Sunday, February 15, 2015

The Gamut, Reconsidered

For as long as I can remember, I have begun my scales with C major. When I practice Sevcik, I typically begin in C and add sharps and flats. I have a feeling that lots of people have been doing this for a long time.

The word Gamut, as defined by Merriam-Webster, comes from the Greek letter Gamma plus Ut, and seems to be the span between G and C. Perhaps if Merriam and Webster were musicians they would have considered other possibilities.

Their etymology doesn't make sense to me, considering the French word for scale is Gamme, and the use of "Ut" as the tonic pitch of a scale goes back at least to Guido D'Arezzo (11th century).

The three-language scale books I used to enjoy reading while I played through my scales during my teenage years prompted me to think that the obvious meaning of "Gamut" was a scale that went from Ut to Ut, whatever that "Ut" might be, since "Ut" is the tonic pitch in a "movable Do" system. When the fixed "Do" came about (sometime before the days of Machaut), "Do" became equal to "Ut."

Why am I thinking about this? Because I decided today to break the cycle (or circle) and begin my journey through the tonal musical spectrum with G, adding sharps, and then subtracting flats. In other words, I played my scales backwards. The beauty of this is that if you go up and down you don't have to read the music backwards (though you certainly can).

What can be gained from this? It forces me to pay more attention to intonation, and it adds variety to my days.


Anonymous said...

This is an interesting notion, which could bear expansion. Let's coin an adjective: key-centric. Various instruments have "home" or natural keys, better suited for beginners than others. The harp's lowest natural key is C flat, which crosses the eyes of a beginning piano student. But the fingering on the fewer strings within an octave of the harp than the twelve oddly spaced on a piano keyboard is just different. Fingerboards on guitars are more like fretted viola da gambas than modern strings, and the modern viola's lowest note is C, while it shares the other three strings with its neighboring violin which stands loftily apart thanks to that E string, of which you wrote in a previous blog entry. Mouthpieces and rim sizes dominate the brass players who are flat key sorts of folks, while cutting reeds is another kettle of fish. And each affects a perspective on keys. But those singers, who so blithely sing in all keys without the worries of others, darn it, what of them? The gamut is broader than one instrument's "nature." Thankfully I had a teacher teach a lesson that all keys were just different pictures of the same thing, and so I shift and clutch (pardon the auto metaphor) rather more easily than some of my colleagues who have remain staunchly key-centric. It's all rather odd, and amusing.

jonathanbrodie said...

Thank you to Anonymous for coining the term "key-centric." That is exactly what I try to help my beginning students not to be. On the contrary, I try to be for my students what Anonymous's teacher was, I suspect, for Anonymous. Five different finger patterns are introduced almost immediately so that the student thinks of them as being equally worthy and equally possible to play. On the A string these patterns are: ABCDE...ABC#DE...ABC#D#E....ABbCDE..ABbCDE
Once those patterns are cognitively in place it is easy to teach one octave scales in various keys. From there...a simple folk tune is taught in different keys.
This approach is inspired by the pedagogy of George Bornoff...a name rarely (and sadly ) not often mentioned in pedagogical discussions these days.

Anonymous said...

Might one add two more patterns? Given the alternation of whole and half steps as in the two octatonic scales? Though the scales' use in music is so often mixed with others, these two additional patterns, ABCDbEb and ABbCDbEb, add to the mix just a little spice, as some 20th century scores employ. Of course the specific pitches change when thinking of the "natural" keys of different instruments.

Elaine Fine said...

I'm afraid that I have to disagree with both Anonymous commenters and Jonathan Brodie! I do not have absolute pitch, but I do find sensational differences between keys when playing scales, especially scales that cover the entire compass of my instrument (whatever instrument that might be).

The instrument resonates differently in different keys. There is the physical sensation of half-steps and whole-steps in different places when playing a stringed instrument. Shifting distances are also different. Since stringed instruments use the natural scales rather than the tempered one (natural meaning that in some places penultimate pitches need to be higher, and other pitches find that they sound best a bit lower--it's all regulated by the ear), it is necessary to explore all the keys in order for the hand to know what to do when it finds itself in any number of sticky musical situations.

With modern wind instruments the schema of the holes in the bore dictates that alterations have to be made all the time in certain keys. With baroque instruments or instruments without keys, cross fingerings sometimes make it impossible to get from one note to the next in certain keys. That's why baroque music for winds is pretty much confined to a handful of keys. Brass instruments have the traditional option of using an instrument that gets all the notes, and transposing the music so that it sounds in the right key.

Fretted instruments are a whole 'nother ball of wax. The frets are fixed, and there is no way that the pitch can be altered. I once heard the Bach Chromatic Fantasie and Fugue played on guitar, and there were sections that were unbearably out of tune because the music was written for a tempered instrument.

Singers also have their resonance points (they build their instruments themselves) though many like keys with multiple flats. Some of the best choral music is written in keys with multiple flats. Singers are also married to their vocal ranges and testier, so sometimes something can sound totally different when it is moved up or down a step (or two, or half).

I don't believe that a person can develop perfect pitch, because from family experience I know that it is really pitch memory. My brothers and my mother could tell you that something is being played in the wrong key. They could tell you the original key and the key it has been transposed into. My father could tell you the original key, and instantly figure out the transposition. I could tell you that something sounded different, and would wonder if it was being played in a different key.

After all my years of making music, I would have to say that thinking about looking at different keys as different pictures of the same thing is kind of like looking at different people (with their different faces, body types, personality types, senses of humor, etc.) as looking at different pictures of the same thing.

Elaine Fine said...

. . . testier should have been tessitura! Dang auto-correct!

Anonymous said...

The comments have themselves run the "gamut." Would that other music blogs have such content as does this.

Of course, instruments have their individual resonances and players will note "sensational differences" between scales, keys and gestures, but much of formal fingering on various forms of fingerboards seems somewhat arbitrary and rooted in history. The piano (harpsichord, organ and more) system of two levels with the imbalances of white (grouped 2-1-2-1-1) and black (grouped 2-3) keys is arbitrary and fingering technique has developed to deal with the levels. Other developments such as the Jankó keyboard as but one example suggest that other fingerings would be necessary to adjust, as experimenters struggled to answer questions about fingering by redesigning the "interfaces." Which is correct? Perhaps a functional a question is, what is correct?

The notion of fingerings and patterns seems wholly related to an individual instrument's "user interface," to borrow a computer term. My wife, a very good pianist, tells me of pianists arguing over fingerings for scales, much less whole passages in the standard repertoire. I know in my own experience of discussions between string players as regards bowings and fingerings of orchestra passages. But as my wife observed, a great deal of conversation like this amounts to "you're wearing your shoes wrong." As one might imagine, in such things I happily defer to her. But when I play pop style piano at parties, she says she simply cannot look at my hands as technically I play something quite different in my odd fingering than her repertoire and education can fathom. While I might be doing it wrong and oh so wrong, it is also effective in its place and time. Show a classical pianist "Fingerbuster," and watch the reaction. My playing is neither, but still good for a round.

Some techniques are different than other techniques for the same instrument, but they are all a matter of patterns practiced repetitively to gain speed, agility and (the magic word) technique. Certainly I have sat around theater and summer festival cafeteria tables and enjoyed the round robin of arguments about which technique is "better." Some of these conversations became rather heated. Was it the summertime?

Keys as tonalities are different in fingering from one instrument to the next, and as such the seeming miseries of reading double sharps and double flats is also a learned thing, the lessons often taught early in a musician's training. But the technique of scordatura for strings is one example of changing tones by changing tunings, such that "tonality" and fingerings become far less identical. Modern developments of new tunings for avant-garde music suggest an even greater disjunction than did the early scordatura techniques.

There are great traditions behind much of technical mastery of various instruments, sometimes differences amounting to taste. Certainly patterns are music, as one looks at fingerboards, designs on printed music pages, and such. Hofstadter devotes a chapter in one of his books to the visually-seen patterns of Chopin pieces. So patterns are what fingerings are, and some are dealt with one way by a smaller hand than by a larger hand. There is no one answer, just better solutions and less effective solutions. I opt for the better, and also for the individual

I also align with the auto-correct error that some singers can be "testier." Perhaps this is why some have said there are musicians and then there are singers?

One small Google'd point. Here is a YouTube of the Bach Fantasy and Fugue rather well played and in tune. Beginning with

It's worth recalling that Jascha Heifetz observed, "If I don't practice one day, I know it; two days, the critics know it; three days, the public knows it."

Which patterns should one practice? It seems to come down to those that work for that individual and the gamut he has had to run.

jonathanbrodie said...

This is indeed a discussion rich enough to warm up a cold Wisconsin morning (currently -7 Fahrenheit windchill) It is a pleasure to be part of it. This response will be the first of several.

To answer Anon’s question: "Might one add two more patterns?"


We start with five because that seems to be enough information for 4th Graders in a large-group class to grapple with. Once those are well under the fingers, we add two more: A B C D# E# (kids love the challenge of extending that pesky 4th finger)…and the ever-popular A Bb C# D E. I confess to not introducing Anon’s sensible A B C Db Eb and A Bb C Db Eb...but we do come close towards the end of the year with this: A Bb B C C# D D# E D E #.

Over the years it has been gratifying to hear the more inquisitive students concoct (with Slonimsky-like vigor) their own finger patterns…some containing Db’s.

With my studio students, however, I do teach Anon’s Db patterns. There is a wonderful little fugue in volume two of the Doflein series in F# minor. The finger pattern warm-up for this piece contains that wonderful Db.

My hope is that these students will not only have the good fortune to someday play Haydn’s Farewell Symphony, but will remember back to their early days; to that little fugue and that quirky Db.

jonathanbrodie said...

Apologies! I must have too many finger patterns rolling around in my aging brain. The little C# minor fugue in the Doflien book calls for B#s and E#s ...not Dbs!
I can't blame this on auto-correct...only my advanced years.

Elaine Fine said...

We share you howling wind and wind chills here in Illinois, Jonathan. And between the swirling howls (of both the wind and my scales) I so appreciate the discussion here.

jonathanbrodie said...

Exciting discovery: Here is the original fugue that Doflein used in his method. The rascal moved the piece from B minor to F# minor in order to force his pedagogical charges to play E#s:

Thank you Professor Doflein!

jonathanbrodie said...

Here is an interesting finger-pattern experience to relate:

A few years ago my long-deceased university violin professor appeared to me in a dream. In this dream his task was to teach me, by rote, a captivating tune in the key of C# major. It was difficult to learn…there were many A# that he insisted that I sound on the D string with an extended 4th Finger. The many repetitions required of me to memorize the tune in the dream gave me an unusual advantage when I woke up, circa 3am. I was able to recall, in my awaked state, the specific notes of what I had just learned. Groggy, but determined, I was able to write down, the entire 16 measure piece. For some reason, perhaps because of my befuddled condition, I didn’t notate it on a staff. Instead I used pitch names like so: C# C# D# D# C# B A#…with dots and dashes to indicate long and short durations. When the entire piece had been faithfully recorded, I plucked through it and was pleased that I had successfully preserved a newly-composed piece of music. It would be fun, I reflected, to admire what I had created when I was more alert the next day. With groggy egotism, I congratulated myself for having created new music; no doubt a masterpiece.

The morning brought a harsh surprise. The tune was indeed wonderful, but it was not mine. It was a 17th century Bergamasca that I had been teaching my 5th Graders intensively for the past two weeks. Not in the key of C# major, but in the less esoteric key of D Major.

Certainly it was my half-awake state that prevented me from recognizing the tune in the middle of the night. But is it possible that If my teacher had taught me the music in D major instead of C# Major, the tune would have been instantly recognizable, If the dream had been a D major dream rather than a C# major dream, I would have been able to save him him time and effort. ; “Master…I already know this piece. You don’t need to teach it too me…."

What bearing does this dream incident have on the current discussion?
I haven’t quite figured that out, but I do know this: The physical struggle it took to play the dream-tune in the remote key of C# major was partly responsible for obscuring the melodic truth; the reality that I was playing the same music that I had played hundreds of times in the previous two weeks.

It was the same music. It just felt different.

Elaine Fine said...

It seems that this discussion has rattled some dust in your subconscious mind! I had a dream last night that the Beethoven Kreutzer Sonata had a development section repeat in the first movement, and that there was a first and second ending. I was relieved to wake up and find out that it didn't. The setting involved some kind of multi-generational meeting in Florida with my various grandparents (all deceased now, by the way) and my husband and children.

It was still in A major, though.