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Topic: Why are 7 individual notes called an "octave"?  (Read 4089 times)

Offline intoresting

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Why are 7 individual notes called an "octave"?
on: June 10, 2005, 07:11:25 PM
You probably guessed that I'm a beginner from my question. One thing that struck me as confusing right off the bat is the fact that there are seven individual notes in an octave. At each octave, the frequency doubles- right? Well if there are really only seven individual notes in an octave (A,B,C,D,E,F,G) then wouldn't it make more sense to call an octave something like a "sept-ave" or a "hept-ave"? (By the way, the number prefixes "sept" and "hept" mean "seven"). When we use the word "octave" (the number prefix "oct" means 8 ) , then aren't we really counting the "A" twice? The reason why this is confusing to me is that it seems to be inconsistant with our base 10 number system. If we were to compare an octave to our number system, then we might call 1-10, 11-20, 21-30 ect octaves. (Or maybe "dec-aves", "dec" means 10, would be more appropriate). But in the case of this hypothetical "decave", it WOULD make sense because each doubling set would have 10 individual "notes".(1,2,3,4,5,6,7,8,9,10) ... with no repeating of the 1's. Could someone explain this to me? Am I missing something obvious here?

Offline intoresting

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Re: Why are 7 individual notes called an "octave"?
Reply #1 on: June 10, 2005, 08:00:29 PM
I'm curious. Are you guys not replying because:

A- what I'm asking doesn't seem to make sense
B- the answer is too complicated and would require an essay

or

C- you're not sure
?

If it's "A", please let me know so that I can try to rephrase my question.

Offline bernhard

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Re: Why are 7 individual notes called an "octave"?
Reply #2 on: June 10, 2005, 08:09:18 PM
You are starting from a false premise, namely that C and C one octave higher are the same note.

They are not.

They sound different, they are written in different locations of the score, they are played in different keys of the keyboard.

Get rid of this initial false assumption and your question vanishes.

Best wishes,
Bernhard.

P.S. Don't be so impatient! ;)
The music business is a cruel and shallow money trench, a long plastic hallway where thieves and pimps run free, and good men die like dogs. There's also a negative side. (Hunter Thompson)

Offline intoresting

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Re: Why are 7 individual notes called an "octave"?
Reply #3 on: June 10, 2005, 09:10:54 PM
Thanks for the reply. I'm still a little confused though. In the example of the "A's" that I used, wouldn't the same be true as what you said about the "C's"? -That is that an A and A one octave higher are not the same note. If that's the case, wouldn't the keyboard have to look something like this? I know I'll probably look back at this question and laugh at myself but, for now, I don't get it.

Offline intoresting

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Re: Why are 7 individual notes called an "octave"?
Reply #4 on: June 10, 2005, 09:25:58 PM
Hmm.. is the highest note in one octave also the lowest note  in the next octave? Therefore the same physical key is counted as twice?

Offline maxy

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Re: Why are 7 individual notes called an "octave"?
Reply #5 on: June 10, 2005, 09:49:42 PM
let's look at the concept considering intervals.

from c to c we call it "unison"  or let's put it as number 1
from c to d "second"   or 2
from c to e  "third"  or 3
from c to f   "fourth" or 4
from c to g "fifth" or 5
from c to a "sixth"  or 6
from c to b "seventh" or 7
from c to c "octave" or 8



Offline sonatainfsharp

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Re: Why are 7 individual notes called an "octave"?
Reply #6 on: June 10, 2005, 09:49:58 PM
count with me:
C (1)
D (2)
E (3)
F (4)
G (5)
A (6)
B (7)
C (8)

From C to C is EIGHT steps, hence OCTAVE, hence OCT. An octave is an "8th," so to speak.

Look at that; two indentical answers at the same time.

Offline bernhard

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Re: Why are 7 individual notes called an "octave"?
Reply #7 on: June 10, 2005, 09:59:56 PM
Er…

An interval is defined as the distance between two notes. Not three, and not four. Just two.

So if you take A and B, two notes are involved, you have a second.
If you take A and C, three notes are involved (A, B, C), so you have a third,

And so on.

If you go from A to A’ (A one octave higher) there are eight notes altogether involved (A, B, C, D, E, F, G, A’), hence an octave (= eighth).

No note is counted twice because there are only two notes defining any interval. (the note on the left and the note on the right; the name of the interval is the total number of notes involved: the start, the end and the ones in between).

Now, when you say: From A to A’ there is one octave, and from A’ to A’’ there is another octave, therefore the A’ has been counted twice, it makes no sense, because you only consider two notes, not three. It does not matter if the note you are starting from is the note you finished on. Such information is not taken into consideration when dealing with intervals, only the two notes involved.

Take the C major triad: C-E-G

From C – E you have a third. (Three notes involved: C-D-E)
From E – G you also have a third (Three notes involved: E-F-G)
And from C – G you have a fifth (Five notes involved: C-D-E-F-G)

The E has not been counted twice. Neither the C, neither the G. They only appear more than once if you look at the three sentences above together, but each sentence is a separate entity, one has nothing to do with the other. The E was the end of the first interval. It was also the start of the second interval. The C was the start of both the first and last interval, and the G was the end of both the second and the last interval. But they have not been counted twice. In each interval they were counted once only.

This is not such an outlandish concept. If you decide to travel from Oxford to London, you will have a stop in Reading. When you measure the distances between Oxford –  Reading; Reading –London; did Reading got counted twice? Of course not. The distance Oxford-Reading is independent of the distance Reading-London. When you measure distances, only origin and destination count. In fact Reading will not even appear if you measure the Oxford-London distance.

I hope this helps.

Best wishes,
Bernhard.


The music business is a cruel and shallow money trench, a long plastic hallway where thieves and pimps run free, and good men die like dogs. There's also a negative side. (Hunter Thompson)

Offline intoresting

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Re: Why are 7 individual notes called an "octave"?
Reply #8 on: June 10, 2005, 10:33:30 PM
Thanks for all the replies.  I think the part that I'm confused about is this "unison" interval. In between which two physical keys on a keyboard can we find a unison?

Offline faulty_damper

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Re: Why are 7 individual notes called an "octave"?
Reply #9 on: June 10, 2005, 10:42:22 PM
The single note is a unison.  There is no interval between a unison.

Offline bernhard

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Re: Why are 7 individual notes called an "octave"?
Reply #10 on: June 10, 2005, 10:48:40 PM
Thanks for all the replies.  I think the part that I'm confused about is this "unison" interval. In between which two physical keys on a keyboard can we find a unison?

Or alternatively, get two pianos and play the same note in both. The interval between these two identical notes (but sounded in two different pianos) would be the unison.

The unison can be used to great effect in an orchestra, all instruments playing the same note at different timbres. :D
The music business is a cruel and shallow money trench, a long plastic hallway where thieves and pimps run free, and good men die like dogs. There's also a negative side. (Hunter Thompson)

Offline intoresting

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Re: Why are 7 individual notes called an "octave"?
Reply #11 on: June 10, 2005, 11:05:57 PM
I think I got it. I could view each octave as a whole pizza cut into eight slices. I have eight choices as far as how much pizza to put on my plate. I can either:

1- put the whole pizza on my plate
2- put 7 slices on my plate
3- put 6 slices on my plate
4- or 5 slices
5- or 4 slices
6- or 3
7- or 2
8- or 1

is that an accurate analogy?

Offline Bob

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Re: Why are 7 individual notes called an "octave"?
Reply #12 on: June 10, 2005, 11:58:26 PM
I don't exactly follow that analogy.


Here's an analogy that makes sense to me...

Why are seven individual notes called an octave?

is like asking..

Why are 5,280 individual feet called a mile?


Another use of the word octave...
In one octave, from the starting note UP TO, but not including, the next note up with the same letter name... that is also another use of the word octave.  C-B would be one octave of the piano.  Then next C-B would be another.

This would be like saying...  This is the first mile, starting at 0 and going an inch over 5, 279' 11".      You could have a first mile, a second mile, etc.

So, octave can refer to an interval OR it can refer to a part of the keyboard -- the lowest octave, higest octave.



You can have unison notes on a piano.

It could be written in the score that way -- one note head with a stem up and a stem down, or the same note written on two different staves.  This is the more notated way.

Another way is all over music...

There are two types of intervals -- melodic and harmonic.

Harmonic intervals occur at the same time, note stacked on top of each other.  A harmonic unison would sound like one note on the piano.

Melodic intervals occur one after the other, like a melody.  So if you have a note repeated, you have a melodic unison between those two notes.



You put a lot of thinking into that original post.  Get a theory book and put that mental effort into that.

There are seven diatonic (notes in the scale) in one octave.   CBDEFGAB, for example.

There are 12 chromatic notes in one octave.  C C# D D# E F F# G G# A A# B


Hope that helps.

Favorite new teacher quote -- "You found the only possible wrong answer."

Offline xvimbi

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Re: Why are 7 individual notes called an "octave"?
Reply #13 on: June 11, 2005, 03:22:36 PM
I think your confusion is well-justified. I agree that the octave system doesn't really make sense. Well, it does, but in a different "sense".

As you said, the doubling of the frequency results in a note with the same name. However, they are obviously not the same. They appear in different spots on the keyboard and on the staff, and they are actually more correctly written as C1, C2, C3, etc. to indicate what frequency range they belong to. Yet, they do have the same names, and since there are eight entities involved (called scale degrees), we call that interval an "octave". I believe the confusion comes from the fact that the distance between identical notes is called "unison", which roughly means "one (and the same)". However the distance between these notes is really zero. To adjust for that, subtract one from each interval name to get the real distance. So, the trick is not to confuse "interval" with "distance" or "difference": Interval = Distance + 1. Or, distance = interval - 1.

Now to your pizza. The pizza analogy is getting close. However, the pizza should have only seven slices. The eigth slice would be identical (in name, but not in frequency) to the first. To illustrate this, one could use a helical pizza. Seven slices make a full turn with every eigth slice stacking perfectly on top of each other.

I'm hungry now ;)

Offline BuyBuy

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Re: Why are 7 individual notes called an "octave"?
Reply #14 on: June 11, 2005, 03:45:26 PM
On this subject, by the way, why was it ever decided that our system of scales should be divided in 7 notes? Why not 5, or 10 (some cultures actually use different scales, like pentatonic etc)? Why is it that most of our Western music is based on a 7 notes scale ?

I mean, I know that Pythagoras supposedly found out the intonation by fifths, eventually circling all twelve notes of our chromatic scale until it got back to the octave (or almost, because intonation by pure fifths is always gonna leave you with the famous Pythagorean comma...). So he got twelve tones from any note to its octave. So how was it decided that out of those twelve notes, only seven would make a proper scale? And it's been this way for a while (even in medieval times, when they used modes, their octave was already divided in 7 tones, so...). Anybody with historic knowledge?...

Offline Bob

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Re: Why are 7 individual notes called an "octave"?
Reply #15 on: June 11, 2005, 03:59:02 PM
I thought it was that the major scale had the strongest and simplest relationships, and that the Greeks had their modes.

From step 1, go up and down a fifth and you've got 4 and 5.

Add a third to those and you get 3, 6, and 7.

2 is a fifth above 5.

Yes, you could use the steps of the minor scale, but the major scale is a little simpler for ratios.  I think the minor scale is just a depressed version of the major scale really.
Favorite new teacher quote -- "You found the only possible wrong answer."

Offline tenn

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Re: Why are 7 individual notes called an "octave"?
Reply #16 on: June 11, 2005, 07:26:36 PM
If you travel around a clock from 12 back to 12 you will pass through 12 spaces. Substitute C for 12, C# for 1 and so on but imagine that when you get back to C it's the next one up. Now change your clock so it has 8 letters, C to C and you will pass through 8 gaps, an octave of gaps (intervals).

Think also about number systems.
Decimal has 9 positive numbers and zero(not a number)
When the units column fills up to 9 and you add 1 it spills over to the next column (octave if you like) and arrives back at 1.
The octal system is the same except it goes from 1 to 7 before spilling into the next column to give 10 ( 8 in decimal )

 

Offline jkristiand

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Re: Why are 7 individual notes called an "octave"?
Reply #17 on: June 11, 2005, 08:47:37 PM
I find this topic very interesting.
Intoresting: Your supposition about the 8th note in a scale being number 1 in the next is correct and thinking about it this way makes sense. I have myself wondered about the scientific reason for the 12 tone system, and tried to gather some information about it. I ended up reading a lot of pretty complicated stuff involving logarithms and so forth. However there a specific reasons why it
is the way it is, and its not a coinsidence.

Offline gorbee natcase

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Re: Why are 7 individual notes called an "octave"?
Reply #18 on: June 11, 2005, 10:31:05 PM
(INTORESTING) YOUR PIANO DOESN'T WORK
(\_/)
(O.o)
(> <)      What ever Bernhard said

Offline ranakor

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Re: Why are 7 individual notes called an "octave"?
Reply #19 on: June 12, 2005, 01:14:09 AM
i think all this talk can only confuse you more so let's be clear

the only thing that seems to confuse you is the unisson (or why beetween one note & another you count the 1st note as an interval) the reason is not a matter of logic but of semantics so a better analogy than the pizza would be our numeric system our system is a decimal system yet it only comprises numbers up to 9 that is because 0 is also a number & that 0 can be used as an analogy to the unisson the interval beetween C & the very same C at the same place on the keyboard is 0 (unisson) but the reason for it to be there is that you often need to name intervals beetween notes & in a melody you may find the same note next to itself... without the unisson you would have no way of naming that inteval but there do are 7 actual steps (C to D D to E etc etc) even thougth there are 8 distinct physical notes & thus the posibility for 8 distinct intervals

also if that may help resolve your confusion think of octavas sometime on sheet music you see a 8 over the staff to indicate you should play an octave highter but when it asks you to play 2 octaves highter it become a 15 (& not a 16) this is because you only add 7 possible intervals with each additionals octave since you already have the interval unission (from the 1st note to the 1st) you only add 7 more each additional octave

here is something that may clear things up :

notes interval        actual steps beetween notes

C C    unisson(1)        0
C D    second (2)        1
C E    third     (3)        2
C F    fourth   (4)        3
C G    fifth      (5)        4
C A    sixth     (6)        5
C B    seventh(7)        6
C C    eight     (8)        7

hence 8 actual notes for 7 physical steps beetween each physically DIFERENT note but 8 actual intervals (adding the one naming the musical interval beetween one note & itself)

next octave:

C D    ninth      (9)        8
etc etc ...
C C    2octaves (15)     14

so there is 8 intervals in an octave & 7 more for each additional octaves

hope this cleared some things up (or at least that it didn't get you confused even more hehe)

Offline jkristiand

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Re: Why are 7 individual notes called an "octave"?
Reply #20 on: June 12, 2005, 08:13:26 AM
Good explanation, a simple rule of thumb I use when figuring out intervals is always count the tonic as number 1. Then naturally the tonic an octave higher has number 8. And the one yet another octave higher number 15 :).

Offline timothy42b

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Re: Why are 7 individual notes called an "octave"?
Reply #21 on: June 15, 2005, 04:04:07 PM
To expand on Bernard's comment just a bit further.

C2 is not the same note as C3.  But they sound like the same note to most people.  I think the definition of an octave is something like "a consonance so perfect it sounds like the repetition of the same note."  So we call both notes C, and may not realize they are really not.  It is just a short hand way of not having 88 different names for the keys.

And why do they sound like the same note?

Ah, this is the good part.

No one knows.

Really. 
Tim

Offline claudio

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Re: Why are 7 individual notes called an "octave"?
Reply #22 on: June 17, 2005, 12:57:51 PM
this discussion reminds me of a little joke in my childhood. when you use your fingers
to count to ten (like: spreading fingers from 1, 2, 3, ... , 10 = 10 fingers) and then use mathematics when coming down you can create a paradox for children (like: right hand closing fingers: 10, 9, 8, 7, 6 + five open fingers of the left hand = 11 fingers)  :D

my reading of the octave phenomenon is actually a physical one; an octave is defined as an intervall of two tones whose frequency has the proportion 1:2.
in addition prime (1:1), quint (2:3) and octace-intervalls appear as perfect consonances as their unique frequency relationsships allow for a good perception of overtones.

in this sense, c2 is part of c1. if you count it as the beginning tone of a new octave or the last tone of the old octave is just a matter of definition.

hope this helps.

Offline timothy42b

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Re: Why are 7 individual notes called an "octave"?
Reply #23 on: June 18, 2005, 10:29:46 AM
my reading of the octave phenomenon is actually a physical one; an octave is defined as an intervall of two tones whose frequency has the proportion 1:2.
in addition prime (1:1), quint (2:3) and octace-intervalls appear as perfect consonances as their unique frequency relationsships allow for a good perception of overtones.


This is closer, but there are still problems with it.  The 3:2 (fifth) sounds consonant, but it doesn't sound like the same note.  There is something unique about how we perceive the octave, and nobody yet knows why.  Or if they do they haven't told me.

Also.

 Two pure sine waves, which have no overtones, still sound like octaves. 

Octaves on tuba, piano, and oboe sound like octaves, even though the overtone series will be considerably different for the different instruments. 

(The overtone series for tuba and oboe will be the same set of frequencies, because all "driven" instruments are forced to have overtones at integral multiples of the fundamental.  But the relative amplitudes will differ.  Piano is not a driven system;  it is struck and then vibrates at it's natural set of frequencies, which are not going to line up at integral multiples.  That is why it is necessary to stretch the tuning at the ends of the piano. 
Tim
 

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