The earliest claimed occurrence of diatonic tuning is in the 45,000 year-old so-called "Neanderthal flute" found at Divje Babe. Although there is no consensus that this is a musical instrument, there has been one claim that it played a diatonic scale.
There is evidence that the Sumerians and Babylonians used some version of the diatonic scale.[citation needed] This derives from surviving inscriptions which contain a tuning system and musical composition. Despite the conjectural nature of reconstructions of the piece known as the Hurrian hymn from the surviving score, the evidence that it used the diatonic scale is much more soundly based. This is because instructions for tuning the scale involve tuning a chain of six fifths so that the corresponding circle of seven major and minor thirds are all consonant-sounding, and this is a recipe for tuning a diatonic scale. See Music of Mesopotamia.
9,000-year-old flutes found in Jiahu, China indicate the evolution, over a period of 1,200 years, of flutes having 4, 5 and 6 holes to having 7 and 8 holes, the latter exhibiting striking similarity to diatonic hole spacings and sounds[citation needed].
Western harmony from the Renaissance until the late 19th century is based on the diatonic scale and the unique hierarchical relationships, or diatonic functionality, created by this system of organizing seven notes. Most longer pieces of common practice music change key, which leads to a hierarchical relationship of diatonic scales in one key with those in another.
Technically speaking, diatonic scales are obtained from a chain of six successive fifths in some version of meantone temperament, and resulting in two tetrachords separated by intervals of a whole tone. For example under this view the two tetrachord structures of C major would be:
[C-D-E-F]-[G-A-B-C]
and of the natural minor of A would be:
[A-B-C-D]-[E-F-G-A]
Temperament and tuning
The diatonic scale has specific properties that mark it out among seven-note scales. David Rothenberg conceived of a property of scales he called propriety, and around the same time Gerald Balzano independently came up with the same definition in the more limited context of equal temperaments, calling it coherence. Rothenberg distinguished proper from a slightly stronger characteristic he called strictly proper. In this vocabulary, there are five proper seven-note scales in 12 equal temperament. None of these is strictly proper, i.e., coherent in the sense of Balzano; but in any system of meantone tuning with the fifth flatter than 700 cents, they are strictly proper. The scales are the diatonic, ascending minor, harmonic minor, harmonic major, and locrian major scales; of these, all but the last are well-known and constitute the backbone of diatonic practice when taken together.
Among these four well-known variants of the diatonic scale, the diatonic scale itself has additional properties of what has been called simplicity, because it is produced by iterations of a single generator, the meantone fifth. The scale, in the vocabulary of Erv Wilson, who may have been the first to consider the notion, is sometimes called a MOS scale.
The diatonic collection contains each interval class a unique number of times. Diatonic set theory describes the following properties, aside from propriety: maximal evenness, Myhill's property, well formedness, the deep scale property, cardinality equals variety, and structure implies multiplicity.
I would like to deal now with one of the foundations of Western music: the diatonic scale. Most of you are probably already pretty familiar with this scale, but I would like to dig a bit deeper than normally since a thorough understanding of this scale is very important for everything that I will point out later.
The diatonic scale like many other musical scales on this planet belongs to the family of the so called "heptatonic" or seven-note scales and has been around for quite a while (several thousand years).
The term "diatonic" in a broader sense refers to notes that belong to a certain key or scale (e.g. all seven notes of a harmonic minor scale in the key of A minor). In a much narrower sense the term "diatonic" refers to just the diatonic scale which basically contains the notes of a major scale. So to avoid confusion I will mainly talk about the major scale in this chapter.
The diatonic scale is a child of its mother, the 12-tone chromatic scale that forms the basis of all common scales within the Western musical system (typically nowadays the twelve-tone-equal-temperament). In this system the smallest musical building-blocks are tones that are one semitone or half-step apart, corresponding to a distance of one fret on a guitar or one key on a piano. Mathematically speaking, each semitone is equal to one twelfth of an octave. If the frequencies of two tones that are a semitone apart are divided one will obtain a ratio of 21/12 (approximately 1.059463094). You will find more harmony theory in one of the next chapters.
However, let's go back to the major scale: the major scale has been and is still used widely in almost every musical context from old greek music to todays Jazz and Heavy Metal. It is definitely one of the most universal scales on this planet. It also has a number of astonishing properties that make it quite unique: for example it is the heptatonic scale whose tones can form the maximum possible number of perfect fifths. Heavy metal guitarists probably like that property a lot, since if allows them to generate a maximum number of power-chords with this scale (six to be more precise) :-)
The major scale is defined by a very characteristic sequence of semitones and whole tones (a whole tone is made up of two semitones).
For guitarists playing all notes that correspond to the white keys on a keyboard - or the C-major scale - is not that simple. If we locate all these notes on a 24-fret fretboard it will look like this:
s you can see, due to the complexity of the guitar, finding a way of memorizing all these notes is far more difficult than just playing the white keys on a keyboard. Since the guitar is not a color-coded instrument like the piano, our only option to learn to play all these notes on the guitar is to either add some sort of color code to our frets or to come up with a comprehensive system that lets you access all these notes. While the idea of a color-coded "piano"-guitar is not per-se bad and could have its uses, a much more general approach would be more helpful.
The typical way of accessing these notes on the guitar is position playing. In the case of a major scale there are 7 unique positions on the fretboard that repeat themselves every other octave. One can now come up with all kinds of regular or irregular scale patterns that make use of 2-note-per string, 3-note-per-string, 4-note-per-string patterns or a mix of these.
But, I would also briefly like to mention, that one of the first steps to familiarize yourself with the C major scale is to play the scale on only one string at a time! This is the most natural and linear way of experiencing the above mentioned whole tone - semitone intervals directly on your guitar! For example go to the B-string and play the C major scale from C through C as depicted in the above fretboard. You can do this for every string and get a pretty good feel for the scale. It is also a good preparation for the more horizontal approach we will take a bit later in this chapter. Adding the horizontal dimension to the more regularly used vertical dimension of position playing will be the main recipe for amazing guitar playing far above average.
But let us for a moment go back to position playing:
One of the systems that I personally like a lot is the 3-note-per-string system that is widely used these days. The main advantage ist that it uses a regular number of notes per string, allows you to quickly cover a lot of terrain on the fretboard in a very fluid manner and unlike the 4-note-per-string system is still very finger-friendly.
Below, the 7 C-major scale positions in 3-note-per-string (3nps) patterns sorted from left to right (without the open strings) are depicted. Please note that I have given the 3nps positions greek mode names (supplemented with some more accessible names based on the starting note on the sixth string in the left lower corner of the red area).
I will not dive too deeply into this mode stuff since it is more complicated then people usually think. I will deal with modal playing in detail in a later chapter, but suffice is to say, that when building a scale from any note of the major scale and returning to it, people like to give it a greek name based on the respective note of the scale and call it a mode. However, all seven modes of the major scale contain exactly the same notes! So far we will just treat these different forms as different positions of the C major scales and not as modes.
Lydian- or F-form
Mixolydian- or G-form
Aeolian- or A-form
Locrian- or B-form
Ionian- or C-form
Dorian- or D-form
Phyrgian- or E-form
So as I already told you, these 3nps patterns are pretty standard and used by a lot of guitarists nowadays. However, the problem with all these patterns is that it is pretty difficult to memorize them. So you have got to learn 7 patterns of the major scale, 7 patterns of the harmonic minor scale, 7 patterns of the melodic minor scale, 7 patterns of any other heptatonic scale that you want to play ..... and then you can only play the positions up and down across the neck but don't still know how to link them together horizontally .... That could probably take you years....
So as I already told you, these 3nps patterns are pretty standard and used by a lot of guitarists nowadays. However, the problem with all these patterns is that it is pretty difficult to memorize them. So you have got to learn 7 patterns of the major scale, 7 patterns of the harmonic minor scale, 7 patterns of the melodic minor scale, 7 patterns of any other heptatonic scale that you want to play ..... and then you can only play the positions up and down across the neck but don't still know how to link them together horizontally .... That could probably take you years....
Fortunately there is a simpler and very systematic approach that can help you a lot and can be easily transferred from the major scale to all the other heptatonic scales. If you break all these 3nps patterns down into single building-blocks, things are dramatically improved.
If we group these patterns into smaller 6-note patterns that are formed by 3nps patterns on two adjacent strings we will find that there are only 6 distinct patterns (however one of them is showing up twice due to the similarity of the Ionian and Mixolydian shape, so functionally we have 7 patterns). In analogy to the above 3nps positions we can name them according to their starting note and the successive part of the scale.
Ionian- or C-form :-----: symmetrical
Dorian- or D-form :-----: asymmetrical
Phrygian- or E-form :-----: asymmetrical
Lydian or F-form :-----: asymmetrical
Mixolydian- or G-form :-----: symmetrical
eolian- or A-form :-----: symmetrical
Locrian- or B-form :-----: symmetrical
Now you can search for these patterns in the above 3nps positions and learn how they repeat themselves horizontally or vertically on a pretty regular basis! Note that two neighbouring horizontal patterns overlap by two notes on one string (4 notes total) which makes the system pretty simple!
Learn these patterns, then you will have total command of the fretboard! You only have to be aware that these patterns are somewhat distorted between the 2nd and 3rd string since the inverval there is only a major third (4 semitones or frets) instead of the regular fourth (5 semitones or frets) between two strings. So when moving from the 3rd to the 2nd string you have to shift the 3nps pattern on the 2nd string up a fret or semitone to the right hand side or vice versa on the way back.
I hope you had a closer look at these patterns on the fretboard and came up with some ideas of how to use them for navigating the fretboard. So if we use a systematic approach we could easily identify how to move in all 4 directions on the fretboard. To demonstrate this we will start off with an interesting experiment. Go to the 10th fret an your D-string which is a C (the starting point of an Ionian- or C-from pattern). Now let's move in all possible directions (left, right, up and down).
As you know if you want to move horizontally you will have to move by one scale degree (either one or two semitones or frets depending on the semitone steps) . So if you move to the left you will go from an Ionian pattern to a Locrian pattern. If you move to the right you will move to a Dorian pattern etc... When moving vertically, you will move one fourth (or five semitones) up or down (except for the interval between the 2nd and 3rd string which is a major third). So if you move from the Ionian pattern towards the high E-string (1st string) the next pattern will be a Lydian pattern. When moving into the opposite direction the next pattern will be a Mixolydian pattern. Basically you have to memorize the order of patterns when moving horizontally or vertically.
So if we put this information into a table and start at the ionian position (bold), here is what we get:
..............................................Aeolian
..............................................Phrygian
..............................................Locrian
..............................................Lydian
Mixolydian,Aeolian,Locrian,Ionian,Dorian,Phrygian,Lydian,Mixolydian
..............................................Mixolydian
..............................................Dorian
...............................................Aeolian
I have depicted the horizontal dimension from Mixolydian to Mixolydian and the vertical dimension from Aeolian to Aeolian. So basically this whole thing is a cycle that is repeating itself over and over and is only limited by the number of strings and frets. While this system looks pretty nice, knowing it and being able to play it effortlessly and without conscious thinking are two different things. It will take you at least months of disciplined practicing to fully digest it. I also would like to encourage you to use this system from the very beginning in a musical context (e.g. playing to a backing track in C major) and not to just run scales or patterns up and down (you should spend about 20 % of your time doing pure technical training and about 80 % of your time practicing within a musical context). This is the best way of training your ears and fingers to make real music. If you don't do this, your playing will sound pretty mechanical....
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