detail.)
The current trend standardizing A=415 for Baroque playing is only minimally based in history, but is practical in some ways: players performing with various ensembles know what to expect wherever they go, instruments can settle in at one pitch, and harpsichords and organs can be tuned at the agreed-upon frequency. In a pinch, a player can even take a modern instrument tuned at 440 and transpose down a half-step to get the same effect. (More info here.)
And so, when I decided to revisit my baroque-violin experience and interest in New York City just recently, it was no surprise that the baroque violin I picked up was tuned to A=415. I tried play some solo Bach. I have rarely felt so inept in my life – stupid, incompetent, frustrated, tangled up: I could hardly play half a measure without mistakes. I could play no more than two measures in a row.
Actually, I do remember when I last felt so gibberished: when I was ten years old, I played as part of the Calgary Fiddlers in the Calgary Stampede Parade. Our hay-wagon blasted our recently-released recording, we fiddled along with it. The stereo was playing the cassette tape (!) too quickly, and everything was a half-tone too high. All the other fiddlers re-tuned their violins up and played their normal fingerings, just fine. I was hopelessly lost, and embarrassed that the crowds lining the street were surely thinking that I, the youngest player there, couldn't really play.
(By contrast, I once had a dream of playing Paganini's first Caprice, the one with the arpeggiated ricochet bowing, with a butter knife instead a bow – and that was perfectly successful.)
Using sheet music, playing at A=415 is not so difficult for me – seeing the notes, I can transpose down a half a step quickly enough that, after a little practice, and writing in 0's for open-strings over pitches sounding to me as Eb's, for example, I can manage the task. But the Sonatas and Partias, which I can sing with letter-names in my sleep, became a laborious exercise. Yes, we have to agree on something to play in ensembles; playing violin solo, however, theoretically gives me the freedom to agree with no-one, so why bother with this difficult task? Well, it became a matter of pride to be able to – at least, for more than two measures - am I really hearing music so differently from everyone else that I cannot perform a task that is easy for almost everyone??
In
Juilliard's ear training classes, we followed a solfège tradition of
singing music with fixed-Do syllables, which is the same as singing
with “A B C D” note-names, except in French. (I'll note that my
strong ear placed me into the third and fourth year courses my
freshman year.) We completed “memory projects”: conducing and
singing with fixed-Do syllables repertoire of our choosing,
essentially re-creating the score by memory in real-time. I still use
this system for any pieces I am learning and playing, especially
anything I memorize: I know that if I have the score clearly in my
head, along with the fingerings and bowings, and can think/feel it
through in real-time, I have great mental security to share it with
the violin in hand. I have no doubt that I would be able to sing all
of the Sonatas and Partias for you in my sleep, where I often
practiced them too!
In my personal theory of music, the meaning of the notes comes from the relationships between them, or the relative pitch (and rhythm). Thus, for example, the sequence of notes “A4-D4” takes its meaning in the form of a rising fourth. O-oh! Most musicians whose relative pitch is stronger than the perfect pitch, will hear the interval (the fourth), first, and then perhaps be able to pin-point it to being A-D. For me, it is the opposite, I hear the notes “A-D” first, and then recognize them as a rising fourth. Movable-Do solfège practices relative pitch, and putting syllables to the scale-degrees (numbers would work too): the tonic, or first note of the scale is called “Do”, the second note is “Re”, the third note is “Mi”, and so on. Movable-Do solfège is very useful, but gets very complicated for any music that modulates (changes key) frequently, or is not clearly in a key. Thus, singing the Sonatas and Partias in movable-Do would require pin-pointing exactly where modulations occur, which is not always unambiguous. Movable-Do also has limited use for corresponding to physically playing the violin, which standardly has G D A E strings regardless of what key one is playing in, and so fingerings do not transpose exactly from key to key. Nonetheless, for me, the feeling, emotion, meaning of a piece is expressed in connections - the motion in time between frequencies (which movable-do highlights) – a rising fourth expresses something, whereas the notes A-then-D are simply frequencies, facts.
In my personal theory of music, the meaning of the notes comes from the relationships between them, or the relative pitch (and rhythm). Thus, for example, the sequence of notes “A4-D4” takes its meaning in the form of a rising fourth. O-oh! Most musicians whose relative pitch is stronger than the perfect pitch, will hear the interval (the fourth), first, and then perhaps be able to pin-point it to being A-D. For me, it is the opposite, I hear the notes “A-D” first, and then recognize them as a rising fourth. Movable-Do solfège practices relative pitch, and putting syllables to the scale-degrees (numbers would work too): the tonic, or first note of the scale is called “Do”, the second note is “Re”, the third note is “Mi”, and so on. Movable-Do solfège is very useful, but gets very complicated for any music that modulates (changes key) frequently, or is not clearly in a key. Thus, singing the Sonatas and Partias in movable-Do would require pin-pointing exactly where modulations occur, which is not always unambiguous. Movable-Do also has limited use for corresponding to physically playing the violin, which standardly has G D A E strings regardless of what key one is playing in, and so fingerings do not transpose exactly from key to key. Nonetheless, for me, the feeling, emotion, meaning of a piece is expressed in connections - the motion in time between frequencies (which movable-do highlights) – a rising fourth expresses something, whereas the notes A-then-D are simply frequencies, facts.
This
brings me to the oft-posed question, “Are keys and tonalities,
imbued with particular characters, personalities, characteristics?”
(You can find countless essays on this online, and even wikipedia
weighs in.) How mysterious a subject - but is it really?
I would answer simply, “It's in the ear of the beholder.”
First-off, there are clearly several empiric factors to this question; three main categories are:
I would answer simply, “It's in the ear of the beholder.”
First-off, there are clearly several empiric factors to this question; three main categories are:
1)
Instruments and their tuning - violins resonate more on the notes the
strings are tuned to, normally G D A and E, and thus keys using those
notes more sound more “open” - or cheerful or upright or ... .
The same goes for wind and brass instruments, and the notes they are
tuned to.
2) Intonation of keys - prior to well-tempered tuning, some keys would sound in tune, and others would be rather more suspect.
3) Our experience with keys – on the violin, G+ D+ A+ are the easiest keys to play and the first ones we learn, and the ones all the fiddle tunes are in and all the easier pieces. On the piano, the same is true for C+; on the saxophone it's Bb+. The more difficult keys become, the more complicated we find them. Something that is written in G# minor on the violin better have good emotional reason to use so many sharps. Ab minor – too many flats, forget about it. And who would play a note as special and rare as Fb with an open (E) string ... (pardon my bitterness as I wrestle with A=415!)
2) Intonation of keys - prior to well-tempered tuning, some keys would sound in tune, and others would be rather more suspect.
3) Our experience with keys – on the violin, G+ D+ A+ are the easiest keys to play and the first ones we learn, and the ones all the fiddle tunes are in and all the easier pieces. On the piano, the same is true for C+; on the saxophone it's Bb+. The more difficult keys become, the more complicated we find them. Something that is written in G# minor on the violin better have good emotional reason to use so many sharps. Ab minor – too many flats, forget about it. And who would play a note as special and rare as Fb with an open (E) string ... (pardon my bitterness as I wrestle with A=415!)
To
put a wrench in the argument – or perhaps a pitchfork, or a tuning
fork, or a pitchpipe, into the mix- consider the following conundrum:
if I listen to a concert at A=415, and thus hear A minor as G# minor,
including with all the associations G# minor has for me rather than A
minor – who's to say which interpretation of the character of the
key is more “correct”? Recently, I heard a 415 concert with
pieces mostly in A D G (or G#, C# F# for me), but one piece in Eb
major, so D major for me. “Ah,” I felt, “At last, open, simple,
resonant, bright, cheerful.” Meanwhile, the performers were likely
experiencing, “Heroic, special, unconventional” and other Eb
associations.
Take the thought experiment a step (or half-a-step) further, and imagine the same piece played on a well-tempered harpsichord in A minor, then G# minor, at A=440, then in A minor at A=415. How would the 440 G# minor be different from the 415 A minor to any ear in the audience? Would the strongly-relative-pitch ear pick up on more sonorities and colours in the sound than the strongly-perfect-pitch ear, which might not hear a difference? Would those who know the piece enjoy the A-minor-ness one way or another, or be jarred by the G-sharp-minor-ness, if having a strong perfect-pitch ear?
And going even further - which colours would a synesthete (think Scriabin) with perfect pitch, see in either case? If A is, say orange, would orange be 415, or 440, or could it move??
I picked the A minor Solo Sonata to slog through, in what to me is clearly G# minor, with F# C# G#, and D# strings. I realized after a frustrating while that I was engaged in a complicated two-step process: 1) transposing the sonata to the new notes, 2) re-fingering the pitches. After about a week of wrestling with the A=415 violin, I could do it when playing with the music, but not so well in-my-head/by memory yet. As I repeated it often enough for mental and sonic associations to take hold, I gradually came to a better solution, which requires more brain gym but is a one-step process: I transpose the Sonata to the unheard-of key of A-flat minor, thinking the “A” loudly and the “flat” as a bend in the pitch. (When I sing with note-names, or solfège I leave off the flats and sharps anyway, and just think them in my head.) Thus my strings are Gb, Db, Ab, and Eb, and I am often playing F-flats and C-flats. Thus my fingering can correspond to my usual fingering, with special attention to open strings and first fingers. I intentionally equate the different resonance of the baroque violin with the extra “flat” in my pitch names, so that garamond and wingding can unite.
Take the thought experiment a step (or half-a-step) further, and imagine the same piece played on a well-tempered harpsichord in A minor, then G# minor, at A=440, then in A minor at A=415. How would the 440 G# minor be different from the 415 A minor to any ear in the audience? Would the strongly-relative-pitch ear pick up on more sonorities and colours in the sound than the strongly-perfect-pitch ear, which might not hear a difference? Would those who know the piece enjoy the A-minor-ness one way or another, or be jarred by the G-sharp-minor-ness, if having a strong perfect-pitch ear?
And going even further - which colours would a synesthete (think Scriabin) with perfect pitch, see in either case? If A is, say orange, would orange be 415, or 440, or could it move??
I picked the A minor Solo Sonata to slog through, in what to me is clearly G# minor, with F# C# G#, and D# strings. I realized after a frustrating while that I was engaged in a complicated two-step process: 1) transposing the sonata to the new notes, 2) re-fingering the pitches. After about a week of wrestling with the A=415 violin, I could do it when playing with the music, but not so well in-my-head/by memory yet. As I repeated it often enough for mental and sonic associations to take hold, I gradually came to a better solution, which requires more brain gym but is a one-step process: I transpose the Sonata to the unheard-of key of A-flat minor, thinking the “A” loudly and the “flat” as a bend in the pitch. (When I sing with note-names, or solfège I leave off the flats and sharps anyway, and just think them in my head.) Thus my strings are Gb, Db, Ab, and Eb, and I am often playing F-flats and C-flats. Thus my fingering can correspond to my usual fingering, with special attention to open strings and first fingers. I intentionally equate the different resonance of the baroque violin with the extra “flat” in my pitch names, so that garamond and wingding can unite.
Will
I ever be able to make it sound as natural (pun intended) as A minor
is?
After about three weeks, I've solved the problem to the satisfaction of my wounded pride, and can play through more or less three movements of the Sonata by heart at A=415. It is still much easier at A=440, and I think I'll go back to my old ways, and rather explore questions of sonority: is it possible to achieve a similar resonance in an A=440–tuned Baroque violin as in an A=415-tuned Baroque violin ... does this require string thickness and length adjustments? Perhaps that difference is minute enough not to be worthwhile. And perhaps that difference of 35Hz just doesn't even half-matter for non-ensemble pieces. And who's to say which pitch Bach would have picked, in the twenty-first century?
After about three weeks, I've solved the problem to the satisfaction of my wounded pride, and can play through more or less three movements of the Sonata by heart at A=415. It is still much easier at A=440, and I think I'll go back to my old ways, and rather explore questions of sonority: is it possible to achieve a similar resonance in an A=440–tuned Baroque violin as in an A=415-tuned Baroque violin ... does this require string thickness and length adjustments? Perhaps that difference is minute enough not to be worthwhile. And perhaps that difference of 35Hz just doesn't even half-matter for non-ensemble pieces. And who's to say which pitch Bach would have picked, in the twenty-first century?
Dear
readers, thank you for having half-a-heart – 1/2-Herz – and
letting my ears maintain their impressions, and characters too, with
the specialness of sharps and naturals and flats Claras and Bkzqzr.
In
my next dream, I plan to record a cassette at A = 415, and then play
it too fast, so that 415 goes to 440 ... then tell me the character
of the keys, please!
Until
next time - Ah!
Tmshk
mdws shld - Zg!
* (Although the pitch for romantic music is currently set closer to A = 425Hz, that is still low enough to sound like G#/Ab compared to 440).
