 The Clarinet BBoard
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Author: Mark Charette
Date: 2003-01-05 00:14
Because their ratios to the fundamental are composed of prime numbers; e.g.:
4th (4:3)
5th (3:2)
octave(2:1)
That should be in any theory 101 book ...
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Author: Suzanne
Date: 2003-01-05 01:54
Mark, I don't understand the ratios you wrote. Can you explain what each number refers to? I actually got out my theory 101 book, and it does not explain this at all. I posted the thread because my student told me yesterday that her piano teacher said the perfect intervals got their name because they "sound the best." That didn't seem like the best answer to me... I want to give her the right answer.
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Author: Mark Charette
Date: 2003-01-05 02:15
Perfect intervals, ones made by the ratios of the prime numbers, do not "beat" against the fundamental and are therefore "perfect". If you draw sine waves (the fundamental and a perfect interval) you'd see that the crests and troughs are coincident after a finite number of cyccles and that coincidence is at a periodic interval.
In "ear terms", they sound "perfect" when played with the fundamental. If they're even a little bit off you'll hear audible "beat notes".
If your fundamental is A=440, the perfect fifth above is E=660. Most of the time we use a well-tempered scale where E=659.26 (or so) and you can hear a beat at about once every 3/4 of a second. If the tones aren't held it's not noticeable, but we'll tend to make it perfect if it's held for any length of time .
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Author: Richard
Date: 2003-01-05 12:51
Suzanne;
I’m afraid the answer to you question goes a little beyond Music 101. Originally, before the equal temperament and just intonation scales were developed Pythagorean tuning was in use. Scales were tuned from one given tone, say 440 Hz, up in fifths and down in fourths from that tone. Thus, up from A are E, B, F#, and so on: Down from A are D, G, C, and so on. The rest of the notes were whole number ratios of these tones.
The problem at this point was that some intervals in some keys didn’t come out right (the infamous wolf tones). To compensate for these inconsistencies, some of the fifths (and fourths) were ‘adjusted’ by a value somewhat less than ‘perfect’.
The use of the term perfect to describe fourths and fifths is a holdover from the original tuning method in the ‘Greater Perfect System.’
For a good discussion on this topic see:
http://www.midicode.com/tunings/index.shtml
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Author: Alphie
Date: 2003-01-05 14:09
Suzanne....in practical terms this would mean that if you are playing together with anything but a piano, organ or mallats that are usually tuned in equal temperament, you would have to play:
major 3rd sharp
minor 3rd flat
4th a little flat
tritonus a little sharp
5th a little sharp
minor 6th (reversed major 3rd) sharp
major 6th (reversed minor 3rd) flat
minor 7th very flat
major 7th sharp
I hope this is clear enough though I think you have different terms for intervals in English.
People who know their maths very well may object and correct me if something is wrong.
Alphie
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Author: Tabbi
Date: 2003-01-05 20:59
The idea of perfect intervals, or consonances, goes back hundreds of years to writers such as Guido and Pythagoreas. The most simple explanation is that it has to do with the division of the string on a lyre or other stringed instrument. The book, Source Readings in Music History, will provide you with excerpts from some of these writers. Thanks to my history of theory professor on this one!
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Author: David Peacham
Date: 2003-01-06 10:43
Sorry, but I shall disagree with everyone (yes, even with Mark C) on this one.
There are two quite separate issues:
(1) Why equal temperament is different from just intonation.
(2) Why we talk about "perfect fifths", but not about "perfect thirds".
In just intonation, but not on a piano, the interval from C up to D is in the ratio 9:8, from D up to E is 10:9, from C up to E is the product of these, which is 5:4. They are all ratios of integers. But none of these intervals would be described as "perfect".
"Perfect" actually relates to something much simpler. Forget about just intonation and let's pretend that equal temperament is all we have. Then we can describe every interval as a "unison", or a "second", a "third" and so on. It turns out to be convenient to say that seconds, thirds, sixths and sevenths come in four varieties, which we call "diminished", "minor", "major" and "augmented". The other intervals - unisons, fourths, fifths and octaves - only come in three varieties, which we call "diminished", "perfect" and "augmented".
So the interval from C up to G is a perfect fifth. From C up to Gb is a diminished fifth. From C up to F# (which in equal temperament is exactly the same thing) is an augmented fourth. From C up to G# is an augmented fifth, which is "the same as" C up to Ab, which we call a minor sixth.
At the end of the day, it's just nomenclature. There's nothing really special about "perfect" intervals. It's nothing to do with equal temperament versus just intonation, and it's nothing to do with integers.
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Author: Ginny
Date: 2003-01-06 15:18
I had thought this was also linked to religion and paralelle organim - the plain chant sung in perfect fifths. That for some reason these intervals where deemed godly... the augmented fourth has been called the devil's interval.
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Author: Ken
Date: 2003-01-06 20:18
Yes, the melody of Berstein's "Maria" is a textbook example of the devil's interval.
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Author: Mark Charette
Date: 2003-01-06 21:03
Ken wrote:
>
> Yes, the melody of Berstein's "Maria" is a textbook
> example of the devil's interval.
As is the opening music to the television cartoon "The Simpsons" ... and I don't think it's by accident.
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Author: Benni
Date: 2003-01-07 01:33
Tritones are even found in literature! ;-)
"He was the Devil's son-in-law, all right, and he was a man who could whistle a three-toned chord . . ."
-Invisible Man by Ralph Ellison
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Author: Abby
Date: 2003-01-10 22:48
I don't entirely understand the physics of it, but from my theory background it seems to me it's more than just nomenclature.
I think Mark was saying something about sine waves. I do distinctly recall a couple of demonstrations from my theory class, which revolved around the speed of the vibrations. If you put one hand on the body of the piano around the strings and play a perfect interval, you can feel the vibrations. Now play an imperfect interval and the vibrations should feel faster.
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David Peacham wrote:
At the end of the day, it's just nomenclature. There's nothing really special about "perfect"
intervals. It's nothing to do with equal temperament versus just intonation, and it's nothing
to do with integers
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