Join GRAMMY® Nominated Music Educator Mike Overly as he presents how to play a two-octave scale on a 4 string bass by applying the Z Angle connector.
Join GRAMMY® Nominated Music Educator Mike Overly as he presents how to play a two-octave scale on a 4 string bass by applying the Z Angle connector.
These five tone numbers are then converted to their 1st octave tone numbers: 1, 3, 5. Tone number 8 of the second octave is also included. Then, these four tone numbers are added to harmony numerals which creates four intervals: Unison, Octave, Perfect 5th and Major 3rd. An interval is harmony of two sounds.
Finally, these intervals are illustrated on the guitar fretboard. However, it should be noted that these intervals have the same pattern on a 4, 5 or 6 string bass.
Guitar is a transposing instrument. It sounds one octave lower than it is written in staff notation. In other words, staff music for guitar is written in the Treble Clef, however, the majority of the guitar sounds in the Bass Clef.
Let’s begin with the first staff note shown in every book 1 guitar method: string 1, fret zero/open, E.
Now, this doesn’t pose a problem unless you’re playing with another treble clef instrument for example, the piano. This is because when the guitar and the piano read and play the same staff note, two different sounds are heard. Remember, the guitar sounds one octave lower than the staff note that is written. This is why guitar staff notation should have an 8 beneath the treble clef. This tell the player to play the staff note one octave lower than written. However, you won’t see it used in guitar method books.
Here’s another common book 1 example: string 2, fret 1, C. Notice that this example uses ledger lines. Ledger lines enable pitches to be written that extend lower, and higher, than the 5 lines of the staff. It should be noted that this is the first staff note presented in the Tone Note™ Music Method for Guitar Book 2.
When the treble clef begins to use ledger lines below the staff, the bass clef becomes useful.
This next example shows how guitar notation writes a treble clef C, how it actually sounds in the treble clef, and how the actual sound is written in the bass clef.
Book 1 guitar methods only teach three open position treble clef staff notes on string 2, B C D. The following example shows how guitar notation writes B C D in the treble clef, how it actually sounds in the treble clef, and how the actual sounds are written in the bass clef.
This next example illustrates the complete range of open position treble clef staff notes that are presented in every book 1 guitar method. Pitch letters and circled string numbers have been added. Now, you can clearly see that the majority of the guitar’s pitches actually sound in the bass clef.
There is only one book that I know of that presents the actual pitches of the guitar in true staff notation: the Johnny Smith Approach to Guitar, published in 1971 by Mel Bay MB93669. Here is a Schoenberg example Johnny included in his book to illustrate that others have acknowledged and used this actual pitch guitar staff notation.
In Johnny’s book, he writes guitar music using two braced treble and bass staves that look like like piano staff music. Here is what a C major chord looks like in actual pitch treble and bass staff notation.
Again, you can again easily see that the vast majority of the guitar actually sounds in the bass clef. And this is why the Guitar Clef ® is not only clever and trademarked ~ it’s true!
’til next time, have some guitar playing fun no matter what clef you use… I’ll be listening!
Ol’ Skool images hand written, cut, taped and scanned by MO. ;~)
Simply stated, the fundamental is the lowest and loudest frequency of a single string vibrating as a whole. It is the pitch by which we identify the letter name of the root, which is also known as the tone 1 scale degree. In Physics, a node is the exact point on a vibrating string where there is no vibration and therefore no sound! On the bass, the nut and the bridge are nodes.
Ratio is the relationship between the length of one whole string to the number of equal parts that it can be divided into. For example, a one-to-two ratio (1:2 ratio) means that one whole string has been divided into two equal parts. Now, if we consider the fundamental to be one string vibrating as one part, that would be a one-to-one relationship or a 1:1 ratio. This 1:1 ratio is also known as a unison interval. For this lesson, our fundamental reference frequency will be E, tone 1 at the nut and bridge of string 4.
Harmonics, also called overtones or partials, are higher frequencies produced by the vibrations of a string divided into any number of equal parts. Harmonics occur because strings not only vibrate as a whole, but they also vibrate in parts or fractions such as halves, thirds, fourths, fifths and so on. Now, whenever a fundamental is sounded, on any instrument whether it is sung, plucked, struck, blown or bowed, there is an entire harmonic series of frequencies that naturally vibrate with it at the same time. This harmonic series is a specific order of frequencies that climb like a ladder through a predictable series of intervals. And each harmonic step of the ladder is a precise multiple of the fundamental frequency.
Notice that tone 8, the 1st harmonic, is a 1:2 ratio that is produced by dividing the string into two equal parts directly over the 12th fret node. The node is the exact point that divides the string into equal parts. This forces the string to vibrate twice as fast as the tone 1 fundamental and to sound one octave higher in pitch, tone 8. Also notice that the same harmonic may be sounded on each side of the 12th fret: the nut side or the bridge side. For example: tone 15, the 3rd harmonic, may be sounded directly over both fret 5 and fret 24 because both frets are the same distance from the 12th fret! Also, notice that some of the harmonics occur directly above frets while other harmonics are in-between the frets or fractions such as 1/4. The reason for this has to do with just temperament, mean temperament and equal temperament, but that’s another lesson.
To produce a loud and clear harmonic on your bass, touch the string very lightly at the node. Do not push the string down toward the fret. Strike the string near the bridge with force. The string will then vibrate in smaller equal parts and this will produce the sound of the harmonic. New strings and perfect intonation, an adjustment at the bridge which assures that fret 12 is at the exact middle of the string, will also help. Be sure to quickly lift your finger off the string after sounding the harmonic, so that you don’t dampen the vibrating string.
Tone 12, which is tone 5 in the second octave, is the 2nd harmonic and has a 2:3 ratio that is produced by dividing the string into three equal parts directly above the fret 7 node. Fret 7 is 1/3 of the strings length. Since it is impossible for a string to vibrate in two unequal parts, the remaining 2/3’s of the string divides itself in half which produces three equal string lengths or parts!
As long as you continue to divide the string into smaller and smaller equal parts, an ever higher and higher series of harmonics will be produced. The sounds of which will be limited only by your strings, hearing and technique. Some harmonics are easy to play, others take more practice.
The important idea to take away from all this, is that the individual timbre (tam-burr) or tone quality of your bass results from the presents or absence of particular harmonics and their relative volumes. It is this balance between the fundamental and its harmonics that makes one bass sound different from another, even when the fundamental pitch they play is the same. In other words, no two basses, no matter how similar, have the same blend of harmonics or the same tone. Each bass is unique!
To learn more about the Bass, please visit: http://www.12tonemusic.com/bass/facts/
Image © C.Chris Peters 2010
Wouldn’t you like to be let in on something that other guitar players don’t know? Imagine what you would be able to do with this hidden information. Well, here are three little known, and rarely understood, secret fretboard angles that will change the way you view your guitar fretboard. Does the following look familiar to you? It should, it’s your fretboard!
Simply stated, X is the horizontal strings, Y is the vertical frets, including the nut and bridge, and Z is the diagonal octaves. This simple fretboard geometry is the key which unlocks your ability to instantly locate any letter on your fretboard. Let’s reveal the first secret angle, the horizontal strings with their letter names:
Next, let’s define the string’s length by revealing the second secret angle, the vertical nut and bridge:
The distance between two pitches, whether letters or tone numbers, is called an interval. The smallest interval is the half step, which on the guitar fretboard is one fret. Here’s a very old discovery made by Pythagoras, 6th Century BCE: when a string is divided in half, the frequency is doubled, and the octave is created. The interval of an octave is 12 half steps or 12 frets. Therefore, fret 12 divides the string in half and creates the 1st octave. Then, 12 frets higher, fret 24, the string is divided again and the 2nd octave is the result as follows:
We can now reveal the third secret angle, the diagonal octave. This simple angle enables us to locate any letter, on any string, faster than we every thought possible. Here are all the E’s within 12 frets connected by the diagonal octave angle:
Remember, although all the letters are the same, they are not all in the same octave, but that’s another lesson. So, let’s end this lesson by showing the 7 letters of music, A B C D E F G on 12 frets:
’til next time, have some fun connecting the diagonal octaves of all 7 letters because it’s a secret no more . . . I’ll be listening!
Music, whether it is seen or heard, has three fundamental parts: rhythm, pitch and dynamics. Each of these parts may be studied in great detail, but for this lesson, let’s simply define them as follows: rhythm is time, pitch is a sound that has a letter name, and dynamics is the degree of sound volume from quiet to loud. That all sounds simple enough, but what is sound?
Non-musical sound has but one name, noise. However, musical sound has many names. Here are a few: letter, tone number, harmony numeral, scale degree, timbre, pitch, octave, harmonics, vibration and frequency.
Let’s look at frequency more closely. The music we hear, in contrast to the silent music symbols we read, is the sound of air moving. This then begs the question, what is moving the air? On the guitar, it’s the strings that move the air. When you pick or pluck a guitar string it oscillates back and forth. It is these back and forth string motions, or vibrations, that are moving the air. These vibrations may be counted and then assigned a frequency number. We’ll skip over all the deep physics and acoustics data, like resonating bodies, air-pressure and amplitude, and instead, we’ll focus on frequency so that you may tune your guitar.
The speed of a string vibrating back and forth is steady, regular and predictable in time. The number of times a string oscillates in one second is called frequency. Frequency is measured as cycles per second (cps) which is also known as Hertz (Hz), named after the 19th century German physicist Heinrich Hertz. The frequency range of the human ear is approximately 20 Hz to 20,000 Hz. This may be written as 20 Hz to 20 kHz. Kilo (k) is the Greek prefix for thousand, 1 kHz = 1000 Hz. The question then becomes, how many times does a string move back and forth in one second? The answer to that question depends upon which string and fret is being played.
Any string played at any fret vibrates faster than the human eye can see and count. So, science has to count for us ~ think electronic tuner. Not only are the vibrations counted and given a frequency number, but they may also be assigned a letter, scale degree tone number, and a note location on the staff. For example, string 5 at fret zero vibrates 110 times a second (110 Hz) and is called A (A). On the guitar, Fret Zero is also known as the nut or open.
An octave is created by doubling the frequency. Therefore, string 3 fret two, which vibrates at 220 times a second (220 Hz), is one octave higher than string 5 fret zero, and is called prime A (1A). String 1 fret five vibrates 440 times a second (440 Hz), is two octaves higher than string 5 fret zero, and is called squared A (2A). Remember, faster frequencies sound higher in pitch, while slower frequencies sound lower in pitch ~ think treble and bass.
It helps if we consider pitch as being Absolute, Perfect or Relative.
Absolute Pitch is an external reference to a definite pitch of a specific frequency upon which everyone agrees. Absolute Pitch may be assigned a letter, scale degree tone number, harmony numeral, or staff note. Here are a few good sources of Absolute Pitch: a tuning fork, an electronic tuner, and a “tune-up pitch” from a play-along CD. Remember, audio tapes are not a good source of Absolute Pitch due to the varying playback speeds of different tape players. Here’s something interesting. The International Agreement, which made A = 440 Hz the Absolute Reference Pitch for the entire world, wasn’t agreed upon until 1939!
Perfect Pitch is the ability of a person to identify a given musical pitch without the benefit of an external Absolute Pitch reference. Those who have Perfect Pitch exhibit some or all of the following capabilities: identify individual pitches by name when played on various instruments; name the key letter of a given piece of tonal music just by listening without reference to an external Absolute Pitch; identify and name all the tones of a given chord or tone cluster; accurately sing any given pitch without an external Absolute Pitch reference; and name the pitches of common everyday sounds such as the honk of a car horn, the ring of a telephone, the chime of a doorbell, or the hum of a refrigerator. Many believe that you must be born with Perfect Pitch because it seems as though it can’t be learned. In contrast to Perfect Pitch, Relative Pitch can be learned.
Relative Pitch, as the name implies, relates to Absolute Pitch and is what is meant when someone says they “play by ear.” In other words, Relative Pitch is the ability to hear an Absolute Pitch, store it in auditory memory, and then match that pitch or relate it to another pitch. In music school they call this ear training. And while it’s true that Relative Pitch can be learned, it sure takes a lot of practice! However, the benefit of Relative Pitch is that it makes tuning your guitar so much easier and faster. The Relative Pitch method of tuning your guitar by matching or duplicating pitches is known as Unison Tuning.
Uni means one and sonus means sound, so, unison means one sound. Said a different way, in Latin uni means one and in Greek iso also means one, therefore, uni + iso(n) = unison. In other words, unison means more than one as one. No matter how we define it, unison is really a coincidence, that is, multiple events occurring at the same time. The prefix “co” means together (two or more as one), and an “incident” is an event. With this said, unison may be further defined to mean: two tones of the same pitch sounding at the same time. One of the greatest things about the guitar is that by playing the same pitch, on two or more different strings of the same guitar at the same time, unison is possible. On the piano, woodwinds, brass and voice, unison is impossible!
Okay, now that we have an elementary understanding of the science of sound, let’s apply it to the tuning of the guitar. We’ll begin by giving each of the six strings of the guitar a letter name and frequency number: string 6 E = 82.41 Hz, string 5 A = 110 Hz, string 4 D = 146.83 Hz, string 3 G = 196 Hz, string 2 B = 246.94 Hz and string 1 E = 329.62 Hz. What follows is the method of Unison Tuning that will enable you to tune your guitar by ear!
From an Absolute Pitch source, determine the reference pitch. For example, if you want to tune string 6, you’ll need to hear the Absolute Pitch of E = 82.41 Hz. Here’s something important. Be sure to use a tuning fork, or some other source of Absolute Pitch and not a piano, as the piano may not be in tune! Think of it this way, why would you tune a tunable instrument to another instrument that needs to be tuned?
Next, assuming that string 6 is in tune, play A = 110 Hz on string 6 fret five. This reference pitch should match string 5 fret zero. If string 5 fret zero, sounds the same as string 6 fret five, they’re in unison and your guitar is in tune. If they don’t match and sound the same, you’ll need to adjust string 5 higher or lower in pitch until they do. Be patient, this is Unison Tuning ~ and the more you practice it, the better you’ll get!
After string 5 is in tune, play D = 146.83 Hz on string 5 fret five. This should sound the same as string 4 fret zero. Again, if it doesn’t, you’ll need to adjust string 4 higher or lower to match the string 5 reference pitch.
After string 4 is in tune, play G = 196 Hz on string 4 fret five. This should sound the same as string 3 fret zero.
Now, once string 3 is in tune, in order to play B = 246.94 Hz on string 3 you must play fret four. This should sound the same as string 2 fret zero. Remember, the B = 246.94 Hz reference pitch on string 3 is located on fret four. This is a different fret than any of the other strings.
Finally, after string 2 is in tune, play E = 329.62 Hz on string 2 fret five. This should match and be in unison with string 1 fret zero.
Congratulations! Your guitar sounds so much better now that it’s in tune.
’til next time, keep playing and have fun… I’ll be listening!
There are many systems used to notate harmony, whether that harmony is an interval, an arpeggio, or a chord. For example, orchestral music uses staff notation, harmonic analysis uses Roman numerals, and the Baroque era used figured bass. However, the most popular harmony symbol used in today’s music is the macro symbol, more simply known as a “chord symbol.”
Simply stated, a harmony symbol consists of two parts: the Letter of the harmony and the Type. And although these symbols are seldom used in classical music, they are universally used to specify the harmony of popular music as found in fake books, lead sheets and chord charts. Therefore, a clear and simple understanding of harmony symbolization is essential.
A quick internet search of harmony symbol notation will present you with an overwhelming amount of confusing, incomplete and, dare I say it, wrong information. So, let’s clean the slate, start at the beginning and discover that harmony notation isn’t overwhelming or confusing at all.
For the examples used in this lesson, we will use the C major scale. Let’s begin by presenting the C major scale as seven letters and seven tone numbers, also known as scale degrees. In the first octave they are 1 C, 2 D, 3 E, 4 F, 5 G, 6 A, 7 B. In the second octave they become 8 C, 9 D, 10 E, 11 F, 12 G, 13 A, 14 B. Now, the first thing we need to realize about harmony is that harmony begins with one sound! To many this just doesn’t seem correct, but it is.
Think of it this way. If we were to begin with a complex harmony symbol, say C major 13, which contains the letters and tones 1 C, 3 E, 5 G, 7 B, 9 D, 11 F, 13 A, we would probably quit because as a beginner, that’s a frightening chord! However, if we were to “reduce” this complex harmony by deleting six tones and letters, then, only one tone and letter would remain: 1 C. And that isn’t complex at all. In fact, it’s very simple. Now you can understand that harmony, no matter how complex, begins with one sound, one letter and one tone number. Let’s continue.
Harmony of two sounds is called an interval. In other words, an interval contains two letters and two tone numbers. For this lesson, we will begin with the following intervals: Perfect Fifth: natural 5, Diminished Fifth: flat 5, and Augmented Fifth: sharp 5.
The Perfect Fifth, P5, is simply the fifth sound of the major scale, tone 5 letter G. And when the perfect fifth is combined with the first sound of the scale, tone 1 letter C, the perfect fifth interval is the result. The perfect fifth interval may be played melodically, which means one at a time, or, harmonically, which means at the same time. Now, to understand the next two intervals, a simple understanding of flat (b) and sharp (#) is necessary. Simply stated, on any instrument, flat is one half-step lower in pitch and sharp is one half-step higher in pitch. To a right-handed player of guitar or bass, flat is one fret lower (to the left) of any letter or tone number, and sharp is one fret higher (to the right) of any letter or tone number. That was easy!
The definition of Diminished is to shrink or make smaller. Therefore, the diminished fifth is simply the fifth sound of the major scale flatted, in other words: tone b5, which is bG in the C Major scale. When the diminished fifth, b5 bG is combined with tone 1 C, the diminished fifth interval is the result. The diminished fifth interval may be played melodically (one sound at a time), or harmonically (at the same time).
The definition of Augmented is to expand or make larger. Therefore, the augmented fifth is simply the fifth sound of the major scale sharped, or, tone #5 which is #G in the C Major scale. When the augmented fifth, #5 #G is combined with tone 1 C, the augmented fifth interval is the result. The augmented fifth interval may also be played melodically or harmonically.
Let’s present the three intervals that are based on tone 3. They are Major: natural 3, Minor: flat 3 and Suspended: sharp 3. You will notice that even though we used the flat and sharp signs with the third intervals, we did not use the designation diminished and augmented!
The Major Third, M3, is simply the third sound of the major scale, tone 3 which is E in the C Major scale. When the major third, tone 3, is combined with the first sound of the scale, tone 1, the major third interval is the result. The major third interval may be played melodically or harmonically.
The Minor Third, m3, is simply the third sound of the major scale flatted, tone b3 letter bE. When the minor third is combined with the first sound of the scale, tone 1, the minor third interval is the result. The minor third interval may be played melodically or harmonically.
The Suspended Third, sus3, is simply the third sound of the major scale sharped, tone #3 letter #E. When the major third is combined with the first sound of the scale, tone 1, the suspended third interval is the result. The suspended third interval may also be played melodically or harmonically.
One more thought. The definition of enharmonic is one sound with more than one symbol. Therefore, it’s important to point out that when C is tone 1, tone #3 is the letter #E and sounds the same as tone 4 letter F, but they are two different symbols. For further clarification of this important concept, see page 102 of Guitar Fretboard Facts http://www.12tonemusic.com/guitar/facts/, or, Bass Fretboard Facts http://www.12tonemusic.com/bass/facts/.
Okay, it’s now time to use the above information to create Nine Triads of Three Types.
Tri is Greek for three. Therefore, triads are arpeggio and chord harmonies which are spelled with three different letters and three different tone numbers. Here’s the essential idea, there are only nine triads upon which all arpeggios and chords are based! These nine triads are created by combining the three third types: major, minor and suspended, with the three fifth types: perfect, diminished and augmented. In the following examples, C is tone 1. Tone 1 is also known as the root, tonic and fundamental. To learn more about the following nine triads, see page 10 of Guitar EncycloMedia http://www.12tonemusic.com/guitar/encyclomedia/, or, Bass EncycloMedia http://www.12tonemusic.com/bass/encyclomedia/.
Now, here is something very important. Notice that the harmony symbol for major is nothing. In other words, there is a harmony letter for major, but there is no type symbol for major. Said a different way, when you see nothing — and yes, you can see nothing — it means something! In other words, in this case, when you don’t see a type symbol after the harmony letter, it means major. Think of it this way, when reading the harmony symbol C, you think, say and play C major.
You will notice that each of the nine triads only have one Type, Name, Tone Spelling and Letter Spelling. However, since there is no standardization of harmony symbolism, some of the nine triads have more than one Harmony Symbol. This really shouldn’t be the case because more often than not, this simply leads to confusion. But, oh well, that’s the way it is.
So, ’til next time, have some nine triad fun… I’ll be listening!