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Thread: By The Numbers

  1. #1
    The Amateur Mandolinist Mark Gunter's Avatar
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    Default By The Numbers

    Quoted from a response by David Brown in another thread:

    Roman numerals indicate chords in a particular key

    A ii chord (no need for the m, if it is major you use upper case II) is the chord built on the second scale degree of a major scale.

    Chords in a major scale:

    I, ii, iii, IV, V, vi, vii dim

    If you use full 4 note chords, it becomes

    Imaj7, ii7, iii7, IVmaj7, V7, vi7, vii half-dim

    Scale degrees are given in Arabic numerals:

    C D E F G A B = 1 2 3 4 5 6 7
    I always try to use the same "numbering scheme" that David mentions here. I know that some folk use IIm to represent ii, and that the Nashville Number System often uses Arabic numerals to represent chords rather than Roman Numerals, but when writing about music, the way that David mentioned above has always been my choice and it's what I learned.

    At any rate, I recently completed an introduction PDF on how numbers are used in music. I think it's a pretty thorough resource for newbies, but certainly not comprehensive. A lot of the music theory concepts had to be simplified, considering space and my own lack of knowledge.

    I'd appreciate it if some of you would read through it and give me suggestions or comments about how to improve it or clarify any of the concepts. I do realize that my writing can be a bit too dry. Click the black box to open it.

    Thanks in advance.

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    formerly Philphool Phil Goodson's Avatar
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    Default Re: By The Numbers

    Mark, I think you've presented the information very nicely. Undoubtedly, there might be some nitpicking (like whether enharmonic notes are the same note), but in practical western context, I like the way you said things.

    Those not well versed in music theory will need to read slowly and repeatedly to let things sink in, but that's just the way it is when you're trying to absorb so much information.

    I think: well done.
    Phil

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    Registered User Tom Wright's Avatar
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    Default Re: By The Numbers

    Wow, fine work and a lot of it! Can't see how to improve it.
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    Default Re: By The Numbers

    A Dominant 7th chord is formed by adding the flatted 7th note to the triad. In our G scale example, rather than adding an F# we would add an F note, which is the flatted 7th degree of the G scale. So a G7 contains the notes G, B, D and F. This chord has a bit more stable sound than the Major7 chord, and still has plenty of motion or pull to it. The G Major chord is the V chord in the key of C—it is the dominant chord of the key of C—the most stable chord other than C Major in the key of C. When playing in the key of C, it is common to encounter a G7 chord, especially as a passing chord to the IV or I chord. The flatted 7th (F note) is common to the key of C, in which G7 is the dominant V chord, while the note F# is not common to the key of C.
    I just skimmed it and it all looks good and clear. I do have a little bit of a problem with referring to a minor seventh as a flatted seventh. (I think it is just me, so I'm not really suggesting a change.) But I would describe a dominant 7th chord as a minor seventh on top of a major triad. To call it a flat seventh (again, to me) seems to imply an accidental, when there is no accidental in a V7 chord. Also, when you truly are lowering an interval (as you describe using the f instead of the f# you would find in the key of G) your are using a natural rather than a flat. I think that could be confusing to a beginner (why aren't you using a flat if you are flatting something?) and for that reason, I personally do not speak of flat intervals, but rather perfect, major, minor, diminished. (Well, I do sometimes say a flat fifth instead of diminished fifth - go figure.)

    Just my random thoughts as requested. Other than that, good job and, "go theory nerds."
    Bobby Bill

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    The Amateur Mandolinist Mark Gunter's Avatar
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    Default Re: By The Numbers

    Thanks for checking this, and for the comment, Phil. I caught some other imprecise stuff when proofreading before, and had to carefully re-word some stuff, but find it very difficult to keep from being imprecise, or to keep from over-simplifying. And the more precise I try to be, it seems the more difficult for a newbie to understand. It would have to be a pretty big book to cover things in depth, and even then I'd be hazy on some things that I myself have difficulty with, and definitely wouldn't satisfy everyone.

    My biggest concern is whether this can help folk with understanding some of the numbering concepts that get thrown around a lot, at least as an introduction.
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    The Amateur Mandolinist Mark Gunter's Avatar
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    Default Re: By The Numbers

    bobby bill, thanks for that. I can see your point, but it differs from the way I normally see it or teach it when I'm talking about building chords. I can see that you are right, though, to approach it from the musical interval angle.

    When showing people about chords, though, I talk about flatting any note by moving it a half step down, regardless of the note name. So if you form an A chord on mandolin, for example, all you have to know is where the third is. Flat that third (move your finger down a fret) and you have an A minor. This method of learning chords will work for any chord no matter where you move the fingering. Works for me anyway.
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    I may be old but I'm ugly billhay4's Avatar
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    Default Re: By The Numbers

    Good work, Mark.
    Bill
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    formerly Philphool Phil Goodson's Avatar
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    Default Re: By The Numbers

    It always seems that there are two chord building schools: 1)Those who modify the major chord in some way, and 2) those who stack intervals.
    Stacking intervals always seemed more confusing to me, probably because I never used "intervals" in my thinking from the beginning (long,long ago ).

    I guess fiddle players and music majors are more likely to think in intervals??
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    Registered User sblock's Avatar
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    Default Re: By The Numbers

    Quote Originally Posted by Mark Gunter View Post
    Quoted from a response by David Brown in another thread:



    I always try to use the same "numbering scheme" that David mentions here. I know that some folk use IIm to represent ii, and that the Nashville Number System often uses Arabic numerals to represent chords rather than Roman Numerals, but when writing about music, the way that David mentioned above has always been my choice and it's what I learned.

    At any rate, I recently completed an introduction PDF on how numbers are used in music. I think it's a pretty thorough resource for newbies, but certainly not comprehensive. A lot of the music theory concepts had to be simplified, considering space and my own lack of knowledge.

    I'd appreciate it if some of you would read through it and give me suggestions or comments about how to improve it or clarify any of the concepts. I do realize that my writing can be a bit too dry. Click the black box to open it.

    Thanks in advance.

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    Nice job, and I'm sure it was a lot of work to write out. So, congrats! Since you asked for suggestions, I will provide two of them

    I did notice that you present notes, such as A# and Bb (and also C#/Db, D#/Eb, F#/Gb), which are enharmonic, as "equivalent." In the 12-tone, equal-tempered scale, notes in these pairs will sound with the same frequency, so they often seem identical, but strictly speaking, the names that we use to call the enharmonic notes are still different, depending on the musical context. In the key of F (one flat), for example, we speak of having a Bb, but no one calls this note an A#. Similarly, the relative minor chord of E is a C#m, and no one calls this chord a Dbm. And, of course, the enharmonic note pairs don't even have the same frequency in other temperaments. At some point, you might want to point out to your readers this fact. Otherwise, sooner or later, they are going to get tripped up.

    I also noticed that you don't introduce the Circle of Fifths in your text. This element is so fundamental, and it goes along so very well with the content that you're already providing, that I wanted to encourage you to write a new section that includes this important topic. It works perfectly hand-in-hand with the Nashville Numbering system, and the most important chords in any tune (I, IV, V, ii) are found in close-by patterns. It also fits beautifully with the tuning of the mandolin in fifths, and further "explains" the recurrent patterns on the mandolin fretboard and all that.

    Anyway, I hope these two suggestions meet with your approval. You are doing a fine job.

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    The Amateur Mandolinist Mark Gunter's Avatar
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    Default Re: By The Numbers

    sblock, thanks for the comments. In writing about what we now call enharmonic equivalents (due to common ETT), I did say that when moving up from A one half-step toward B we arrive at A#, and when moving down one half step from B toward A we arrive at Bb. I do see your point, but I'm not certain whether I'll expand much more on that for this article. I tackle it again in the section where I invite the reader to write out two major scales (homework). For the serious student, it becomes apparent that the enharmonic equivalent note is determined by context.

    As for the Circle of Fifths, I published a COF primer in the Woodshed group last year, and a video to go along with it.

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    This type of critique you've given is very helpful; I'd appreciate the same on this COF primer as well. After reading comments and suggestions, I may do some editing on these articles.

    The COF video was pretty much off-the-cuff, and the video quality is not great, so I've thought about updating these materials eventually. For what it's worth, here is the video:



    Video direct link: https://www.youtube.com/watch?v=escuoOICSoY
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    The Amateur Mandolinist Mark Gunter's Avatar
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    Default Re: By The Numbers

    I just re-read my COF primer, and realized that I was even more sloppy when writing it, for instance:

    "F## is the same note as G."
    "I wrote out the scale for Cb, which contains 7 flats—I wouldn’t want to have more than that. This is the same notes of the B scale, since B is a half-step less than C, and so these scales overlap."

    I know this type of sloppiness will make somebody's head explode, and I apologize. What I mean is that the enharmonic equivalents are the same notes physically positioned on your instrument of choice, and not that they are the same, musically.
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    Default Re: By The Numbers

    In your description of the dominant (major/minor) seventh chord, you twice describe it as "stable". You say it is more stable than a M7 chord. That is just not so. The tritone in the dominant 7 chord makes it very UNstable, wanting to resolve to the tonic. You also call the V7 the next most stable to the tonic. Again, that is not the use of "stable" that most people in music theory use. The V7 is considered the LEAST stable chord.

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    The Amateur Mandolinist Mark Gunter's Avatar
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    Default Re: By The Numbers

    David, I didn't intend to call the V7 the most stable chord, but rather the V chord, which is probably not right either. The V is the dominant chord. I'll have to re-read what I wrote there. This is the type of problem that occurs when a non-expert like me gets in over his head a bit with terminology. Thanks for pointing out the problem.
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    Default Re: By The Numbers

    Very good job of presenting what can be difficult material in an easy to understand manner.

    Mark, I enjoyed reading it and I learned a lot from it. I'll give you an augmented 5 stars.
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    formerly Philphool Phil Goodson's Avatar
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    Default Re: By The Numbers

    Quote Originally Posted by Philphool View Post
    ..... Undoubtedly, there might be some nitpicking (like whether enharmonic notes are the same note), but in practical western context, I like the way you said things.....
    What did I tell you Mark?
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    formerly Philphool Phil Goodson's Avatar
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    Default Re: By The Numbers

    Quote Originally Posted by sblock View Post
    ....In the key of F (one flat), for example, we speak of having a Bb, but no one calls this note an A#. Similarly, the relative minor chord of E is a C#m, and no one calls this chord a Dbm.....
    While I totally agree with you about what's right and wrong, sblock, you obviously haven't been to some of the jams that I go to.....
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    Registered User Simon DS's Avatar
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    Default Re: By The Numbers

    Hi Marc, excellent job! It’s so good to see groups of people working together to help others. And the details, whatever, it gets people thinking, well done!

    Ideas, for example mention something and then build on it, ie ‘12 frets on the fretboard, 12 notes in the chromatic scale.’ And first thing mentioned in the sentence is the most important. And everything linked to the ears and the hands, there’s a list, but for me the interesting part would be the practical side. How about to maybe not talk about note names at all. Crazy idea, I know. But how about numbers for notes, intervals, chords and only use the one major scale, ‘the scale that shall not be named’, the one that begins at 4 string fret 0, or better, string3 fret5? AND it’s described as the feeling of where your hand is. No looking at the fretboard but at a computer graphic and sounds of the intervals to play? Then if necessary graphics/photos from the PLAYER’S perspective. Then scrap the circle of fifths, as it is a circle (pianist-thought) and design a fretboard of fifths, a MANDOLIN fretboard and use the FFcP system of spatial associations, chord tones movements (a bit like Tai Chi). And maybe use other media too, video, app exercises...
    And remember that not everyone will like this but we could try it. It could be interesting.
    One of the reasons I’m trying to think like this (and it’s not easy) is that apparently at the moment/last couple of years there’s a big jazz scene just blooming in London, lots of very different people and diverse ideas but all playing some amazing jazz. And they say that this is very unusual.
    So I’m trying to understand how they see the music. This could be really good for the mandolin. All we need is for Gibson to understand this, ha, ha.

  25. #18
    Registered User sblock's Avatar
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    Default Re: By The Numbers

    Quote Originally Posted by Philphool View Post
    While I totally agree with you about what's right and wrong, sblock, you obviously haven't been to some of the jams that I go to.....
    Yup, I hear ya! I've been to plenty of those jams.

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    Registered User sblock's Avatar
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    Default Re: By The Numbers

    Quote Originally Posted by Mark Gunter View Post
    sblock, thanks for the comments. In writing about what we now call enharmonic equivalents (due to common ETT), I did say that when moving up from A one half-step toward B we arrive at A#, and when moving down one half step from B toward A we arrive at Bb. I do see your point, but I'm not certain whether I'll expand much more on that for this article.
    ...
    I am not sure that I quite agree with this, at a least as phrased here. Whether one chooses to call a note A# or Bb does not depend on whether you happen to arrive at the note in question by coming up from below, or down from above, which is what you seem to be saying here. Or perhaps I misunderstand you?

    The note naming depends, for example, mainly on the choice of the home key, and sometimes the type of melodic line, or -- to pick another important example -- how the chord (in harmony) is being formed, and so on. This is why, in fact, you often see double flats (bb) indicated in a diminished chord or arpeggio: the scale note is already a flat, and you "diminish" it by flattening it still further, according to the usual rule for forming a diminished chord, resulting in a double flat. Does this really matter? No, not in most cases, if you ask me! But folks learning music should be prepared to see things like double sharps and flats on occasion, and be ready to understand why.

    That said, it is VERY HARD to state things simply for beginners, when the facts on the ground are rather more complicated! There are a number of different heuristic approaches one can take. One is to deliberately over-simplify from the start, in order to get the main points across, but suffer from a certain amount of incorrectness. Another is to state the simpler/broader case, but then take the time (perhaps in footnotes or digressions) explain why there are exceptions. Another is to teach everything more rigorously from the outset (but risk losing some folks, and/or taking longer to convey the information). In practice, ones sees every approach imaginable.

    Music theory is actually pretty hard material to grasp, even for some accomplished musicians. I think it requires a somewhat 'mathematical' mindset. And not everyone gets it at first. Or even ever. But I think it's a great idea to get everyone you know thinking about Nashville Numbering, which is a wonderful starting point for anyone who plays folk/bluegrass/oldtime/country/popular music. It's handy, portable, more intuitive, and in certain ways superior to our older/conventional system of staff notation.

    If Western music had evolved differently, and perhaps had came up with 12TET from earlier on, we might not be saddled with the silly systems of ABC or solfegio that we have, and instead be using a "portable" numbering system for all of music that was independent of the key. That would make transposition a snap. We would also have a less cumbersome notation system to go along with that, say, one that described musical intervals, and not the absolute notes. When you think about it, sharps and flats are silly things, forced upon us by the tyranny of our awkward staff notation, and not really necessary for 12TET music at all!

    P.S. The link you supplied to your COF article generates an "Error 404 - page not found" error on my computer. Perhaps the link is stale?
    Last edited by sblock; Apr-13-2018 at 4:46pm.

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    formerly Philphool Phil Goodson's Avatar
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    Default Re: By The Numbers

    I just have to say that I think that it's easy to be too dogmatic in the beginning and discourage folks who are just trying to figure out some basics and want to have fun.
    (That doesn't change the facts, and honest and complicated discussions with those students need to happen when they're ready.)
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    Default Re: By The Numbers

    As sblock says, it is difficult to simplify complex matters. I also was not entirely happy with the "Moving up it's a sharp;moving down it's a flat" but the complete explanation is both complicated and argued over. You could perhaps say in the text that this idea is a way to remember the function of the accidental---the sharp moves the note up, after all. But also say it is not a full explanation of why there would be an A# instead of a Bb,

    Since your subject is mainly the numbers, you have license to gloss over accidentals, I'd say.

    But on the question of harmonic notation, the #9 chord is a good example of why one might use the sharp over the flatted higher name. Because there is already a major 3rd in the chord, the minor third in the higher octave is conventionally given a different note name, the sharped 9th instead of a minor 10th. But if you're like me, you hear the 10th, not an augmented 9th.
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    Default Re: By The Numbers

    In the key of F we have a note between A and B. We call this a Bb so we don't have sharps and flats in the same key, it's just neater. Someone said you didn't go to the same jams as they did. A lot of old time and bluegrass musicians playing by ear know almost no theory, so they may not speak about the music the same as some of us but that don't mean they can't play.

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    Default Re: By The Numbers

    in the key of F the only flat is B flat, your argument is moot.

    In the key of F to conform to the 2212221 format we need a note 1 step above A, we already have an A in the scale. It would be hard to notate that sometimes you play A and sometimes play A#. It is simple to say play A and Bflat. Likewise in the key of G we need a note 1 step below G it would be difficult to say g flat sometimes, g all other times. however no issue to say F# always and G always
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    The Amateur Mandolinist Mark Gunter's Avatar
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    Default Re: By The Numbers

    Quote Originally Posted by sblock View Post
    I am not sure that I quite agree with this, at a least as phrased here. Whether one chooses to call a note A# or Bb does not depend on whether you happen to arrive at the note in question by coming up from below, or down from above, which is what you seem to be saying here. Or perhaps I misunderstand you?
    It's not my words that confuse you, but my intent, I believe, so you may be misunderstanding me. What I mean is that you misunderstand my intent, because I've worded it incorrectly. The way I have written this can cause confusion, and I can see that. The movement up or down that I am conveying has to do with what happens to the note you begin with, I'm conveying a downward movement of the starting note value - not the ascending or descending motion of playing a scale or melody.

    When you lower a B one half step toward A, you get Bb. When you raise A one half step toward B, you get A#. This is simple, and this is the idea I'm conveying. In a given musical context, any enharmonic equivalent is named according to whether the note name is derived by lowering or raising its position relative to the natural note from which its name is derived. We know it could be lowered or raised more than once from the natural note position, we can encounter double sharps or double flats, but the naming convention is based on the position of the natural note being moved up or down to account for the proper intervals in a specific musical context.

    The note naming depends, for example, mainly on the choice of the home key
    It must be understood that the "home key" has been derived a priori from the raising upward or lowering downward of certain notes to maintain the correct intervals of that key, unless the key is C major or one of its modes. It still holds true that note values have moved either upward for sharp notes or downward for flat notes.

    At any rate, I didn't intend to convey ascension/descension of scales, melodies, etc. but rather the raising or lowering of a note. I'll have to be more precise in that regard in the future. If you look at my invitation to do "homework" on page 8 you'll more readily understand what I'm getting at. In fact, that type of homework will do more for the reader's understanding than any words I can write about it. And in this, I practice what I preach. For years, whenever I found myself with idle time, I'd write out scales on scratch paper. Some folk do crossword puzzles, some doodle, I often am reading, but I write out musical scales. This is only the beginning of understanding sharping and flatting. Chord building moves you further along. Musical direction (moving a note up or down, south or north of the natural note from which its name derives) is important for knowing the difference between a minor interval, an augmented note, a diminished note, etc.
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  32. #25
    The Amateur Mandolinist Mark Gunter's Avatar
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    Apr 2014
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    Default Re: By The Numbers

    sblock, it seems that I capitalized "of" in the document name in that link I provided. Here it is corrected.


    http://www.markgunter.net/MMC/The_Ci...ths_Primer.pdf


    As I mentioned in an earlier post, I was even less precise with my language in that one. I can see that it really should be re-written, but I'd still welcome critique, comment, suggestions. You folk have already been very helpful on "By The Numbers", and I'll definitely be making a few changes to the text.
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