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Playing Guitar - Numbers Instead Of Letters For Musical Notes

This is the June edition of Uncle Tim's Newsletter. This month we are going to dabble with expressing notes as numbers instead of letters. Sometimes great accuracy is needed when describing notes and linear pathways. If you have an understanding of how notes are actually wavelengths expressed in cycles per second, you can learn the differences between notes that share the same name and occur in different octaves. This can improve your overall understanding of the fretboard.

This actually can affect the quality of a solo and the choice of pathways for the lead. Even though this edition deals with numbers, this is actually a lite column. As we get closer to Autumn we will go a little deeper. So lets take a look at the numbers and attach them to notes. I promise no addition, multiplication, division or subtraction. Okay maybe a little addition.

Numbers Instead Of Letters

Most of the time when people describe notes on a fretboard, they describe them in terms of letters. If you are trying to tune a guitar, you might ask someone to give you an A. Usually that means striking the open A string so another person can tune to that note. Once that person tunes their guitar to the A note, it is a simple matter to tune the other strings relative to the A note provided.

Sometimes you will hear someone say, give me a 440. That is a more precise way of saying give me an A. The A string is tuned to 440 cycles per second. No other string is tuned to this number of cycles per second, so it identifies this string as tuned to an A. A specific A note too. But that is just the beginning. There are at least four octaves of an E note on any guitar. That means there are usually at least four different A notes. I really do mean different A notes, because even though they are all still A notes, they occur in different registers (octaves). So you can refer to these four different A notes as A, but that is imprecise. If you refer to an A note as 440, you know exactly which A note it is. But there is even more to this than just identifying the A note that lives at the open A string. It also lives somewhere else too (more on that in a minute).

So by using numbers as identifiers, you can gain some additional accuracy in describing these notes. In case you might be thinking this is just an academic exercise, there is an important concept that will help you understand the fretboard more precisely. That concept is the difference between A notes and the different places the identical note resides. It is also the difference between all notes that share the same name.

From the first low E note to the second E note on the high E string there are 12 letters used to describe 72 notes in a three octave range. These notes occur at different places over the fretboard. Looking at numbers can help to identify where each note is duplicated and where notes of the same name differ.

This can be enormously important when you are constructing a lead line. If you need to pick up the 440 A note, you have the choice of playing an open A note or choosing the A note that lives at the fifth string of the low E string.

They are both tuned to 440! They are the identical note. This plays a big role when you try to determine what scale fragment you want to use. How high do you climb on a string before switching over to the adjacent string for higher notes. Both ways are quite acceptable, depending on what effect you are after. But sometimes, more importantly, is the pathway you choose to travel. The mechanics of what your hand can do is limited and the notion of where you choose to switch will greatly affect the sound of the run. So spending a little time on this will sharpen your awareness and hopefully give you some sensitivity on choosing routes of travel.

Lets go look at the different tunings of the strings of a guitar. This should help us understand cycles per second and the duplication occurring on the fretboard.

Disclaimer: I am not trying to turn you into a math major. Do not feel like you have to memorize these numbers. All I am trying to do is point out how the same exact notes occur on different strings. For some people, if they see numbers, they can understand this easier. Look at this information as a broad picture.

These numbers represent how many cycles per second the sound wave makes for each note. This is how notes differ in pitch.

Cycles Per Second

E String		A String		D String		G String		B String		E String
Note	Cycles	Note	Cycles	Note	Cycles	Note	Cycles	Note	Cycles	Note	Cycles
E	329.63	A	440.00	D	587.33	G	783.99	B	987.76	E	1318.52
F	349.23	A#	466.16	D#	622.25	G#	830.61	C	1046.50	F	1396.92
F#	370.00	B	493.88	E	659.26	A	880.00	C#	1108.74	F#	1479.98
G	392.00	C	523.25	F	698.46	A#	932.32	D	1174.66	G	1567.98
G#	415.31	C#	554.37	F#	739.99	B	987.76	D#	1244.50	G#	1661.22
A	440.00	D	587.33	G	783.99	C	1046.50	E	1318.52	A	1760.00
A#	466.16	D#	622.25	G#	830.61	C#	1108.74	F	1396.92	A#	1864.64
B	493.88	E	659.26	A	880.00	D	1174.66	F#	1479.98	B	1975.52
C	523.25	F	698.46	A#	932.32	D#	1244.50	G	1567.98	C	2093.00
C#	554.37	F#	739.99	B	987.76	E	1318.52	G#	1661.22	C#	2217.48
D	587.33	G	783.99	C	1046.50	F	1396.92	A	1760.00	D	2349.32
D#	622.25	G#	830.61	C#	1108.74	F#	1479.98	A#	1864.64	D#	2489.00
E	659.26	A	880.00	D	1174.66	G	1567.98	B	1975.52	E	2637.04

 

Here are the important concepts to walk away with.

1. All strings contain some of the notes on the next lower string.

2. All strings contain some of the notes on the next higher string.

3. Notice that the A note is expressed as 440, 880 and 1760. Each higher octave will double the number. If you want to figure out the next octave, (high E string, 17th fret), you would double the last A note of 1760.00 cycles per second. That means the fourth octave of A would be 3520.00.

4. If you look at the colored number, you may notice one of the notes on each string coincide with the frets used when you tune a guitar using the other strings (cream colored box). All of these are on the fifth fret except one, the fourth fret on the G string.

5. Not all A notes are alike. You can have four different A notes and each one is in a different octave. Each note in the different octaves has a different number attached to it. All other notes will also share this behavior.

6. When you change strings to pick up additional notes in a scale, there are logical points to switch strings. You can switch wherever you want, regardless of any pattern you may be using for a scale passage. The typical patterns for scales passages are designed to make it easy to switch. But you can make up your own mind and switch wherever it makes sense to you. You can also just climb the string you are on, and play a vertical scale.

7. Notice that when you increase in pitch, the cycles per second also increase.

The Numbers

Most of these numbers do not end on whole numbers. They have decimal points.

There is a little fudge factor involved here. This was done so that the spacing of the notes is consistent over one octave as well as several octaves (among other reasons). If the numbers do not exactly double as you move up an octave, your ear will begin to notice the notes are not exact octaves. This will really confuse your ear. So they fudge the numbers a little to make it all work out. There are many good web pages available that will explain these concepts in terms of physics and math, so I am not going to go into this detail here. All we are trying to do is understand how the numbers equate to the notes and gain a simple understanding of pitch and octaves.

Strings

There are a few other concepts that should be explained as long as we are on the subject. For this example we are going to use the A notes on the low E string and the A string.

If you play an open A string you will hear the note ring out. If you try to duplicate that note by hitting the A note on the low E string, you may hear slight differences when doing so. Usually there are two reasons for this slight difference in note quality.

The first reason has to do with the thickness of the string. The E string is thicker than the A string and will sound slightly different than the open A string note. So the notes are identical but slightly different! As strings get thinner, the sound quality diminishes. So thicker strings move more air and create slightly better sound quality.

The second reason is when you press down a string at a fret, it will also ring differently than striking an open string. The open string has nothing touching it and it will ring clearer longer.

When you hold down a note at a fret, the note does not ring out as clear, in part because it is now a shorter vibrating string. This means the note will not sustain as long as the open string. The note sounds as long as the string is vibrating. A longer string will vibrate for a longer period of time thus producing a longer sustaining note.

Also if you move your finger off the fret, even slightly, it may affect the note. If you move it high enough off the string, it will muffle or mute the note. But there is another consideration. If you play the A note on the low E string, it should ring out as 440. But if you bend the string, even slightly, you will raise the note. It will no longer be 440. It may be 442, or 448 or something along that line. This depends on how far you bend the note. Often times, the guitarists is unaware they are bending and changing the note. They mean to press the string directly down and play a 440 but since their technique is slightly off, they may bend the string slightly, which will produce a slightly different note.

The difference between 440 and 448 is very slight. This is very hard for your ear to pick up. Some people claim they can tell the difference, but during a song you will be hard pressed to do so. You can however pick up this slight difference when tuning. So be aware of this little problem and concentrate on hitting the note by pressing it straight down, not bending it. This problem can become a little more pronounced as your fingers get stronger. They may have a tendency to bend the string more as the muscle groups gain proficiency.

For some people this information may not seem so important. But as you are learning to play scales and training your ear, you will eventually wonder about some of this. If you become aware of this, you will find ways to use this information to gain a deeper understanding of notes. All of this stuff works together. Sometimes it will contribute to what you are doing and sometimes it just hangs in the background until deeper scrutiny is required. I would not advise turning this into a major math study, unless you are very interested in the minutia, but it does add valve to understanding notes and music.