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Thread: Guni's Intervals (the Key to HU)

  1. #1
    Afro-Cuban Grunge-Pop Bongo Boy's Avatar
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    Guni's Intervals (the Key to HU)

    Can't thank Guni enough for taking the time to do this document. It's a wonderful thing to make sense of something that really doesn't seem to be explained in a lot of places. Had a few questions tho.

    1. I understand the rules you've outlined for determining the note name for the 4th interval, and understand how to apply the rules. But re: the "2 note names must occur between the root and P4 note" restriction, why is this restriction needed?

    To ask it another way, if A# and Bb are equivalent (I'm assuming these are truly two names for EXACTLY the same thing), then why was the 'grammatical' distinction ever made? Are there circumstances where the distinction is important and therefore the convention for interval naming was adopted?

    2. If the 4th and 5th intervals are perfect and perfect ONLY, then why would anyone ever make reference to a "P5" or a "P4"? I see why the need to discuss 'perfect intervals' as a topic unto itself, and as a family or class of intervals. But why ever refer specifically to the "perfect 4th" or the "perfect 5th"? Is that not redundant? I mean, there are no other kind of 4th or 5th intervals, right?. Is this common practice in everyday verbal dialog?

    Thanks again for such a great resource.

  2. #2
    Afro-Cuban Grunge-Pop Bongo Boy's Avatar
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    ...and I also wanted to verify:

    1) The rules for naming intervals apply for absolutely ANY root interval chosen?

    2) A diminished major is always a minor, and an augmented minor is always a major?

    3) If the answers in 2) above are 'yes', is this a case where, while it may be true, it's also a fact of utterly no practical value or meaning?

    I know these are really dumb-*** questions, but I just want to nail the lid down on this wacky bizniss.

  3. #3
    Ibreathe Music Advisor EricV's Avatar
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    Re: Guni's Intervals (the Key to HU)

    Originally posted by Bongo Boy

    To ask it another way, if A# and Bb are equivalent (I'm assuming these are truly two names for EXACTLY the same thing), then why was the 'grammatical' distinction ever made? Are there circumstances where the distinction is important and therefore the convention for interval naming was adopted?
    Hi Bongo Boy...

    I´ll leave most of those answers to Guni, since he wrote the article you´re referring to, and I liked the way he explained all the stuff there.
    But about the question you asked ( the one I quoted above )... that used to confused me too, until someone taught me that system...
    Well, one rule when naming intervals and i.e. listing the notes in a given key, there are two rules that are the cause for things like the distinction between A# and Bb...
    1. Do not mix up #´s and b´s. If you look at the circle of fourths / circle of fifths, you´ll see that each key has either b´s or #´s ( flats or sharps ), despite the key of C Major, which has none.

    And since you shouldn´t mix up #s and bs, the Bb is named Bb in the key of F ( as an example ), while in the key of B, it is A#... on the fretboard, it is the same note, but regarding to the key you´re in, it is named differently, which is an organisational thing.

    The second rule would be: Each note should appear only once.

    That means, you shouldn´t write down the Fmajor scale ( example ) like this:
    F-G-A-A#-C-D-E-F
    Instead, name every note only once, and to do so, you´ll need to use a b instead. So this is how it looks the right way:
    F-G-A-Bb-C-D-E-F

    Of course there are exceptions to that rule, and in some rare cases, you´ll even see double accidentals ( i.e. Gbb or A## )...
    I hope this makes sense, and I hope I didn´t confuse you even more.

    Warm regards
    Eric

    NP: Planet X- Live From Oz

  4. #4
    Ibreathe Music Advisor EricV's Avatar
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    Another addition

    Before I forget about it... I wanted to add something for all of you, since Guni just published that article about intervals.

    Here is a helpful tool called the "chord clock".
    What you do is: Print out those two graphics, cut them out and connect them. Do so by putting a hole through the middle of both circles, put the small one on top of the big one and put in something like those small clamps that are sometimes used to close envelopes... the purpose is to connect those two circles so you can still turn the small one.

    Once you´re done, you can use it as some kind of a flash card to learn about intervals... If you turn the clock i.e. to the note C, you can immediately see the interval between the C and all the other notes...

    Hope this helps
    Eric




  5. #5
    Afro-Cuban Grunge-Pop Bongo Boy's Avatar
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    Thumbs up

    ...we owe so much to those who have gone before us

  6. #6
    i Breathe ... Admin Guni's Avatar
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    First a note about the interval article. My idea is that we all see it as an 'in progress' paper and not as an article 'written in stone'. So, as you bring in more input the article will grow.

    Eric, you did a wonderful job in ansering Bongo's questions and I am thinking of adding these 2 rules. Well, I had them in there but somehow it didn't reallty fit as the article doesn't really cover the construction of scales (maybe it should with the c major example)..... I'll have another thought about this ........

    Hey Bongo, I think these are great questions and actually show that you understand the topic:

    Originally posted by Bongo Boy
    ...and I also wanted to verify:

    1) The rules for naming intervals apply for absolutely ANY root interval chosen?

    2) A diminished major is always a minor, and an augmented minor is always a major?

    3) If the answers in 2) above are 'yes', is this a case where, while it may be true, it's also a fact of utterly no practical value or meaning?

    I know these are really dumb-*** questions, but I just want to nail the lid down on this wacky bizniss.
    1) yep

    2) well, yeah you could see it in this way ...

    3) your observation are 100% correct but are of no real practical value (except that you have a clear understanding of how this stuff works.)

    Guni

  7. #7
    Resident Curmudgeon szulc's Avatar
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    my $.50 worth

    I felt the need to chime in on this..
    Following are some excerpts from my book "Escape From The Cage{d}", which may be helpful in your understanding of music theory.

    CHROMATIC SCALE
    The chromatic scale is an even (actually logarithmic) distribution of twelve unique tones throughout the octave.
    An octave is the unit given to a doubling of frequency, since notes which are multiples of two times the frequency sound similar.
    The distance between two adjacent tones in the chromatic scale is called a Half Step (H), and the distance of two Half Steps is called a Whole step (W).
    To our ears, two notes which are separated by exactly one or more octaves have the same note value. We therefore give them the same note name ie. C.
    Now since the chromatic scale is composed of twelve tones, we must have twelve note names.
    The names chosen for these notes are A, (A sharp, B flat), B, C, (C sharp, D flat), D, (D sharp, E flat), E, F, (F sharp, G flat), G, (G sharp, A flat).
    Notice that the notes in parenthesis are enharmonic, (different names for the same tone) in other words, A sharp and B flat sound the same.
    The chromatic scale sounds the same no matter where you start to play it, because all of the tones are equally spaced. The chromatic scale is therefore atonal (having no tonal center, or tonal magnetism, some would call this pan-tonal since it has all possible western music tones)

    MAJOR SCALE FUNDAMENTALS
    If you are familiar with a piano keyboard, you will notice the keys which are white have unaltered letter names (A, B, C, D, E, F, G), and the black keys are the sharps or the flats.
    The white keys on the piano form the C major scale (starting on C [C, D, E, F, G, A, B]), the arrangement of half steps is 2, 2, 1, 2, 2, 2, 1 or W, W, H, W, W, W, H.
    It is this arrangement that gives the major scale its sound (tonality), and tonal magnetism (tendency for a particular note to follow another ie. the root following the seventh. This really has to with the concept of tension and resolution. Within a major scale, the seventh tone has tension which is best resolved by following it with the root, thus tonal magnetism.).

    KEY CENTER / KEY SIGNATURE
    Now since the chromatic scale has twelve unique tones, and each one can be the starting note of a major scale, we must have twelve unique major scales.
    Looking at the interval spacing, 2, 2, 1, 2, 2, 2, 1, we can make it 2, 2, 2, 1, 2, 2, 1 by raising (sharping) the fourth degree (fourth scale tone) a half step, now the fifth degree becomes the new root (note from which the new major scale takes its name and begins on).

    By a similar, but inverse, process we can make the interval spacing 2, 2, 1, 2, 2, 1, 2 by lowering (flatting) the seventh degree a half step, the new root becomes the fourth degree.

    Notice in the first example we sharped the fourth degree and started on the fifth degree, and in the second we flatted the seventh and started on the fourth.
    This produced two new major scales which each differ from the first by one altered (sharped or flatted) tone.
    These two processes can easily be shown to be inverses of one another by observation of the intervals (sharping the fourth tone F in C major we get G major, by flatting the seventh tone F# in G major we get C major).
    By continuing each of these processes seven times starting with C major, we can build a structure called the circle of fifths which contains all seven sharp scales, all seven flat scales and C major. Notice that this adds up to fifteen and we know there should be twelve, this is due to enharmonic spelling of three of the scales (C flat=B, G flat=F sharp, D flat=C sharp).
    When building the scales it is important to remember the guidelines ; each letter name must be used exactly once ; only one type of accidental (sharps or flats) allowed per scale ; no note can have more than one accidental.

    INTERVALS
    We call the distance between two notes an interval. Intervals are named for the distances which occur in the major scale from the root to any scale tone. All the intervals from the root in the major scale except the unison, octave, fifth, and fourth are called major intervals (2nd, 3rd, 6th, 7th), these exceptions are called perfect.
    Perfect intervals are so called because any perfect interval which is inverted (bottom note is now on top and vise versa) remains perfect (perfect fifths become perfect fourths and vice versa, octaves remain octaves, unisons remain unisons).
    Guni I know this is not in agreement with your explanation here, but this is how I learned it.

    Minor intervals are flatted versions of major intervals, diminished intervals are flatted perfect intervals, augmented are sharped perfect intervals.
    Non-perfect intervals change their prefix (major or minor) when inverted (minor sixths become major thirds, major sixths become minor thirds, minor seconds become major sevenths, major seconds become minor sevenths and of course vise versa).

    I hope this gives a concise explanation of the circle of fifths and scale degree naming conventions.

    James

  8. #8
    i Breathe ... Admin Guni's Avatar
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    Re: my $.50 worth

    [QUOTE]Originally posted by szulc
    Guni I know this is not in agreement with your explanation here, but this is how I learned it.
    [QUOTE]

    Hi szulc,

    Thanks for this lengthy reply. This might be really helpful to some of us. I think that it is good to see things from as many different point of views as possible, as there are no real standard ways of learning these things.

    Thanks

    Guni

  9. #9
    just some dude nateman's Avatar
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    howdy, folks! i'm a new fella here, but i ran across this old thread while browsing, and i wanted to add a few comments and see what the big brains think. some of the points i'd like to make may well have been brought up in other places, but what's redundancy without a little repetition! Bongo Boy has probably already figured this stuff out based on his more recent posts, but i wanted to add a little more commentary for other new folks who might read this.

    here goes nuttin'...

    1. I understand the rules you've outlined for determining the note name for the 4th interval, and understand how to apply the rules. But re: the "2 note names must occur between the root and P4 note" restriction, why is this restriction needed?

    To ask it another way, if A# and Bb are equivalent (I'm assuming these are truly two names for EXACTLY the same thing), then why was the 'grammatical' distinction ever made? Are there circumstances where the distinction is important and therefore the convention for interval naming was adopted?
    to some degree, it is a matter of historical precedence. at one time, musical instruments were not well-tempered beasts, and A# and Bb were not necessarily the same thing. furthermore, on fretless stringed instruments, you can play A# and Bb and not be playing the same exact pitch.

    on a well-tempered instrument like the guitar, one reason to maintain the distinction is so that you talk the same language as the crazies out there playing other instruments. another reason that has struck me and made me work to maintain these dinstinctions is that it can help you remember scales and intervals if you know your key signatures; your musical alphabet forwards, backwards, and around both ends; your musical alphabet math; and the patterns of sharps of flats that get added as you walk through the keys.

    say you know that the key of D major has two sharps and you know that the first two sharps that get added are F# and C#. then these interval naming conventions help in a couple of ways...

    example 1a: calculating intervals. what's the sixth of D major? it will take you five tonal steps to get there from D going up, or two tonal steps going down. so first, walk up five letters from D (EFGAB) or down two letters from D (CB), and this puts you at B. since that's not C or F, either of which would need to be sharped, you've already got your answer: B is the major sixth of D.

    example 1b: calculating intervals. what's the third of D major? up two letters from D (EF) or down five letters from D (CBAGF) gets you to F. you know it has to be sharped based on the key signature, so the major third of D is F#.

    if you get to a point where you can quickly do that kind of letter math (like "D + 5 = B"), which is sort of like imagining the C-major scale as numbers, and you can remember the key signatures, you can quickly figure out intervals. if you didn't maintain the one-interval-per-letter rule, it would take more memorization to come up with those because you'd have special cases to consider.

    example 2: scales. using D major again, you can relatively easily blurt out the scale forwards or backwards by walking from D to D through the letters (DEFGABCD, DCBAGFED), remembering that C# and F# are the oddballs. up: D-E-F#-G-A-B-C#-D. down: D-C#-B-A-G-F#-E-D.

    don't know if this will help anyone, but it has been useful to me. someone once stated to me the two basic rules that Eric and James outlined, and that's when some of this stuff started to click a lot better for me.


    2. If the 4th and 5th intervals are perfect and perfect ONLY, then why would anyone ever make reference to a "P5" or a "P4"? I see why the need to discuss 'perfect intervals' as a topic unto itself, and as a family or class of intervals. But why ever refer specifically to the "perfect 4th" or the "perfect 5th"? Is that not redundant? I mean, there are no other kind of 4th or 5th intervals, right?. Is this common practice in everyday verbal dialog?
    perfect fourth and perfect fifth intervals are used in the major scale and the minor scales and lots of other places, but there are times when they are modified. this is usually (in my experience) in triad/chord construction or modes. in those cases, there may be references to augmented fourths/fifths or diminished fourths/fifths. therefore, it is possible that just saying "fourth" or "fifth" may be ambiguous in some cases.

    you are definitely correct, however, that it can be redundant as well. for example, saying "F is the perfect fourth of C major" could be seen as over-emphasizing the point. if it's well established that you are talking about the key or scale of C major, it is not strictly necessary to use the word "perfect" to describe the fourth or fifth intervals unless you really want to drive the point home or you are referring to it after having referred to an augmented or diminished fourth for some reason.

    in fact, once you establish the scale you are talking about, you can even be a little more lax with words like "major" and "minor"...but not too lax. if you start getting vague about stuff and junk, people won't know what you mean about the things and the other things!


    2) A diminished major is always a minor, and an augmented minor is always a major?

    3) If the answers in 2) above are 'yes', is this a case where, while it may be true, it's also a fact of utterly no practical value or meaning?
    Guni's response was "yeah you could see it in this way," and i think it's worth elaborating on that. i don't know if Bongo Boy meant to ask it the way he did, but i haven't seen any examples i can think of where people referred to an augmented minor or a diminished major. typically, the interval itself is referred to as being augmented (a half-step above the major or perfect interval) or diminished (a half-step below the minor or perfect interval).

    so, a diminished major sixth would technically be a minor sixth and would probably always be referred to as a minor sixth, and therefore the term "diminished major sixth" would not be of practical value. but a diminished sixth is another animal that might be of practical value...just not to me.

    this actually leads into another area where the interval naming rules come into play. if, for whatever reaon, you wanted to distinguish between a perfect fifth and a diminished sixth, you could do it by the name. for example, G would be the perfect fifth of C, and Abb would be the diminished sixth of C. they are the same pitch on the guitar, but the different names denote that they are derived from different intervals.

    hopefully i didn't misstate anything and provided some tangible value to at least one poor soul out there.

    cheers,
    nathan

    NP: Inspiral Carpets / Life

  10. #10
    Afro-Cuban Grunge-Pop Bongo Boy's Avatar
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    I think it's great you brought this one back to life. Aleternate or simply re-worded explanations are, for me, one of the best ways to get to understand something.

    Many times I've thought I understood something quite completely--come to find out I understand a particular explanation quite completely, but not the whole topic, really. It's good to know, for example, that two names are equivalent from a strict definition point of view, but not used interchangeably because of convention or even common slang. This is just an example.

    What's unfortunate, in a way, is that I already care less about the topic than I did when I posted it because I think I understand it. Of course that's not true, and it highlights the challenge of retaining a beginner's mind! Your thoughts help me do that.
    Pulsing the System with Confirmed Nonsense.

  11. #11
    Resident Curmudgeon szulc's Avatar
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    2) A diminished major is always a minor, and an augmented minor is always a major?
    Technically this is not a true statement for the following reason:

    The term diminished is used only in conjunction with PERFECT intervals and the term augmented is used only in conjunction with PERFECT intervals.
    Minor intervals are flatted versions of major intervals, diminished intervals are flatted perfect intervals, augmented are sharped perfect intervals.

    Any non-perfect interval that is lowered is called flatted and any non-perfect interval which is raised is called sharped. Major and Minor are equivalent to these terms but not Diminished and Augmented, which are reserved for Perfect intervals.
    "Listen to the Spaces Between the sounds."
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  12. #12
    Afro-Cuban Grunge-Pop Bongo Boy's Avatar
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    Originally posted by szulc
    The term diminished is used only in conjunction with PERFECT intervals and the term augmented is used only in conjunction with PERFECT intervals.
    Maybe it's fair to say this is true in the case of common usage and in any practical applications--but in books, at least, I see augmented used to qualify both perfects and majors, and diminished with both perfects and minors.

    I'm not sure any of this matters too much, though, since I think the underlying idea that's being communicated is the raising or lowering of an interval by a semi-tone, and everyone would understand one another using either terminology (given they'd seen the terms used in any of the ways we've just talked about).
    Pulsing the System with Confirmed Nonsense.

  13. #13
    Resident Curmudgeon szulc's Avatar
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    You do not refer to Minor 4th, Minor 5th, Minor Unison or Minor octave. ( Or for that matter Major 4th, 5th, unison or octave)

    Only 2nds, 3rds, 6ths, and 7ths are prefixed with major or minor.
    Major being the case for the interval taken from the Major scale from the root, minor being the major scale interval flatted 1/2 step.

    Minor interval become major intervals when inverted. M3 inverted = m6

    Perfect intervals are Perfect interval when inverted. P4 inverted = P5.

    Raised Major intervals are named by the next higher interval. raised M3 = P4 or raised M2 = m3 or raised M6 = b7 or raised M7 = Octave.

    Lowered Minor intervals are named by the next lower note.

    Perfect intervals have no Major or minor quality.
    Lowered Perfect intervals are called Diminished.
    Raised Perfect intervals are called Augmented.

    Lowered 5th = Augmented 4th
    Lowered 4th = M3 (Called Major 3rd, not minor or diminished 4th)
    The one exception to this is raised 5th which is commoly called minor 6th. This could also be called Augmented 5th, but other than in altered chords it rarely is.
    "Listen to the Spaces Between the sounds."
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    Registered User jesus's Avatar
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    Hi folks,

    Maybe it's a matter of language but in spanish you can speak about a diminished second for instance.
    In my opinion the rules are as follows:

    - For perfect intervals:

    diminished --> perfect --> augmented

    That is, a perfect interval flatted a half step is a diminished interval, and raised it gives you an augmented interval. Example: Gb is a diminished fifth of C, G is a perfect fifth of C and G# is an augmented fifth of C.

    - For non perfect intervals:

    diminished --> Minor --> Mayor --> augmented

    So Bbb is a diminished seventh for C (think of chord Cdim7), Bb is a minor seventh of C, B is
    a mayor seventh of C, and B# is an augmented seventh for C.

    I think, that we must take care with the enharmony, which applies exclusively to the sound,
    but harmonically the function of the notes could be different. Thus, despite Bbb is enharmonically the same as A, its harmonic function is different,
    that's the reason of Bbb is a diminished seventh for C and A is a mayor sixth, but the sound is the same. Tecnically speaking, A does not belong to a
    Cdim7 chord, since it has no sixth degree, but the same sound or pitch (named as Bbb) does belong it, since Bbb is the seventh degree (is B note).

    See you. Jesus

  15. #15
    just some dude nateman's Avatar
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    it may be a matter of technicalities vs. practicalities.

    like Bongo Boy, much of my learning has come from reading books and asking questions...and many of the people i ask have also learned in non-traditional ways.

    many books and a lot of the on-line lessons out there definitely talk about being able to augment or diminish any interval, as Jesus showed. as for how often one does that, that's usually not discussed in the beginner material.

    James is probably correct that such things are rarely done in the real world (i certainly never do it), but i think it's fair to say that it's still technically possible to make those alterations and distinctions.

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