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Interval changes if you go to the same chord one octave higher
Old 17th February 2019
  #1
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Interval changes if you go to the same chord one octave higher

I am continually reading on music theory and I came across something that puzzled me.

Let's say you have two chords in your progression, C and F.

If you go to from C to F you are moving up 5 semitones. If you go from F back to the C below it, you are moving 5 semitones.

But if you go from F to a C chord and octave above, you are moving 7 semitones up.

So from F you could go to two C chords but the intervals are different.

Is there a name for this and is this significant in composing music?
Old 17th February 2019
  #2
That's why the flatted fifth -- six halftones up, six halftones down from the keynote of a given key -- is the most beautiful of intervals. Perfect symmetry!

With regard to the complementary relationship you ask about, I'm afraid I don't know the name of that fundamental aspect of organizing music as we do. But I'll bet someone has given it a name. I'm not at all sure knowing that name will make me a better musician, but now you got me curious, too.
Old 17th February 2019
  #3
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Quote:
Originally Posted by theblue1 View Post
That's why the flatted fifth -- six halftones up, six halftones down from the keynote of a given key -- is the most beautiful of intervals. Perfect symmetry!

With regard to the complementary relationship you ask about, I'm afraid I don't know the name of that fundamental aspect of organizing music as we do. But I'll bet someone has given it a name. I'm not at all sure knowing that name will make me a better musician, but now you got me curious, too.
I found the name in one book- apparently it is called “interval inversion”, but there was no explanation as to how this can be used.

I will research it further but basically my thinking is- you can take two chords, and by using them in different octaves, they become four, this way you can add more interest and movement with major scale palette without even looking outside the key. In a way, it opens up the major scale...
Old 18th February 2019
  #4
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The important word is "inversion." A C Major chord for example, without getting into all the silly spread-out possibilities, has three inversions; it can either be CEG, or EGC, or GCE.
Old 18th February 2019
  #5
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Quote:
Originally Posted by Brent Hahn View Post
The important word is "inversion." A C Major chord for example, without getting into all the silly spread-out possibilities, has three inversions; it can either be CEG, or EGC, or GCE.
No, this is not the same as chord inversions! It’s about movement and how major interval can become minor interval, and vice versa.
Old 18th February 2019
  #6
I don't understand your point.
The F isn't half way between the two C's. Therefore there is a bigger distance when going from F up to the higher C, than back down to C. It really has no effect on the sound, except the upper C chord sounds higher.
It sort of sounds like you are overthinking this.
The interval of an octave doesn't change the relationship of the notes. It's still CEG (in c major). F to C 3, or F to C4 doesn't change any notes either, it just makes the C sound higher register. The harmonic structure isn't changed and the ear hears it as na subtle difference only.
In terms of melody, C to F, or F to C can work in both minor and major keys. Minor and major are determined by the 3rd in the triad, E or Eb in the key of C. Therefore the F is irrelevant to major or minor intervals.
Old 18th February 2019
  #7
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Quote:
Originally Posted by chrisso View Post
I don't understand your point.
The F isn't half way between the two C's. Therefore there is a bigger distance when going from F up to the higher C, than back down to C. It really has no effect on the sound, except the upper C chord sounds higher.
It sort of sounds like you are overthinking this.
The interval of an octave doesn't change the relationship of the notes. It's still CEG (in c major). F to C 3, or F to C4 doesn't change any notes either, it just makes the C sound higher register. The harmonic structure isn't changed and the ear hears it as na subtle difference only.
In terms of melody, C to F, or F to C can work in both minor and major keys. Minor and major are determined by the 3rd in the triad, E or Eb in the key of C. Therefore the F is irrelevant to major or minor intervals.
Well, this is what I find interesting and apparently it does have an effect on sound so you can view the next octave as a new set of chords as the interval is different.

I found this and he seems to agree:

Old 18th February 2019
  #8
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Quote:
Originally Posted by dc_r View Post
Well, this is what I find interesting and apparently it does have an effect on sound so you can view the next octave as a new set of chords as the interval is different.

I found this and he seems to agree:

I haven't watched the vid yet, so forgive me if I'm missing what's being said in it, but it's not correct to say that there is a new set of chords in the next octave. However, you could think of it in terms of inversions (yes, I know you've already said you're talking about interval inversion, rather than inversions of chords, but bear with me) like this:

An F major chord, root position, is F A C - the interval between the F and the C is a fifth. Now change to second inversion, and it becomes C F A, and the interval between the C and F is a fourth. Yes, these two inversions will sound different, but they are still the same chord.

Nothing is going to change it to a minor, except flatting the A, no matter what octave any of the notes are in.

Last edited by littleeden; 18th February 2019 at 02:59 PM..
Old 18th February 2019
  #9
Quote:
Originally Posted by dc_r View Post
Well, this is what I find interesting and apparently it does have an effect on sound so you can view the next octave as a new set of chords as the interval is different.

I found this and he seems to agree:
No, the video just agrees with what I said.
The distance between low C and F is shorter than the distance from that F to the next C.
It doesn’t change the chord. It doesn’t turn anything major to minor, it just changes the inversion.
Effectively the chord and the harmony are unchanged, but different inversions have a slightly different sound.
Old 18th February 2019
  #10
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Quote:
Originally Posted by dc_r View Post
No, this is not the same as chord inversions! It’s about movement and how major interval can become minor interval, and vice versa.
I explained it in the clearest way I know how, and I don't have the patience to take it further.
Old 18th February 2019
  #11
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I think you are all missing the point here.

Try playing C3 - F3 - C3 notes.

Then try C3 - F3 - C4.

The last interval changes so you alter the sound a bit. Works with chords as well as single notes.

To me at least, this is an interesting realisation.
Old 18th February 2019
  #12
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Thank you for taking time to record the video. This is what I was saying and I was hoping someone could elaborate.

I think some people got confused with the word "inversion", as in changing order of notes in a chord.

What happens here is that root notes change their relationship when you go an octave higher- a major interval becomes a minor interval.

This is something I have been hearing in practice but now I also stumbled across it in theory. In practical terms- I can see why it would be very important to know chords all over the neck.
Old 18th February 2019
  #13
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I think you are confusing some terms here. Perhaps C and F were not the best example.

If you go from C to D, this interval is called "major second", id you go from D to C one octave higher, it is called "minor seventh".

This is what I found interesting and was hoping someone could tell me more about it. However, this seems to be a slightly more advanced topic so maybe someone classically trained could help...
Old 19th February 2019
  #14
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The answer is in the Major scale which is the KEY of reference.

The 3rd interval of a key is also a Minor type scale based on triads; a mode if it is now the tonic. It's second interval is up a semitone and is the 4th of the Key, a Major chord based on it's triads.

When you go up from the Key tonic, the next note is a Minor chord based on triads and if you now refer to that minor as a tonic the octave above has to follow it's new relationship with the new tonic, now called a Dorian mode and it is minor and the octave above down the whole step is referred to this mode.

The Key hasn't changed but the relationship of the intervals are now being referred to this mode to agree but it is still in the same key.

If you go from the Key's 4th to 5th, it is the dominant 5th degree based on triads and referenced to KEY.
Up an octave back down is technically called a minor interval or a flat 7 based on the second triad of the Dominant mode and it can become confusing. If it was called a whole step Major, you'd know it was the dominant. And Music over the ages has been made confusing on purpose.
It is what it is; referencing the key to go up and the mode to go down isn't always the case, depending what is agreed upon. Different Schools different rules.

If you played from any note as a Tonic up a 5th interval and up again another 5th interval it is called a 9th more often based on the agreed tonic as an extension of that mode and a modern iteration.
Old 19th February 2019
  #15
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Quote:
Originally Posted by dc_r View Post
[IMG]If you go from C to D, this interval is called "major second", id you go from D to C one octave higher, it is called "minor seventh".
No offense but um...duh.

Let's draw a circle on the floor that will take 12 steps to walk around, and then name each step after a note in the chromatic scale. So if we start at C, and take two steps, we are still 10 steps away from getting back to C if we continue forward, but only 2 steps from C if we turn back around. Only the tritone is equidistant to the octave above and below.

In the sense of the physics here, each interval is represented by a ratio. An octave is double the frequency of the octave below. If we go up a fifth the relationship is 3/2. So if the root note was 100hz (to make easy math), the octave above that is 200hz, and the fifth above 100hz is 150hz- 100*(3/2).

Frequency is a logarithmic scale so the 'distance' of 50hz here does not represent the midway point between 100 and 200. So the 4th above 150hz is not a ratio of 3/2 again (obviously that would be 150*1.5=225hz, which is a whole step above the higher octave). Instead the nominal ratio of a 4th is 4/3 (1.3333). (4/3)*150 is 200.

I say nominal ratios because everything but octaves are squished just slightly out of perfect ratios (called just temperament) a little bit to accommodate the even tempered scale (aka the 12 tone scale).
Old 19th February 2019
  #16
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Quote:
Originally Posted by dc_r View Post


I think you are confusing some terms here. Perhaps C and F were not the best example.

If you go from C to D, this interval is called "major second", id you go from D to C one octave higher, it is called "minor seventh".

This is what I found interesting and was hoping someone could tell me more about it. However, this seems to be a slightly more advanced topic so maybe someone classically trained could help...
I think a study of modes might be of use for you. Obviously, it is not possible, in an ascending melody, to go from D to C without going into the next octave up. You can go from C to D in the same octave, but that is not the same thing. If you play the same notes as occur in the key of C, but take the D as the tonal centre of the melody - as could be the case in your example above - you would be playing in D dorian, which is a minor mode. This is down to the way the intervals in a major scale are laid out (tone-tone-semitone-tone-tone-tone-semitone).

Remember also, if you add the note C to a D major triad, the result is a D7 (or dominant) chord - note, not a minor chord, even though the interval between the 3rd of the D major triad (F#) and the 5th (A) is a minor third, as is the interval between the 5th and the minor 7th (C).

The nomenclature used for major/minor can seem a little confusing - you can play a minor melody using only notes from a major scale, and major chords contain at least one minor interval. In short, it depends where you start, and which direction you're heading.
Old 19th February 2019
  #17
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The F chord is the 4th chord of the C major scale. It stands to reason that there will be a larger number of semitones to reach the unity (tonic) C note of the next octave as the F chord is based upon the 4th of the major scale. If it was the fifth, or G chord, then the number of semitones would be less to reach the unity (tonic) octave note of the next highest C.

The higher voicing of a C chord in combination with a lower C chord in any progression that is in the "key of C" is a unity tonic, or doubling of the frequency, but in perfect consonance with the other C chord (as long as the inversion is identical). It is a form of harmony in it's most simple manner. Try playing C triads with identical inversions in 3 octaves, as it is possible on the guitar. The "octave above", or "octave below" unity harmony can be a delicious texture to make use of when it fits the music. Sometimes changing the inversion from a "C-E-G" to a "E-G-C", or a "G-C-E" voicing can be the most desirable for whatever emotion, mood, or feeling that you wish to impart upon the composition.
Old 28th February 2019
  #18
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I don't even know why I'm in this forum... but I do know the answer... if I'm not misunderstanding the question as I've done before...

Fourths and Fifths and Octaves are special intervals. They are Perfect. There is no major fourth or fifth or octave and no minor fourth or fifth or octave. All other intervals, 2nds, 3rds, 6ths, and 7ths have major and minor forms.

When you invert a major interval, you get a minor interval.

When you invert a perfect interval, you get another perfect interval.

So, a major 2nd becomes a minor 7th and a minor 2nd becomes a major 7th. A major 3rd becomes a minor 6th and a minor third becomes a major 6th, etc.

A perfect fourth gets you a perfect fifth and vice versa. An octave gets you... an octave. This is why these intervals get the designation "perfect" rather than "major" or "minor."
Old 1st March 2019
  #19
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Quote:
Originally Posted by Poopypants View Post
I don't even know why I'm in this forum... but I do know the answer... if I'm not misunderstanding the question as I've done before...

Fourths and Fifths and Octaves are special intervals. They are Perfect. There is no major fourth or fifth or octave and no minor fourth or fifth or octave. All other intervals, 2nds, 3rds, 6ths, and 7ths have major and minor forms.

When you invert a major interval, you get a minor interval.

When you invert a perfect interval, you get another perfect interval.

So, a major 2nd becomes a minor 7th and a minor 2nd becomes a major 7th. A major 3rd becomes a minor 6th and a minor third becomes a major 6th, etc.

A perfect fourth gets you a perfect fifth and vice versa. An octave gets you... an octave. This is why these intervals get the designation "perfect" rather than "major" or "minor."
You understand the question! Are there any commonly used ways to use this for any sort of effect in music composition?
Old 1st March 2019
  #20
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I think you might be expecting to learn some secret, but I don't believe there is one. C and E in the key of C will function the same way, no matter which note is on top. The difference is the voicing, and you can do fun things with chord voicings, but you can't change the nature or function of a chord by changing it's inversion or voicing. You can still create variations in the sound. Hard to describe, but practice some chord inversions in the context of a song and see what sounds different. Play something with closed voicings and then try it again with open voicings.
Old 4th March 2019
  #21
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It's not that placing things in different octaves makes zero difference, of course, but there's a reason that people will say, when talking about chords/harmonic material that "Down a fourth is 'the same' as up a fifth," "Down a third is 'the same' as up a sixth" etc.

It makes a bigger difference when you're talking about a melody.

With chords, especially with traditional orchestration or arranging, where we're writing for string sections, horn sections, etc. the exact octave where we'll place different pitches in a chord will have a lot to do with the range of the instruments in question, and the way that timbre changes in different parts of those ranges.
Old 13th March 2019
  #22
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Somewhat crazy thread.

Up is different than down, O.K.?

And G7 still resolves to C, no matter what octave the respective chords lie in. One may say its just lousy voice leading to jump to different octaves between chords, but, then again, it may be useful as an effect.



Best,

audioforce
Old 9th April 2019
  #23
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The major scale has that weirdness of a sense of two tonics (take the key of C) the interval of C to F as fourth is an inverted 5th F to C.

So that for example in C - diatonic notes resolve to the tonic - play C to D and then D wants to return to C.
But play C to F and it sounds like it's resolved upwards to the F and doesn't want to return to the C as the other diatonic notes do as the ear is also hearing F to C (V-I)

it's a funky thing really and makes the major scale very restless - something we can exploit when we compose.

See George Russell Lydian Theory.

Lydian doesn't have this issue as C to F# is the same interval distance as F# to C.

I always love the progression for example.

A - G - D

Which feels like you could be in A majoy/mixolydian) or D major because of the weirdness of the 4th being an inverted 5th.

It drove me a bit crazy as a young composer until I got a handle on it and worked out what was going on with the 4th acting as an inverted 5th and therefore giving a major scale two potential key centres.

Isn't music fun :-)
Old 9th April 2019
  #24
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Quote:
Originally Posted by thehightenor View Post
...Isn't music fun :-)
Yes, it is - emphatically! Well said.
Old 9th April 2019
  #25
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Quote:
Originally Posted by dc_r View Post


I think you are confusing some terms here. Perhaps C and F were not the best example.

If you go from C to D, this interval is called "major second", id you go from D to C one octave higher, it is called "minor seventh".

This is what I found interesting and was hoping someone could tell me more about it. However, this seems to be a slightly more advanced topic so maybe someone classically trained could help...
No, WITHIN THE SCALE OF C MAJOR, if you go from C to ANY D, it is still a major second interval; same goes for D to C.(all relative to tonic C)

D to the C above is a minor seventh interval IN THE SCALE OF D MAJOR if we're talking in the context of scales!
Absolutely speaking it would be correct, but then you should leave scales, tonic, etc., out of the equation, since those are RELATIVE expressions.


It's about the position that the notes have on the particular scale, always starting from the tonic at the 1 position and all other notes of the scale in relation to the tonic, IN WHATEVER OCTAVE.
You always count up from the tonic BELOW the other notes of the scale.
A0, a' or a", though in different octaves, are all major sixt in the C major scale.

You're probably confused by the fact that one can tell a musician to play a certain interval, in reference to a particular note, like play the second major above F; then the musician is supposed to play G.
However when playing in the key of C major, telling the musician just to play the second major, he'll play D (because that's it's position on the C major scale).

So, there is a difference in what is understood with:
- an interval RELATIVE to the tonic (scale) and
- an interval in reference to any particular note (which is an ABSOLUTE interval).


I hope this helps clarify it for you.

Regards.
Old 9th April 2019
  #26
Seems to me the problem is that there are multiple, conflicting 'standards' and 'definitions' that music pedagogues have allowed (and sometimes encouraged) to flourish -- and the consequence of that is confusion and -- quite often the sort of he-said/he-said conflicts we see over and over again in discussions of 'music theory' and associated terminologies.

If music pedagogues cannot even agree on what 'Middle C' is -- how can we not expect musicians to be confused and use conflicting terminologies?

(I have literally had an academically trained musician insist to me that C5 on their instrument ['middle C' to their way of thinking because it's in the middle of their range] was the same note as C4 on a piano. This individual insisted that that was how he'd been taught and that settled it. But, of course, they are different pitches. One is an octave above the other. But you couldn't tell this guy that. It's that kind of nonsense that has fostered a push among some contemporary music pedagogues to insist on universal terms and definitions -- that is, that 'Middle C' should be C4 [261.6 Hz] -- but at this time, there is no one 'official' definition of Middle C. If ya can believe that.)


FWIW, with regard to intervals and scales, what I mostly seem to see is people talking about absolute intervals on the one hand -- simple difference between two notes, independent of context -- and scale degrees on the other.

And that comports with the common definition of a musical interval:
Quote:
In music theory, an interval is the difference in pitch between two sounds. An interval may be described as horizontal, linear, or melodic if it refers to successively sounding tones, such as two adjacent pitches in a melody, and vertical or harmonic if it pertains to simultaneously sounding tones, such as in a chord.
Interval (music - Wikipedia)

Quote:
Interval - The distance between two pitches. The term ‘harmonic interval’ (as opposed to ‘melodic interval’) indicates that they are thought of as being heard simultaneously. Intervals are traditionally labelled according to the number of steps they embrace in a diatonic scale, counted inclusively: thus from C up to D or down to B is a 2nd, another step up to E or down to A makes a 3rd, etc. These names are applied in non-diatonic contexts so that an interval embracing five degrees of a pentatonic scale is still called an octave (from Lat. octavus : ‘eighth’)
Search Results | Oxford Music


Scale Degrees
Quote:
In music theory, scale degree refers to the position of a particular note on a scale relative to the tonic, the first and main note of the scale from which each octave is assumed to begin. Degrees are useful for indicating the size of intervals and chords, and whether they are major or minor.
Degree (music - Wikipedia)
Old 10th April 2019
  #27
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Quote:
Originally Posted by theblue1 View Post
[...] If music pedagogues cannot even agree on what 'Middle C' is -- how can we not expect musicians to be confused and use conflicting terminologies?

(I have literally had an academically trained musician insist to me that C5 on their instrument ['middle C' to their way of thinking because it's in the middle of their range] was the same note as C4 on a piano. This individual insisted that that was how he'd been taught and that settled it. But, of course, they are different pitches. One is an octave above the other. But you couldn't tell this guy that. It's that kind of nonsense that has fostered a push among some contemporary music pedagogues to insist on universal terms and definitions -- that is, that 'Middle C' should be C4 [261.6 Hz] -- but at this time, there is no one 'official' definition of Middle C. If ya can believe that.) [...]
Perhaps this may help you.

Guitar Theory Resources Where Is Middle C
Old 10th April 2019
  #28
Quote:
Originally Posted by Herr Weiss View Post
Good thing he had pictures.

And don't even start me on how there are different High C's for different types of singers...
Old 10th April 2019
  #29
Before the Internet took off and filled in, the often bizarre conflicts (and sometimes nasty arguments) regarding music terminology and some aspects of theory drove me just about nuts. Because I thought it was me who just couldn't wrap my head around this stuff.

But once I was able to 'lay it all out' and see stuff side-by-side, I realized that music pedagogy is just one big klusterfudge of confusion, differently defined terms, and often pointed conflicts between parties who are absolutely sure they are right, not the other guy.
Old 17th April 2019
  #30
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C to F ascending is a Perfect Fourth. 5 semitones
C to F descending is a Perfect Fifth. 7 semitones
Perfect Intervals, when inverted, as Octave, 4th and 5th change naming to Unison, 5th and 4th respectively.

Interval Inversions always sum 9. Perfect 4th + Perfect 5th = 9

Augmented turns to Diminished when inverted. Augmented 4th (F to B) + Diminished 5th (B to F) both ascending = 9
Consonances as 3rds and 6ths change from Mayor to Minor and viceversa when inverted. Mayor 3rd ( C to E) + Minor 6th (E to C) both ascending = 9

When you go C to F is an ascending 4th and F to C descending is still a 4th. 5 semitones.
If you F to C you are ascending a perfect 5th and C to F descending is also a Perfect Fifth. 7 semitones.
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