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why is the major scale constructed like it is?

Posted by expuddle 
Re: why is the major scale constructed like it is?
August 18, 2013 09:03PM
Ty Wrote:

> But I believe this begs the question. The heart of
> the matter is why such a preference is
> running 400 years and counting?

What about the THOUSAND years of preference for modes prior to the advent of the Major/Minor scale system. And what about MINOR. What about the rediscovery of modes in the 1800s? The modern preference for Major and Minor scales is not as strong as it was in the CPP (so really Major only represents about 66% of 200 years), and we have just as much preference for Dorian and Mixolydian, as well as Blues Scales, and all the other ethnic scales out there.


>
> Looking for an acoustical, objective basis for
> aesthetic preferences in music seems to me a very
> honorable and intelligent thing to do.

Why? Are you looking for an objective physical science reason for the preference for Poodle Skirts in the 50s versus mini-skirts in the 60s versus Skorts in the 90s? Is there some scientific reason people preferred Grey Flannel Suits in the 40s and 50s, or why Tweed Jackets are common in X period.

No one in any other field tries to explain stylistic choices "scientifically" (well, OK, some do, but...). I've never seen it to any degree compared to what happens with music. As I said, even in the visual arts no one's sitting around trying to say that the wavelengths of colors have anything to do with choice of and combination of colors in a painting. Why do musicians have this pre-occupation with trying to explain "why" with acoustic principles that have no actual bearing on the choices being made. It's silly.




Folks are
> looking for the frame that undergirds what we like
> in music.

I guess, maybe because music hits us at such a "gut" level - it connects with us in a way that's essentially unexplainable, so the attraction of explaining the unexplainable is always going to attract attempts at explaining it.

But for 1000 years or so, people "liked" music that never had a Major scale in it. What about that? All these people are so focused on the Major Scale as "the" scale, or "the perfect" scale, or, what ends up as what they're saying, "the apogee of western invention" So their premise, "The Major Scale is Best, so now I'm going to explain why using flawed arguments supposing the support of Acoustic properties to make everyone believe it".

I know many people who will say the Blues Scale has more soul and power than any "plain vanilla" Major Scale. In fact, I've seen people on other forums who would argue with you until their fingers turn blue about how the Septimal Seventh used in blues aligns with the crystal lattice of the heavenly spheres and because of this blues musicians choose this exact note to connect with our inner harmony and souls it's "better" than any old Major scale.

And any good Romanticist will tell you that the most powerful music is all in Minor anyway! Beethoven 5, 9, Pathetique, Moonlight, etc. It was the minor movement of Beethoven's 7th that was encored at it's premiere.

And what's funny is, all these acoustic arguments are made in support of Major, but when if comes to Minor, they have nothing to say. It's all because there's a Major-centric way of thinking and these people are conditioned to believe that it is somehow superior for no other reason than someone told them so. So they have to look for ways to prove it to themselves.

But, believe what you will.

Steve
Ty
Re: why is the major scale constructed like it is?
August 18, 2013 11:13PM
Quote
SteveL
The purpose of counterpoint (from which that style of writing evolved) was to maintain the independence of the voices. When you use parallel intervals of any type for too long, one voice becomes dependent on the other - it gets "subsumed" into it. This is especially true of 5ths, and even more so for Octaves (and obviously, unisons!).

In essence, nothing destroys independence of the voices like parallel 8ves or 5ths.

Exactly. We know from an acoustical basis that voices become subsumed into one another if their intervallic relationship too closely mirrors the overtone series of the lower-sounding pitch. Basic acoustics. The imperative of the style, the holy grail, is voice-independence, but voice-independence hinges on fundamental, natural laws of physics.
I don't believe great CPP-era composers sat around looking for scientific and mathematical reasons to write such-and-such pitch here or there. That's not my point, nor the point of anyone looking for an acoustic basis for musical practices.

What we are interested in is whether art is more or less effective according to its relationship to nature. The example of 5ths/8ves prohibition deftly illustrates how acoustics is the domain for musical/aesthetic choices. Acoustics necessitate ingenuity on the part of composers who wish for richer texture, they must beware of certain pitfalls of the natural harmonic order, they must wrestle and grapple with the natural world in which the sound lives; contrary motion is paramount in counterpoint for the same reason.
Ty
Re: why is the major scale constructed like it is?
August 18, 2013 11:17PM
Another example, Steve, is how intervals must widen as you descend the keyboard (or the orchestra). The aesthetic choice to compose a piece with octaves or 5ths instead of 2nd or 3rds when writing below E2 is contingent upon acoustics.
Ty
Re: why is the major scale constructed like it is?
August 18, 2013 11:25PM
Quote
SteveL
However, many people find DaVinci's work to be too "academic" - in much the same way as people see Bach's music. Although it's a Romantic ideal, people tend - still - to favor more "emotion" in their art. La Giaconda's appeal seems to be less about it's *supposed* architectural positioning and more about the "enigmatic smile" which has nothing to do (that I've ever heard) with any scientific or physical elements - it's purely the emotional aspect of that smile which "connects" with people.

There is plenty of music out there written *very specifically* using acoustical principles in a far more obvious manner than other styles of music. It just does not connect with people in any significant way that would lead one to believe that what little intentional acoustic elements included in more popular music have any impact on a listener - it's ultimately leaning towards the "art" side.

Steve

Steve, it's quite difficult to respond meaningfully to this post, because it relies on so many slippery suppostions.

Who, exactly, are the "many people" who find DaVinci's work too academic or lacking emotion?

What music, which composers, have written "very specifically'" using "acoustical principles in a far more obvious manner"? And who said anything about using acoustics prescriptively as a method for composing?
Ty
Re: why is the major scale constructed like it is?
August 19, 2013 12:04AM
Quote
SteveL
No one in any other field tries to explain stylistic choices "scientifically" (well, OK, some do, but...). I've never seen it to any degree compared to what happens with music. As I said, even in the visual arts no one's sitting around trying to say that the wavelengths of colors have anything to do with choice of and combination of colors in a painting. Why do musicians have this pre-occupation with trying to explain "why" with acoustic principles that have no actual bearing on the choices being made. It's silly.

Again, DaVinci, arguably the most influential and important visual artist in human history, meticulously applied his scientific discoveries to his artistic endeavors. Mona Lisa is a triumph of perspective, created from a deep understanding of not only human anatomy but the processes of visual perception. He didn't just "feel" his way into painting the most influential masterpiece in the history of painting.

All this talk about acoustics, and I forgot to mention something quite important. It's not just acoustics -- the physical properties of sound -- that's important, it's the way the human brain psychologically relates to various manipulations of that natural order. WNYC covered a very interesting study on Beethoven's tempos. In it, they discuss Vierordt's Law about human perception of time; as it pertains to music, at 80bpm the average person rushes, at 120bpm the average person drages, for example. At around 94 or 96 bpm is the "indifference point," where the average person neither rushes nor drags. One argument for why Beethoven's tempo indications were so fast was that he deliberately intended on unsettling the listener, and consequently posthumous conductors and interpreters misapprehending this have settled toward the "indifference point," comfortable tempos. Given his meticulousness, should we be surprised to learn Beethoven may have a) intuited where the indifference point was and b) deliberately indicated pieces to be performed at tempos unsettling close to it for emotional effect?

Joyce and Proust in literature were no strangers to psychology or science, and the modern art of branding and marketing relies upon both.
Ty
Re: why is the major scale constructed like it is?
August 19, 2013 12:11AM
But, getting back to the OP, "why is the major scale constructed like it is?"

Ostentatiously blathering about modes and pre-CPP musical practices doesn't answer this question, it only evades and mocks the question.

Looking for the relationship between the major scale and acoustic properties of sound, not to mention studying the various scale-resource possibilities in an octave, within the domain of equal temperament tuning, is a valuable and worthy endeavor. I just don't get, Steve, why you are so knee-jerkingly and rudely opposed to such investigation. Schenkerian theory begins with precisely that investigation; you should read Harmony, seriously.
nicholovich
Re: why is the major scale constructed like it is?
December 20, 2013 06:56PM
I need a good reference that states that the notes of the major scale sound good together because their intervals are simply mathematically related. I did not understand what you wanted to say when you wrote


There's also the harmonic series to consider. Any piano string vibrating at any frequency will also contain other (fainter) vibrations (overtones) which are multiples of the fundamental vibration. The closest and strongest of these correspond to a large degree to those simple ratios mentioned above.

As far as I know, the overtones are primarily octaves apart, is this not true?
Would appreciate any reference that a novice could easily understand.
Re: why is the major scale constructed like it is?
December 20, 2013 09:46PM
nicholovich Wrote:
-------------------------------------------------------
> I need a good reference that states that the
> notes of the major scale sound good together
> because their intervals are simply mathematically
> related. I did not understand what you wanted to
> say when you wrote
>
>
> There's also the harmonic series to consider. Any
> piano string vibrating at any frequency will also
> contain other (fainter) vibrations (overtones)
> which are multiples of the fundamental vibration.
> The closest and strongest of these correspond to a
> large degree to those simple ratios mentioned
> above.
>
> As far as I know, the overtones are primarily
> octaves apart, is this not true?
> Would appreciate any reference that a novice could
> easily understand.

No, it's not true.The overtones' frequencies (as mentioned above) are multiples of the fundamental note.

For example, if the fundamental is 100 vibrations per second, the first overtone is 200, which is indeed an octave because it's twice the frequency, but the next overtone is 300 (3x the fundamental) 300. It's not twice as high as the previous overtone but one and a half times the frequency (300/200). That makes a perfect 5th, not an octave, above that overtone).

Fundamental note = 100
1st overtone = 200 (an octave above the fundamental)
2nd overtone = 300 ( an octave plus a perfect 5th above the fundamental)
3rd overtone = 400 (two octaves above the fundamental)
4th overtone = 500 (two octaves plus a major 3rd)
5th overtone = 600 (two octaves plus a perfect 5th)

Here's a diagram of the overtone series from a source that's almost as reputable as us :-)
[www.phy.mtu.edu]

It agrees with ALL of the above, but it doesn't say that that's why the notes of the major scale sound good together. Good and bad are subjective terms that lie outside of the realm of physics. I don't think anyone on this thread says the major scale's notes sound good together, but that they work well together (within our musical system). Any two notes can sound good or bad together depending on context and personal taste.
Re: why is the major scale constructed like it is?
December 21, 2013 03:05AM
nicholovich Wrote:
-------------------------------------------------------
> I need a good reference that states that the
> notes of the major scale sound good together
> because their intervals are simply mathematically
> related. I did not understand what you wanted to
> say when you wrote
>
>
> There's also the harmonic series to consider. Any
> piano string vibrating at any frequency will also
> contain other (fainter) vibrations (overtones)
> which are multiples of the fundamental vibration.
> The closest and strongest of these correspond to a
> large degree to those simple ratios mentioned
> above.
>
> As far as I know, the overtones are primarily
> octaves apart, is this not true?
> Would appreciate any reference that a novice could
> easily understand.

Here's my chart of the harmonic series of A=110 (same frequency as guitar 5th string, octave and 3rd below middle C)
HARMONIC - FRET - FREQUENCY - NEAREST NOTE - cents away from ET
 1st        0       110 Hz          A
 2nd       12       220 Hz          A
 3rd      7, 19     330 Hz          E  (329.6)   2 cents sharp
 4th      5, 24     440 Hz          A 
 5th    4, 9, 16    550 Hz          C# (554.0)  14 cents flat
 6th        3       660 Hz          E  (659.2)   2 cents sharp
 7th 2.7, 9.7, 14.5 770 Hz          G  (784.0)  32 cents flat
 8th       2.3      880 Hz          A  (880)
 9th        2       990 Hz          B  (987.8)   4 cents sharp
10th       1.8     1100 Hz          C# (1108)   14 cents flat
11th               1210 Hz          D# (1244.5) 49 cents flat
12th               1320 Hz          E  (1318.5)  2 cents sharp
13th               1430 Hz          F  (1396.9) 40 cents sharp
14th               1540 Hz          G  (1568.0) 32 cents flat
15th               1650 Hz          G# (1661.2) 12 cents flat
16th               1760 Hz          A  (1760)
17th               1870 Hz          Bb (1864.7)  5 cents sharp
18th               1980 Hz          B  (1975.5)  4 cents sharp
19th               2090 Hz          C  (2093.0)  3 cents flat

Ignore the second column, only of interest to guitarists!
As you can see, the lower order harmonics - the loudest ones - align very closely with the tones of an A major triad.
Only the octaves are exactly in tune, but the E is very close (a negligible 2 cents out), and the C# (14 cents out) is "close enough" for most ears.

The 7th is the first odd one out, and seems to imply a natural basis for the dominant 7th chord; but it's significantly flat of a tuned A-G minor 7th. In western music, we use dom7 chords as tensions, so there is no need (IMHO) to explain them as natural consonances.
However, there is an argument for this overtone as a natural basis for blues harmony, perhaps for folk mixolydian mode, and that barbershop habit of ending on a dom7 chord (tuned by ear, so probably aligning with this harmonic).
(The site Fretsource linked to suggested avoiding this overtone. Multiples of 7 are not considered in western theory, in which scales are constructed - historically - from ratios involving factors of 2, 3 and 5 only. If you want more of this, google "5-limit" and "7-limit" tuning.)

BTW, in the last column I describe the harmonics as flat or sharp of equal tempered (ET) pitches. You may like to look at it the other way round: it's the artificial system of equal temperament that is out of tune with "pure" harmonics!



Edited 3 time(s). Last edit at 12/21/2013 03:09AM by JonR. (view changes)
Re: why is the major scale constructed like it is?
December 21, 2013 10:43AM
JonR Wrote:
-------------------------------------------------------
"
>Here's my chart of the harmonic series of A=110 (same frequency as guitar 5th string, octave and 3rd below middle C)

HARMONIC - FRET - FREQUENCY - NEAREST NOTE - cents away from ET
1st 0 110 Hz A
2nd 12 220 Hz A
3rd 7, 19 330 Hz E (329.6) 2 cents sharp
4th 5, 24 440 Hz A
5th 4, 9, 16 550 Hz C# (554.0) 14 cents flat
6th 3 660 Hz E (659.2) 2 cents sharp
7th 2.7, 9.7, 14.5 770 Hz G (784.0) 32 cents flat
8th 2.3 880 Hz A (880)
9th 2 990 Hz B (987.8) 4 cents sharp
10th 1.8 1100 Hz C# (1108) 14 cents flat
11th 1210 Hz D# (1244.5) 49 cents flat
12th 1320 Hz E (1318.5) 2 cents sharp
13th 1430 Hz F (1396.9) 40 cents sharp
14th 1540 Hz G (1568.0) 32 cents flat
15th 1650 Hz G# (1661.2) 12 cents flat
16th 1760 Hz A (1760)
17th 1870 Hz Bb (1864.7) 5 cents sharp
18th 1980 Hz B (1975.5) 4 cents sharp
>19th 2090 Hz C (2093.0) 3 cents flat "

It is somewhat incomprehensible why the minor scale is considered although the question was referred to major scale. IMHO, it is valid for both scales: for decrease of possible dissonances the scales' notes frequencies must possibly correspond overtone series.

Yuri Vilenkin
Re: why is the major scale constructed like it is?
December 22, 2013 04:19AM
vilen Wrote:

> It is somewhat incomprehensible why the minor
> scale is considered although the question was
> referred to major scale. IMHO, it is valid for
> both scales: for decrease of possible dissonances
> the scales' notes frequencies must possibly
> correspond overtone series.

"must"?

I think there's an issue here between scale and chord construction. Scales are not dependent on consonance between their pitches
(relative to the root or not), at least not in the way that chords are. It may be that, once chords (and harmony) became an essential component of music, then the kinds of scales - or modes - that produced harmonious chords (consonant as well as
pleasantly dissonant) became favoured.

(I guess many of these musings may have been expressed - and dealt with - earlier in the thread, or at least in previous threads...)

Obviously all modes of the diatonic scale produce the same chords, but major, Ionian, seems to make them perform in the clearest,
most satisfying way, dissonance to consonance. They all seem to fall happily into place. And the major chord, of course, as a "tonic", aligns well with the harmonic series, so the rest of the scale and chords seem to line up in support.
With the other major modes (lydian, mixolydian) the dissonances are more ambiguous: the tritone is there in the extended tonic chord, seeming to want to resolve elsewhere. The "pull" of the dissonances - in chords, or implied by melodies - is all towards an Ionian tonic. B goes to C and F to E. The natural root of a C-E interval is C.

The problem with explaining minor chords and scales from the overtone series is that the minor 3rd is not among the prime harmonics. It doesn't appear until way up at the 19th harmonic, which is (IMO) a neglible part of the fundamental. Therefore, if we used the harmonic series as our sole foundation for scale (or chord) construction, we would never arrive at the idea of a minor scale/chord. It simple makes no sense, from that perspective.
And yet obviously minor keys form a large part of our music (almost half). So some other explanation is required.
It still must (IMO) be connected - in some way - with the HS, but more indirectly. (I mean, obviously minor chords, scales and keys are used because we like the sound! But - I guess this is behind your question - why do we like the sound? Is it purely cultural familiarity? Or is there some acoustic science that can at least partially explain it?)

We can certainly see that the tones of a minor chord (tuned pure) are in relatively simple ratios (10:12:15), albeit not as simple as major (4:5:6). That might seem to explain why a minor chord "sounds OK" - and its more complex ratios might even explain (in part) its more mysterious or intriguing sound.
But if we look at the common factor of those ratios - the "acoustic root" of which the chord tones could be overtones - we get a note that is not in the chord. Eg, the virtual acoustic root of an A minor triad (ACE) is F. That doesn't seem to make a lot of sense, because intuitively we feel A is the root (thanks to the strong A-E 5th, of which A is clear root).
The problem (for HS adherents) - as mentioned - is that C is not part of the harmonic series of A - at least not audibly. So why does it sound OK? Why doesn't it sound totally out of place?
ttw
Re: why is the major scale constructed like it is?
December 23, 2013 06:45AM
The actual vibrations of piano strings is noticeably anharmonic. Still, fifths and thirds, etc., have their "musical" meanings.
Re: why is the major scale constructed like it is?
December 23, 2013 07:08AM
Here's a neuro-scientist who's put forward a biological explanation for why we perceive consonant and dissonant intervals in much the same way worldwide.
[www.dukemagazine.duke.edu]

He (and his team) analysed loads of speech patterns (including Chinese) and discovered a high correlation between frequency ratios of speech formants present in vowel sounds and frequency ratios of the most consonant intervals in music.
He's not a musician and sometimes confuses consonant with pleasant, but I found it quite interesting, although I'm far from convinced yet. I just thought I'd add some more fuel to the fire ;-)
Re: why is the major scale constructed like it is?
December 23, 2013 07:29AM
Are you saying vilen is Purves?
Re: why is the major scale constructed like it is?
December 23, 2013 08:32AM
JonR Wrote:
-------------------------------------------------------
> Are you saying vilen is Purves?

Hmmm - never thought of that... but nah...no way. That article doesn't mention harmonics anywhere. Can you imagine Vilen writing an article on consonance and dissonance without ever mentioning harmonics? - impossible. No offence Vilen :-)
Re: why is the major scale constructed like it is?
December 24, 2013 03:05AM
Sorry I just realised I misread your previous post! You said "Here's" and I read it for some reason as "He's"! (Must be the dementia setting in... :))
Re: why is the major scale constructed like it is?
February 24, 2014 06:07PM
quick answer to expuddle:

Your questions were right on the mark.

The (t t s t t t s) sequence of the major scale directly creates the two '3-tone' segments of opposite 'temperament' (, temper, color, or mood,) that are found in the scale. They are C_D_E and g_a_b, and are 7 semitones apart. You jump from one 3-tone to the other. No other scale has such a simple and powerful structure.

There are two 6-tone series on the keyboard, C_D_E_F#_G#_A# and g_a_b_c#_d#_f. By playing using all 6 tones from one series, and none from the other, it did not sound good. You were using too many tones from one temperament, and not enough from the other.

The major scale uses the alternating 4-tone series, but selects 3 tones from the first, 4 tones from the second, and then a 4th tone one octave above the first. C_D_Ef_g_a_bC_. This creates the 3-tone, transition tone, 3-tone, transition tone, sequence found in C.

The simplicity, symmetry, and power found in the major scale makes it easy to learn and play. It is a solid base to study other more complex or subtle scales.

I will go into the details in another post called: The structure of the major scale, long answer to expuddle.


note to modellpq:

I agree with you "that a major scale consists of two identical phrases, one following the other". I discovered this 3 years ago, to my own stupefaction. The next post summarizes my findings on the scale since then. (Summary of the summary: "But these phrases are of a different color !") Do these findings make any sense to you? Are they understandable? They have transformed the way I learn music, and have given me solidity and depth. Nothing is too difficult when you work with these tools.
Jack
Re: why is the major scale constructed like it is?
April 11, 2014 11:08AM
The major scale was just one of several modes. I think the popularity of the major (ionian) scale came with the evolution of harmony and established rules of the common pracrice period starting in about 1600 AD and the importance dominant-tonic relationship. This would explain why the major mode wasn't as popular before this period. Two things I think we're important to composers in that period (1600-1900): the leading tone such that the seventh key in the scale was a semitone away from the tonic key and the dominant 7th chord which has a strong pull to the tonic.

The major modes are (Ionian, Lydian, and Mixolydian)

The major (ionian) scale naturally has both of these qualities. The 7th chord which is 5 keys away from the tonic is a dominant 7th chord on the major scale. Also, the major scale naturally has a leading tone. The Lydian mode also has a natural leading tone, however the 7th chord 5 keys from the tonic is a major 7th chord, not a dominant chord.
The Mixolydian mode has no naturally leading tone and the 7th chord 5 keys from the tonic is a minor 7th chord, not a dominant chord. Because of this, both the Lydian and the Mixolydian fell out of favor.

The minor modes are (Dorian, Phrygian, and Aeolian)

None of the minor modes have a natural leading tone or a natural dominant 7th chord. Phrygian can be ruled out because it's fifth chord is a diminished chord. At least Dorian and Aeolian both have a minor fifth chord and a minor 7th fifth chord. Changing the third note in the chord to major with make the chord a dominant 7th chord, which is the goal. This is done by raising the 7th key a semitone which also creates a leading tone. Doing this on the Aeolian mode creates the harmonic minor (the reason the harmonic minor was invented). However, doing this on the Dorian mode also meets the requirements of the dominant 7th chord and leading tone.

So the real question is why was the Harmonic "Aeolian" minor chosen over the Harmonic "Dorian" minor?
Re: why is the major scale constructed like it is?
April 11, 2014 12:26PM
Me again. I decided to go ahead and register.

I had another thought. If we're primarily concerned about the dominant-tonic relationship such is the case in western music, then we can construct our own scale based on that. If we use C as an example, the dominant 7th chord must be G7 which contain the notes G, B, D, and F. And of course we must have C. So far we have 5 required notes for the scale: B, C, D, F, and G. What is missing is A and E, either of which can be flatted or natural. If both A and E are natural, then you have the major scale. If both A and E are flatted, you have the harmonic minor scale. If E is flatted and A is natural, you have the melodic minor scale (turns out this is the same as the Haromonic "Dorian" scale which kinda answers my previous question). If A is flatted and E is natural then you have some type of new weird major scale, which have the chords: I, iidim, iii, iv, V, VI+, viidim, I.
So, I think that dominant-tonic relationship is responsible for the major/minor scale being what it is.
Re: why is the major scale constructed like it is?
April 11, 2014 01:40PM
Jack Wrote:
-------------------------------------------------------
> The major scale was just one of several modes. I
> think the popularity of the major (ionian) scale
> came with the evolution of harmony and established
> rules of the common pracrice period starting in
> about 1600 AD and the importance dominant-tonic
> relationship.


Not quite. By the time the terms "Ionian" and "Aeolian" appeared, the other modes had been in use for centuries.
And those modes weren't always 100% "pure".

The Lydian mode, in practice, often lowered the fourth degree (from B to Bb, or transposed equivalents) to avoid the tritone from the root. This produced music which might look to us, on first glance at least, to be in the "major key" - and this is still several centuries before the term "Ionian" came into existence. In fact, the addition of Ionian and Aeolian was largely a theoretical matter, and didn't really make any appreciable difference to music practice.


> So the real question is why was the Harmonic
> "Aeolian" minor chosen over the Harmonic "Dorian"
> minor?

Like above, music in the Dorian mode often lowered the sixth degree in practice.

So in actual fact, the true origins of "major" and "minor" are actually better described as being "Lydian" and "Dorian" modes rather than Ionian and Aeolian.

Check out this textbook on Four Part Harmony.
Lola
Re: why is the major scale constructed like it is?
April 22, 2014 10:59AM
What is the history of the major scales? Im intrested in theory and analysis as to how and why they are used. Google hasn't been much of a help in my search to understand how the scales came into being and why. I'd love some help with this.
Re: why is the major scale constructed like it is?
April 22, 2014 11:26AM
Lola Wrote:
-------------------------------------------------------
> What is the history of the major scales? Im
> intrested in theory and analysis as to how and why
> they are used. Google hasn't been much of a help
> in my search to understand how the scales came
> into being and why. I'd love some help with this.

You really need a good book on this, but meanwhile this is my favourite site on the history of scales in western music:
[www.yumpu.com]
It's from a technical perspective, of course, focussed on tuning and temperament, but seems pretty good on the evolutionary process.

Essentially, you can say the major-minor key system developed out of the medieval modal system. The modal system itself evolved over the 1000 years (or so) that it existed in Christian Europe (600-1600 very approximately), and gave way to keys (dominated by the major scale) very gradually, as our system of tonal harmony developed. The major scale - based on Ionian mode, one of the later additions to the modal system - and its associated system of tonality (major and minor "keys") - [en.wikipedia.org] - has ruled western music for around 400 years (again very approximately), and is the system that our standard musical theory is based on - the so-called CPP, or Common Practice Period:
[en.wikipedia.org]
As that page states, 1900 is considered to mark the end of that period - as avant garde composers such as Schoenberg sought alternatives - but popular music since then is still broadly tonal, if rather freer with the old CPP rules.



Edited 2 time(s). Last edit at 04/22/2014 11:34AM by JonR. (view changes)
Thomas Hopwood
Re: why is the major scale constructed like it is?
May 24, 2014 12:49PM
The major scale exists in nature, just like the major triad exists in nature (blow a bugle and that's what notes are produced-a major triad). Mother nature can't be fooled---bugles came from animal horns, and they don't change--always turning out a major triad. (No "accidental" keys on a bugle).

Listen to the triad C (on a piano for example), resolve to the triad F. C resolves to F because it sprang from F in the harmonic series of F (it's a perfect 5th of F, it's number 3 in the series of F, and it's surrounded by F's).
Then listen to the triad G resolve to C (for the same reason that C resolved to F).
These 3 triads revolve around the tone C and have only 7 different notes, which produce the scale of C. A scale of all "natural" keys.

Is this complicated?

That's my story and I'm sticking to it (unless I'm missing something).

Tom Hopwood
Re: why is the major scale constructed like it is?
May 25, 2014 05:32AM
Thomas Hopwood Wrote:
-------------------------------------------------------
> The major scale exists in nature

No it doesn't.

> just like the
> major triad exists in nature (blow a bugle and
> that's what notes are produced-a major triad)

Yes - that's the harmonic series, which produces a "pure" major 3rd and perfect 5th (along with octaves) as the lower overtones.
Both are a little out of tune with modern equal tempered scales, but horn players can "lip" notes into tune if they have to.
The remaining notes produced by the harmonic series don't align with the major scale, or indeed with any of our modern tempered scales. (They're close to what's known as the "overtone scale", aka "lydian dominant", but in equal temperament it's not close enough.)

> Mother nature can't be fooled---bugles came from
> animal horns, and they don't change--always
> turning out a major triad. (No "accidental" keys
> on a bugle).
>
> Listen to the triad C (on a piano for example),
> resolve to the triad F. C resolves to F because it
> sprang from F in the harmonic series of F (it's a
> perfect 5th of F, it's number 3 in the series of
> F, and it's surrounded by F's).

The C note is a strong overtone of F, yes, and is arguably behind the sense of resolution when the single notes move in that way, at least when C goes down a 5th to F.
But the C triad has no natural tendency to move anywhere. It's a stable sound in its own right (due in part to the harmonic series as mentioned).
If a key centre of F has already been established, then yes a C triad will act as dominant and resolve to F.
But that's largely (if not entirely) down to our cultural familarity with the major key system - which is not natural, it was only introduced to European music around the 16th century. No other culture, and no time in Europe up to then, regarded it as in any way fundamental. Of course, we feel it' "natural" now because it's central to our culture and we've all grown up with that "do re mi".

Try telling an Indonesian gamelan player that the major scale is "natural". He/she might well shrug and say "if you say so", but what is natural is beside the point in any musical culture, including our own. "Natural" doesn't cut it. We need tension and dissonance.

Our scales do have a kind of connection with overtones of root notes (the harmonic series IS an important natural phenomenon affecting perception of pitch and harmony), but it's not direct or simple.

> Then listen to the triad G resolve to C (for the
> same reason that C resolved to F).
> These 3 triads revolve around the tone C and have
> only 7 different notes, which produce the scale of
> C. A scale of all "natural" keys.
>
> Is this complicated?

No, it's just wrong. :-)

> That's my story and I'm sticking to it (unless I'm
> missing something).

It's the history and the mathematics you're missing. ;-)

This site will fill in some background for you:
[www.yumpu.com]



Edited 1 time(s). Last edit at 05/25/2014 05:35AM by JonR. (view changes)
ttw
Re: why is the major scale constructed like it is?
May 25, 2014 06:51AM
[www.youtube.com]

[www.youtube.com]

[www.youtube.com]

[www.youtube.com]

Counter examples. Later, counter-tenor examples.
Adrian Allen
Re: why is the major scale constructed like it is?
June 10, 2014 08:04PM
The major scale formed out of the diatonic sequence wwwhwwhw of Lydian whch is the first scale/mode that is formed out of the Pothagorean circle of fifths. If you replace the augmented fourth in Lydian with a P4 you get Ionian. The dominant seventh chord being the only V chord not containing a b5 indicative of the key led to it's choosing as the definitive mode to develop tertiary harmony out of as well as it's relationahip of the I6 chord being a vi7 inversion and the vi7 chord containing the I triad led to it's prodominance to it's relative Aeolian.

However now that we have opened our ears to dissonance and to intervallic relatinships that used to be considered unmusical, we can see that Phrygian with it's half diminished v (vii) chord would possibly be a better minor counterpart to Ionian.

Phrygian- 1 m2 m3 P4 P5 m6 m7 Ionian- 1 M2 M3 P4 P5 M6 M7

Phrygian has all minor intervals and two perfects while Ionian has all major intervals and two perfects.

The vii7 half diminished chord is equally indicative of Key as the V7 dominant chord as there are only one of each in each natural key.

The Phrygian would hold prodominance over the Ionian and Ionian would be it's relative due to the relationship of the chord functions associated with each mode.

iii6 chord is an inversion of a I7 chord and a iii triad is contained within a I7 chord. The same relationship as I and vi but with the I relative to the prodominant iii.

I have this further detailed in my book "Modal Diatonicism" available at Amazon.com Also with diatonic sets for each mode as prodominant and relative with parallels and secondary functions for each.

Adrian Allen
Re: why is the major scale constructed like it is?
June 28, 2014 08:38AM
Thomas Hopwood Wrote:
-------------------------------------------------------
> The major scale exists in nature

The music is artifact and any music scale is artifact. Music scale is built specially for music production on common music instruments (inclusive human voice ) which sounds correspond roughly to harmonic oscillation. Our ET music scale is results of artificial compromise between necessity contain some ratios of natural row which correspond partials of harmonic oscillation and necessity to have same ratios between all neighboring scale point. Second one is required for possibility to reproduce melodies in different frequency diapasons.
The major scale is one of diatonic scales and get advantages thank to development of music (secular music) and technology. In end of 16 century
H. Glarean noticed that composers use accidentals in other scales which aren't required by use of major scale (then Ionian) and elicited it together with minor scale (then aeolian). Possibly most important advantage of major scale is leading note to tonic. Concerning euphony major an minor triad are roughly equal and better as other possible in diatonic scale triads. Both scales have their characteristic triads on most important positions of tonic, subdominant and dominant. Of course, these properties of major and minor triad were discovered thank to use of new music instruments of clavichord type from begin of the 15 century. Of source, chords ( and triads) are artifacts.

>major triad exists in nature (blow a bugle and that's what notes
> are produced-a major triad)

You can believe in it but it can't serve as argument.

Yuri Vilenkin
ttw
Re: why is the major scale constructed like it is?
June 28, 2014 03:30PM
The Lydian mode has a leading tone.
Re: why is the major scale constructed like it is?
June 29, 2014 02:45AM
ttw wrote:
>The Lydian mode has a leading tone.

Yes, but it hasn't note with fourth consonant interval to tonic and has on subdominant position most dissonance triad b-d-f.

Elevation of major and minor triad in Renessance era may be explained by
development of secular music. Church modes were used for definite melodies as psalmes. They have recitation tone-tenor and same initial and final tone-finalis. By it pitches of tenor and finalis had considerable difference, which served for indication of begin and final. The pitches in the middle part are little differed from tenor and altered in intervals of 1-2 semitones. So the smoothness of sound and indicaion of initial and final parts were provided.
It is interesting that the word psalm descend from Greek werb for playing on the single string. Such playing provided absence of dissonances from overlapping of neiboghbouring tones (possibly,especially important for primitive instruments) but determined melody alteration in little diapason.
The secular music required significant more diapason for melodies. In these conditions chords becam a means for support of music smoothness and punctuation and leading note to tonic becam especially valuable for punctuation in melody itself together with rythm alteration.

Yuri Vilenkin
ttw
Re: why is the major scale constructed like it is?
June 29, 2014 10:02PM
In one sense, the question of the structure of the major scale isn't really complete. What are the putative starting points for the analysis. If one starts with all possible 1/1 to 2/1 ratios, the question arises why the particular notes chosen? If one takes 12 approximately equal (to avoid questions of temperament for the nonce) one can ask, why chose 7 notes as "diatonic" and 5 as "chromatic"? One can say, "It sounds good," but that's somewhat subjective. One could put (using octave equivalence), 2 half step and 5 whole steps, but why spread out as they are? The Harry Partch stuff I linked to didn't use a 12 part division, but rather a 43 part division, non equal. (One could 53 parts which is interesting, an exercise for the reader.)

All the medieval modes (and their modern derivatives) use the same 7 out of 12 arrangements in the same order with different starting points. If taken circularly, there is no difference in the modes. Pelog and Slendo use a different arrangement (sounds like a law firm.)

One can only answer why (based on lots of reading and listening) as a historical question, not a physics. Major and minor (common practice) treat some tones a mutable (like in c-minor, the notes A, Ab, B, and Bb can be treated as diatonic or chromatic, even in the same piece.)
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