Grantville Gazette - Volume XIII, page 23
part #13 of Grantville Gazette Series
It is common musical practice that for a given key, the sharps or flats for that key will be placed at the beginning of each line of music in the piece. It makes it easier to print and easier to read. Of course, the musician has to keep in mind what key he or she is in, or it starts to sound a little strange. Seriously, if you've played or sung for very long, it becomes second nature to you.
Everything said so far also applies to minor keys, except that the half-steps are in different places in the scale.
Harmony
Most Western European music is based on what's known as tertiary harmony. As you can tell by the name, it has something to do with thirds. To explain that, let's go back to the piano keyboard. We talked about octaves and steps. The musical term usually used to describe those is "interval." An interval is a measurement of distance between one tone and another.
So, let's start with middle C again. From middle C to the adjacent black key (which is called either C-sharp or D-flat, depending on what key we're in) is a half step, which is a minor second interval. Moving from low to high/left to right, from C to D is a whole step, which is a major second interval. From C to E is two whole steps, which is a major third interval. From C to F is two and one-half steps, which is a perfect fourth interval. From C to G is three and one-half steps, which is a perfect fifth interval. From C to A is four and one-half steps, which is a major sixth interval. From C to B is five and one-half steps, which is a major seventh interval. And from C to C is six steps, which is a perfect octave. You can continue past that point (ninth, tenth, etc.), but for our purposes we'll stay within the octave.
First question is probably why the octave, fifth and fourth are perfect, while the others are major or minor? The answer goes way back into early music history, to the time when the church was the sole repository of musical learning. Gregorian chant is monophonic—only one melody, everyone singing the same thing. For a long time the church wouldn't accept the concept of multiple lines of music. Finally, they accepted the concept of a second line, but they still insisted there could not be dissonance of any kind, so they sang the second line on the same notes, only an octave higher. And lo, they blessed it, and it was perfect.
So more time passed, and some musician wanted to make the music richer. He probably was listening to some of that low class street music, liked what he heard, and wanted to sneak it into the church music. The next interval that they allowed was the fifth. They didn't understand why it sounded good to them—the understanding of acoustics was pretty limited back then. They didn't realize that the fifth interval is one of the major harmonics of a tone, and that by singing at the fifth they were singing at one of the acoustically harmonious points. It just sounded good. And lo, they blessed it, and it was perfect.
Pretty soon someone realized that a fifth is just a fourth turned upside down (or vice-versa). From low C to G is three and one-half steps, but from that G to the higher C above it is only two and one-half steps, which is a fourth. And lo, they blessed it, and it was perfect.
It's psychology interacting with acoustics. It sounds good.
Yes, you can sharp or flat a fourth or fifth, but you don't call it major or minor. If you sharp it, it's augmented, if you flat it, it's diminished. I supposed technically you can augment or diminish an octave, but in six years of formal training in music theory I never heard it.
Back to harmony. The next interval inserted into the harmonic mix was the major third, but when you put a major third in the middle of a fifth—C-E-G, for example—you get a structure called a triad, which is the first real musical chord. From C to E is a major third, from E to G is a minor third—hence the tertiary harmony label that we mentioned at the beginning.
Most music that people enjoy listening to today is built on tertiary harmony—maybe with some added tones, but still recognizably built on thirds.
As you might imagine, there are quite a few rules on how to build chords, and which chords must precede or follow other chords, which is a level of detail we're not going to dive into for this discussion.
Last thing I will mention is to go back to the fifth interval. If I'm in the key of C, using the C scale as the foundation for my harmonies, the fifth tone of the scale is G. Musically, that is referred to as the dominant. It goes back to the psychology/acoustics thing again . . . it is the strongest harmonic to C, the root of the scale. It took on a special place in the minds of the early musicians, hence the dominant name. Likewise, a chord that is built on the fifth of the scale is referred to as the dominant chord in that key. In C, the dominant chord would be G-B-D, maybe with an added seventh or ninth.
Tempering/Temperament/Temperatur
Okay, this is going to be way simplified. For a more thorough but still reasonably brief discussion of the issues, see the Acoustics and Temperament articles in the Harvard Dictionary of Music.
This issue has to do with the physics of sound generation. In nature, there is no such thing as a pure tone. All natural tone generating objects, whether animate or inanimate, resonate when they generate tones. They generate complex wave-forms consisting of the primary tone and then the secondary harmonics or partials that are associated with it. The only way I know to get a pure naked tone without harmonics is to use a sine-wave generator, although modern tuning forks come close.
This generation of harmonics is not an issue as long as we are producing monophonic music. However, as soon as we move to polyphonic or homophonic music (more than one note sounding at the same time), we have a problem. (See the musical lexicon section.)
The human ear is capable of discerning some pretty subtle distinctions in tonality. When two different tones are generated, we instinctively want them to be consonant, to sound good, so we want the higher-pitched tone to match into one of the partials of the lower-pitched tone. The closer the match, the more consonant/less dissonant the harmony, the more "perfect" it becomes.
The problem is the proportion of tones one to another to produce "perfect" consonance is not consistent if you change the lower tone. If my lower tone is a C, to achieve perfect consonance with a G the pitch of the G will be slightly different than the pitch of a G will be if it is perfectly consonant with a lower D tone.
This isn't normally a problem for vocalists, obviously. They tend to adjust their sound to blend without even thinking about it. This is also true of good wind musicians. Players speak of "lipping" a tone, of shifting the "embouchure" (position of the mouth in relation to the mouthpiece) to make a subtle difference in the pitch. And of course standard string players can just slide a fingertip a hair one way or another to blend in.
However, for hammered or plucked instruments (bells, glockenspiel, piano, harpsichord, harp, etc.), this is not possible. This means that practically speaking, their "palette" of available tonalities would be limited to one base key with perfect tuning and at most three or four keys closely related to it. As you get farther away from the base key that the tuning of the instrument is perfect for, the less consonant/more dissonant its music would sound within itself. Needless to say, it's rather laborious to retune one of these instruments, if it's possible at all. And the thought of trying to adjust the tuning of a pipe organ can't even be seriously considered.
The limitations of this approach are pretty self-evident. Composers chafed at being limited to a handful of keys/tonalities.
A number of "temperament" systems were proposed over the years with different methods of adjusting pitch ratios and dropping certain keys from usage.
Eventually, however, the system that won out is the "Equal Temperament" system. It had been proposed in one form or another as far back as the early 1500s, but it didn't gain dominant status until about 1800 in Germany and about 1850 in France and Britain. In this system, the only truly perfect interval is the octave—A to A, B to B, etc. Between the two tones of an octave, the frequency spectrum is divided into twelve equal semitones (a/k/a half steps), each of which corresponds to one of the white and black keys of a piano in that octave.
The net result is that the non-octave intervals in equal temperament are never "perfect," but many of them are so close it's hard for even the human ear to detect the difference. The big thing is that all keys/tonalities are just a little bit off, instead of some of them being nearly perfect and some of them being rather dissonant. This opened up the full musical palette for composers, which made for the richness of the classical and romantic periods of music.
This was a very serious subject in musical circles of the 16xx era. Lots of debate (i.e., impassioned arguments) occurred over this.
Of course, even today, you will sometimes hear wind instrumentalists muttering that equal temperament is a folly, and we should go back to the true Pythagorean/just tunings. J
Pitch and tuning
Standard international pitch today is a' (the a above middle c) = 440 Hz. This was established in 1939 by an international conference under the sponsorship of the International Standards Association. (Precursor to ISO?)
Prior to that, the standard was a'=435 Hz, established by the Paris Academy in 1859 and ratified by a conference in Vienna in 1885.
Prior to that, there was no international standard. It was whatever the local musicians decided. Most probably, it was whatever the local pipe organ had been tuned to, as that would be the instrument that would be hardest to re-tune. It was not unknown for composers to have to transpose works if they took them to a different locale because the tuning in their new location was significantly off compared to their old location.
Historical evidence is that in the early 1700s, the closest thing to a standard was b' = to something around 422 Hz. 16xx probably was not too different. This means that the a' would probably have been around 370 Hz. This is a difference on the order of a full step. The down-time a' would be around the up-time g', maybe even lower.
Net effect = down-time musicians playing up-time music with local tuning values would generate music that was actually lower in pitch than the up-time performance of the same piece. This actually gives a break to sopranos, tenors, trumpeters, and anyone else who was performing in their personal upper register. A difference of a step is a huge difference. It would also explain why composers would sometimes produce copies of the same work in multiple keys, as the local organ might have a different pitch than the organ in the last place he was at, so to get the sound he wanted he'd have to change to a different key.
Why was the international move to raise the pitch? One suggestion is that they wanted a brighter sound.
What Does All This Mean?
Okay, we've talked about all this to get to this point: the music from the future is going to sound very different to 1632 ears. This is the part that is hardest for our generation to understand. I'm actually going to quote some words I wrote for one of my characters, Marla Linder, in the story "Suite for Four Hands," which was published in Grantville Gazette, volume 5. I can't think of a better way to describe what's what.
" There has always been a difference between the music done for art's sake, and the music done to please the common man. You know that's true. The music you create for patrons, and I include the church in that category, is different from the music you create on street corners and in taverns. It may be related—you know as well as I do that melodies from the street and the taverns have a way of sneaking into even the music written for the churches—but there is a definite difference in complexity between the two. The more complex the music grows, the smaller it seems the audience is who can truly appreciate it.
"As I said, this has pretty much always been the case, but until the early 1900s the music of the streets was more of an undercurrent in the stream of music. That changed with the invention of mechanical devices that could record music played in one place onto some kind of medium, such as wax or types of plastic—" They all nodded at the reference to the magic stuff that was so prevalent in Grantville. "—or even the CDs.
"What happened was once the average citizen could own a device that would play whatever music he wanted whenever he wanted it, he began buying the music he liked. That changed the way music was created and performed. By the 1970s, it was becoming difficult for many orchestras to exist, partly because people were buying different music than what the orchestras played, and partly because even the music the orchestras did play could be recorded, bought and played any time.
"The popular music, the outgrowth of the music of the streets, took many forms. Most people would like a few types. Very few people liked them all. But in almost every case, the popular musicians became like heroes, and it became a status symbol to people to have a lot of these recordings. The more you had, especially of rare or new or avant-garde musicians, the more status you had among your friends. By the time I was in high school, a ridiculously large amount of money was being spent every year by people all across our nation to purchase these recordings.
"The styles of music diverged for a while, but inevitably they began influencing each other again, both between different types of popular music and between the popular music and the art music."
Another conversational quote from the same source.
After they regained their composure, Friedrich said, "How can so many different styles have developed so quickly? Our music develops slowly, changes slowly. Why did theirs change so rapidly?"
"We've already talked about the access to mechanical and electrical systems to play music," Marla said as she walked back into the room. "Another factor, though, is the changes in the place and authority of the church in society. For most of its existence, the church has been a conservative institution. That can be a good thing, at times. However, it can also be a drawback, for conservative organizations tend to be very slow to change. Ultraconservative organizations actively resist change. Hence the boiling pot of Europe that Luther and Calvin have lit a fire under."
She moved to the stereo, and continued speaking while she searched for a CD. "One of the areas where the church exerted its control was in the arts. Musical forms changed very slowly over the years. But as a result of the changes that occurred beginning with Luther, the influence of the church—whether Roman, Lutheran or Reformed—over music began to ebb, and musical evolutions began to cycle faster. By the 1800s, musical generations were occurring on a level with human generations. By my lifetime, musical generations were occurring every five to ten years."
There you see the evolution of modern music described in a nutshell. Now to talk about what the down-timers would hear.
There are three factors that define what sounds "good" to people: using notes that fall within the harmonic series of the previous note, using notes that fit within the harmonic series of the chord in place at that moment of the music, or using notes and intervals that are acceptable within the cultural experience of the people. The first two do have some grounding in acoustics. The last is purely a factor of what the people have learned to be acceptable, and please do not underestimate it.
Singable melody carries with it implied harmony, created by the intervals between the notes of the melody line. Even if all you ever heard sung was the melody line, if you can hear the melody well enough to pitch-match and sing along with it, you gain a feeling for the key the song is in. It's an unconscious thing—most people don't even realize that it's happening. And in the street music of the 1632 era, changes of key during a song just weren't common, whether sung, played on a pennywhistle or played on a bagpipe. I won't say they didn't occur, but they weren't common.
As an example of something that would really affect the down-timers, let's look at the old standby, "Do, a Deer," from The Sound of Music. Even performed with only the melody, I think that song would drive most of the down-timers nuts. It seems so simple to us, but we grew up with it in the twentieth century. If you really listen to the melody, though, that song seems to shift keys about five or six times in the verse and chorus, and then it starts over and does it again. You don't have to be a trained musician to hear that, and it would just sound "weird" to them.
