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Beginner Circle (or cycle) of 4ths and 5ths

as a logician 1
Logically it should be zero because that's how old you are when you are born.
A child between 12 and 24 months is one year old, a child before 12 months is zero, so you count your age from zero.
 
Logically it should be zero because that's how old you are when you are born.
A child between 12 and 24 months is one year old, a child before 12 months is zero, so you count your age from zero.

you missunderstood me.... :p

In boolean logic
1=true
0=false

So 1 meant I was agreeing with him. :sax:

But... We play on the double meaning of 1 here. :mrcool
 
Why fourths instead of fifths? Jazz guys tend to work that way.

A large percentage jazz tunes are in flat keys, while most
blues tunes that guitarists play are in sharp keys.
 
Sharp sounds up and feels right. Flat sounds down and feels left. Clockwise feels right and anti feels uncle.

There's a lot of maths in music. Looking at harmony through an oscilloscope was a revelation to me. Jagged lines resolving into geometric shapes.
.
 
As for the word mathematics, please forget it.
That's neither possible nor desirable for me.
That simply puts people off.
Am I not a person, then? ;). The people who are put off (usually by some very bad teaching in the past) are missing out, big time. It's a beautiful and powerful tool.
Music is a natural element and owes nothing to mathematics
Oh man, where do we start?
Yes his infamous 12 rules of database are actually 13, counting from zero is a nonsense.
That's a very different application of the number system. Absolute versus relative. Your example involves counting things. Intervals are a kind of distance measure between two pitches. I could launch into a discussion of affine versus linear spaces here but, in light of the the comments I quoted above, I'll restrain myself.

A perfect unison is no interval at all, and should be labelled zero rather than one. I really don't see how there's any room for argument other than "It's always been done that way".
 
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I respectfully disagree:
The cycle of fourths is also known as cycle of dominants (that is not a sport event for perverts).
Each key is the dominant of the next one.
I know it's called that, but the dominant of any scale is the 5th, not the fourth. So I'm being dumb, but why is the circle of fourths also known as the cycle of dominants?

Dominant chords are 1 3 5 b7, but I don't see a fourth in there,

Yours confused.
 
I'm guessing really but it's depends on your standpoint and how you draw your circle*:
Fourths
C is dominant of F is dominant of Bb is dom of Eb etc. (1 flat - 2 flats - 3 flats - 4 . . . )
or Fifths
G is dominant of C - D is dom of G - A is dom of D (1 sharp - 2 sharps - 3 sharps - 4 . . . )

(P.S. Edith)
@Kev - * I guess again what I'm trying to say is C up to F is a fourth and C down to F is a fifth.
and vice versa C up to G a fifth and C down to G a fourth.
but when you get to six o' clock you have to change from C# to Db or Db to C# then your sharps or flats diminish numerically 7,6,5,4,3,2,1 back to C
 
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Dominant chords are 1 3 5 b7, but I don't see a fourth in there,

Yours confused.

If someone allows you to touch a piano, try this:

C E G C
C E G Bb
F C F A
F C Eb A
Bb Bb D F

...

(Inversions could be better and first note is on LH)

This gives you an idea of how one key dominates the next one.

Moving by fifths does not show candenzal relation.
 
A perfect unison is no interval at all, and should be labelled zero rather than one. I really don't see how there's any room for argument other than "It's always been done that way".

First of all mathematic is just a language more ore less useful to describe an empirical reality and a tool (see my previous link to Galileo's father). Nothing obeys to mathematical laws, mathematical laws successfully describe things, as long as they work.

About zero, I am not sure that Pitagora knew it when he first described harmonic intervals.

Among the lucky coincidences in the western music system, the 7th, 8th, 9th, 10th 11th 12th 13th harmonics, are the 7th, 8th, 9th, 10th 11th 12th 13th grades of a scale.
As the Greek mathematician pointed out, if you divide a string in seven parts, you get (roughly) what is now called "7th"

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.


edit: I did an error.
The harmonic numbers are the denominator of the original string length. 2nd harmonic is 1/2 string, 3rd is 1/3 and so on. so they start from 1.
 
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First of all mathematic is just a language
A commonly-held misconception. It's a collection of languages and a vast body of knowledge expressed in those languages. What we're dealing with here, however is a simple matter of counting.
Nothing obeys to mathematical laws, mathematical laws successfully describe things, as long as they work.
Well, that's pretty much what a law is (in the scientific sense), isn't it?
About zero, I am not sure that Pitagora knew it when he first described harmonic intervals.
I really don't care what he knew or dodn't know. We've moved on a bit since then. And did Pythagoras ever talk about thirds and fifths, etc, in the sense we use the ternms now (genuine question)?
If you want to be really logical
Yes, please!
do like a friend of mine and divide the octave in 6 equal steps.
That's horrible, and it's nothing like what I'm asking for. All I want is to subtract 1 from all the interval names so that they acually mean something sensible and can be added together in a straightforward way. I understand I can't have it but it annoys the hell out of me.
 
A commonly-held misconception. It's a collection of languages and a vast body of knowledge expressed in those languages. What we're dealing with here, however is a simple matter of counting.
I was also referring to the semitone function debatable 12th root of 2. A bare tool to approximate an acceptable tempered system.

Well, that's pretty much what a law is (in the scientific sense), isn't it?
I wish... Often prescriptive and descriptive laws get confused.


I really don't care what he knew or dodn't know. We've moved on a bit since then. And did Pythagoras ever talk about thirds and fifths, etc, in the sense we use the ternms now (genuine question)?

Not sure about his theory, but Pitagorean tunings have been in use for a long time. I seem to remember that the scaling of guitar frets are Galileo's take on Pitagora's calculations.
Here lies the actual problem of music theory. Starting from Pitagora formulations, we need a system that works both horizontally and vertically, that is useful to describe chords and scales, in a system that is forcefully tempered.
Also it has to cover several centuries, from just after Gregorian chant to nowadays.
The denominator thing is a good approximation, so you don't have a /0 number. The root is a full string 1/1 of its length. Using a different starting point if we talk harmonics or scales is just impractical.

That's horrible, and it's nothing like what I'm asking for. All I want is to subtract 1 from all the interval names so that they acually mean something sensible and can be added together in a straightforward way. I understand I can't have it but it annoys the hell out of me.

How con you cope with the major scale? It's like having a week where Tuesday and Sunday are only 12 hours long, and if you work Wednesday to Wednesday you need to adjust Friday! :)
 
There appear to be two simultaneous threads here - I'll leave the mathematical one to the brain surgeons and rocket scientists.
This gives you an idea of how one key dominates the next one.
Moving by fifths does not show candenzal relation.
I'm flying by the seat of my piano stool, but let's see if I'm grasping this ?
In the circle of fourths each succesive chord "dominates" its predecessor.
C to F changes the key center.
Whereas in the circle of fifths each successive chord is "dominated" by its predecessor.
C to G doesn't change the key center.

I play by ear - music theory goes in one ear and out the other.
 
How con you cope with the major scale? It's like having a week where Tuesday and Sunday are only 12 hours long, and if you work Wednesday to Wednesday you need to adjust Friday! :)
Yes, but I can see (and more importantly, hear) the need for those quirks. I can even live with the rather arcane major/minor/diminished/augmented nomenclature for intervals. But the numbers are just wrong. I can see no downside to the doublie-frequency = (perfect) seventh system other than the historical one. I understand why we're stuck with the current system but I really, really don't like it. That's all I'm saying.
 
In the circle of fourths each succesive chord "dominates" its predecessor.

C to F changes the key center.
Whereas in the circle of fifths each successive chord is "dominated" by its predecessor.
C to G doesn't change the key center.

I'd say the other way round...

I can even live with the rather arcane major/minor/diminished/augmented nomenclature for intervals.

My favourite!
Inversions work a dream: 9-(original interval), major becomes minor, perfect stays the same. Augmented becomes diminished. Some genius elaborated the system.

I can see no downside to the doublie-frequency = (perfect) seventh system other than the historical one.

I told you, since there is a relation with the denominator, the root cannot be expressed as 1/0. That would be seriously irrational.
 
@ArgoPete

This is typical of our threads. If a question's been answered (or even before) we tend to digress around and off the subject. Feel free to shout and bring it back on track.
 
I told you, since there is a relation with the denominator, the root cannot be expressed as 1/0. That would be seriously irrational.
What denominator? I'm talking about interval names. What are you dividing by what?
 
What denominator? I'm talking about interval names. What are you dividing by what?

Look at the fundamental as a string.
At full length its frequency f is f/1. Its first harmonic (the octave) is half length, f/2. And so on.
When we get to f/7 we start having a relation between harmonics (vertical approach) and scale (horizontal approach). f/7 is the seventh note of the scale starting on f/4. same as f/8, f/9... debatable f/11 (see George Russel). So the denominator at that point is also the grade name.
Interval names are based on grade names.

I seem to remember more complex mathematical gizmos to calculate consonances and dissonances, but all fell apart with the tempered system.

Now I am curious to know who first formalized music intervals as we know them. I would guess 15th century at some point.

edit: obvious error on f/x
 
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Interval names are based on grade names.
Eh?

How is the interval of a (major or minor) second based on a grade name? (This is the first I've ever heard of a grade name by the way. Niotice how this is not the way the names are taught to us in modern times).
f/7 is the seventh note of the scale starting on f/4.
Say what? If that's why they called a seventh a seventh, those guys were even crazier than I thought.
 
Eh?

How is the interval of a (major or minor) second based on a grade name? (This is the first I've ever heard of a grade name by the way. Niotice how this is not the way the names are taught to us in modern times).
Something is gone amiss.
CDEFGABC
12345678
D is the second grade of C. There is a second between C and D
Between C and F there is a 4th. F is 4 of Cmajor
Between F and B there is a 4th, although augmented, because B does not belong to the F scale, but a Bb is the 4th grade of the F scale.
Interval is still a 4th.
Between G# and Fb there is still a 7th. G1 A2 B3 C4 D5 E6 F7

Major minor perfect augmented are a different matter.

If you are referring to names like "supratonic" another can of worms is to be opened.
In Italian and English a melodic tradition gives names like tonic (1) supratonic (2) mediant/characteristic/modal (3)
In German, a harmonic approach is Tonic (1) (spelling?) Subdominantparallel (2) Tonicparallel/Dominantparallel (3)
Different concepts, different traditions.
To explain this in English is really hard for me. Also it is more useful when composing or analizing than it is when improvising on a standard jazz form.

I studied in the 80s, a different century. Not sure what they teach now.

Eh?Say what? If that's why they called a seventh a seventh, those guys were even crazier than I thought.

Not sure that's the reason, but it is a lucky coincidence.
 

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