#77776
08/06/2002 12:16 PM
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Attention, music and math lovers. I found this fascinating site while trying to find something else. He starts off with how fractions are used to denote intervals in music; for ex., 5/12 = 5/6 = 5/3 = 10/3 = 20/3. The last section is one I thought you might be particularly interested in, Musick: "4. What Do Pure Intervals Sound Like?"
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#77777
08/06/2002 1:16 PM
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Running perty fast and loose with them equalses there, Jackie. Gonna post the site's url to back them up?
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#77778
08/06/2002 8:14 PM
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I don't know what pure intervals are, but I would guess that octaves, perfect 4ths and perfect 5ths might be good contenders for the title.
Will be interesting to read here whether 'tis so...
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#77779
08/06/2002 8:18 PM
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About to check it out, but it looks like http://home.earthlink.net/~kgann/tuning.htmlis the one. Entry #2 on a Google search.
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#77780
08/06/2002 8:44 PM
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"What Do Pure Intervals Sound Like?"Am I right in thinking it's impossible to get a "pure" interval? I recall (possibly incorrectly) that all tunings - including the well-known Well-Tempered - deviate from "purity" to favour particular keys. In fact that definitely strikes a chord. 
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#77781
08/07/2002 2:08 AM
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you can have pure intervals, just not a whole string of them(no pun intended. yeah, right!) stacked on top of each other. you can tune all the octaves(say "C"), and the 5ths to them, but if you try to tune the 5ths of the 5ths, bingo! trouble. the math just doesn't add up. the 5ths of the 5ths would be the seconds and ninths of the octaves, and the frequencies wouldn't quite add up. you are left with a hole. or too much, I forget.  Well-Tempered tuning alters all of the tunings so that all the intervals work pretty well; all your major thirds are fairly major like, etc. it's a huge and deep topic, and if you get a chance to hear a group play with Just Intonation, it's really quite interesting. it can be hard to accept to our compromised ears, however. this of course, really only deals with music from Western Civilization, as other cultures use different tuning systems, with different numbers of notes between the "octaves".
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#77782
08/07/2002 2:31 PM
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Uh oh. Don't get Faldage started on Pythagorus.
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#77783
08/07/2002 2:36 PM
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Don't get Faldage started on PythagorusYeah, we don't want the summation of squares. 
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#77784
08/07/2002 6:11 PM
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It's certainly not impossible to get a pure interval. THe fifth you get out of a well tuned piano won't be one. It'll be close but.
The fifth of the fifth isn't where the problem is noticed. The fifth is not half an octave so we shouldn't expect two fifths to make an octave. If you tune a perfect fifth (it's a wee tiny bit sharp of your piano fifth) from a C and call it a G, then tune a fifth from that to a D and so on, you'll get the famous circle of fifths:
C-G-D-A-E-B-F#-C#-G#-Eb-Bb-F-C
but the C you end up with won't be the same C you started with. If you read the page wofa posted you'll see that the pure interval fifth is 702 cents (Don't panic folks, one cent is one one-hundredth of a half step. That's the half step on your well tuned piano.) Add up the seven half steps in the fifth and you get only 700 cents. This is two cents flat of the pure interval fifth. Add up all those two centses in the circle of fifths and you'll see that the C you get when you're done with piling all these pure interval fifths on top of each other is 24 cents sharp of the C you started out with. Oh, oops. This is called the Pythagorean comma and it's not a problem as long as you're only playing in one key with no accidentals, but as soon as you want to modulate or have an instrument that will play in any key (such as a piano) you're in big trouble. It took us a couple of hundred years to get this all settled out. We got a lot of compromises along the way that left us with the idea that different keys have different characters. They used to even as recently as Mozart's time. If they still do, it is merely because composers think they do and write music accordingly.
There. Din't even sum no squares.
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#77785
08/07/2002 6:34 PM
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I read this three times and for the first time in many years I am at a loss as to how to translate it. My job is to take complicated stuff and reduce it to simple stuff, but in the beginning I have to have English language. Whatever this stuff is it AIN'T English.
To me a fifth of a fifth is nothing more than a damned strong drink, about 6 oz. A cent is a hundredth of a dollar, not of a half step.
A comma is used for punctuation, Pythagorean has to do with right triangles and other stuff like that, and accidental is how Sasha (well never mind about that.)
TEd
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#77786
08/07/2002 6:39 PM
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I read this three times and for the first time in many years I am at a loss as to how to translate it.
Don't worry your pretty little head about it, then. Sorry there's no puns in it.
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#77787
08/07/2002 9:29 PM
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"...when you're done with piling all these pure interval fifths on top of each other is 24 cents sharp of the C you started out with..."Mathematically this may be true, but your issue is only worth a penny less that two-bits as it manifests seven octaves apart, which *nobody in their 'right minds' will be juxtaposing for its fullest effect... let alone be able to discern it. The tuning adjustments are done at a smaller intervals and more accurately by ear by listening to a combination of ratios or a more complex ratio (such as 5/6 instead of 2/3), or so it is to my ear... On the note of different keys have different characters: A piano's sounding board and stringing has also had a lot to do with the character of key centers. The b natural (or b flat depending) below "mid" c is the point at which the note on a piano changes from comprising of three tuned strings to two tuned strings per note. This has a clear effect on how we (for example) relate c-major and a-minor (keys which share the same notes, but not the same "resting" point). This effect of timbre is minimized by correctly tuned instruments of the finest caliber... but how many of those are out there?
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#77788
08/07/2002 9:29 PM
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It's certainly not impossible to get a pure intervalAhh, that's it - I was thinking about the impossibility of getting perfect intervals right the way across a keyboard, as you so eloquently describe, Faldagious One. Yeah, just getting one pure interval so you can hear how it sounds is easy (ish). Mind you, you should hear a guitar I've tuned.  We got a lot of compromises along the way that left us with the idea that different keys have different charactersThis interests me. Are you saying that, in a non-well-tempered universe, all keys would sound more or less the same, and have the same "feel"? In other words there would be no advantage to writing music in any particular key (other than, perhaps, to fit in comfortably with vocal ranges). Edit: ackshully I think musick just answered my question (ta mate)
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#77789
08/07/2002 11:27 PM
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In reply to:
The fifth of the fifth isn't where the problem is noticed.
I used this just as a starting point; to show that it was the adding up of continued "pure" intervals, that ended up causing the trouble. you finished my thought. thank you.
In reply to:
We got a lot of compromises along the way that left us with the idea that different keys have different characters.
I always thought that it was the other way around. the Greeks knew that each tonal center(key) had a different sense to it. Db sounded different than C because it was different. the frequency variations would cause a different resonance with the listener and the space around them. this is still true today, though since we have forced the keys to behave, the resonances don't ring true anymore. frankly, I think we lost a major part of what music could do to people. it is a testament to the power of vibration that music still moves people today.
musick: your idea of timbre is a good one, but I think it goes deeper than just two or three strings. think about the different instruments/voices that are used...
so Onabi, I think it is crucial to pick the right key for each song, not only for the instruments and voices that are to play it, but for the deeper resonances of nature that reside in each key.
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#77790
08/08/2002 9:00 AM
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I think it is crucial to pick the right key for each song, not only for the instruments and voices that are to play it, but for the deeper resonances of nature that reside in each key.
Nice way of putting it, eta.
I agree, albeit from the perspective of one who has never really heard much of alternative tunings.
A friend has a Korg keyboard that you can easily set to a variety of tunings; quite interesting to hear the same music "filtered" in different ways. But we tend to agree that one tuning system is the best for any given tune, even if it's not the same for each.
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#77791
08/08/2002 10:18 AM
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the frequency variations would cause a different resonance with the listener
I have been trying to find out what the characters of each of the keys are. Do you know them all? I know that D major, for example, is supposed to be martial and F major pastoral (I think) but that's about as far as I can go. I think the point about certain keys sounding good on certain instruments is a valid point but is it cause or effect? D is martial because D is a good key for brass instruments and brass instruments sound martial so when one wishes to write martial music one does so in D so it will sound good on the martial instruments. Perhaps, at some point during the tweaking of the scales to get around the Pythogorean comma, D was more martial feeling because of its particular thirds and fourths and sixths and what-all, so when brass instruments were designed they were designed with the key of D in mind. But would a piece written in D sound less martial if transposed to F and played on a brass instrument designed for F the way a normal brass instrument was designed for D?
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#77792
08/08/2002 10:27 AM
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Then there's the consideration of keys that are naturally set for strings.
The violin's strings are G, D, A, and E, a fifth apart. Those keys, both major and minor, are easiest to play for the violinist--or perhaps a better way to state this would be, they're more available. And there are countless works set around those keys.
It works for the cello and viola, too, though there's a little difference here:
C, G, D, and A being the tunings of their strings.
I don't offer the above to suggest that other keys are avoided in any way--instead, just to point out that a great deal of the literature is built around those keys because of how the string instruments are set up.
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#77793
08/08/2002 11:03 AM
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Those keys, both major and minor, are easiest to playThis gets me thinking - major and minor are significantly different (even to non-musicians), but with "modal" music you end up with something that's neatly in between, that easily flips either way. Major and minor are more like opposite poles on a continuum than discrete entities. Flipping between major and minor would probably be expressed by "accidentals" in musical notation, but in a way this is cooking the books to make the notation work. And here's the thing - the same applies to keys in general. Guitar is a good instrument to "suss" this one: the chord Gsus4, for instance, is somewhere half-way between G and C. I could be playing a song that is officially written in G or in C, yet the chord that fits that song best overall is Gsus4. You can't say "this music is written in the key of Gsus4" as there's no way to express that in standard musical notation - it's nonetheless meaningful, and also very useful to musicians aware of other chord-shades that they've found to work well with Gsus4. Musical notation, like language, is a convention that enables understanding and communication. But marvelous as it is, it's still just a finger pointing at the moon - and it shouldn't be confused with a reality where its rules don't necessarily apply. Errr IMHO
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#77794
08/08/2002 12:51 PM
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First; a question: What notes are in a Gsus4 chord?
OK. Modes.
The major and minor keys are probably about 99% of modern western music but they are just two of seven different modes possible with the note distibution (two half steps scattered amongst all the whole steps) available to western music. They are often described in relation to the white notes on a piano. The standards are the major (C to C on a piano) and minor (A to A on a piano, but there are variations called harmonic and melodic minor that would just confuse things so we'll stick to what we can call the pure minor, A to A). These are not the only possibilities and, in fact, in the days of Gregorian chant, were not used very much, if at all. The modes have been given Greek names (that have nothing to do with anything the ancient Greeks called any corresponding modes but). These modes can be roughly divided into major and minor modes based on whether they had a major or minor third.
Starting with the one we call Ionian they are:
Ionian - This is the major mode. C to C on the piano.
Dorian - D to D. A minor mode. D minor has one flat, Bb. This is the sixth. It is a B natural in Dorian, so Dorian is minor with a raised sixth.
Phrygian - E to E. A minor mode. E minor has one sharp, F#. The F is natural in Phrygian, so Phrygian is minor with a minor second.
Lydian - F to F. A major mode. F major has one flat, Bb. The B is natural in Lydian, so Lydian is major with an augmented fourth.
Mixolydian - G to G. A major mode. G major has one sharp, F#. The F is natural in Mixolydian, so Mixolydian is major with a flatted seventh.
Aeolian - A to A. This is the pure minor.
Locrian - B to B. This is where things get scary. It's a minor mode but. B minor has two sharps, F# and C#. They are both natural in Locrian so Locrian is minor with a flatted second (the C#) and a diminished fifth (the F#). Since the perfect fifth is so basic to Western music use of the Locrian is almost unheard of and, indeed, thought by some to be Evil.
Anyone still awake can go back to sleep now, and pleasant dreams (as if)
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#77795
08/08/2002 1:13 PM
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I don't have the time today to research this as much as I'd like, but a quick search for "tonal center" brought up several interesting sites, this one in particular: http://www.sohl.com/sohl/mt/maptone.htmlit's not quite what I'm looking for, but has some neat ideas, and both verbal and graphic explanations. perhaps a search for Greek music might give up something worthwhile. I'll be gone all day(sheesh, I have to go to the lake and spend time with the family ), but I'll get back to this. it's going to make for some possible lesson plans with my middle school music classes! ok, how about this: http://www.unconservatory.org/articles/hexperience.htmlscroll down to The Dark Sidewell, here's a list for you!  http://www.xs4all.nl/~huygensf/doc/bib.htmlthis will take days to get through, a huge bibliography(with many links) of tuning and temperament. yeeha!
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#77796
08/08/2002 1:55 PM
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Musical notation, like language, is a convention that enables understanding and communication. But marvelous as it is, it's still just a finger pointing at the moon - and it shouldn't be confused with a reality where its rules don't necessarily apply.This is the most sensible thing I've heard all *day! musick: your idea of timbre is a good one, but I think it goes deeper than just two or three strings. think about the different instruments/voices that are used...Much deeper! I suppose should have put the words "for example" a little earlier in that paragraph. Your comments on resonance are exactly what timbre is *about! Wordwind makes it clear for strings and Faldage makes it clear for brass. The answer is: there is a reason why things are set into certain keys: because they sound better. The fundamentals and the harmonics are both more pronounced. A stringed instrument will resonate the fullest as certain keys provide the most direct (mathematical) relationship with the open strings. Whether or not a Tenor sax, a b flat instrument, would be considerably different if it was constructed to be a c "concert" instrument is not worth much argument, but "built into" its physics certain frequencies resonate better, and I would suspect those would *transpose as well. I doubt if one would be able to make much sense anymore out of any historical description of what key is called what "emotion", as they probably were labled before "just" tuning, but each instrument will have more overall "pastoral" sounding collections of notes... that may just *suggest a key. The modes are a different story. I'd be guessing also, Faldage, but your descrition of F (lydian) and D sounds like Plato's (that's the guess) description of the modes... where F is pastoral and D (dorian minor, not major) is the mode they played for soldiers to prepare them for battle, as it had a focusing effect. Dorian sure can't be used to get anyone pumped up, unless you really don't like (for example) the pop singer Sade. Fishy - "Alternate tunings" should be split into two concepts. Techniques like tuning your guitar's lowest string to a "D" so the first three strings produce a D - A - D (or *open fifth) structure is a technique employed by *rockers who need to spend more energy on tounge than finger extensions (and rightly so!) is what is generally called alternate tunings (ie. using the same notes just grouping them differently). This is much different than Harry Partch http://partch.edition.net/Bhpsv1n2.htmlor other microtonal tunings that takes years of exposure to get be *functional, and even then only personally (but, then again, is there any other kind of *functionality?). Music, by definition, is structural and repetitive. Vary too far and you risk getting *it called noise... but then again, that's not saying much for the "three B's" is it? It is the only way most relate to some music as being a "sad" song or a "happy" song (and I'm not talkin lyrics here) but these are environmental effects and repetitive contexts - not intrinsic qualities.... IMHO, of course.
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#77797
08/08/2002 2:07 PM
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...indeed, thought by some to be Evil.This explains my comment about the "three B's"...[eg] First; a question: What notes are in a Gsus4 chord?= G, C, D, (F) Depends on the song / arrangement you are playing. The (F) may or may not be appropriate to the implied key center, it may contradict or overpower the melody note (or erroneously anticipate it). In rock it'd be difference between, say, Journey and AC/DC. In Jazz, the 7th in this case is *available cuz there ain't no rules, and nobody seems to care much. In Folk, it is just as written (three notes). In other traditional styles, well that's not traditional notation. EDIT : tsuwm - You'll like this one. I did a search for 37 note tunings ...and found one!http://www.seriouscomposer.com/Tunings.htmI can't stop laughing...
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#77798
08/08/2002 3:22 PM
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What notes are in a Gsus4 chord?
= G, C, D, (F)That would certainly be technically correct, muso, but fairly difficult to achieve in pure form. I suppose it's always an issue [a delightful one, mind ] that playing the same notes simultaneously on 2 or more strings of a guitar isn't equivalent to playing the note on one string. The chord takes on a drone, a different flavour, and different compatibilities with other chords (and shades thereof). As such most chord-shapes are trade-offs, even the beginner's "standards". The sort of shapes I'd use for Gsus4 would be: 6th String 3rd fret (G) 5th String 2nd Fret (B) 4th & 3rd Strings open (D & G) 2nd String 1st Fret (C) * only difference from a basic G 1st String 3rd Fret (G) or - 6th String 3rd fret (G) 5th String open (A) 4th String 2nd Fret (E) 3rd String open (G) 2nd String 1st Fret (C) 1st String 3rd Fret (G) - to go more in an Am7/C direction. Then take your finger off the 6th String (making an E) and move it down to the 5th string 3rd Fret (making another C) and - hey presto! - you have a C (add G) shape. You can also make a totally different Gsus4 by doing an Esus4 shape (3rd, 4th & 5th strings 2nd fret, rest open) barred on the 3rd fret. That makes the notes G,D,G, C,D,G - closer to a pure version. You may gather that I just love the "shadiness" or "merginess" of guitar. For any guitarists out there, here's my favourite recent discovery. It's a luvverly Am shape (I think Am7+9 ish) that stretches your fingers a bit, but worth the effort! 6th String open (E) 5th String open (A) 4th String 2nd Fret (E) [2nd finger] 3rd String 4th Fret (B) [4th finger *this is the stre-etch] 2nd String 1st Fret (C) [1st finger] 1st String 3rd Fret (G) [3rd finger] Works brilliantly with the Eurythmics' Here Comes The Rain Again... 
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#77799
08/08/2002 4:50 PM
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Speaking of picking nits... er... notes:
5th String 2nd Fret (B)
... 'taint no sus with a "B" in there!
... and if Faldage thinks a 'tritone' is the devil's interval he'll really *enjoy a 'minor 9th' (artfully 13 half steps)
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#77800
08/08/2002 4:53 PM
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if Faldage thinks a 'tritone' is the devil's interval
Interestingly enough, a good quarter or more of the works we do in the community chorus, and most of them religious, have a demented fifth tucked away somewhere in them. And that's just counting the bass part.
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#77801
08/08/2002 10:30 PM
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Y'all want fries with that? [snapping gum-e] a demented fifth tucked away somewhere in them. And that's just counting the bass part.That 'splains a lot. You know, for me, reading this thread is a little like trying to read a newspaper in Danish. I keep getting cream cheese on the comics but it is fun to imagine that I am understanding something, even if it is only my personal interpretation.
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#77802
08/08/2002 10:48 PM
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An algae-bra is something that a buxom plankton wears. But the moosick part is interesting! I'll try out that guitar chord, shona! :)
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#77803
08/08/2002 10:58 PM
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#77804
08/08/2002 11:00 PM
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'taint no sus with a "B" in there![sigh] Have you learned nothing? [points finger skyward]
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#77805
08/08/2002 11:01 PM
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That sounded suspiciously like the mating call of a pezcyclando What key would that be in?
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#77806
08/08/2002 11:11 PM
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the mating call of a pezcyclando What key would that be in?Bottom sea flat, con - a Bass key, of course.
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#77807
08/09/2002 2:15 AM
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In reply to:
there is a reason why things are set into certain keys: because they sound better.
I would say that it goes even deeper than just a relationship to the instrument being used. the different frequency energies based around each key center will resonate with various life experiences. if D is martial, perhaps there is some correlation between the combined energy of marching(simplistic picture, I know) and the emotions necessary for battle with the frequencies most prominently found in the key of D. likewise, those keys which seem more pastoral may relate directly to the life energies found in a meadow or field. etc., etc. this may seem like a bunch of hokey, but I would like to see some thought about it. I've read(somewhere, wish I could find the source) that whale song and many natural vibrational processes(Earth's orbit) are centered around the key of Db.
anyway, I guess I believe there are connections to be found, and patterns hidden deeply within those things that move us most.
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#77808
08/09/2002 2:32 AM
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RE: You know, for me, reading this thread is a little like trying to read a newspaper in Danish. I keep getting cream cheese on the comics but it is fun to imagine that I am understanding something, even if it is only my personal interpretation
you and me both connie.. i have been thinking of demanding wav files so i can have a clue... or else get emanuala in here, and give me frequencies in Hz, and let me generate the tones.. so i have some sort of clue.. (i might not always here the difference, but i might be able to parse the math..) still its like godel, esher and bach.. every once in a while a word or two strung to gether make some sort of sense.... goodness knows i found that book to be one of many i have encountered that consisted of words strung together, and while each indivigual word worked, the string were meaningless!-- but i still think i might have been able to understand it as a multi media presentation.. if i could hear, and read, and see, all at once.. maybe, maybe something would make some sort of sense, even if only temporarily. (like quantum mechanics.. when is see it on TV show, or hear a lecture (a really good lecturer) it perfectly clear, and i can fully understand it.. and 24 hours later, its back to being mush!)
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#77809
08/09/2002 4:57 PM
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Joined: Dec 2000
Posts: 2,661
Carpal Tunnel
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Carpal Tunnel
Joined: Dec 2000
Posts: 2,661 |
'taint no sus with a "B" in there!
[sigh] Have you learned nothing?
[points finger skyward]
I know, I know... it was a weak attempt at trying to pick at the word used to *prescribe it.
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etaoin - The *only hard thing to 'believe' is that emotions vibrate at specific frequencies for all preceivers.
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Algebra Schmalgebra!
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#77810
08/09/2002 6:12 PM
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Joined: Jul 2000
Posts: 3,467
Carpal Tunnel
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Carpal Tunnel
Joined: Jul 2000
Posts: 3,467 |
Oh that was good! I prostrate myself before you, trebling in awe.
TEd
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#77811
08/09/2002 6:39 PM
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Joined: Oct 2000
Posts: 1,346
veteran
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veteran
Joined: Oct 2000
Posts: 1,346 |
trebling in awe
Well, every good boy deserves favour, TEd, but don't quaver, don't even semiquaver. It's a breve feeling and I'm sure you can stave it off.
Get down the bar and take a rest for a minim.
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#77812
08/09/2002 7:48 PM
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Joined: Dec 2000
Posts: 2,661
Carpal Tunnel
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Carpal Tunnel
Joined: Dec 2000
Posts: 2,661 |
Interestingly enough, a good quarter or more of the works we do in the community chorus, and most of them religious, have a demented fifth tucked away somewhere in them. And that's just counting the bass part.They're so much more tasty in the lower register! A demented fifth seeks to resolve itself... I'd be even more interested if you sing any deficient ninths down there. I think you'd be *edging toward a virtual reformation. 
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#77813
08/10/2002 12:35 AM
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Joined: Mar 2000
Posts: 11,613
Carpal Tunnel
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Carpal Tunnel
Joined: Mar 2000
Posts: 11,613 |
Running perty fast and loose with them equalses there, Jackie. Gonna post the site's url to back them up? Ohmigawd, how horribly embarrassing. I am so sorry. Thanks, wofa--that is indeed it. I had had a message that day that frightened me not a little (it's not every day that I hear someone say, "Don't make enemies unless you're prepared to kill them."), and then got an unrelated one which was devastating, and which I am still reeling from. I am glad the belated find sparked the good discussion I'd hoped it would.
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#77814
08/10/2002 4:27 PM
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Joined: Mar 2000
Posts: 6,511
Carpal Tunnel
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Carpal Tunnel
Joined: Mar 2000
Posts: 6,511 |
Jackie, I'm saddened to hear of the threatening message.
Back to demented fifths: musick, I might take a lickin' from Faldage on this, but I agree they need to be resolved, sort of a suspended devil if you will. For example: "Ma-ri-a" from West Side Story... you gotta have it go on.
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#77815
08/11/2002 4:51 PM
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Joined: Mar 2001
Posts: 36
newbie
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newbie
Joined: Mar 2001
Posts: 36 |
Perhaps I read the posts too hurriedly, but I didn't see any mention of the recently published book "Temperament" by Stuart Isacoff. A very readable book, it discusses tuning down through the ages, engaging "such great thinkers as Newton, Kepler, and Descartes as well as musicians, craftsmen, church leaders, and heads of state. At the heart of their dispute is the question of how the tones of a musical scale should be selected."
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