Trying to relate the concepts of pitch without the use of an instrument is sometimes difficult. In last week's lecture the topic of pitch was discussed. This week we apply the concept of "musical pitch" to the keyboard and guitar.
Soon it will become apparent that the keyboard was designed to implement the "7 letter name -12 tone system" in keyboard form. The names of the white keys are the musical alphabet letters A-G, in a repeating pattern. Once you know where "A" is located, you can find all of the other Keys. The white key to the immediate right of "A" is "B", the next white key is "C" and so on.
So, where is A? Well, strange as it may seem, our system is usually taught from a different perspective than letter "A". Usually music theory starts with the letter "C" and later when we study scales, we start with a C major scale. The keyboard is visually and tactually layed out in a repeating pattern. Look at the keyboard diagram, do you see the repeating pattern in the center portion of the keyboard? The pattern at both ends of the diagram is "chopped off" to coincide with the pitch range of the exercises used in this course. The diagram above is not as large as the standard 88 key layout of a grand piano but the repeating pattern is the same. The key "C" is an easily recognizable landmark on the keyboard. Notice the pattern of black keys that are intermixed with the white keys. Two black keys, three black keys, two black keys, three black keys etc. We will define the letter "C" as the white key to the immediate left of the group of TWO black keys. ALL of the keys to the immediate left of the group of two black keys are named "C". There are several "C" keys on a full size keyboard. By the way, the white key to the immediate left of the group of THREE black keys is named "F". Now that you know where "C" and "F" are, you can figure out where "A" is located, can't you?.
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At the risk of sounding redundant, let me say that each time the pattern (2 black keys, three blacks) repeats, you are moving up (or down) to a new octave. The keys within any single pattern use all of the letter names of the notation system. These names are repeated in each octave. In other words not only are there several octaves of "C"s there are several octaves of all of the letter names.
On a scientific level, when you jump up an octave the frequency of the note is doubled. We use a tuning standard of A-440, which means that the note A, above middle C should be tuned to vibrate at 440 vibrations per second (hertz). The next A, one octave up, is tuned to 880 hertz. The A one octave lower is tuned to 220 hertz. The 2:1 ratio of frequencies with regard to octaves is an important musical truth. We can then divide up a single octave into several smaller parts using that same division in each octave up and down the range of any instrument. This allows us to learn patterns in a single octave that can be repeated in each octave range.
Maybe you've figured it out already, but those black keys are the sharps and flats. Hmmm, but there are only 5 black keys in each octave. Last week we learned that each letter name can be sharped or flatted. It seems that there should be 7 black keys, one for each sharp or flat. The explanation goes back to last week's discussion about the fact that the distance between each of the letter names is NOT the same. Let me show you again in table form. This table represents all of the letter names in a single octave (one full pattern on the keyboard). In keeping with tradition, the letter names start on C.
| 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 |
| C | _ | D | _ | E | F | _ | G | _ | A | _ | B |
Notice that there is space between only 5 of the adjacent 7 letter names. This pattern is replicated on the keyboard. The letter names of the table equate to the white keys and the blanks equate to the black keys. Do you see the pattern? Of course the black keys have names.
Here is a table of all the notes names, similar to last week but this time starting on C. Can you find all of the letter names on the keyboard?
| 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 |
| C | C# | D | D# | E | F | F# | G | G# | A | A# | B |
| B# | Db | _ | Eb | Fb | E# | Gb | _ | Ab | _ | Bb | Cb |
This link is to a keyboard diagram that you can print out for reference.
This is a good question, I'm glad you asked. Unfortunately a good answer is beyond the scope of this course. Here's a short discussion on the topic. First I should assure you that this section (2.3) contains material that will NOT appear on any test so don't sweat it if you find it confusing.
Our 12 tone equal temperament system evolved over time. Since we don't have recordings of the music that was being made a century or two ago, we rely on surviving documents and historical accounts of the musical reality of the time. We do know that music notation DID NOT start with the 5 line staff system. First there was a single line and melodies had a limited range. Then another line was added to the notation system but still providing only a limited pitch range. These are the characteristics of early melodic chants used for church services. Over time another line was added then another and so on, eventually evolving into the 5 line system we use today.
The issue of the 12 tone equal temperament is a little different. It is related to physics and our desire to overcome some of the characteristics of the nature of sound.
A single musical tone is made up of many different pitches sounding simultaneously. You might not be aware of it but that is just the way it is. When you play a note on a piano, for instance an octave below middle C (C3), that note also has a little bit of the next octave C (C4 - middle C). Not only that, the original C3 has a little bit of the next G (G4) and a little of C5, E5, G5, Bb5 and more. This is not a hoax. It is simply the nature of vibrating strings and air chambers and other physical ways of creating sound. I'm talking about acoustic instruments here, synthesizers are a different animal. Back to the piano example, the various ratios of volumes of the additional sounds (called overtones) to the original (called the fundamental) will determine the tone quality of the piano. Of course the quality of materials and construction play a large part in the instrument's tone quality. But usually a piano is recognizable as a piano and not confused with a clarinet, right? This is primarily because of the overtone content. The ratios of the overtones in the sound of a clarinet is different from the ratios of the overtones in the sound of a piano.
What does this have to do with 12 tones per octave?
Nothing, it's just background material, here comes the real discussion of the 12 tone equal temperament. Notice, that most of the overtones are not the same letter name as the fundamental note. In the example above the fundamental is C and the overtones include the notes C, G, E, Bb ( and even more). Here was the problem before our 12 tone equal temperament system. When you tuned up the instrument so that the G key on the keyboard was "in-tune" with the overtone G (from the C fundamental) and the E Key was "in-tune" with overtone E (from the C fundamental) the key of C sounded great. So what is the problem? Well the problem occurred when you wanted to play in a different key. When you tuned the instrument for the key of C, the other keys sounded out-of-tune. If you wanted to play a piece in the key of A you had to tune up for the key of A instead of C. The bottom line is that the notes in one key were out-of-tune with the same letter named notes of a different key. Weird, huh? This is the result of a tuning system known as "pure" intonation. When using pure intonation, the choice was to either stay in a single key or retune for each different key. As composers started creating more complex compositions this tuning situation caused serious restrictions in the use of different tonalities within a single composition. As you shifted into a different tonality the music started sounding sour. In order to find a solution to this dilemma musicians started experimenting with new tuning systems that eventually lead to our 12 tone equal temperament system of tuning. In the equal temperament tuning system, most everything is slightly out-of-tune when compared to the overtone series (nature) but all keys sound sort of OK (to most people) and you don't have to retune for different keys.
That explains equal temperament, but what about 12 tones per Octave?
Well, some people say that dividing the octave into 12 parts will create the smallest interval that humans can recognize as a separate and distinct pitch. However in the late part of the last century a composer named Harry Patch was writing music that had 43 notes per octave!! He had to design and construct the instruments that were used to perform his music. Quite a task. Rumors are that Harry was a human ;-) So much for the "we can't hear more than 12 tones per octave" theory. As it turns out many musicians throughout history have used "quarter tones", the notes inbetween the half steps of the 12 tone system. The Harvard Dictionary of Music listing of "Microtones" cites several examples of using quarter tones some dating back centuries.
Additionally, some cultures have created music that uses only 5 notes per octave. Go figure.
So, it comes back to this: Why 12 notes per octave?
Gee, I don't know, ....why not? I suppose western music could have evolved differently, but it didn't. Sorry I took so much of your time with this tail chasing exercise.
In this class we will study the 12 tone system without any further questioning of the merits of the system. It's kind of like having faith in one's chosen religion, you may not have a complete understanding of "how and why", but you still believe none-the-less.
If you are interested in different viewpoints of music with regard to tuning systems, there is a considerable amount of information and many opinions on the subject. As a start you can look up the topics of "Intervals, calculation of", "Microtones" , and "Temperament" in the Harvard Dictionary of Music. There you can find a very technical and scientific discussion. It might even be interesting, no guarantees however. But as I stated at the beginning of this section, it is beyond the scope of this course.
Open MIDI file
Open mp3 file
Play file
[ C scale - uses the white keys only ]
[ Chromatic scale - uses all the white and black keys]
[ Whole tone scales - two different whole tone scales,
each note is a whole step away from the next note of the scale.]
[ II-V-I jazz pattern - this is a basic jazz pattern that outlines a common chord progression. ]
Open quicktime presentation of the above pitch contours
Each fret on the neck of the guitar is one half step in distance. The twelfth fret is one octave higher than the open string.
There are six strings on the guitar, numbered 1-6 counting from the highest sound string E. The letter names are shown below.
| 1 | 2 | 3 | 4 | 5 | 6 |
| E | B | G | D | A | E |
An important concept in this type of instrument (all string instruments) is the overlapping ranges of the different strings.
There are two or more versions of most of the pitches within the range of the guitar. As an example, consider the open first string, "E". That same note is found at the 5th fret of string two, the 9th fret of string three and the 14th fret of string four! These are not an octave higher or lower, all four "E"s are in the same octave, they are written at the same location on the staff (fourth space of the staff). These multiple versions of the same pitch create many interesting compositional possibilities that cannot be duplicated on a keyboard.
Shown below is one octave range on strings 1, 2, and 3. These strings are shown written as naturals and sharps. Each string has more range than an octave but even using this limited pitch range one can see the multiple versions of pitches available on the different strings. Notice that all three strings can play the notes of E5, F5, F#5, and G5. These are only some of the many possibilities.
string 1
string 2
string 3
To see the written range of each string along with guitar tablature, use the following links to the text.
Naturals and Sharps on the Guitar
Naturals and Flats on the Guitar
On a keyboard the sharps and flats are visually and tactually distinctive. It is fairly straight forward, with the trickiest part being the Fb, E#, Cb, B# letter names (all are white keys, seemingly of a different letter name!).
On the fretboard, visual and tactual characteristics for chromatics are not apparent. Each fret is one half step in distance and there is no distinguishing characteristic for sharps or flats. As an example, the sixth fret of string 1 is A#/Bb yet the sixth fret of string 2 is F. One fret higher at the seventh fret, string 1 is B yet the seventh fret of string 2 is F#/Gb. There is NO easy rule such as "all notes at the even numbered fret are chromatics" or whatever..., NO WAY, forget it. No black or white key to help you out. You just have to learn the names.
One of the essential differences between the keyboard and the fretboard is that a keyboard gives you one and only one choice of each note. You want to play middle C, there is ONE middle C on the keyboard. You want to play a C major scale starting on middle C? There is ONE place on the keyboard that you can play that scale. However, on the fretboard it is different. Since each string has a range that overlaps with the range of the adjacent strings, there are many possiblities for each note. It is common to have two, or more choices as to where on the fingerboard you will play a specific note or scale. The only exception being the extreme low or high range of the instrument.
The lack of black keys on the fretboard also illustrates another difference in the two instruments. It becomes apparent when you play music in a variety of keys. The keyboard fingering for a C major scale and a C# major scale would be quite different. However, there are several fingerings for C major on the guitar fretboard that you could simply move one fret higher and re-use for C#. The exact same fingering. Keyboard player are jealous. Do you hear them whining?
A guitarist is generally a little more into the maintenance of the instrument. Certainly more involved in maintaining the tuning and restringing of the instrument. Most pianists hire a professional tuner to tune their instrument. These pianists are connected to their instrument on an artistic level but not on a "nut and bolts" level. I guess an analogy might be the people who do their own car's oil change vs. the people who go to the local Jiffy Lube. I don't change my own oil but I do change my guitar strings, it's sometimes dangerous work.
A note to guitarists: We guitarists are the butt of some jokes. Unfortunately it is true that many guitarists don't learn to read music very well. I've even read articles about respected guitarists who say "Fortunately, I don't read well enough to hurt my playing any." What a load of CRAP! Remaining ignornant of this important language of music notation is an unnecessary limitation on one's musical horizons. If the following joke describes you accurately and you don't do anything about it... well, SHAME ON YOU!
Q. How do you make a guitar player be quiet?
A. Put some written music in front of him.
Years ago one of my favorite Jazz instructors said to a Jazz combo class, " Most guitarists only know three chords, The E chord, the A chord and the cord that plugs into their amp."
PPPsssstttttt---
Arrogant Sax player. But he sure could play (and read!). And unfortunately there was some truth to what he said. Let's prove him wrong.
I'm having problems with this section of this file. The last line should be the address of the page, but frequently the last few lines are not shown in the browser. I haven't been able to track down the problem, if you don't get the address to the quizzes for this week (there are two), PLEASE EMAIL ME, mikesult@guitarland.com
Here are the links to this week's reading from the text. Note that the chapter is spread out over two files. You can link to part two from part one using the 'next' link found in these files.
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