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Notice that a standard guitar fretboard extends only about 1.8 octaves.



THE NOTES OF MUSIC:

Any octave is further divided into 12 mathematical segments / increments that makes the sound wave frequency of each increment harmonic with the other increments;  Meaning that the sound waves frequencies of each increment are in sync  with each other.  Those 12 increments are the notes of music;  So each octave has 12 notes.  The frets on a guitar or the keys on a piano represent those 12 increments in each octave.  Those 12 notes are the very basis for Euro-American (aka Western) music.

Seemingly odd, but true to physics, an octave's 12 increments / notes are not in sync with each other in all cominbations.  Only 7 of the 12 notes in an octave are harmonic / in-sync with each other in any / all combinations.  So these 7 notes were long ago used to make a sequence of notes which we build upon to derive all of the kinds of scales and chords used in Western music.  The remaining 5 notes are used when and where a composer or musician desires;  And they are also needed for the full compliment of 12 notes neccessary to afford 7 notes in all keys of music.  There are 7 different, distinct, most popular and most used scales that can be made from the long ago and well established sequence of  7 notes;  But the evolution of music and the physics behind it has established one of those 7 scales as the "Master" scale.  That master scale is called the Major-7 scale.  Most people recognize the Major-7 scale as the do, re, mi, fa, sol, la, ti, do we learned and sang or played in elementary school.

When the science of music created orchestras of instruments beginning about 600 years ago they could only play a Major scale in only one key ....because that key had the best harmonious notes for that Major-7 scale;  And thus certain other kinds of scales for harmony in certain other keys that were derived from the Major-7 scale, by starting their #1 aka Root note on a particular Major-7 scale note to create a new scale of a different sound character known as 'Quality' (Different kinds of major and minor scales), because the science of music back then had not yet figured out how to make all notes within an octave more harmonious to each other, and particularly get all other octaves to more closely match.  That one Major scale key has evolved to what we know today as C Major-7 scale.

Over time with several different evolving methods, that arrangement of Major-7 scale notes has been retuned slightly out of harmony to give us notes that we use today which more closely match each other in each and all octaves, and thereby now allows us to play any type of scale and chord in any key.  The tuning method (the frequencies of notes) we use today is called Tempered Tuning and Stretched Tuning (derived from strething the full spectrum of octaves of tempered notes so that they all come closer to matching each other;  Ironically, some of the notes are quite out of tune with exact harmony which is neccessary for them to be the closest harmony to all notes.  And it's ironic that some music is still written in perfectly in-tune tunings and keys, and it sounds quite unusual to our ears that have become used-to hearing the Tempered / Stretched tuning that's been used for about 150 years now.

THE NUMBER OF POSSIBLE NOTES IN AN OCTAVE:

There are 12 possible different notes in an octave;  The 7 that make C Major scale plus the 5 sharps/flats (called accidentals) that are not notes in C Major scale.  There are actually 13 when you consider note 13 is the same as the 1st note but an octave higher in pitch than #1.  EACH OF THOSE 12 NOTES ARE SAID TO BE 1/2 STEP APART.  NOTES THAT ARE 2 NOTES APART FROM EACH OTHER ARE A WHOLE STEP.  In other words, playing any note and then another note 1 fret higher or lower on a guitar would be playing a half step;  And playing any note and then a note 2 frets apart on a guitar would be playing a whole step;  1 fret is one half step, ....while 2 frets are one whole step.

NUMBERING THE NOTES IN A SCALE:

We do not number all 13 notes in an octave.  For the purpose of common music theory that covers the vast majority of music, and for the purpose of the mechanical science of music / sound, we only use 8 notes to form the common scales from their #1 / Root note up or down to their same note one octave higher or lower.  So we use numbers 1 through 8 to describe a scale, with notes 1 and 8 being the same note 1 octave apart (lower / higher respectively) in pitch from each other.  For all practical purposes we can say that a scale has only 8 of the possible 13 notes in an octave.

The 8 notes of C Major 7 scale are C, D, E, F, G, A, B, C.  We number any scales 8 numbers as 1, 2, 3, 4, 5, 6, 7, 8 ......upon which we can make other notations to define the Quality of any certain quality scale.

More advanced music theory also uses numbers 9, 11 and 13 to specify special CHORD conditions upon notes 2, 4 and 6 respectively.  There is more on these notes in the advanced sections below.

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SCALES:

Songs are written around a scale quality (types of major or minor scales) with the scale's specific 'alpha character' (C, D, E, F, etc) root note  (#1 note in the scale) chosen by the composer for a number of reasons a musician will come to understand with experience, ....usually the voice range of singers, or the range of instruments' voices (particularly in orchestras), or the timbre desired in the composition (the highness or lowness and/or the tones of the composition in the spectrum of sound we can hear).

EVERY SCALE HAS A NUMBER SEQUENCE 1 THRU 8 REPRESENTING THE NOTES AND/OR
STEP SEQUENCE STRUCTURE
OF THE SCALE.  USING NUMBERS ALLOWS MUSIC TO BE REFERENCED (WRITTEN OR TALKED ABOUT) REGARDLESS OF ANY PARTICULAR ROOT NOTE AND/OR KEY.

THE NOTES 1 THRU 8 ARE CALLED AN OCTAVE, WITH NOTES 1 AND 8 BEING THE SAME LETTER AND NUMBER NOTE, AN OCTAVE APART, AND UP OR DOWN 1 OCTAVE IN PITCH FROM EACH OTHER.  Note 8 is the last note of an octave but also the first note of the next higher octave.  The number 1 note of an octave is also number 8 note of the next lower octave.  The number 8 note is most commonly just referred to as the 1 note in the number system;  You will hardly ever see a note labeled #8 except in writing a scale for illustration purposes such as this:

A two octave C Major scale would look like this:
C  D  E  F  G  A  B  C  D  E  F  G  A  B  C
1   2  3   4   5  6   7   1   2  3  4   5  6   7   8

THE NUMBER 1 NOTE IN A SCALE IS CALLED IT'S ROOT.  CHORDS ARE MADE BY USING ANY OR ALL OF NOTE NUMBERS 1, 3 AND 5, (CALLED THE TRIAD NOTES) OF A SCALE AND THEN ADDING WHATEVER OTHER NOTES (CALLED EXTENSIONS) OF THE SCALE THAT MIGHT BE DESIRED OR CALLED FOR.  So C Major chord would be notes 1, 3 and 5 of C Major Scale, which are notes C, E and G.

NOTES STEP SEQUENCES:

Once again, playing any note and then another note 1 fret higher or lower on a guitar would be playing a half step;  And playing any note and then a note 2 frets apart on a guitar would be playing a whole step;  1 fret is one half step, ....while 2 frets are one whole step.

THE VERY FOUNDATION OF MUSIC IS THE MAJOR SCALE.  See figure 092301-1.  The Major scale is made up of a sequence of whole and half steps.  THE MAJOR SCALE STEP SEQUENCE BETWEEN EACH NOTE NUMBER GOING UP THE SCALE IS:
1 - whole step - 2 - whole step - 3 - half step - 4 - whole step - 5 - whole step - 6 - whole step - 7 - half step - 8/1.
Easier to remember:  W W h W W W h.

ANOTHER EASY WAY TO REMEMBER THIS IS TO NOTICE THAT IN THE MAJOR SCALE THE HALF STEPS FALL ONLY BETWEEN 3 AND 4 AND BETWEEN 7 AND 8/1.

Making all the other different kind of scales (and their chords) is a matter of altering the Major scale STEPS.  To alter the step sequences we SHARP "#" (raise) or FLAT "b" (lower) one or more note NUMBERS by one half step.  As an example;  To make a simple minor scale we flat the 3rd note which results in a scale numbering:
1  2  b3  4  5  6  7  1

When we reference specific alpha letter notes (such as C, D, E, F, G, A, B) the "#" or "b" goes BEHIND THE LETTER (Gb or C# for example), but when referencing notes in the number system the "# / b" goes IN FRONT OF THE NUMBER (#5 or b7 for example). So the chord "C sharp flat 9" would be written C#b9.  If the extension notation would be confusing, then the potentially confusing part is often written in parentheses, such as C(b9) rather than Cb9 where you could not tell whether the flat belongs to C or the 9.

A simple minor scale has it's 3rd note flatted;  So the scale becomes 1, 2, b3, 4, 5, 6, 7, 8/1.

A dominant 7 scale, more commonly known simply as a 7th scale (such as G7), has a flatted 7 note;  So the scale becomes 1, 2, 3, 4, 5, 6, b7, 8/1.  NOT TO BE CONFUSED WITH THE MAJOR 7 SCALE WHOSE 7th NOTE IS NATURAL / NOT FLATTED.

Here is how other scales are formed by the altering notes and thus altering the scales step sequence:

THE WORD "MAJOR" WITHOUT ANY OTHER NOTATION TO THE CONTRARY, SIGNIFIES THAT ALL THE NOTES IN THE SCALE ARE NATURAL (not having sharp or flat scale NUMBERS).  THE TERM MAJOR 7 ALSO MEANS THE SAME THING.  A SCALE OR CHORD IS UNDERSTOOD TO BE MAJOR UNLESS OTHERWISE NOTATED.  So if you see the notation "C scale", CMaj or C Maj 7, they all mean derived from the Major 7.

THE WORD MINOR BY ITSELF WITHOUT ANY OTHER NOTATION TO THE CONTRARY, MEANS SIMPLY THAT THE NOTE 3 IS FLATTED.

HERE ARE THE COMMON SCALE / CHORD ALTERATIONS:

Major (Maj) = For scales it means Maj7.  (For chords, it means simple Major triad.)
Major 7 (Maj7) = Same as the Major scale.
Dominant 7 or simply 7th (7) = b7
Minor 7 (min7 or -7) = b3, b7.
Augmented 5th (aug5 or +5) = Maj#5.
Augmented (Aug or +) = Maj#4#5#6,
Diminished (dim or small "o") = minor b5 b6 bb7 b9 (double flat 7 = 6), which is the same as saying the scale is 1  b2  b3  4  b5  b6  6  8/1.
Half Diminished (h-dim or small "o" with a slash through it) = minor b5 b6 (1  b2  b3  4  b5  b6  b7 1).

Here are the 4 common types of minor scale / chord alterations from the Maj scale:
MELODIC MINOR = b3
HARMONIC MINOR = b3, b6 and either b7 or natural 7;  Is sometimes said in theory that natural 7 is more appropriate when ascending and b7 is when descending.  Commonly used that way in practice exercises.
MINOR 7 = b3, b7.
PURE MINOR = b3, b6, b7.

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BASIC CHORD STRUCTURE REVIEW:

BASIC CHORDS ARE THE TRIAD NOTES. TRIAD NOTES ARE NOTES 1, 3 AND 5.

We can then add notes 2 (also called 9), 4 (also called 11), 6 (also called 13) and 7 ...or any alteration (# / b) of any of those notes ....to the basic chord as we wish or are directed.

When we add notes 2, 4, and  6, for musical sound reasons they are commonly added in the octave higer than notes 1 through 8/1 (Though 6 is common in the triad octaves).  So we have a number system that goes higher than 7.

ANY TIME NUMBERS 9, 11 AND/OR 13 ARE USED, IT IS UNDERSTOOD THAT A b7 IS ALSO IN THE SCALE OR CHORD;  UNLESS THE WORD "add" IS NOTED, such as C(add9) which would not have a b7 in the chord nor would it be neccessary in the scale.

Now let's review the chord building process (C chord is just example;  The numbers fit any chord root letter name):

IT IS NOT NECCESSARY TO MEMORIZE ALL OF THESE CHORDS;  This list is more to show how chords are constructed and notated.  Ones in red ARE important to memorize:

C chord (aka CMaj) is simply the notes 1, 3, 5 (C, E, G) of C major scale.
C Maj7 would be the notes 1, 3, 5, 7.
C7 chord would be the notes 1, 3, 5, b7.
Cmin would be 1, b3, 5.
Cmin7 would be 1, b3, 5, b7.
C6 would be 1, 3, 5, 6.
Csus (suspended) would be 1, 3, 4, 5.
Csus7 would be 1, 3, 4, 5, b7.
C9 would be 1, 3, 5, b7, 9.
C(add9) would be 1, 3, 5, 9.
C11 would be 1, 3, 5, b7, 9, 11.
C(add11) would be 1, 3, 5, 11.
C13 would be 1, 3, 5, b7, 9, 11, 13.
C9(add13) would be 1, 3, 5, b7, 9, 13.
C9(add13) could also be notated C9(13), as could any other 'add' notation.
Cmin7b9 would be 1, b3, 5, b7, b9.
Cmin7(addb13) ...or Cmin7(b13)... would be 1, b3, 5, b7, b13.

Augmented and diminished chords are not difficult either:

The augmented scale simply has all whole steps:  1, 2, 3, #4, #5, #6, 7.  So Caug chord would be 1, 3, #5, #6 .....and a 7 if appropriate in the song, composition or scale. (Usually only 4 notes are used)

The Diminished scale is 1, b2, b3, 4, b5, b6, bb7(=6), 8/1.  So Cdim chord would be made by the C scale notes 1, b3, b5, b6, bb7 (bb7 = 6).  (Usually only 4 notes are used).

The half diminished scale / chord is 1, b2, b3, 4, b5, b6, b7, 8/1;  The same as diminished but uses a b7 rather than a bb7.

Scale and / or chord "Voicing" refers to what notes are played in what order in a scale, chord, passage, musical line, etc.

Now is a good time to mention that technical music theory comes from Classical Music, because it is the oldest technical music.  Formal Jazz also conforms to technical ideas for the most part.   But technical music theory does not always apply to the guitar in the practical sense of Popular Music.  One of the main reasons for this is because the guitar does not always afford easy "correct" technical voicing of notes in the 2 octaves voiced by the vast majority of chords on the guitar.  For instance, a proper technical E9 chord would be voiced 1 3 5 b7 9 ;  But the open E chord on a guitar is voiced 1 5 1 3 5 1 and adding a 9 on the 1st string gives us a voicing of 1 5 b7 3 5 9 ; ..close but no cigar;  And the more common blues 9 chord with roots on the 1st and 6th strings is 1 3 b7 9 5 1 .far from the technical cigar .but still quite proper for Popular Music.  Another reason technical theory often does not apply to the guitar in Popular Music is the nature of Popular Music itself where anything is OK although good music theory still has to be applied if a person wants their music to be pleasantly harmonic and melodic.  Indeed technical music theory holds a cornucopia of discovery of why and how melody and harmony works.

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ADVANCED CHORD THEORY REVIEW:

THE REMAINDER OF THIS BASIC MUSIC THEORY REVIEW IS RATHER ADVANCED THEORY AND SHOULD NOT BE WORRIED ABOUT IF YOU ARE NOT UP TO SPEED ON THIS LEVEL OF THEORY ...but should be studied if you want to get up to speed.

EXTENSION NOTES.  In order to write, express and know to play the EXTENDED OCTAVE NOTES (Extensions) in chord structures, we have to extend the scale numbers beyond 1 octave;  In other words higher than the number 8.  Now, notes 1, 3, 5 and 7 are already expressed in the basic chord notation, and notes 2/9, 4/11, and 6/13 in the higher octave are all that's left, therefore the numbers don't go higher than 13;  So we use the extended octave numbers 9, 11 and 13 to represent them in chord structure (D9 for example).  So we only commonly need numbers 1 through 7 plus 9, 11, and 13 (though we might rarely see the other numbers in some exotic notations).  If it is not notated to the contrary, any 9, 11, or 13 extension notation means that the 7 is dominant (a b7) and all the extensions below the extension notated are also included in the voicing.  Example, the notation G9 means the 7 is flatted and 9 is added in the higher octave.  G11 means the 7 is flatted, AND THERE IS A 9 AND 11 in the higher octave.  If an extension is meant to be added all by itself the notation "add" will be used, ...such as G7add13 which would mean G7 with 13 in the higher octave but not 9 nor 11.

So, going over this again, a 9 chord such as D9 for example, should (for notation and "exotic" musical reasons) also have a b7 unless otherwise noted (I will get to the otherwise part in a little bit);  And an 11 chord such as D11 should also have a b7, and a 9 as well as the 11;  And a 13 chord should have b7, 9, 11, and 13.  The chord D9 therefore would be the basic notes 1, 3, 5, b7 with 9 added.  The chord G13 would be made by the notes 1, 3, 5, b7, 9, 11, and 13.  The reasons for this is because the higher number chords are more harmonic when stacked that way.  It's easier in the long run to allow rules for automatically including the forms of the extensions in writing out  chord notations, and otherwise indicate the fewer circumstances when certain of those notes are not desired when writing the notation.  If we should desire to eliminate the b7 in an E9 chord for instance, we would write the chord Eadd9.  Similarly if we wanted to eliminate the 11 note we would write the chord E9add13.  BUT THESE EXTENSION NOTE RULES ARE USUALLY STRICT ONLY IN DISCIPLINED MUSIC CONFORMITY.  IN THE REAL WORLD OF LOOSER MUSIC, THEY ONLY APPLY TO THOSE MUSICIANS THAT CARE TO BE THAT METICULOUS.  HOWEVER, WE SHOULD BE AWARE OF THESE NOTATION RULES SO WE CAN RECOGNIZE THEM IN NOTATIONS if not for the hunger of knowing how and why music works in it's most melodic and harmonic forms.

Now refer to chart 102101-1CHORDS ALSO HAVE SPECIAL ROMAN NUMERAL DESIGNATIONS:  I, II, III, IV, V, VI, VII.  THESE NUMBERS REPRESENT THE CHORDS OF A COMPOSITION BASED UPON THE KEY OF THE COMPOSITION BEING NUMBER "I" (THE TONIC) AND EACH OTHER CHORD NUMBER CORRESPONDING TO THE NOTES IN THE KEY'S SCALE.  ROMAN NUMERALS CAN ALSO BE USED TO DESIGNATE CHORDS DERIVED FROM A PARTICULAR SCALE.  IF THE KEY IS A MAJOR KEY, THEN THE ROMAN NUMBERS WOULD FOLLOW THE MAJOR SCALE SEQUENCE.  IF THE KEY WERE MINOR THE ROMAN NUMERALS WOULD FOLLOW THE MINOR SCALE SEQUENCE;  In other words if the composition key was C Melodic minor, the roman numeral sequence would correspond to 1, 2, b3, 4, 5, 6, 7, 8/1;  And although we usually will, we would not NECESSARILY see 'b' preceeding the III because III is technically understood as being bIII in a minor key (although in the less technical practical world of music notation, the flatted or sharped chords are usually marked as such).  Also common is for a minor III to be notated iii.

If we want to play a chord that is harmonic to, and follows the tone direction of each note in a scale (or melody or musical passage), all we have to do is write the scale out (or know it by heart) and use the scale's notes to derive the harmonic chords.  In other words, if we want to play harmonic chords to C scale, then the first chord would be C, built on our choice of 1, 3, 5, 6, 7, 9, 11, 13 of the C MAJOR scale.  Now for the chord harmonic and tonal to the note D, we would STILL build the D chord on the notes in C MAJOR scale, but use the note D as note number 1 for the D chord we need:  So our D scale would be D, E, F, G, A, B, C, D .  Looking at that scale AS A "D" SCALE we see note numbers 1, 2, b3, 4, 5, 6, b7;  So the basic triad chord would be 1, b3, 5,  and the fuller chord would be 1, b3, 5, b7 which is Dmin7.  To do the same thing for the note E we would have the notes E, F, G, A, B, C, D, E to work with (still the notes of C Major scale that we want to harmonize with);  And looking at those note numbers for E chord we see 1, b2, b3, 4, 5, b6, b7, 8/1;  So our chord notes would be 1, b3, 5, b7 which is Emin7.  Repeating the process for each note/chord we would discover the following sequence FOR MAJOR SCALES:
IMaj7, IImin7, IIImin7, IVMaj7, V7, VImin7, VII half-dim, IMaj7 !!!!!
To make it even more simple we could drop the 7 extensions and simply remember:
I,   IImin,   IIImin,   IV,   V,   VImin,   VIIminb5, I;
(Although keeping the 7s adds much musical color and definition).

If we did the same thing for the Pure Minor aka min7 aka Dorian (1, 2, b3, 4, 5, 6, b7) we would find that the SIMPLE TRIAD chord sequence up the min7 scale would be Imin ,  IImin ,  III ,  IV,  Vmin,  VImin(b5),  VII, Imin;  The same step sequence as the Maj7 but slid down a whole step like a slide rule.  If the Pure Minor / min7 scale step sequence had a D root note we could clearly see the TRIAD-plus-7th-notes sequence as a CMaj7 scale sequence slide rule slid down one whole step with the TRIAD-plus-7th-notes being:  Dmin7, Emin7, FMaj7, G7, Amin7, Bmin7(b5), CMaj7, Dmin7, ....which are the identical chords, scales and sequence as CMaj7, .....just starting on D.  And of course if it works in a Dmin7 to CMaj7 relationship, IT WILL WORK IN ANY SCALE / CHORD QUALITIES SEQUENCE.  MEANING that we can play pretty darn jazzy sounding chords simply by playing the correct triad or 7th chords upon moments in the melody, or in harmony with the melody, or point in harmony with the melody, or moments in counter-melody, or timing notes in a measure, or accent points in a song, etc etc !

There are more exotic compositions where the key is written in / on / around more exotic Major and minor scales that require close scrutiny to determine the correct chords for each of those scale's step sequences.  In any event the harmonic chords will conform to the parent scale of the composition or part of the composition or passage in the composition by analyzing and treating the "mother" scale's step sequence chords just like done in the above examples.

The keys and scales in a composition can change, such as in Classical Music;  But in popular music the key and theme scale structure will usually remain the same.

SOME SUGGESTIONS & COMMON "RULES" ABOUT 4/11 NOTES:

The 4/11 extension note will occur often when you start studying / using chord substitutions and you will need to avoid playing those notes in the chords when they are not called for, because they have a STRONG effect of suspending and causing tension in songs / compositions that weren't written for that specific tension.  So we need to know some things about the 4/11 notes.  Any notes IN A MODAL CHORD will be nicely harmonic to each other EXCEPT FOR THE 4/11 EXTENSION ...unless the suspended or 11th chord is intended (it's probably the most used suspended chord).  In SCALES, the 4/11 note is normal and used extensively in melody, and passages, etc, ...but not often in chords unless specifically intended because it suspends a chord and thereby applies tension to what else is going on musically.  The tension is one of "confusing" the resolution of a musical line, keeping anticipation "hanging in the air", as opposed to an augmented or diminished chord's tension that affords anticipation of where the musical line is going.  So we will need to practice knowing where that 4/11 note is to avoid it IN CHORDS, by ear and by practice, which comes quite natural with a bit of woodshedding.  If you are interested in scale and chord substitution and/or modes;  Then you should see my short lessons on scale / chord substitution via modes.

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ALOHA !





Notice that a standard guitar fretboard extends only about 1.8 octaves.



THE NOTES OF MUSIC:

Any octave is further divided into 12 mathematical segments / increments that makes the sound wave frequency of each increment harmonic with the other increments;  Meaning that the sound waves frequencies of each increment are in sync  with each other.  Those 12 increments are the notes of music;  So each octave has 12 notes.  The frets on a guitar or the keys on a piano represent those 12 increments in each octave.  Those 12 notes are the very basis for Euro-American (aka Western) music.

Seemingly odd, but true to physics, an octave's 12 increments / notes are not in sync with each other in all cominbations.  Only 7 of the 12 notes in an octave are harmonic / in-sync with each other in any / all combinations.  So these 7 notes were long ago used to make a sequence of notes which we build upon to derive all of the kinds of scales and chords used in Western music.  The remaining 5 notes are used when and where a composer or musician desires;  And they are also needed for the full compliment of 12 notes neccessary to afford 7 notes in all keys of music.  There are 7 different, distinct, most popular and most used scales that can be made from the long ago and well established sequence of  7 notes;  But the evolution of music and the physics behind it has established one of those 7 scales as the "Master" scale.  That master scale is called the Major-7 scale.  Most people recognize the Major-7 scale as the do, re, mi, fa, sol, la, ti, do we learned and sang or played in elementary school.

When the science of music created orchestras of instruments beginning about 600 years ago they could only play a Major scale in only one key ....because that key had the best harmonious notes for that Major-7 scale;  And thus certain other kinds of scales for harmony in certain other keys that were derived from the Major-7 scale, by starting their #1 aka Root note on a particular Major-7 scale note to create a new scale of a different sound character known as 'Quality' (Different kinds of major and minor scales), because the science of music back then had not yet figured out how to make all notes within an octave more harmonious to each other, and particularly get all other octaves to more closely match.  That one Major scale key has evolved to what we know today as C Major-7 scale.

Over time with several different evolving methods, that arrangement of Major-7 scale notes has been retuned slightly out of harmony to give us notes that we use today which more closely match each other in each and all octaves, and thereby now allows us to play any type of scale and chord in any key.  The tuning method (the frequencies of notes) we use today is called Tempered Tuning and Stretched Tuning (derived from strething the full spectrum of octaves of tempered notes so that they all come closer to matching each other;  Ironically, some of the notes are quite out of tune with exact harmony which is neccessary for them to be the closest harmony to all notes.  And it's ironic that some music is still written in perfectly in-tune tunings and keys, and it sounds quite unusual to our ears that have become used-to hearing the Tempered / Stretched tuning that's been used for about 150 years now.

THE NUMBER OF POSSIBLE NOTES IN AN OCTAVE:

There are 12 possible different notes in an octave;  The 7 that make C Major scale plus the 5 sharps/flats (called accidentals) that are not notes in C Major scale.  There are actually 13 when you consider note 13 is the same as the 1st note but an octave higher in pitch than #1.  EACH OF THOSE 12 NOTES ARE SAID TO BE 1/2 STEP APART.  NOTES THAT ARE 2 NOTES APART FROM EACH OTHER ARE A WHOLE STEP.  In other words, playing any note and then another note 1 fret higher or lower on a guitar would be playing a half step;  And playing any note and then a note 2 frets apart on a guitar would be playing a whole step;  1 fret is one half step, ....while 2 frets are one whole step.

NUMBERING THE NOTES IN A SCALE:

We do not number all 13 notes in an octave.  For the purpose of common music theory that covers the vast majority of music, and for the purpose of the mechanical science of music / sound, we only use 8 notes to form the common scales from their #1 / Root note up or down to their same note one octave higher or lower.  So we use numbers 1 through 8 to describe a scale, with notes 1 and 8 being the same note 1 octave apart (lower / higher respectively) in pitch from each other.  For all practical purposes we can say that a scale has only 8 of the possible 13 notes in an octave.

The 8 notes of C Major 7 scale are C, D, E, F, G, A, B, C.  We number any scales 8 numbers as 1, 2, 3, 4, 5, 6, 7, 8 ......upon which we can make other notations to define the Quality of any certain quality scale.

More advanced music theory also uses numbers 9, 11 and 13 to specify special CHORD conditions upon notes 2, 4 and 6 respectively.  There is more on these notes in the advanced sections below.

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SCALES:

Songs are written around a scale quality (types of major or minor scales) with the scale's specific 'alpha character' (C, D, E, F, etc) root note  (#1 note in the scale) chosen by the composer for a number of reasons a musician will come to understand with experience, ....usually the voice range of singers, or the range of instruments' voices (particularly in orchestras), or the timbre desired in the composition (the highness or lowness and/or the tones of the composition in the spectrum of sound we can hear).

EVERY SCALE HAS A NUMBER SEQUENCE 1 THRU 8 REPRESENTING THE NOTES AND/OR
STEP SEQUENCE STRUCTURE
OF THE SCALE.  USING NUMBERS ALLOWS MUSIC TO BE REFERENCED (WRITTEN OR TALKED ABOUT) REGARDLESS OF ANY PARTICULAR ROOT NOTE AND/OR KEY.

THE NOTES 1 THRU 8 ARE CALLED AN OCTAVE, WITH NOTES 1 AND 8 BEING THE SAME LETTER AND NUMBER NOTE, AN OCTAVE APART, AND UP OR DOWN 1 OCTAVE IN PITCH FROM EACH OTHER.  Note 8 is the last note of an octave but also the first note of the next higher octave.  The number 1 note of an octave is also number 8 note of the next lower octave.  The number 8 note is most commonly just referred to as the 1 note in the number system;  You will hardly ever see a note labeled #8 except in writing a scale for illustration purposes such as this:

A two octave C Major scale would look like this:
C  D  E  F  G  A  B  C  D  E  F  G  A  B  C
1   2  3   4   5  6   7   1   2  3  4   5  6   7   8

THE NUMBER 1 NOTE IN A SCALE IS CALLED IT'S ROOT.  CHORDS ARE MADE BY USING ANY OR ALL OF NOTE NUMBERS 1, 3 AND 5, (CALLED THE TRIAD NOTES) OF A SCALE AND THEN ADDING WHATEVER OTHER NOTES (CALLED EXTENSIONS) OF THE SCALE THAT MIGHT BE DESIRED OR CALLED FOR.  So C Major chord would be notes 1, 3 and 5 of C Major Scale, which are notes C, E and G.

NOTES STEP SEQUENCES:

Once again, playing any note and then another note 1 fret higher or lower on a guitar would be playing a half step;  And playing any note and then a note 2 frets apart on a guitar would be playing a whole step;  1 fret is one half step, ....while 2 frets are one whole step.

THE VERY FOUNDATION OF MUSIC IS THE MAJOR SCALE.  See figure 092301-1.  The Major scale is made up of a sequence of whole and half steps.  THE MAJOR SCALE STEP SEQUENCE BETWEEN EACH NOTE NUMBER GOING UP THE SCALE IS:
1 - whole step - 2 - whole step - 3 - half step - 4 - whole step - 5 - whole step - 6 - whole step - 7 - half step - 8/1.
Easier to remember:  W W h W W W h.

ANOTHER EASY WAY TO REMEMBER THIS IS TO NOTICE THAT IN THE MAJOR SCALE THE HALF STEPS FALL ONLY BETWEEN 3 AND 4 AND BETWEEN 7 AND 8/1.

Making all the other different kind of scales (and their chords) is a matter of altering the Major scale STEPS.  To alter the step sequences we SHARP "#" (raise) or FLAT "b" (lower) one or more note NUMBERS by one half step.  As an example;  To make a simple minor scale we flat the 3rd note which results in a scale numbering:
1  2  b3  4  5  6  7  1

When we reference specific alpha letter notes (such as C, D, E, F, G, A, B) the "#" or "b" goes BEHIND THE LETTER (Gb or C# for example), but when referencing notes in the number system the "# / b" goes IN FRONT OF THE NUMBER (#5 or b7 for example). So the chord "C sharp flat 9" would be written C#b9.  If the extension notation would be confusing, then the potentially confusing part is often written in parentheses, such as C(b9) rather than Cb9 where you could not tell whether the flat belongs to C or the 9.

A simple minor scale has it's 3rd note flatted;  So the scale becomes 1, 2, b3, 4, 5, 6, 7, 8/1.

A dominant 7 scale, more commonly known simply as a 7th scale (such as G7), has a flatted 7 note;  So the scale becomes 1, 2, 3, 4, 5, 6, b7, 8/1.  NOT TO BE CONFUSED WITH THE MAJOR 7 SCALE WHOSE 7th NOTE IS NATURAL / NOT FLATTED.

Here is how other scales are formed by the altering notes and thus altering the scales step sequence:

THE WORD "MAJOR" WITHOUT ANY OTHER NOTATION TO THE CONTRARY, SIGNIFIES THAT ALL THE NOTES IN THE SCALE ARE NATURAL (not having sharp or flat scale NUMBERS).  THE TERM MAJOR 7 ALSO MEANS THE SAME THING.  A SCALE OR CHORD IS UNDERSTOOD TO BE MAJOR UNLESS OTHERWISE NOTATED.  So if you see the notation "C scale", CMaj or C Maj 7, they all mean derived from the Major 7.

THE WORD MINOR BY ITSELF WITHOUT ANY OTHER NOTATION TO THE CONTRARY, MEANS SIMPLY THAT THE NOTE 3 IS FLATTED.

HERE ARE THE COMMON SCALE / CHORD ALTERATIONS:

Major (Maj) = For scales it means Maj7.  (For chords, it means simple Major triad.)
Major 7 (Maj7) = Same as the Major scale.
Dominant 7 or simply 7th (7) = b7
Minor 7 (min7 or -7) = b3, b7.
Augmented 5th (aug5 or +5) = Maj#5.
Augmented (Aug or +) = Maj#4#5#6,
Diminished (dim or small "o") = minor b5 b6 bb7 b9 (double flat 7 = 6), which is the same as saying the scale is 1  b2  b3  4  b5  b6  6  8/1.
Half Diminished (h-dim or small "o" with a slash through it) = minor b5 b6 (1  b2  b3  4  b5  b6  b7 1).

Here are the 4 common types of minor scale / chord alterations from the Maj scale:
MELODIC MINOR = b3
HARMONIC MINOR = b3, b6 and either b7 or natural 7;  Is sometimes said in theory that natural 7 is more appropriate when ascending and b7 is when descending.  Commonly used that way in practice exercises.
MINOR 7 = b3, b7.
PURE MINOR = b3, b6, b7.

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BASIC CHORD STRUCTURE REVIEW:

BASIC CHORDS ARE THE TRIAD NOTES. TRIAD NOTES ARE NOTES 1, 3 AND 5.

We can then add notes 2 (also called 9), 4 (also called 11), 6 (also called 13) and 7 ...or any alteration (# / b) of any of those notes ....to the basic chord as we wish or are directed.

When we add notes 2, 4, and  6, for musical sound reasons they are commonly added in the octave higer than notes 1 through 8/1 (Though 6 is common in the triad octaves).  So we have a number system that goes higher than 7.

ANY TIME NUMBERS 9, 11 AND/OR 13 ARE USED, IT IS UNDERSTOOD THAT A b7 IS ALSO IN THE SCALE OR CHORD;  UNLESS THE WORD "add" IS NOTED, such as C(add9) which would not have a b7 in the chord nor would it be neccessary in the scale.

Now let's review the chord building process (C chord is just example;  The numbers fit any chord root letter name):

IT IS NOT NECCESSARY TO MEMORIZE ALL OF THESE CHORDS;  This list is more to show how chords are constructed and notated.  Ones in red ARE important to memorize:

C chord (aka CMaj) is simply the notes 1, 3, 5 (C, E, G) of C major scale.
C Maj7 would be the notes 1, 3, 5, 7.
C7 chord would be the notes 1, 3, 5, b7.
Cmin would be 1, b3, 5.
Cmin7 would be 1, b3, 5, b7.
C6 would be 1, 3, 5, 6.
Csus (suspended) would be 1, 3, 4, 5.
Csus7 would be 1, 3, 4, 5, b7.
C9 would be 1, 3, 5, b7, 9.
C(add9) would be 1, 3, 5, 9.
C11 would be 1, 3, 5, b7, 9, 11.
C(add11) would be 1, 3, 5, 11.
C13 would be 1, 3, 5, b7, 9, 11, 13.
C9(add13) would be 1, 3, 5, b7, 9, 13.
C9(add13) could also be notated C9(13), as could any other 'add' notation.
Cmin7b9 would be 1, b3, 5, b7, b9.
Cmin7(addb13) ...or Cmin7(b13)... would be 1, b3, 5, b7, b13.

Augmented and diminished chords are not difficult either:

The augmented scale simply has all whole steps:  1, 2, 3, #4, #5, #6, 7.  So Caug chord would be 1, 3, #5, #6 .....and a 7 if appropriate in the song, composition or scale. (Usually only 4 notes are used)

The Diminished scale is 1, b2, b3, 4, b5, b6, bb7(=6), 8/1.  So Cdim chord would be made by the C scale notes 1, b3, b5, b6, bb7 (bb7 = 6).  (Usually only 4 notes are used).

The half diminished scale / chord is 1, b2, b3, 4, b5, b6, b7, 8/1;  The same as diminished but uses a b7 rather than a bb7.

Scale and / or chord "Voicing" refers to what notes are played in what order in a scale, chord, passage, musical line, etc.

Now is a good time to mention that technical music theory comes from Classical Music, because it is the oldest technical music.  Formal Jazz also conforms to technical ideas for the most part.   But technical music theory does not always apply to the guitar in the practical sense of Popular Music.  One of the main reasons for this is because the guitar does not always afford easy "correct" technical voicing of notes in the 2 octaves voiced by the vast majority of chords on the guitar.  For instance, a proper technical E9 chord would be voiced 1 3 5 b7 9 ;  But the open E chord on a guitar is voiced 1 5 1 3 5 1 and adding a 9 on the 1st string gives us a voicing of 1 5 b7 3 5 9 ; ..close but no cigar;  And the more common blues 9 chord with roots on the 1st and 6th strings is 1 3 b7 9 5 1 .far from the technical cigar .but still quite proper for Popular Music.  Another reason technical theory often does not apply to the guitar in Popular Music is the nature of Popular Music itself where anything is OK although good music theory still has to be applied if a person wants their music to be pleasantly harmonic and melodic.  Indeed technical music theory holds a cornucopia of discovery of why and how melody and harmony works.

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ADVANCED CHORD THEORY REVIEW:

THE REMAINDER OF THIS BASIC MUSIC THEORY REVIEW IS RATHER ADVANCED THEORY AND SHOULD NOT BE WORRIED ABOUT IF YOU ARE NOT UP TO SPEED ON THIS LEVEL OF THEORY ...but should be studied if you want to get up to speed.

EXTENSION NOTES.  In order to write, express and know to play the EXTENDED OCTAVE NOTES (Extensions) in chord structures, we have to extend the scale numbers beyond 1 octave;  In other words higher than the number 8.  Now, notes 1, 3, 5 and 7 are already expressed in the basic chord notation, and notes 2/9, 4/11, and 6/13 in the higher octave are all that's left, therefore the numbers don't go higher than 13;  So we use the extended octave numbers 9, 11 and 13 to represent them in chord structure (D9 for example).  So we only commonly need numbers 1 through 7 plus 9, 11, and 13 (though we might rarely see the other numbers in some exotic notations).  If it is not notated to the contrary, any 9, 11, or 13 extension notation means that the 7 is dominant (a b7) and all the extensions below the extension notated are also included in the voicing.  Example, the notation G9 means the 7 is flatted and 9 is added in the higher octave.  G11 means the 7 is flatted, AND THERE IS A 9 AND 11 in the higher octave.  If an extension is meant to be added all by itself the notation "add" will be used, ...such as G7add13 which would mean G7 with 13 in the higher octave but not 9 nor 11.

So, going over this again, a 9 chord such as D9 for example, should (for notation and "exotic" musical reasons) also have a b7 unless otherwise noted (I will get to the otherwise part in a little bit);  And an 11 chord such as D11 should also have a b7, and a 9 as well as the 11;  And a 13 chord should have b7, 9, 11, and 13.  The chord D9 therefore would be the basic notes 1, 3, 5, b7 with 9 added.  The chord G13 would be made by the notes 1, 3, 5, b7, 9, 11, and 13.  The reasons for this is because the higher number chords are more harmonic when stacked that way.  It's easier in the long run to allow rules for automatically including the forms of the extensions in writing out  chord notations, and otherwise indicate the fewer circumstances when certain of those notes are not desired when writing the notation.  If we should desire to eliminate the b7 in an E9 chord for instance, we would write the chord Eadd9.  Similarly if we wanted to eliminate the 11 note we would write the chord E9add13.  BUT THESE EXTENSION NOTE RULES ARE USUALLY STRICT ONLY IN DISCIPLINED MUSIC CONFORMITY.  IN THE REAL WORLD OF LOOSER MUSIC, THEY ONLY APPLY TO THOSE MUSICIANS THAT CARE TO BE THAT METICULOUS.  HOWEVER, WE SHOULD BE AWARE OF THESE NOTATION RULES SO WE CAN RECOGNIZE THEM IN NOTATIONS if not for the hunger of knowing how and why music works in it's most melodic and harmonic forms.

Now refer to chart 102101-1CHORDS ALSO HAVE SPECIAL ROMAN NUMERAL DESIGNATIONS:  I, II, III, IV, V, VI, VII.  THESE NUMBERS REPRESENT THE CHORDS OF A COMPOSITION BASED UPON THE KEY OF THE COMPOSITION BEING NUMBER "I" (THE TONIC) AND EACH OTHER CHORD NUMBER CORRESPONDING TO THE NOTES IN THE KEY'S SCALE.  ROMAN NUMERALS CAN ALSO BE USED TO DESIGNATE CHORDS DERIVED FROM A PARTICULAR SCALE.  IF THE KEY IS A MAJOR KEY, THEN THE ROMAN NUMBERS WOULD FOLLOW THE MAJOR SCALE SEQUENCE.  IF THE KEY WERE MINOR THE ROMAN NUMERALS WOULD FOLLOW THE MINOR SCALE SEQUENCE;  In other words if the composition key was C Melodic minor, the roman numeral sequence would correspond to 1, 2, b3, 4, 5, 6, 7, 8/1;  And although we usually will, we would not NECESSARILY see 'b' preceeding the III because III is technically understood as being bIII in a minor key (although in the less technical practical world of music notation, the flatted or sharped chords are usually marked as such).  Also common is for a minor III to be notated iii.

If we want to play a chord that is harmonic to, and follows the tone direction of each note in a scale (or melody or musical passage), all we have to do is write the scale out (or know it by heart) and use the scale's notes to derive the harmonic chords.  In other words, if we want to play harmonic chords to C scale, then the first chord would be C, built on our choice of 1, 3, 5, 6, 7, 9, 11, 13 of the C MAJOR scale.  Now for the chord harmonic and tonal to the note D, we would STILL build the D chord on the notes in C MAJOR scale, but use the note D as note number 1 for the D chord we need:  So our D scale would be D, E, F, G, A, B, C, D .  Looking at that scale AS A "D" SCALE we see note numbers 1, 2, b3, 4, 5, 6, b7;  So the basic triad chord would be 1, b3, 5,  and the fuller chord would be 1, b3, 5, b7 which is Dmin7.  To do the same thing for the note E we would have the notes E, F, G, A, B, C, D, E to work with (still the notes of C Major scale that we want to harmonize with);  And looking at those note numbers for E chord we see 1, b2, b3, 4, 5, b6, b7, 8/1;  So our chord notes would be 1, b3, 5, b7 which is Emin7.  Repeating the process for each note/chord we would discover the following sequence FOR MAJOR SCALES:
IMaj7, IImin7, IIImin7, IVMaj7, V7, VImin7, VII half-dim, IMaj7 !!!!!
To make it even more simple we could drop the 7 extensions and simply remember:
I,   IImin,   IIImin,   IV,   V,   VImin,   VIIminb5, I;
(Although keeping the 7s adds much musical color and definition).

If we did the same thing for the Pure Minor aka min7 aka Dorian (1, 2, b3, 4, 5, 6, b7) we would find that the SIMPLE TRIAD chord sequence up the min7 scale would be Imin ,  IImin ,  III ,  IV,  Vmin,  VImin(b5),  VII, Imin;  The same step sequence as the Maj7 but slid down a whole step like a slide rule.  If the Pure Minor / min7 scale step sequence had a D root note we could clearly see the TRIAD-plus-7th-notes sequence as a CMaj7 scale sequence slide rule slid down one whole step with the TRIAD-plus-7th-notes being:  Dmin7, Emin7, FMaj7, G7, Amin7, Bmin7(b5), CMaj7, Dmin7, ....which are the identical chords, scales and sequence as CMaj7, .....just starting on D.  And of course if it works in a Dmin7 to CMaj7 relationship, IT WILL WORK IN ANY SCALE / CHORD QUALITIES SEQUENCE.  MEANING that we can play pretty darn jazzy sounding chords simply by playing the correct triad or 7th chords upon moments in the melody, or in harmony with the melody, or point in harmony with the melody, or moments in counter-melody, or timing notes in a measure, or accent points in a song, etc etc !

There are more exotic compositions where the key is written in / on / around more exotic Major and minor scales that require close scrutiny to determine the correct chords for each of those scale's step sequences.  In any event the harmonic chords will conform to the parent scale of the composition or part of the composition or passage in the composition by analyzing and treating the "mother" scale's step sequence chords just like done in the above examples.

The keys and scales in a composition can change, such as in Classical Music;  But in popular music the key and theme scale structure will usually remain the same.

SOME SUGGESTIONS & COMMON "RULES" ABOUT 4/11 NOTES:

The 4/11 extension note will occur often when you start studying / using chord substitutions and you will need to avoid playing those notes in the chords when they are not called for, because they have a STRONG effect of suspending and causing tension in songs / compositions that weren't written for that specific tension.  So we need to know some things about the 4/11 notes.  Any notes IN A MODAL CHORD will be nicely harmonic to each other EXCEPT FOR THE 4/11 EXTENSION ...unless the suspended or 11th chord is intended (it's probably the most used suspended chord).  In SCALES, the 4/11 note is normal and used extensively in melody, and passages, etc, ...but not often in chords unless specifically intended because it suspends a chord and thereby applies tension to what else is going on musically.  The tension is one of "confusing" the resolution of a musical line, keeping anticipation "hanging in the air", as opposed to an augmented or diminished chord's tension that affords anticipation of where the musical line is going.  So we will need to practice knowing where that 4/11 note is to avoid it IN CHORDS, by ear and by practice, which comes quite natural with a bit of woodshedding.  If you are interested in scale and chord substitution and/or modes;  Then you should see my short lessons on scale / chord substitution via modes.

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ALOHA !





1998wdt
~ Basic Music Theory Review via The Number System ~



WHAT MAKES OCTAVES AND THEIR NOTES:

A tensioned string will have a certain and set vibration inherent to the string's mass, length and tension.  A piano has a large set of strings ....longer and thicker ones for lower frequencies and shorter thinner ones for higher frequencies.   We can take any string and divide it's length in half, into 2 equal lengths, by  "clamping" the string to a stationary edge placed in the middle of the string.  Fretting a guitar string at the 12th fret "clamps" that string in half .  This causes each equal half to have a new, set, inherent and exact same frequency that is twice the number of vibrations per second than the original unclamped string.  The original frequency and the new frequency sound very much alike except that the new frequency vibrations are twice as fast and thus twice as high in pitch than the original unclamped frequency.  They sound very similar because they are whole / half proportional to each other in vibrations frequency / sounds.  The original string frequency, and the new frequency twice as fast, are defined as being an octave apart;  The new frequency an octave higher than the original.  The word 'octave' means 8 consecutive notes .....and we'll get into that later on this page.  Double a frequency and you get one octave higher ( while halving a frequency makes an octave lower).   If  / when we divide such a new string length in half again we get yet another new frequency that's yet again twice as fast and sounds very much the same as the previous two but is yet another octave higher.  We can keep dividing the string in half, achieving a series of higher octaves until the frequency gets so high that humans cannot hear it.

Let's prove it:  Look at a guitar's frets.  The 12th fret is half way along the strings bridged lengths.  There is only one octave on each of the strings below the 12th fret, BUT each octave between the 12th fret and the bridge, occur by repeatedly dividing that distance in half until we get so close to the bridge where octaves are so tiny and high that the frequencies are higher than our ears can hear.