Temperments...Circle of 5ths..OTHER fun stuff!

[zbalz]

I am reading the Tuning section (along with all the extra links) in chapter five. I never knew that music got so deep...as into mathematics! However I don't quite understand what exactly "dead in tune is".

1)For example (based on Stephen Bicknell's article SD has as a link from the Chapter 5 tunings page) the 17th century meantone temperment has all the thirds perfectly in tune.Being that we work in an equal temperment phase today where everything is slightly out of tune...how do we know what is IN tune? Who...over time...determined what is IN tune and what isn't.

2)Also in the meantone era, assuming someone wanted to play a score in G flat...were they just like, "Oh crap...theres no such thing as G flat right now because we tuned it out so I guess I'll just use something else."? Or was it that the style of music of that time didn't call for those notes.

3)Anyone really know why all these guys in the past didn't use equal temperment? Or if composers today know they are not playing in a certain key (that that style of temperment excludes); do they deliberately tune in a different temperment to make their music sound more pure?

4)Also a quick question on modulation. Do most songs actually follow smooth transition shown by the circle of 5ths. For example, SD mentions for the smoothest transition from C..one should go to G..then D...etc. However, I was taking a look at stairway to heaven by led zeppelin and they seem to go from the chords D to Fmaj7 to C which doesn't follow the circle of 5ths idea (i think) but still sounds like a smooth change.

5) According to the circle of 5ths...12 5ths equals 7 octaves....similarly..if going counterclockwise...shouldnt 12 4ths equal 7 octaves? however it is closer to 5 octaves.

5th=702 cents. 4th=498 cents. octave=1200 cents.

1200 x 7 = 8400 cents
702 x 12 = 8424 cents (equals when temperment applied)

yet. 498 x 12 = 5976...closer to 5 octaves.
Why is this so when on the circle of 5ths it seems different. Also, this may seem stupid, but how come equal temperament doesn't divide the cents out through 4ths rather than 5ths.


:http://www.zentao.com/ubb/smilies/biggrin.gifeep breath:: Thats it for now...sorry for all the questions. I have a feeling some of these questions will be answered further in the lessons or on the supplimentary material which I havent finished. If so, please state that.

Thanks

-zbalz



[This message has been edited by zbalz (edited November 13, 2000).]

[StoneDragon]

Heh heh... I was wondering if anybody even bothered to read through that stuff.

Im cetainly not a "musical scientist", myself, so I've only delved into this side of things enough to get a "basic" understanding of how things work. With that in mind, I'll attempt to answer each of your questions.

1) Pitches are "in tune" or "out of tune" based on the harmonic overtone series... or how they occur in nature. I've run into information here and there that suggests that the Ancient Greeks (Pythagorus?.. he seems to get all the credit) had a fairly deep understanding of overtones and their influence on sound... and therefore music. Western music is founded on the bits and pieces that survived from Ancient Greece.

2) I've never really dug through a lot of music from that period, but most of the music I have seen tends to revolve around a few basic keys. Those were the "accepted" keys for music. If you whipped up a sonata in a weird key (like Gb), you were probably going to find yourself unemployed.... pretty much how it still is today.

3) I read something to the effect that at least the idea of equal temperament was kicking around for quite some time before it actually caught on. But keep in mind that equal temperament would have sounded as "out of tune" then as those "other" tuning systems will sound to you now, because you have spent your entire life listening to equal temperament.

I'm not sure what you are getting at with "Or if composers today know they are not playing in a certain key (that that style of temperment excludes)"

There are entire "societies" and whatnot that devote themselves to playing "period" music exclusively on "period" instruments that are constructed and tuned as close to the original a possible. I find the sound of the music done this way very interesting... but my ears are pretty stretched out from listening to weird music anyway http://www.zentao.com/ubb/smilies/wink.gif

4) Well... it's nice to know that things have come a long way from the idea that music must do this or that. If you listen to some of the late 18th century - early 19th century classical music, you'll find experimentations that deviate a lot farther than Zepplin ever did.

Still... if you take the entire body of music... not just rock and roll music... you'll find that things pretty much stick to the tried and true formulas. More songs have been written around the V chord resolving to the I chord than deserve mentioning.

5) Don't confuse the idea of a circle with what is actually happening if you lay the octaves out in a straight line from low to high. If you start on C and move higher using 5ths, it will take you 7 octaves to "get back to" C (because you're taking bigger steps... your going to pass over more C notes before you land on one). If you proceed in 4ths (smaller steps) you'll land on C with "less octaves" traveled.

Why 5ths? good question. I think it is because the 5th is a "power note" as far as music is concerned. The 5th is more consonant than the 4th.... lower vibrational ratio or something like that.

Keep asking questions... it's good for you.

[zbalz]

Thanks for taking the time to read through that mess. Yeah Im sure there are better conducted songs than stairway to heaven http://www.zentao.com/ubb/smilies/tongue.gif. I was just analyzing pieces of that song at the time so I used it as an example.

This isn't really guitar related...but can any of you guys give good suggestions for good collections of classical music? Preferably done on piano or something?

Also, is it possible to play guitar under different temperments or is the fretting spaced so it must be played that way...if its possible..you guys know of anyone who has tried it?

Just quicker questions this time http://www.zentao.com/ubb/smilies/smile.gif

-zbalz

[StoneDragon]

If you're interested in checking out classical music, your local library is the best place to start. See if you can find a book on the subject. There are many out there that attempt to teach you what to listen for etc... Cybe bought me this really nice book (put out by Gramaphone... I believe) that takes you through the entire history of classical music and details not only the most "famous" composers and their "best" works, but gives you some insight into what the social conditions were that helped to shape the musical styles of the day.

If you can find a book like that... then you can use it as a guide for digging through the library's CD collection. You'll undoubtedly find lot's of stuff that is HO-HUM, but you'll most likely run into several composers and pieces that you really like. That will give you a better idea of what type of stuff to investigate further.

As far as temperaments on the guitar, I have seen guitars that were built this way... even one that had a removable fingerboard so you could change between different temperaments. A standard guitar won't work though. The frets are positioned for equal temperament. The only way that you could get around this is to use a slide or get really good at bending notes.