why our scales have seven notes, part 2

[jancivil]

No. To sing these earliest chants, you needed the six notes. My teacher had us do this and from the neumes. In practice, six mutated into seven thusly:

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

Starting in the 14th century, these three hexachords were extended in order to accommodate the increasing use of signed accidentals on other notes.[6]

The introduction of these new notes was principally a product of polyphony, which required the placing of a perfect fifth not only above the old note B♮, but also below its newly created variant, this entailing, as a result of the 'original sin' committed by the well-meant innovation B♭, the introduction of the still newer respective notes F♯ and E♭, with as consequences of these last C♯ and A♭, and so on ad infinitum, nisi ad montem formosum.

[MadBrain]

Wait, you're telling me how F#/Eb/C#/Ab came into being and how they were understood (as part of extended hexachords)... Fine but that is NOT the same as how the hexachord fell out of use, replaced by the octave based scale...

[IncarnateX]

Wait, you're telling me how F#/Eb/C#/Ab came into being and how they were understood (as part of extended hexachords)... Fine but that is NOT the same as how the hexachord fell out of use, replaced by the octave based scale...

No but isn't the burden of evidence on you if you wish to convince us they fell out due to principles like these?

- No clusters (ie no consecutive half steps)
- Scale isn't a subset of some other scale that doesn't have clusters (so pentatonic scales are excluded because they're subsets of the major/minor scale)

Or is it me who has lost track of the discussion here?

[JumpingJackFlash]

Probably because western music scales are derived from chords (and not the other way around)?

The earliest written music we have (gregorian church chant) has the classic 7 step scale and pretty much nothing else.

But it_does_not.
Confer:

http://en.wikipedia.org/wiki/Guidonian_ ... iddle_Ages

so, the thread at that time will have been 'why our scales have six notes', isn't it. Yet you want these things to form a foundation. It's just not a foundation, it's reverse-engineering from some notions you have and they seem pretty inchoate even.

There's a lot of confusion here.

The Hexachord was a practical tool used for singing (much like the Do-Re-Mi that some still use today). It is not quite the same as the "scale" in the theoretical sense that we now use the term. Music was never written using hexachords.

And, incidentally, there are examples of written music from a lot earlier than Gregorian Chant. The earliest example that I know of dates from 1200 BCE which is an example of a solo voice accompanied by a harp or lyre. It is made up of 7 different notes and harmonic intervals that we still regard as consonant.

[stringtapper]

And, incidentally, there are examples of written music from a lot earlier than Gregorian Chant. The earliest example that I know of dates from 1200 BCE which is an example of a solo voice accompanied by a harp or lyre. It is made up of 7 different notes and harmonic intervals that we still regard as consonant.

I'm curious as to what that example is. The earliest papyrus examples I'm aware of only date to around the mid-3rd century BCE and other stone examples such as the Delphic hymns dating to the 1st century BCE.

[jancivil]

Notice I used 'confer'. The hexachord is not the same as scale but it is how the rows of tones discussed here were remembered at the time MadBrain wants to say there was nothing but seven note scales. I don't know what that means, but the notion they were dealing with it just as we would today is a bit off. As a rhetorical question 'wasn't it six notes then?: NB., the idea of scales as we have it today doesn't really tell us what they were doing. The reasons for choices will be odd to us today and it is tied to religious practice.

- but the 'music theory' there shows a process of moving past a range of a sixth which is useful if one wants to grasp what went on coming up with this sort of scalar material.

A melody moving a semitone higher than la (namely, from A to the B♭ above) required changing the la to mi, so that the required B♭ becomes fa.

I personally would not call the Gregorian Chant type of music 'diatonic'. It is not really a subject to be glib about and the assumptions there aren't so good.

I read this more than once, that 'si' didn't come about until some time in the 18th century; really the 'hexachord falling out of favor' is another thing than talking about seven notes as a basis.
At CCM we were immersed in this. We sang a lot of six note tunes and one of the things we were to write about was this. I forget most of it. But 'the earliest Gregorian Chant' as much resembling diatonic seven note scalar sort of music doesn't stand up for me.

[JumpingJackFlash]

I'm curious as to what that example is.

A cuneiform tablet unearthed on the site of an ancient Babylonian city in modern Syria.

I read this more than once, that 'si' didn't come about until some time in the 18th century; really the 'hexachord falling out of favor' is another thing than talking about seven notes as a basis.

It's certainly true that 'si' came a lot later - there were several different words for it at the time, but it's important to realise that this was just adding an extra syllable to the solmization that singers used. It was NOT in any shape or form adding a seventh note to an existing 6-note "scale".

The equivalent of our "scale" was the the ecclesiastical modes, which all had seven different notes in them (though obviously it gets more complicated than just that).

But 'the earliest Gregorian Chant' as much resembling diatonic seven note scalar sort of music doesn't stand up for me.

Well the term "diatonic" in this context can be misleading. Modes didn't work the same as our scales do.
In practice, it was fairly common to alter certain notes of the mode - one of the earliest examples being the lowering of the 4th of the Lydian mode to avoid the tritone form the root (but it was still considered to be in Lydian mode - the Ionian mode didn't come until much later).

Also, it's worth remembering that the medieval modal system was originally devised as a means of cataloguing existing music, not as a "how to" manual for composers.

...that is NOT the same as how the hexachord fell out of use, replaced by the octave based scale...

This is completely inaccurate historically. The hexachord used in solmization was a different thing to the octave based scale (or mode) used in composition (and analysis). The two things co-existed for centuries, one did not replace the other.

[stringtapper]

I'm curious as to what that example is.

A cuneiform tablet unearthed on the site of an ancient Babylonian city in modern Syria.

Ah, I was thinking you were talking about the Greeks.

Taruskin describes it… very similarly to the way you did…

[IncarnateX]

Gentlemen!
First of all thank you for bringing the discussion back to an educational level. I really enjoy your lectures.

Secondly, I am no music theoretician myself but a psychologist and thus generally miss that perspective in this topic. So I searched the Google scholar and found this very interesting article, Psychology and Music by Diana Deutch

http://wiki.dxarts.washington.edu/sandb ... eutsch.pdf

on the subject with regard to the development of western music. As far as I get it, it resembles many points by the historicist in this thread and counter those of the mathematical universalists. Among other things it displays the arbitrariness of ancient numerological approaches to music that actually are not far from the math approaches offered in this thread. Among the conclusion we find this important paraphrase:

To place this concern in historical perspective, the development of Western music
may be viewed as a constant struggle between innovative composers on the one hand
and establishment critics on the other, who have argued against various innovations on
the grounds that they are unacceptable to the listener. Some examples of "new" music
that were considered unacceptable would surprise a modern audience. For example, J.
S. Bach was considered in his time to have "confused the congregation with many peculiar and foreign tunes [Portnoy, 1954, p. 144]." Another composer who was censured by his contemporaries was Monteverdi [……].Yet the works of Bach and of Monteverdi appear to us as outstanding examples of traditional cultivated music. Clearly, the way that music affects the listener is at least to some extent a function of experience.

The conclusion thus refer to the critic's ideas that innovation in music (including use of scales) in some way were unacceptable to the listeners. To make such criticism, I would say it follows that you have to be a universalist exactly like the math theoreticians in this thread. If any of the historicists around have interest enough to read this artice, I would love to hear your take on it.

Cheers

[murnau]

why we have scales please and notes?

[jancivil]

The hexachord used in solmization was a different thing to the octave based scale (or mode) used in composition (and analysis). The two things co-existed for centuries, one did not replace the other.

This is the crux of the biscuit. First of all, we have to draw a distinction between the people that sang and the composers. Yes, it's plain enough that the material was a version of the modes we receive as 'the ecclesiastical modes' which we receive as seven to an octave today.

However the octave wasn't the thing to the singers. When they exceeded the range of a sixth, this is the conceptual framework, some mental work was done and another level was established. That is where that 'new notes' ideation came from, via the wiki article and the Grove New Dictionary. What that kind of thing tries to do however is encapsulate something rather tricky for us in a small space.

One of the outcomes particularly early on was tunes where a seventh note, as we would frame it, was less frequent and ought to have been as it was reserved as a more expressive device; in a MODAL practice where there are reasons for choices [by composers working for The Church and under its guidelines] that do not gibe so well with a modern ideation 'it's one of the seven in the scale, go for it'.

[IncarnateX]

why we have scales please and notes?

Has your mother not told you not to interfere in grown-up's conversations? Be a good boy now and go play on the freeway.

[IncarnateX]

Another important conclusion from the aforementioned article

it must remain the prerogative of the composer to experiment with any new rules that he wishes; psychology cannot provide prescriptive answers and can only explain how existing music is perceived. However, by the same token, music theory cannot provide prescriptive answers either. As Aristoxenus (1902, p. 195) wrote over two millennia ago: "We shall advance to our conclusions by strict demonstration." If there is no strict demonstration, then there can be no conclusions.

That basically sums it for me. So much for any empirical support for mathematical universalism in music. Quite in accordance with common sense to anyone who have experienced the phenomenon of not liking a piece of music before being exposed to it several times or vice versa, disliking a piece of music after several exposures. So why do our scales have 7 notes in this perspective? Answer: because that is where the cultural development of western compositions has landed so far, while at the same time training our brains to like music made upon these scales. However development is not over, so where we are in about 200 years cannot be predicted. Possibilities are endless from a psychological perspective.

[jancivil]

I'm not a 'theoretician', certainly.
There is scarely any such thing as 'music theory'. The word 'theory' connotes some kind of scientific endeavor or something like it, and music isn't done like that usually. 'Music theory' happens when we codify practice, make what happened [which is believed to work consistently and well] available in terms for study, and in order to form language in order to convey the sense of what you're DOING.

I'm a composer. I want to hear things a certain way, I want to explore sound and surprise myself and come up with some new shit, because I got bored with the old shit.

There are things to know about sound and there are numbers used in this. The numbers however SERVE THE FVCKING MUSIC, serve the SOUND. It's not a little intellectual game, music is made to hear and the people that drive new ideas in music want to hear it. It seems strange to have to point this out but this is where we are in this thing.

Psychologically what happens is people that are not built to do music - I hate to say this because I think 'talent' tends to be a kind of excuse - but that do not have the talent for music, that have this impulse to try and knock things down to their level. The phenomenon of a 'music technology', 'plugins' forum gives a platform for such bullshit. Music theory qua music theory is bullshit.

The statement by 'aciddose', 'if you believe music is an irrational art, go away' is so arrogant and it's an arrogance based in cluelessness and a special kind of stupidity. What does that even MEAN? Go over this in your head a little bit, it's idiotic, isn't it.
Where is music that is just a product of sorting or collation or arithmetic? What asshole would do that?

Sure we have dodecaphony and some of it is deeply satisfying as music. But the ideas served someone, and the next someone trying to break new ground: first, Schoenberg in terms of harmony. He was a harmony freak, he was steeped in history and tradition. As a 'theory' it arose out of a perceived emergency, the dissolution of tonal center as things became extremely chromatic - itself a product of the artifice 12-equal-to-the-octave, so 'let's make them truly equal'.
For me and many others, Webern is the more refined achievement in dodecaphonic serialism. But the practices, the manipulation of rows etc, doesn't amount to a cart strong enough to pull the horse. These are musicians trained and steeped in tradition and practice with refined ears and refined TOUCH. It's not a product of better math qua math.

When you get down to talking about 'the octave', that's a convention. Yep, it describes seven notes and then we repeat. But what it is physically is 2:1. If you're going to talk about 'the fifth' as an essential dividing point 'in the octave' you're already in dodgy territory, as what this physically is based in is 3:2, which geometrically is at odds with 2:1. So we have two areas of maths, the physics of the third partial in the acoustical description OF SOMETHING WE FIND PLEASANT* - "consonant" - and the ratios that the ancient Greeks had such naive and clueless high hopes for, at odds. If we go with the somewhat later decision to break 2:1 into twelve - which is a contrivance, an artifice - a 'perfect' fifth is 7/12ths. So we have a contrivance that makes a kind of sense of the physical thing we like. There is nothing essential about this, this was intentional. Seven out of twelve? It works. But if you study this you find a whole lot more detail we can perceive inside 2:1 than twelve! Cf., Danielou's 53! (There's some science. But he was interested in the intonation in Hindustani practice and there were always various notions floating around but typically not written, in a very much oral tradition). (*: and is one of the first things we notice, 'harmonically'. When we get to music featuring the higher partials eg., 'the lydian chromatic concept' that's obviously someone that hears more better. Then you go on a bit further and here are 'microtonalists' that want to hear more. And that drives some 'theory', from say Cowell, then Partch onwards.)

12?; so it's convenient to the mind in a certain way.
It's making sense of sound, though, the entire exercise serves The Human Wants To Hear This Thing This Way.

[jancivil]

Music and the Power of Sound - Danielou

here is someone with certainly a belief in numbers as an ideal, and it's a religious ideal at that. but the inadequacies of western 'music theory' are dealt with devastatingly in service of his universality. it's an excellent read and very educational. His belief was in raga as a spiritual quest, a religion out of music really and he believed in things being TRULY IN TUNE so this is what his numbers were about.

So here is a middle path.