Intervals, from: The Circle - Fifths versus Fourths

kernewegor

Bon vivant, raconteur and twit
If you want to be really logical, do like a friend of mine and divide the octave in 6 equal steps. His piano (he could not patent it, because the original idea dates back to 16th century) has a white key followed by a black key. All intervals are simpler, as is the system (common in computer music) of dividing the octave in 12 steps. In the good old days we used to say that a third is "5 strings", as is a diminished fourth, and a plus-that-augmented second.
You just need to learn two fingerings and you have all the major scales (a mark is needed on C).
Quite useless in performing western music.

Some time ago I got irritated that medieval organ and other keyboard makers couldn't be bothered to put a complete set of black notes on their instruments, giving birth to the ludicrously complicated notation system used in (most) Western music (Highland pipers, I believe, used at one time to use something which looked like Arabic written by a drunk...)

So I decided to rename all the notes of the octave (ABCDEFGHIJKL) and drew up a stave which had more lines and enabled music to be written without the need for signs for sharps and flats....

I never got around to modifying a piano and accidentally used my notes (in which I wrote out a few tunes in the system) to light the fire.

The fire caught all right, but I don't suppose the idea would have caught on...

PS

In the USA a 757ml bottle of spirits is known as a 'fifth'....

.....and talking about fifths, Eddie Condon once said "Beboppers flatten their fifths. We drink ours."
 
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JBT's note is a good one.

The other thing is that the perfect intervals are all simple ratios such as 1:1, 1:2, 2:3 etc., whreas the non-perfect intervals are not.
 
A minor interval "stretched" by adding a half step becomes a major interval.
A major interval "shrunk" by taking away a half step becomes a minor interval.
A perfect interval "stretched" by adding a half step becomes an augmented interval.
A perfect interval "shrunk" by taking away a half step becomes a diminished interval.

Great pedagogy - using the visualisable concept of shrinking and stretching makes an abstract concept and its terminology instantly memorable.
 
Many musicians do just that but when they get the basics they suddenly realise that 12 hours a night in a Hamburg night club over 3 years learning what works could be replaced with a few hours study.
"A few hours study" crack me up man - I beg to differ - I never did Hamburg - and study - whoosh - there's a lot more to earning your daily bread than swotting up on theory. I studied on stage - live - music is emotional - this whole theoretical crap gets up my nose. If you don't move 'em you lose 'em. and if you can't move 'em you don't get the gig!
 
I see that someone chose birth as a guide and completely misinterpreted it. At birth one is already some period older. The Zero point is passed at partition when you breath.
The nurse notes the time you are born, you must be zero at that point in time.
You don't breathe at parturition, (or breath at partition), you take your first breath when some sadist holds you by the ankles and hits your backside until you start crying.
 
I can't find the 0 on my piano did Yamaha rip me off or should I call John Cage or Nicolas Slonimsky?
Feel free to write a 0 anywhere you like on the keyboard. Most people would probaably put it on middle C if forced to choose. But those flappy things on your keyboard represent notes, not intervals. If I ask you to play me an octave, I expect to hear two notes separated by the interval of an octave.

@BigMartin - you find it ugly ? does it sound ugly ?
"A third plus a third is a fifth" does sound ugly to me if you say it out loud. The notes don't sound ugly (depending on who sings or plays them) but that's not what I'm talking about.

It's rather like cubism and the use of perspective in ancient Chinese art.
What is? And in what way?
 
this whole theoretical crap gets up my nose
Sorry to hear that. The way I see it is: theory is something that can help you plan your practice. Practice forms the habits you use when performing. Works for me at my admittedly relatively low skill level. Gigging 5 nights a week would possibly work even better, but it's not a option for many reasons. Of course, if you're thinking about theory while you perform, you're in trouble.
 
apart from the octave/unison, not exactly true in equal temperament
If A = 440 then 3/2 of that frequency would be the "true" E a fifth higher or 660 hz.

If one multiplies the product of 440 X 1.059464309435 7 times it produces the tempered pitch 659.225 hz which is .745 hz or about 2 cents lower than the "true" pitch.

I think "close enough for jazz" is the commonly used expression. 🙂
 
If A = 440 then 3/2 of that frequency would be the "true" E a fifth higher or 660 hz.

If one multiplies the product of 440 X 1.059464309435 7 times it produces the tempered pitch 659.225 hz which is .745 hz or about 2 cents lower than the "true" pitch.

I think "close enough for jazz" is the commonly used expression. 🙂
True, but my cello teacher tries to get me to tune the 5ths on the open cello strings to remove the slight 'wow' from ET tuning, i.e. to widen the interval very slightly.
 
I'm rapidly coming to the conclusion that calling the circle of fourths the circle/cycle of dominants is simply sloppy English. Calling the circle of fifths the circle/cycle of dominants - yes, that's OK as you move to the dominant of the previous scale with each step, so that fits properly.
 
@aldevis
Sorry, maybe it's language, but the first harmonic is the fundamental. Second harmonic has double the frequency of the fundamental.

Indeed.
I messed up terms, contradicting the whole point of rational numbers.

1st harmonic is the fundamental, a vibrating string of length l/1
2nd harmonic (1st overtone?) l/2
3rd l/3
and so on

Calling the first harmonic "harmonic zero" cannot relate it with the string length (l/0)


A minor interval "stretched" by adding a half step becomes a major interval.
A major interval "shrunk" by taking away a half step becomes a minor interval.
A perfect interval "stretched" by adding a half step becomes an augmented interval.
A perfect interval "shrunk" by taking away a half step becomes a diminished interval.

But the saucy part comes when you stretch a major interval and get an augmented one, or shrink a minor one and get a diminished.
This allows the rule of inversions:
9 - (original interval). and major becomes minor, augmented diminished.
for example if we want to invert a diminished 7th
9-7=2, diminished becomes augmented. We have an augmented second.
 
So I decided to rename all the notes of the octave (ABCDEFGHIJKL) and drew up a stave which had more lines and enabled music to be written without the need for signs for sharps and flats....

You discovered the piano roll.
Cubase or Logic have it as a primary function to edit notes. DJs and computer programmers love it.
Also it counts semitones from zero, so an augmented 4th is simply "6"

We called this intervals "strings" because is like counting the strings inside a piano, but I am not sure how it is in English.
 
I studied on stage - live - music is emotional - this whole theoretical crap gets up my nose. If you don't move 'em you lose 'em. and if you can't move 'em you don't get the gig!
Sorry to hear that. The way I see it is: theory is something that can help you plan your practice. Practice forms the habits you use when performing. Works for me at my admittedly relatively low skill level. Gigging 5 nights a week would possibly work even better, but it's not a option for many reasons. Of course, if you're thinking about theory while you perform, you're in trouble.

There are classical musicians that forget almost all the theory as soon they finish the academy.
As performers they just don't need it, and they surely make more money than I do.

As jazz improvisers and composers, theory is essential to know what you are doing.
Also the more awareness you have of the music you are contributing to make, the more complete you feel.

The way we call intervals reflects the harmonic concept behind. An augmented fourth is not a diminished fifth (often chords are miswritten), and knowing it allows me to play a better solo and hope to get the next gig.

In some context theory (actually theories) can be superfluous but having it handy never hurts.
 

Similar threads... or are they? Maybe not but they could be worth reading anyway 😀

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