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Upon reading Mark Levine's Jazz Theory Book, on the chapter of the diminished scale, there a footnote that says:

The diminished scale is artificial in the sense that it is not derived from the overtone series, as is the major scale, and has no particular ethnic origin, as does the melodic minor scale, which has an Eastern European ancestry.

footnote #68, page 77

But I cannot understand what the overtone series are. How is a major scale derived from it? If a scale is not derived from this, is it always an artificial one?

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Overtones are the notes found when you play natural harmonics.Sometimes called upper partials. I've grouped these names together, but they're not strictly synonyms. Using a guitar (or bass) string, open gives note. Let's call it the root. The first harmonic, half way along it is an octave above the root. Next, at 1/3 comes a fifth. The next, at 1/4 is another octave above the root. 1/6 gives a major third. 1/7 finds another fifth interval note.At 1/8 there is a note close to b7, then another octave root. From then, and they are not easy to play clearly, are more, very close together. They make up a whole octave of diatonic notes - a major scale. Some of these notes are slightly out of tune to our familiar TET, but close enough for jazz. I'm jesting!

The diminished scale can't be found using natural harmonics, and the notes in it are non diatonic. Think C, Eb, Gb, Bbb. Yes, the Bbb is a sort of diatonic sounding A, but that's all.

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    I was preparing an answer but I think Tim has said it well (once again). The only other thing that I was going to mention is the symmetrical nature of diminished chords, which is also prevalent in whole-tone chords, which are also artificial. These chords and scales are very interesting but their artificial nature can be heard when they are used, ie, they usually desire some resolution and tend not to work well as tonal centers, though Debussy wrote some interesting music along those lines. Maybe more anecdotal but they are rarely used in pop songs, probably because of that artificial feeling. – Basstickler Feb 11 '15 at 21:29
  • The notes in the ninth through sixteenth partials are not a diatonic scale. It's actually an eight-note scale in which every step is slightly smaller than the last, and it isn't what the quote in the OP is referring to. The Ptolemaic version of the Major scale can be derived from the overtone series (by the way, harmonics are a result of the overtone series, but not its definition) simply by building above the tonic using ratios from the early partials. 1/1, 9/8, 5/4, 4/3, 3/2, 5/3, 15/8, 2/1. – Pat Muchmore Feb 12 '15 at 0:40
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Why is the diminished scale 'artificial'?

In the sense of the quote you gave, it is artificial because it was not constructed from the overtone series.

What is an overtone series?

http://en.wikipedia.org/wiki/Harmonic_series_%28music%29 explains it very well.

How is a major scale derived from it?

There isn't a direct step by step method. It is easier to justify a pentatonic scale from the harmonic series than anything else. If our western major scale more directly followed the harmonic series it would have a # 4th, much like the lydian scale.

Harmonic series for C

C-C3-G3-C4-E4 G4-B-Flat4*-C5-D5 E5-F-Sharp5*-G5-A5*-B Flat5*-B5-C6.

Now the corresponding C major scale is:

C D E F G A B C

And taken literally the note collection above is:

C D E F# G A Bb B C

If you investigate 18th century counterpoint, you will learn why we do not use this scale, or why the current set of scales is a product of contrapuntal thinking. Often, ethnic, or traditional music will use scales or note sequences more closely following the above. Also, if you are interested in Jazz check out the "lydian chromatic theory" by George Russell.

Long story short:

F# is a no no. Causes a tritone.

Bb is a no no. Causes a tritone.

Now, allow me to deconstruct the author's quote for you:

The diminished scale is artificial in the sense that it is not derived from the overtone series, as is the major scale, and has no particular ethnic origin, as does the melodic minor scale, which has an Eastern European ancestry.

Sadly, music instruction textbooks are not always proofread by ethnomusicologists. Sometimes knowledge of the origins of musical constructs (for performers) is more passed down than maintained via rigorous inquiry.

The diminished scale is artificial in the sense that it is not derived from the overtone series

This is a confusing statement for multiple reasons. First, technically any scale can be justified by the harmonic series, since it producing a series of all possible notes, including thousands of microtones.

as is the major scale

Actually the history of the major scale is far, far more complicated than this and diverges from the "harmonic" series justification often. Like I said, nearly any scale can be justified by the harmonic series. Our major scale has as much to do with arguments over proper cadences in church music as it does the harmonic series. In that sense it is just as "constructed" as the diminished scale.

http://en.wikipedia.org/wiki/Diatonic_scale

and has no particular ethnic origin

This is just wrong:

http://en.wikipedia.org/wiki/Octatonic_scale#History

Diminished scales have existed for as long as diatonic scales, in various cultures around the world. They were also used widely by the romantics. Slonimsky wrote extensively about the scale. At any rate it goes way back, and has been used in Western classical music since at least 1823.

which has an Eastern European ancestry.

Also completely wrong. The melodic minor scale was, again, created by composers in Western Europe for properly resolving cadences. It's history and usage, and justification can be traced back to 18th century counterpoint practices throughout western Europe in the 18th century. Perhaps he just thinks it has a vaguely eastern sound?

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An artificial scale is a constructed scale, usually showing a lot of symmetry. The diminished scale is a perfect example: it alternates whole tone and half tone steps (e.g. starting from C):

C D Eb F Gb Ab A (Bbb) B

Note that the odd notes (1, 3, 5, and 7) as well as the even notes form a diminished seventh chord. Due to the symmetry there are only three different diminished scales (the ones starting on C, on C#, and on D; the one starting on Eb has the same notes as the one starting on C). Another example of an artificial scale is the whole tone scale with its obvious symmetry. There are only two different whole tone scales.

The above explanation of what an artificial scale is, is different from Levine's definition that it is scale which is not constructed from the overtone series. I believe that it is very hard to argue that the major scale is somehow derived from the overtone series. The first seven-note scale which comes up when looking at the overtone series is (with some approximations) the lydian dominant scale, which sounds to most people quite a bit less natural than the major scale. In this context, the lydian dominant scale is also referred to as the acoustic scale. Note that unlike a complete major scale, a major triad is definitely related to the overtone series, because already the first 4 overtones make up a complete major triad.

Note that the overtone series (or harmonic series) is simply the series of integer multiples of some fundamental frequency. They are not only found when playing natural harmonics, but any tone played by a natural instrument contains overtones. The timbre or 'color' of a tone is determined by the relative strengths of these overtones. This is why the same note sounds different when played on different instruments. E.g., a distortion effect does nothing but add more overtones, which changes the characteristic of the tone.

One consequence of the diminished scale being an artificial scale is that in a diatonic context, some of the tensions it implies when played over a diminished chord are non-diatonic. For this reason, for diminished chords with a diatonic function (i.e. resolving to a diatonic chord), the diminished scale is often replaced by other scale choices.

  • +1. I agree that the quote in the OP isn't super well-worded, but I think what they mean is that the Major scale (Ptolemaic) scale derives quite easily from ratios of lower harmonics - 1/1, 9/8, 5/4, 4/3, 3/2, 5/4, 15/8, 2/1. In other words, the intervals formed not just in sequence, but between various members of the overtone series create a just version of the major scale. Although the fourth above the fundamental doesn't show up until the 11th partial (and it's so sharp it's practically a tritone), the interval of a P4 is quite early, between the 3rd and 4th partial. – Pat Muchmore Feb 12 '15 at 0:45
  • @PatMuchmore: Thanks for you comment. I agree that this is probably what people mean by "derived from the overtone series". However, I think it doesn't make much sense, because in this way you can also "derive" many other scales, and it seems to me that the major scale is not "more naturally" derived from the overtone series than others. – Matt L. Feb 12 '15 at 9:05
  • Yeah, I agree for the most part. I don't think there are that many scales that can be derived from lower partial relationships, but the major scale isn't exclusive nor does the overtone series represent its historical genesis. Although pure 3/2 fifths tempered by pure 5:4 major thirds does. – Pat Muchmore Feb 12 '15 at 13:52

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