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

aldevis

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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.
 

aldevis

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You should see mine after trying to use a language in which numbers have no gender.
A sex-free language.
 

BigMartin

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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
Yes I know that, but here's how it should go:

C is the first grade of C
D is the second grade of C.
The interval between them is 2 - 1 = 1, so that should have been called a first (just a one or something else reflecting the number 1, not two). Intervals are not notes, they are the vertical "spaces" between notes.
F and A are the 4th and 6th degrees of the C scale. The interval between them is 6 - 4 = 2. Calling it a third is just horrid.

And I don't see anything in my system that leads to division by 0.
 

aldevis

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And I don't see anything in my system that leads to division by 0.
Root is a vibrating body... it is not a nothing. It has a rational relation with the other degrees (in a non tempered system)
"One" has to be the same in both approaches.
You have to throw the harmonic theory down the drain, not relating it to the scale.

free to do it, but I find the current system exceptionally integrated.
 

jbtsax

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Now you folks even have me confused talking about "grades" and such and I know this stuff. :)

It doesn't have to be complicated if one looks at intervals in terms of the diatonic (major) scale.

Do Re Mi Fa Sol La Ti Do or 1, 2, 3, 4, 5, 6, 7, 8

From step 1 of the scale to step 2 is a major 2nd (1 whole step)
From step 1 of the scale to step 3 is a major 3rd (2 whole steps)
From step 1 of the scale to step 4 is a perfect 4th(2 1/2 (whole) steps )
From step 1 of the scale to step 5 is a perfect 5th(3 1/2 steps)
From step 1 of the scale to step 6 is a major 6th (4 1/2 steps)
From step 1 of the scale to step 7 is a major 7th (5 1/2 steps)
From step 1 of the scale to step 8 is a perfect 8th (6 steps)

I also think that to use the language that a certain chord "dominates" another can be confusing. The V or V7 "leads or pulls" back to I or the tonic. The 3rd of the V chord pulls up to the root of the 1 chord, and the 7 of the V7 chord pulls down to 3rd of the tonic. The 3 and the 7 of the V7 alone create a "tritone" (3 whole steps) which in music is a very unstable interval. It wants to "resolve" to a more stable interval. It is this "tension and release" that produces the characteristic sound of the V7 - I or the ii V7 I that we hear in all styles of music. If the ii is major instead of minor then we have a II - V - I, or II7 - V7 - I which is called "secondary dominance" [there's that confusing word again]. :)

Did this help anyone, or did I make it even more confusing.
 
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BigMartin

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Root is a vibrating body... it is not a nothing.
But it's a note, not an interval. The interval from root to root is nothing. (Or amultiple of a "septave" in my newly-invented terminology)
"One" has to be the same in both approaches.
But note one is (or shouldn't be) the same as an interval of one.
It doesn't have to be complicated if one looks at intervals in terms of the diatonic scale.
But the problem comes when a 3rd plus a third is a fifth etc. I know that's how it is, I'm just saying I find it ugly.
 

kevgermany

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@aldevis
Sorry, maybe it's language, but the first harmonic is the fundamental. Second harmonic has double the frequency of the fundamental.

However the first overtone is double the frequency of the fundamental.

Back to numbering from 0 or 1...

But I still don't get the tie between fourths and dominants, sorry.
 

spike

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Thanks jbt - C to F is a perfect 4th and C to A is a major 6th
and by the same token - F to A is a major 3rd (2 whole steps)
I can't find the 0 on my piano did Yamaha rip me off or should I call John Cage or Nicolas Slonimsky?
@BigMartin - you find it ugly ? does it sound ugly ?
It's rather like cubism and the use of perspective in ancient Chinese art.
@kevgermany - yes I've been hacking around on my old johanna all afternoon and I still don't get the tie between fourths and dominants either - seems back to front for my ears although maybe correct in theoretical terms.
"Ear, Ear" that's all I can say me lords.
 

spike

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You'll get more explanations - I'm quoting:
It was considered a sacred interval in medeval times which earned its title of "perfect". The perfect fourth is also well known as the "Amen" at the end of many hymns which are still sung in churches today. It has a "major" sound but also has an open quality to it and some have even described it as meditative.
I'll get my coat, take the dogs for a walk and whistle a few hymns.
 

kevgermany

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I'm confused by the word "perfect". What make those notes perfect? Forgive me as I have a limited theory background. I also get confused with what makes a dominate.
Originally used to describe intervals that are the same number of semitones in major and minor keys like octaves, fourths, fifths.

As opposed to thirds which are a semitone smaller in a minor key than they are in a major key. So a major third is 4 semitones(e.g. C to E), while a minor third is only 3(e.g. C to Eb).

But the terminology is abused - so you get a minor second of 1 semitone, even though a second is 2 semitones in major and minor scales.

Another explanation is that the perfect intervals sound, harmonically, perfect, as opposed to the others which don't (especially thirds in equal temperament).
 

aldevis

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If we consider Monday as "day zero" we may end up with a week of only six days...
 

Jeanette

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If we consider Monday as "day zero" we may end up with a week of only six days...

Well as long as we don't lose Friday like you were threatening here

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! :)
I like that Friday feeling :)
 
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