We have scales but why??

[jopy]

funny how cultural relativism often goes hand in hand with complete resigned nihilism, unwillingness to acknowledge any artistic merit involved in the tradition of music.

Huh? Not sure who or what in this thread this is directed at.

[egbert]

For a wave, speed of transmission = frequency x wavelength.

The speed of transimission of sound waves varies with the properties of the medium they are passing through - particularly the density and temperature of the medium. Even changing the air temperature changes the speed of sound (and hence the wavelength but not the frequency). Passing through solid or liquid media, sound typically travels much faster than it does through air. The frequency is constant through all this - assuming the source and the observer are stationary.

The upshot of all this is that nobody talks about wavelengths when it comes to musical scales - they talk about frequencies. The wavelengths in the bones and liquid media of the inner ear are not those in the air around you but the frequencies are the same everywhere in the system.

[izonin]

I know, if you use a root key, you have your "home" but WHY you can hear this home and why it has this effect?
Why we dont use all notes without selection? why is minor and minor the scales which are the best in our culture?

Miles Davis was an important part of our culture, and he favored the chromatic scale.

[HordePrime]

there isn't any indication in your posts that you understood what I was saying at all.

Maybe cause you were just talking rubbish?

Just a thought.

[egbert]

I know, if you use a root key, you have your "home" but WHY you can hear this home and why it has this effect?
Why we dont use all notes without selection? why is minor and minor the scales which are the best in our culture?

Miles Davis was an important part of our culture, and he favored the chromatic scale.

Where? He is associated with modal music. He used a lot of diatonic scales - dorian and natural minor etc - and blues scales and blue inflections (blue third etc).

[izonin]

I know, if you use a root key, you have your "home" but WHY you can hear this home and why it has this effect?
Why we dont use all notes without selection? why is minor and minor the scales which are the best in our culture?

Miles Davis was an important part of our culture, and he favored the chromatic scale.

Where? He is associated with modal music. He used a lot of diatonic scales - dorian and natural minor etc - and blues scales and blue inflections (blue third etc).

Listen to his records with Charlie Parker. Miles is a master of the chromatic scale. He was using it a lot during his modal/fusion period, too. Scofield, who was playing in his band, admired Miles' ability to play chromatically.

[egbert]

A run on the chromatic scale is often used to lead into a destination note and individual chromatic tones are used to lead into chord tones. When he played with Parker he was a very young kid and he was following the ideas of his mentors. When he came into his own, Miles stripped away a lot of melodic ornamentation and every note he played counted. Look at the trumpet solos for Kind of Blue. They are pretty inside mostly - chord scale tones dominate completely - look at Freddie Freeloader - he has great phrases and lines but they are myxolydian mode and pentatonic major stuff mostly - here and there he anticipates the arrival of the next chord by a beat or two.

Same sort of thing with So What - the opening phrases over the E minor 7 is all on the notes of the Dorian. He plays one phrase with a blue fifth in the second last E mi 7 section and he anticipates the change to the new chord - plays notes from E dorian over the last couple of beats of Fmi7 and holds a high Bb straddling the end of the Emi7 section into the last Fmi7 section.

These would be two of his best known tunes from his (and anyone's for that matter) most successful jazz album.

[izonin]

A run on the chromatic scale is often used to lead into a destination note and individual chromatic tones are used to lead into chord tones. When he played with Parker he was a very young kid and he was following the ideas of his mentors. When he came into his own, Miles stripped away a lot of melodic ornamentation and every note he played counted. Look at the trumpet solos for Kind of Blue. They are pretty inside mostly - chord scale tones dominate completely - look at Freddie Freeloader - he has great phrases and lines but they are myxolydian mode and pentatonic major stuff mostly - here and there he anticipates the arrival of the next chord by a beat or two.

Same sort of thing with So What - the opening phrases over the E minor 7 is all on the notes of the Dorian. He plays one phrase with a blue fifth in the second last E mi 7 section and he anticipates the change to the new chord - plays notes from E dorian over the last couple of beats of Fmi7 and holds a high Bb straddling the end of the Emi7 section into the last Fmi7 section.

These would be two of his best known tunes from his (and anyone's for that matter) most successful jazz album.

I'll use this quote (from memory) from an interview with Scofield: "Miles used the chromatic scale as a basis of a lot of the things he played." Yes, those chromatic tones can also link diatonic scales. Artist like Davis and Metheny use the chromatic scale as a basis of their improvisation. In an interview Metheny explains how he can hear every chromatic tone, regardless of the chord he solos over. The impro is not limited only to the scale tones, although they have more gravity.

[egbert]

The ability to employ all twelve tones is sometimes referred to as the definition of bebop. Bird certainly could find contexts for any tone over any chord and several generation of musicians have followed him down that path. I have been reading transciptions and articles on ideas about improvisisations over changes and the examples are full of this stuff.

I am just surprised that this is being said about Miles because he clearly moved away from Bebop ideas and played his own stuff. I have some of his later albums like Decoy, Tutu, Amandla and Aura - perhaps he got into this stuff again when he was a playing with Chick Corea and Herbie Hancock and those 60s groups (eg ESP and Bitches Brew) or later when he returned after a long break in the 70s and played with guitarists like Schofield and Mike Stern.

[D.Josef]

I had no idea what equal temperament tuning meant.

I rest my case.

bwa ha ha, too funny. The whole time you've been saying math and physics can't explain scales. You brought up this equal temperament thing to try to "support" your argument. Turns out, you had no clue what you were talking about, because equal temperament is purely math and physics based. I had no idea what equal temperament was, but NEITHER DID YOU. I'm the one that looked it up and explained it to you. Now you use that quote? Yes, you should rest your case.

Guys, this was hands down the ugliest shitflinging I've ever seen, and that includes monkey houses in zoos all over the world.

I happen to be quite well educated in physics and mathematics... And yes, the equal temperament IS based on mathematics, but is in fact wildly divorced from the "traditional, hands-on" aspect of physics.

The traditional western tuning systems were based on the harmonic series, or more specifically, on what happens when you take a resonating string, and reduce its length to half, one third, one quarter, etc. of the original. This is the basic-basic of ALL tuning, and the way people have created music without knowing jack shit about mathematics or even what a frequency is.

Now fast forward a hundred thousand years, and we are now in the time of Johann Sebastian Bach. Western music is highly advanced, and people write pieces in various keys that the tuning system was not designed for. Most intervals and chords sound beautifully in tune, but SOME are really off. They were called the WOLF intervals, because they "howled" horribly.

That is because just intonation, a tuning system refined without a paradigm shift from the above mentioned way of using discrete ratios to shorten strings - but no longer using only the natural harmonic frequencies, but subdivisions as well, giving out the 12 intervals of the chromatic scale - does not play nice with octaves.
To demonstrate this, take a pair of compasses, draw a circle, then set it to an arbitrary length, and start subdividing the circle. See what happens when you get back where you started.

Now this is where the whole "Wohltemperiertes Klavier" came into play. An instrument maker had the idea of making ALL intervals slightly out of tune. In equal temperament, you take the octave, which is a factor of 2, and cut it up into 12 equal steps. Now a step (ie. a minor second) is not an addition, but a multiplication, so one step is the 12th root of 2 (around 1.059xxx).
So say, A4 = 440Hz, then A#4 = A4*s, B4 = A4*s*s, C5 = A4*s*s*s, and A5 = A4*s^12 = 880Hz.
(EDIT: According to some music historians, Bach's "Wohltemperiertes Klavier" was not based on the equal temperament. But that's the way I learned it in school, and as far as I know, it is an undecided question even among music historians.)

So it has NOTHING to do anymore with ratios of string length. It is an approximation to let musicians play in any key they wish, on the same instrument. This approximation was necessary BECAUSE the very subdivision of 12 intervals was in fact an arbitrary.

That said, even with this approximation, most of what we consider harmony is in fact somewhere based in the physical fact of the harmonic series, but no longer exact, only approximated. (That is why a chord sung by a barbershop quartet sounds so much richer than one struck on a piano. A good barbershop quartet aligns their chords in just intonation, as will a virtuoso solo violinist.)

[NKF]

that is for modern piano. 1 instrument tuned 1 way. An orchestra is not bound by the limitations of the piano. Also the "Wohltemperiertes Klavier" did not use equal temperament.

[egbert]

The above is absolutely right. I think it is worth looking at how close these tempered scale intervals are to the integral ratios. The perfect fifths are pretty close the thirds are not so close. There some interesting consequences even for the integral ratios.

Look at a 5 string violin or cello. It is tuned C G D A E. The E is actually a harmonic of the bottom string - ratio 5:1.

Violinists often tune the strings to a series of perfect fifths. A perfect 5th has frequencies in the ratio 3:2. If you do this for all 4 pairs of strings starting from C-G and moving all the way up to A-E you are raising the pitch 4 times over by that factor of [3/2]^4 = 81/16 = 5 1/16.

So there - if you tune the E directly to the harmonic of the bottom string you get a quite different result to what you get with perfect 5ths between the strings.

[NKF]

5 string violin / cello ?

I think that is where you've erred,

You don't tune E to the harmonic of C because you don't actually have a C string. For cello it would be A to C. Either way, that harmonic is barely audible and not used to tune. String players use pythagorean tuning. All of the strings are perfect 5ths and all the strings are tuned exactly to their associated frequency. They don't reference E with G as you would first of all not be able to play that and it would not provide the sort of potential for beating to make that comparison worth while. Which is why use the previous string. Unless they are tuning to a piano.

[egbert]

5 string violin / cello ?

I think that is where you've erred,

You don't tune E to the harmonic of C because you don't actually have a C string.

Can you count? I said 5 string cello or violin - and I gave the tunings for each of the 5 strings. Do you doubt the existence of such things? There are plenty of examples of electric and acoustic 5 string violins and cellos. If you have not heard of either of these instruments - or their history (look up Bach's 6th cello suite for a start) you might want to acquaint yourself with this thing called Google before you presume to correct others.

And when it comes to tuning, of course you can listen to the interval created by any two strings and tune them in relation to one another - you needn't bow them. Guitarists - other than Jimmy Page - seem to manage without the horsehair and so could you. You don't need to tune with unisons or fifths either.

My point related to the sort of problems that tunings with integral ratios get into - the issue here is similar to what happens after a few of modulations around the cycle of fifths on keyboard instruments tuned in perfect fifths.

[NKF]

no you actually do bow them and listen to the beating. That is really how you do it. You will not find 1 violinist that tunes the way you just described using the low string to tune the high. It makes no rational sense when you can use the actual string that was previously tuned and use the precise beating method to get it perfect.

And a 5 string violin or cello is so esoteric that to make a point with such a rare instrument is sort of weird. And that fabled notion of bach's 6th being written for a 5 string cello is considered a myth. There is no evidence for the claim.

I don't need to use google as my information comes from the actual source. I trust that more than google. I would say your reliance on google is symptomatic of a very small understanding of a complex topic. I work with orchestras on a daily basis. Nobody tunes the way you describe.

Guitarists , well lets be honest, they don't have to be as exact as an orchestral player. They aren't blending with 70 other musicians as a result they can and are usually out of tune. But you were talking about stringed instruments. Your point assumes that the lowest and highest are tuned by perfect 5ths therefore they should be harmonics of each other. That doesn't quite work that way because 99.9% of people playing strings have a 4 string violin.