We have scales but why??

[pj geerlings]

The traditional western tuning systems were based on the harmonic series

It's worth pointing out that the harmonic series was not discovered or described until the eighteenth century, so any implication of early musicians being consciously aware of this is woefully ahistorical.

...

You might want to find out what Pythagoras has to say about that! You might owe him an apology

While you are at it please familiarize yourself with the monochord... There is a whole-lotta-musical-theory (and history!) before the 18th century.

[JumpingJackFlash]

The traditional western tuning systems were based on the harmonic series

It's worth pointing out that the harmonic series was not discovered or described until the eighteenth century, so any implication of early musicians being consciously aware of this is woefully ahistorical.

...

You might want to find out what Pythagoras has to say about that! You might owe him an apology

While you are at it please familiarize yourself with the monochord... There is a whole-lotta-musical-theory (and history!) before the 18th century.

Here we go again...

Did you actually read what I said?
Here it is again: "the harmonic series was not discovered or described until the eighteenth century." That is not my opinion but a statement of fact.

The legend of Pythagoras has him discovering pleasing ratios (although, like all legends, this needs to be taken with a pinch of salt) , but that's not the same as saying he discovered the harmonic series. - In other words, he did not explain why certain ratios sounded good, only that they did. - Basically, he just liked the sound (he probably linked it to the divine and mystical nature of the universe)

Furthermore, no one knows what Pythagoras "had to say" because none of his writings have survived.

[pj geerlings]

Did you actually read what I said?

No ...
I read what you wrote

but, pedantry aside ...

The research that Pythagoras and others did with the monochord (100s of years before the 18th century) has survived

[JumpingJackFlash]

The research that Pythagoras and others did with the monochord (100s of years before the 18th century) has survived

To the best of my knowledge, the monochord was first theorised in a treatise completed in 391 (AD) by Aurelius Augustinus (St. Augustine).

This was quite some time after Pythagoras!

Not that it constituted the discovery of the harmonic series in any case.

[Gillman]

Ancient Greek Music



xviiith century music



Method of music by Heinichen:

http://www.sheetmusicplus.com/title/18t ... ng/5126120

Ancient Greek Music



xviiith century music



Method of music by Handel:

http://www.amazon.com/Continuo-Playing- ... rough+bass

[NKF]

That's interesting. What about the pieces for piano and orchestra, or for guitar and flute? I've always thought that equal is the new standard.

every instrument has its own ways of adjusting intonation. Some instruments actually have their own kinks that players already account for.

I honestly could not think of an actual source that had this all in one place.

http://www.petersontuners.com/index.cfm ... =14&sub=85

There is a bit there to sort of give you an idea.

But yes, a piano or guitar will introduce tuning issues and requires a very good orchestra to do right.

[egbert]

Pick up a guitar, double bass or cello and you can play play very audible harmonics using a finger on each string's nodal points - these are quite loud and sustain well on the heavier strings. On the double bass these are really quite loud even off the end of the fingerboard.

I would be amazed if nobody had ever happened upon these until the 18th century. Playing a lyre with fingers of both hands - it would have been no problem at all.

The mathematical theory about integral ratios of frequencies would have come later but it would not have been all that hard for the greeks to measure and discover that the nodal points for successive harmonics divide the string into two halves, three thirds etc.

[JumpingJackFlash]

To put it simply, the essential principle of the harmonic series is that notes are composite sounds containing not only a basic frequency (the fundamental) but multiples of that frequency. To put it slightly less simply, a string or air-column doesn't just vibrate throughout its whole length, but also in aliquot parts of that length (in two halves, three thirds, four quarters etc.) at the same time. The frequency of each harmonic is in inverse proportion to the size of its fraction (so, half the length produces twice the frequency for example).

This produces a series of higher, fainter pitches (harmonics or overtones) which 'colour' the sound of the fundamental. These are tabulated in the order in which they are produced, starting with 1/2 the frequency of the fundamental which sounds one octave higher, then 1/3rd the length of the fundamental which is an octave plus a fifth higher, then 1/4, 1/5, 1/6, 1/7 etc.). Every sound produced by natural means consists of a blend of the fundamental and its harmonics. Different instruments stress different harmonics, thus giving each instrument its own distinctive timbre (for example, the oboe is rich in harmonics, the flute has few).

The harmonic series continues indefinitely, with intervals becoming progressively smaller (some of the harmonics/overtones/partials are definitely "out of tune" with equal temperament). The series starts with what we would call perfect consonances, then imperfect consonances, and then dissonances.

Interestingly. this actually leads to two sizes of whole tone (8:9 and 9:10) and two sizes of semitone (15:16 and 16:17).

Also, although some people regard the major triad as a product of nature as it contains the first six harmonics, the same can hardly be said of the minor triad as the minor third does not appear until the 19th of the series, and this partial cannot be distinguished by the human ear.

Some of this was researched by Hermann Helmholtz who, in the nineteenth century, wrote:
"the system of Scales, Modes, and Harmonic Tissues does not rest solely upon unalterable natural laws, but is at least partly also the result of aesthetical principles, which have already changed, and will still further change with the progressive development of humanity".

Early musicians certainly knew about proportions and ratios and so on, but the scientific proof of overtones was not fully discovered until the eighteenth century. That's not to say that earlier musicians weren't aware that voicing a chord in the order root, octave, fifth, third (for example) produced the most pleasing sound; they realised that, they just lacked the scientific reason as to why it did so. (It wasn't until the work of people like Joseph Sauveur (1653-1716) that such science could be appreciated).

Some writers use their own justifications. Even as late as 1725, Johann Fux for example writes:
"The greater the proportional numbers that determine an interval, the brighter the sound of this interval, the higher therefore, too, the register that it requires. The proportional numbers of the fifth are 2 and 3 which equal 5. Those of the third, 4 and 5 which equal 9. From this it is clear that according to the natural order the fifth should be used in the lower register, the third in the upper."

Gioseffo Zarlino is another good example of an early theorist who would have been thrilled to have his theories confirmed with the science of the overtone series, but (and this is the crucial point) nobody knew about overtones at the time.

[qa2pir]

he just liked the sound

there is no research suggesting people had hearing back then.

[JumpingJackFlash]

there is no research suggesting people had hearing back then.

There quite obviously is. Written music has been discovered as early as 1200 BCE. Later pictures portray a variety of musical instruments and there were surviving treatises of Greek music theory (especially tunings for the lyre). And of course this is before you consider language and so on.
All of this would have been completely pointless if nobody could hear anything!

Do you have a point?

[jopy]

Do you have a point?

i don't think he does. i think if you go back and read qa2pir's prior posts you'll see why i draw that conclusion.

[qa2pir]

Do you have a point?

yeah

your doubt concerning pythagoras' knowledge of tonal ratios is as warranted as my doubt concerning hearing in antiquity.

pythagoras was a mathematician so I think it's quite safe to assume he saw the connection between pleasing consonance and simple ratios.

[fmr]

When a caveman wanted to sing along with a cavewoman but couldn't sing as high, he sang an octave below. He had no idea his wavelengths were twice as long as hers, he just knew it sounded right. Why? Because of the physics. Another, more talented caveman started harmonizing and got laid.

That might explain the octave, but why in the west has the octave always been divided up into 7 different basic notes? Why not 5 or 15? - That's just one example.

Why do you say that westerners divided the octave in seven parts? I'm pretty much convinced that when music was sung, people used mainly six notes. And scales are theoretical constructions derived from the music built previously. Melodies came first.

[JumpingJackFlash]

your doubt concerning pythagoras' knowledge of tonal ratios is as warranted as my doubt concerning hearing in antiquity.

pythagoras was a mathematician so I think it's quite safe to assume he saw the connection between pleasing consonance and simple ratios.

You do not understand.

According to legend, Pythagoras did indeed see connections between ratios and consonances. I am not disputing that (although it is only a legend). What he definitely did not do however was invent or discover the overtone series. That came over two thousand years later.

To claim that Pythagoras discovered the overtone series is as historically inaccurate as claiming that Pope Gregory invented "Gregorian chants", or that J.S. Bach invented equal temperament, or that Tonality was invented in 1650, or that the Violin replaced the Viol, or that Palestrina single-handedly saved music after the 19th Council of Trent.

[JumpingJackFlash]

Why do you say that westerners divided the octave in seven parts? I'm pretty much convinced that when music was sung, people used mainly six notes. And scales are theoretical constructions derived from the music built previously. Melodies came first.

You're right in a way, but the 7 different notes certainly existed in theory, even if not (always) in practice.

Also, imagine this: You play up 6 notes from G: GABCDE. Another time, you play 6 notes up from C: CDEFGA. Even though each individually may only have 6 notes, when you sum them together, you get 7 different notes.

It's obviously more complicated than that, but I am reluctant to post in any more detail when it is obviously not appreciated.