Intervals ~ what's in a name ?

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ChrisMusicChrisMusic Frets: 1093
I thought it about time to check whether my understanding of the names of intervals is actually correct, or to put it right if I have it wrong.  So if any of you good folks on here with a bit more theoretical knowledge than me (and that's not difficult!), like @viz ; @missmisstreater @Lestratcaster @Clarky ; and others, could put me straight, I would be immensely grateful.

I would like to compile a list of all the acceptable names for each interval if possible, it's always nice to have a choice  ;)

So here goes, moving up by chromatic steps (frets/semitones) from the root

0 ~ root, tonic
1 ~ minor 2nd, flat 2nd
2 ~ major 2nd, 2nd
3 ~ minor 3rd
4 ~ major 3rd
5 ~ perfect 4th
6 ~ augmented 4th, flat 5th, diminished 5th
7 ~ perfect 5th
8 ~ minor 6th, flat 6th
9 ~ major 6th, 6th
10 ~ Dominant 7th
11 ~ Major 7th
12 ~ Octave of root, tonic (again)

How do the naming conventions apply beyond the octave ?
I know 2nd becomes 9th, 4th becomes 11th, and 6th becomes 13th, are they named the same for sharp and flat, and what about the even numbers, 10th, 12th 14th ?
Are there any conventions once you span more than 2 octaves ?

Thanks for your help  :)



I will start a second post to contain the corrected list of interval names (if appropriate) so that it is easy to find.  Hopefully that makes sense and won't be too confusing...   
:-B

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  • ChrisMusicChrisMusic Frets: 1093
    edited January 13
    Corrected list of interval names, so that it is easy to find.
    Sorry if it looks a bit more complicated with some other options added.
    Thanks for the help with this ~ see comments below for the source of the changes.

    0 ~ root, tonic, unison
    1 ~ minor 2nd, flat 2nd
    2 ~ major 2nd, 2nd,  8ve=9th
    3 ~ minor 3rd
         ~ also #2, Augmented 2nd, 8ve=#9
    4 ~ major 3rd
         ~ also diminished 4th
    5 ~ perfect 4th, 8ve=11th
    6 ~ augmented 4th, #4th, flat 5th, diminished 5th
         ~ also, tritone, devil's interval !!! & 8ve=#11
    7 ~ perfect 5th
    8 ~ minor 6th, flat 6th
         ~also #5th, augmented 5th
    9 ~ major 6th, 6th
         ~ also diminished 7th, 8ve=13th
    10 ~ Minor 7th, flat 7th
           ~ also augmented 6th
    11 ~ Major 7th
    12 ~ Octave of root, tonic (again), 8ve, perfect octave, diapason

    note: 8ve = octave

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  • There are no mistakes in there man!

    It might be worth remembering that the b3 is also a #2 (or #9 for all those 7#9 chords)

    Your b6 will also sometimes make more sense to be called a #5

    I wouldn't call a b7 a "dominant 7" though, it's the b7th or the minor 7th. Yes, it's in a dominant chord, but it's the 7th degree flattened - the 7th is a major 7th, and when you flatten a major interval, it becomes a minor interval.

    If you flatted a minor interval... it also becomes diminished. So that 6th is also a diminished 7th! (confusing right?)

    You're on the money with naming conventions beyond the octave.

    the 9th, 11th, and 13th are correct. You'll rarely see a 10th, and I don't think I've ever seen a 12th, or 14th.

    This convention comes from stacking intervals - 1 3 5 7 9 11 13 - when you put a note a 3rd higher on the 13, you're back at the 1.

    As a guide, you use 9, 11 and 13 when the 7th is present (Cmaj9 contains R 3 5 7 9), and 2 4 and 6 when it's not (C6 contains R 3 5 6)

    Make sense?
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  • As what was mentioned above, also for extended intervals I just add 7 to whatever it is beyond the octave. e.g 2nd + 7 is a 9, 4th + 7 is an 11th, etc.

    So in C major the 2nd is D so you add 7 to get 9 which is the same note.
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  • kinkin Frets: 503
    Thanks very much to both of you, very helpful !
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  • ChrisMusicChrisMusic Frets: 1093
    Thanks guys  :D 

    I'm glad I wasn't a million miles from convention
    (cripes Geeves, that's such an un rock and roll thing to think, let alone say!)

    I have no idea why I put the flat 7th down as dominant 7th, just the sort of common misunderstanding from picking it up as I went along I guess, and a primary reason for asking for clarification right now.  I may as well get it right from here on in.  Hopefully it is helpful to others on here too.

    Those alternative names are very helpful too (#9 etc).  I wondered about the diminished, i.e.  6th is also a diminished 7th, makes sense, so I must be getting somewhere with this.

    Cheers  :D 

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  • ChrisMusicChrisMusic Frets: 1093
    I guess #Major would be augmented then ?

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  • I guess #Major would be augmented then ?
    Yes it would be as you're raising (sharpening) and not lowering (flattening) the note.
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  • NeillNeill Frets: 239
    I understand why the perfect 4th is so named but why do we call the major 5th a "perfect" fifth and why is the note a semitone below always referred to as a flat or diminished fifth but never a minor fifth?
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  • Because you can't have a "major 5th" or "minor 5th" or any other change above the root note. Regardless of key it will always be constant.
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  • Phil_aka_PipPhil_aka_Pip Frets: 7121
    perfect interval = when the MD buys the drinks
    "Working" software has only unobserved bugs.
    Parroty Error: Pieces of Nine! Pieces of Nine!
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  • TheBigDipperTheBigDipper Frets: 633
    Neill said:
    I understand why the perfect 4th is so named but why do we call the major 5th a "perfect" fifth and why is the note a semitone below always referred to as a flat or diminished fifth but never a minor fifth?
    The fifth note in a major scale and a minor scale are the same.  For example, in A major, the fifth note is E natural. Same in A minor. Unlike the third - in the A major scale it's C#, in the A minor it's C natural. 

    I call the flattened 7th in a major key the "dominant 7th", BTW. For long and historical reasons...
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  • Phil_aka_PipPhil_aka_Pip Frets: 7121
    Perfect intervals are perfect because they retain their quality when inverted. Perf 4th -> perf 5th and vice versa. Whereas other intervals eg maj 3rd -> minor 6th. The numbers always add up to 9 :)
    "Working" software has only unobserved bugs.
    Parroty Error: Pieces of Nine! Pieces of Nine!
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  • CarpeDiemCarpeDiem Frets: 87
    Really helpful thread - thanks all.
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  • ClarkyClarky Frets: 2492
    couple of things..
    8 - can also be an augmented 5
    10 - is not a dominant 7 cos that is the name of a chord. This is a minor 7
    play every note as if it were your first
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  • ChrisMusicChrisMusic Frets: 1093
    Thanks for the extra input, much appreciated  :)

    I have put an amended list in the 2nd post now (hopefully easy to find for reference) and hopefully correct too !

    http://thefretboard.co.uk/discussion/comment/1755837/#Comment_1755837

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  • ChrisMusicChrisMusic Frets: 1093
    Diapason (for octave), now there's a word for you @Phil_aka_Pip   ;)

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  • ChrisMusicChrisMusic Frets: 1093
    Neill said:
    I understand why the perfect 4th is so named but why do we call the major 5th a "perfect" fifth and why is the note a semitone below always referred to as a flat or diminished fifth but never a minor fifth?
    Let me have a crack at explaining the Perfect 4th and perfect 5th thing...

    Take a trip back to school daze, and good old Pythagoras, and no nodding off at the back there !
    Yes that's the guy with the triangles and pyramids.

    He is credited with early work on musical scales, and the most fundamental part of that is the Diapason, or Octave.
    (although we are getting a bit ahead of ourselves there as an octave is by definition: the eighth note)

    OK then we'll call it an octave, as that is what we are all used to.


    The octave is basically a doubling (or halving) of the fundamental frequency.  So if we took for instance A 440Hz concert pitch, that is A from the 4th octave of (A4) vibrating 440 times per second then an octave above (doubled) will be 880 Hz (A5) and an octave below will be 220 Hz (A3).  Are you still with me so far ?
    (BTW ~ middle C is C4 for reference)

    The next most obvious harmonious frequency relation is the original root x1.5 (or 3/2), so multiply 440 Hz by 1.5 gives 660 Hz or E, which happens to be the fifth note of the diatonic scale, perfect !
    (which in the equal tempered scale (another story for another time) is adjusted to 659Hz)
    Alternatively you could look at it as the root plus a fifth.

    Now if you divide the root by 1.5 you get 293Hz which happens to be a D note, which although an octave below, also happens to be the fourth of A, perfect (yet again!).  Or multiply by 4/3 = 587Hz = D5.  Alternatively you could look at it as the root minus a fifth = a fourth an octave below.  I do hope that makes some sort of sense ?


    Another way to look at this, or an alternative perspective of the same thing if you like...

    If you take a fourth (which is 5 semitones above the root), and add a fifth (which is 7 semitones above the root); 5+7=12 which magically is the number of semitones in an octave.  So these frequency relations are fundamental to the way we hear and appreciate the harmonious nature of music.  Octave, fourth and fifth.  They also appear as pleasing harmonic overtones in vibrating strings, and columns of air in wind instruments.

    They are a more fundamental flavour to music than either major or minor, and are inextricably related.


    OK ~ you can wake up now  D 

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  • ChrisMusicChrisMusic Frets: 1093
    Or maybe more concisely from the Wikipedia page:

    The perfect fifth is more consonant, or stable, than any other interval except the unison and the octave. It occurs above the root of all major and minor chords (triads) and their extensions.

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  • Phil_aka_PipPhil_aka_Pip Frets: 7121
    Diapason (for octave), now there's a word for you @Phil_aka_Pip   ;)
    wow! I didn't think anyone else (other than smart-arse dictionary people) bothered with such words. yes, indeed "octave" only applies in the western diatonic system when you just happen to go up 8 note names before you halve the string length / double the fundamental frequency. So many people get hung up on the octave, I'd rather talk about diapasons before we get to dividing up the string length into other fractions ...

    About "So these frequency relations are fundamental to the way we hear and appreciate the harmonious nature of music.  Octave, fourth and fifth.  They also appear as pleasing harmonic overtones in vibrating strings, and columns of air in wind instruments." - they do, but equal temperament spoils them!
    "Working" software has only unobserved bugs.
    Parroty Error: Pieces of Nine! Pieces of Nine!
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  • HAL9000HAL9000 Frets: 3295
    I was told that a 9th contains the 7th as well as the 2nd, an 11th contains the 7th as well as the 4th, and a 13th contains the 7th as well as the 6th. Not sure if that's right but certainly something I've heard.
    It might look like I'm listening to you, but in my head I'm playing my guitar.
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  • LestratcasterLestratcaster Frets: 213
    edited January 8
    There wouldn't be enough fingers to play 2 of the same note (an octave apart) so there's no 2nd in a 9th chord, it'll also clash with the 3rd and the extension is normally fretted higher than the root and lower intervals (3rd, 5th and 7th).
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  • stratman3142stratman3142 Frets: 632
    There wouldn't be enough fingers to play 2 of the same note (an octave apart) so there's no 2nd in a 9th chord, it'll also clash with the 3rd and the extension is normally fretted higher than the root and lower intervals (3rd, 5th and 7th).
    Steely Dan often use the 2nd with the 3rd. The so called 'mu major' chord.

    It's not a competition
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  • There wouldn't be enough fingers to play 2 of the same note (an octave apart) so there's no 2nd in a 9th chord, it'll also clash with the 3rd and the extension is normally fretted higher than the root and lower intervals (3rd, 5th and 7th).
    Steely Dan often use the 2nd with the 3rd. The so called 'mu major' chord.

    With a 5th, 7th, and 9th as well?
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  • stratman3142stratman3142 Frets: 632
    There wouldn't be enough fingers to play 2 of the same note (an octave apart) so there's no 2nd in a 9th chord, it'll also clash with the 3rd and the extension is normally fretted higher than the root and lower intervals (3rd, 5th and 7th).
    Steely Dan often use the 2nd with the 3rd. The so called 'mu major' chord.

    With a 5th, 7th, and 9th as well?
    Sorry I may have misunderstood. I was just picking up on the point that the 2nd and 3rd don't necessarily clash.
    It's not a competition
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  • There wouldn't be enough fingers to play 2 of the same note (an octave apart) so there's no 2nd in a 9th chord, it'll also clash with the 3rd and the extension is normally fretted higher than the root and lower intervals (3rd, 5th and 7th).
    Steely Dan often use the 2nd with the 3rd. The so called 'mu major' chord.

    With a 5th, 7th, and 9th as well?
    Sorry I may have misunderstood. I was just picking up on the point that the 2nd and 3rd don't necessarily clash.
    Yeah well it depends on how you play it, sometimes when I play certain extended chords I omit the 5th to make room for another interval. I just didn't think you could fit all 6 intervals in one shape!
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  • ChrisMusicChrisMusic Frets: 1093
    edited January 8
    HAL9000 said:
    I was told that a 9th contains the 7th as well as the 2nd, an 11th contains the 7th as well as the 4th, and a 13th contains the 7th as well as the 6th. Not sure if that's right but certainly something I've heard.
    I started this thinking about melodic intervals for simplicity, just to clarify the terminology, but you are right, there is the whole other issue of harmonic intervals, and their rules too.  Luckily rules are made to be broken (if there was ever a justification for the phrase "truism" then that must be it).  Just play around with the voicings and inversions, there are some lovely sounds to be had on the guitar, and a lot of "interesting" ones too.  Then there is the whole issue of sequencing, melodic or harmonic, and emotional response (which is where the power of music lives IMO)...

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  • ChrisMusicChrisMusic Frets: 1093
    An interval is the distance (in scale steps) between two pitches. A harmonic interval occurs when two notes are played at the same time. Intervals can also be melodic, meaning that the two notes are played in sequence, one after the other.

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  • stratman3142stratman3142 Frets: 632
    edited January 8
    An interval is the distance (in scale steps) between two pitches. A harmonic interval occurs when two notes are played at the same time. Intervals can also be melodic, meaning that the two notes are played in sequence, one after the other.
    The topic of harmonic intervals and chords would be good topic as well, perhaps on another thread.
    Sorry to derail the thread but the 13th chord is one I'm never sure about. The formula would say you can include the 9 and 11 as well. I can buy the inclusion of the 9, but the inclusion of the 11th makes it a very different sounding chord to my ear. If I saw 13th in a chord chart I'd probably omit the 11 unless my ear told me differently.
    It's not a competition
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  • BradBrad Frets: 183
    edited January 9
    HAL9000 said:
    I was told that a 9th contains the 7th as well as the 2nd, an 11th contains the 7th as well as the 4th, and a 13th contains the 7th as well as the 6th. Not sure if that's right but certainly something I've heard.
    Not quite. For example a 2nd and a 9th are the same thing but it depends on the chord type that generally dictates whether you'd call it a 2nd or 9th. If the 3rd and 7th are included in the chord, then 9th 11th and 13th are used, rather than 2nd 4th and 6th. Although I have seen them used on occasion, e.g Cmaj7#11 or Cmaj7#4.

    So C9 doesn't have both a 2nd and 9th because they are the same thing. We say 9th because we are extending above a 7th. So C9 is C E G Bb and D (1 3 5 b7 9).

    From a theoretical perspective, 11th and 13th chords are built on this principle so C11 is C E G Bb D F (1 3 5 b7 9 11) and C13 is C E G Bb D F A (1 3 5 b7 9 11 13). But this doesn't work in practise as depending on the chord type there are clashes between certain notes and a 13th chord has 7 notes. Because of this we alter some notes or omit some altogether.

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  • ClarkyClarky Frets: 2492
    edited January 11
    Brad said:
    HAL9000 said:
    I was told that a 9th contains the 7th as well as the 2nd, an 11th contains the 7th as well as the 4th, and a 13th contains the 7th as well as the 6th. Not sure if that's right but certainly something I've heard.
    Not quite. For example a 2nd and a 9th are the same thing but it depends on the chord type that generally dictates whether you'd call it a 2nd or 9th. If the 3rd and 7th are included in the chord, then 9th 11th and 13th are used, rather than 2nd 4th and 6th. Although I have seen them used on occasion, e.g Cmaj7#11 or Cmaj7#4.

    So C9 doesn't have both a 2nd and 9th because they are the same thing. We say 9th because we are extending above a 7th. So C9 is C E G Bb and D (1 3 5 b7 9).

    From a theoretical perspective, 11th and 13th chords are built on this principle so C11 is C E G Bb D F (1 3 5 b7 9 11) and C13 is C E G Bb D F A (1 3 5 b7 9 11 13). But this doesn't work in practise as depending on the chord type there are clashes between certain notes and a 13th chord has 7 notes. Because of this we alter some notes or omit some altogether.

    another little angle on this [which is not related to modern music theory] is that the 2nd, 4th and 6th are [rather, were in classical music] more typically used for suspensions..
    so they'ed be a momentary dissonance that then moves  to a consonance..

    for example, the sus4 [Root, 2nd, 5th] would resolve to a triad [Root, 3rd, 5th]
    play every note as if it were your first
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