1. #1
    This method depends on knowing the fret-number / note-name for each fret on (either) E string. (i.e. Fret 8 is C. Fret 2 is F#, etc.

    By “cold”, I mean “seemingly instantly”. We know our names “cold”.

    Knowing (cold) that fret 8 is C on the E strings, how can I know-cold the note-name of fret 8 on strings A, D, G and B?


    We get our answer by adding or subtracting from 8 (in this C example). The sum is our fret-number/note on the E string. What we add or subtract depends on which string’s 8th fret we’re naming.

    The method depends on memorizing (well) the following.
    A) +5 or -7
    D) +10 or-2
    G) +3 or -9
    B) +7 or -5

    Let’s try it:
    A)
    8+5=13 -> 1**
    8-7=1
    Answer:F (E-string fret #1 is F)

    D)
    8+10=18 -> 6**8-2=6
    Answer:Bb (E-string fret #6 is Bb)

    G)
    8+3=118-9=-1 -> 11
    Answer:Eb (E-string fret #11 is Eb)

    B)
    8+7=15 -> 3**8-5=3
    Answer:G (E-string fret #3 is G)

    ** Guitarists need to routinely do “modulo 12” arithmetic. This is just clock arithmetic. So-called “Military time”. 15:00 is 3:00. 22:00 is 10:00.
    So fret 19 is 7. And fret 13 is 1.
    Negative modulo arithmetic gives answers like these: -2=10, -7=5, -3=9. Google it for more info.
    Last edited by GuitarStudent; 08-18-2019 at 09:42 AM.

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    The Jazz Guitar Chord Dictionary
     
  3. #2

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    I feel this is a strange way to learn notes on the fingerboard. Learn them by reading music and perseverance. It’s kinda hard, but not impossible, I get better by baby steps continually.

    And I really connect modulo 12 for music , with the music analysis that favors pitch class relationships over traditional harmony. I have recently read Straus’ Introduction to Post Tonal Theory, a textbook on the use of pitch class and modulo 12 techniques to study dissonant or difficult modern classical music.

    In that book, the clockface is always C = 0, C#=1, D=2, D#=3 etc. You learn to transpose with “ math”, invert, find common tones under transposition, find common tones under inversion, create arrays for twelve tone rows that dispenses transposed, inverted, retrogrades or inverted retrograde rows based on the original. Addition usually assumes transposition, so 8+7 assumes you start at G#/Ab and move up 7 semitones or a perfect 5th ( D#/Eb). Or in modulo 12, 8+7=15 and 15-12=3 and like above 3=D#.

    It is all about reducing real pitch to pitch class (0-11) and looking at relationships other than tonic/ dominant.

    I hate to confuse that system of analysis with a gtr fingerboard memory tool. Since there is a trend towards this approach for serious analysis I think I will defer to that system. Still your post is intriguing, I just already have a clear visual/tactile/sonic memory already in a place for gtr notes.

  4. #3
    Quote Originally Posted by cubistguitar View Post
    I feel this is a strange way to learn notes on the fingerboard. Learn them by reading music and perseverance. It’s kinda hard, but not impossible, I get better by baby steps continually.
    ......
    Still your post is intriguing, I just already have a clear visual/tactile/sonic memory already in a place for gtr notes.
    I am somewhat new to JazzGuitar.be. I don’t recall how I decided to post this silly method/discussion. I probably just wanted to share my “wow” about modulo. I love studying guitar “math”. Then I realized: This is dreadful. This post doesn’t belong on JazzGuitar.be! But I didn’t know how to delete it! So I instead tried to improve it (and lessen the embarrassment). The whole post isn’t important.

    For a long, long time, I’ve wanted to finally know “cold” the notes on frets 8-11 on the 4 inside strings. I still have a short delay in naming them. I have no delays on frets 0-5.

    Basically, this silly post was born out of my never-ending enthusiasm for guitar layout and for great fretboard knowledge.

    A mistake.
    Progress can be imperceptible. And I’m impatient to KNOW-COLD all 72 notes.

  5. #4

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    I think just sight read everything in 8th position for a bit. Stuff you could read fine in open.

    It’s a common problem. We call it ‘the dusty end’

    But then the notes in the low positions sound better and more in tune anyway. 3rd position is the best position for most stuff up to a Bb it turns out...

  6. #5
    I wanted to add one thing:
    I would think what excited me about the interval/fret-distance stuff is this:
    I also want to get faster at identifying the chord-tones in “grips”.

    In other words, I’d like to instantly know which string holds which tone. For example, there are (R,3rd,7th) grips with the root on 6 and the b7 on string 4. And the 3rd on string 3. I wanted to be able to more quickly chord-tone-analyze grips. That’s where my interest in this fret-distance stuff arose.

    Around the same time, I had been pulled to Shell Voicings. Finding the chord tones in a 6-tone open G chord was nuts. 3 Roots, 2 3rds. So I started playing tunes using only Shell voicings for a while. I played Body and Soul like this. I feel it was illuminating.

    I’d learned grips before I’d learned notes. I could grip a 6,4,3,2 m6 chord but I didn’t quickly know which chord tones were where. R on 6, 6th on 4, b3 on 4, 5th on 2. So finding fret-counting shortcuts to the chord tones attracted me. 9 frets to the 6th, 15 (3) frets to the b3, 19(7) frets to the
    5th.

    Then change this m6 chord to put the root on string 1 was also cool. The same analysis yields -5 frets (from the root on string 1) to the 5th onnstring 2, -9 frets to the b3 on string 2, -15(9) frets to the 6th on string 3. This employs “modulo” or clock arithmetic on negative amounts. -1 is 11, -8 is 4. -15 (or -3) is 9.

    Then I sa standard tuning from string 6 to 1 as 4th, b7, b3, 5th, octave. Somehow I imagined that could help me in Jazz guitar study.

    I guess I’m addicted to that sort of analysis. I’m like The Count on the Sesame Street kids TV program. The Count can’t stop counting. Me neither.

    Interesting instrument. I wonder if anybody has written about how Standard Tuning arose.
    Last edited by GuitarStudent; 08-26-2019 at 09:55 AM.

  7. #6

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    Quote Originally Posted by GuitarStudent View Post
    I wanted to add one thing:
    I would think what excited me about the interval/fret-distance stuff is this:
    I also want to get faster at identifying the chord-tones in “grips”.

    In other words, I’d like to instantly know which string holds which tone. For example, there are (R,3rd,7th) grips with the root on 6 and the b7 on string 4. And the 3rd on string 3. I wanted to be able to more quickly chord-tone-analyze grips. That’s where my interest in this fret-distance stuff arose.

    Around the same time, I had been pulled to Shell Voicings. Finding the chord tones in a 6-tone open G chord was nuts. 3 Roots, 2 3rds. So I started playing tunes using only Shell voicings for a while. I played Body and Soul like this. I feel it was illuminating.

    I’d learned grips before I’d learned notes. I could grip a 6,4,3,2 m6 chord but I didn’t quickly know which chord tones were where. R on 6, 6th on 4, b3 on 4, 5th on 2. So finding fret-counting shortcuts to the chord tones attracted me. 9 frets to the 6th, 15 (3) frets to the b3, 19(7) frets to the
    5th.

    Then change this m6 chord to put the root on string 1 was also cool. The same analysis yields -5 frets (from the root on string 1) to the 5th onnstring 2, -9 frets to the b3 on string 2, -15(9) frets to the 6th on string 3. This employs “modulo” or clock arithmetic on negative amounts. -1 is 11, -8 is 4. -15 (or -3) is 9.

    Then I sa standard tuning from string 6 to 1 as 4th, b7, b3, 5th, octave. Somehow I imagined that could help me in Jazz guitar study.

    I guess I’m addicted to that sort of analysis. I’m like The Count on the Sesame Street kids TV program. The Count can’t stop counting. Me neither.

    Interesting instrument. I wonder if anybody has written about how Standard Tuning arose.
    I think a grasp of the relationship between intervals and graphical shapes is pretty important.

    On the other hand, there are more shapes than you would think.

    And I don’t find that terribly helpful for learning note names.

    I can help on standard tuning. The guitar belongs to an extended family of instruments derived from the Spanish Vihuela, which includes things like the viol (aka the viola da gamba) as well as the guitar. Other instruments such as the theorbo, renaissance lute and all sorts of things have similar tunings which is to say 6+ frettable strings tuned mostly in fourths but with a major third located either between strings 2 and 3 or 3 and 4.

    (This is in contrast to the uniform fifths and fewer strings of the violin family that you also find in the mandolin, banjo and eventually the tenor guitar.)

    Anyway why not uniform fourths, which makes more sense? I think the answer lies in open position playing. Basically having the same note on two strings facilities use of open strings which was important I think for two reasons:

    1) string technology of the time meant it was more workable to add strings than frets. Less tension....

    2) equal (or even well) temperament wasn’t yet in use so some keys are much more common than others and modulations were very limited. Early strings have moveable frets allowing purer intonations of the time.

    3) the polyphonic style became prevalent at the end of the 16th century. It’s easier to play polyphonic music if you had access to more open strings. So the lute turned into a multi stringed monster tuned to an open Dm chord - that’s what Bach wrote for btw.

    Now of course, we don’t need to think about this so much as jazz players, but otoh we still need to play Freebird.

  8. #7

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    Also no one read notation on these instruments. Was all tab unless it was continuo from bass clef.... (Basically the 16th - 18th century version of chord symbols.)

    These were largely considered amateurs instruments.

    Less changes than you think. What chance do we have lol? 500 years, man!

    (I know what you are thinking- the double bass!

    4 strings in uniform fourths. Favourite pub quiz tie break is that it is a member of the viheula or viol family not the violin. This may in fact be not true, it’s a lot more complicated... some early basses had 3 strings tuned in 5ths which suggests the violin family but that sounds like a bastard to play. Early bass strings were things like the violone which was a contrabass viol with 6 strings iirc.

    So I reckon the modern double bass is the product of compromise.... and some double basses have a low 5th string as well, although a bass extension is more common for orchestral instruments.)

    Not sure what’s going on with the Brazilian 7 string with the bottom C. Drives I mad!

    Sorry you asked? :-) Anyway, Rob will be by in a second to fact check me as he plays all of these bloomin things.

  9. #8

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    The connection to set theory has already been made but it is a bit more extendable to music in styles other than modern concert music.

    What you describe is working with the full chromatic-literally the integer residues modulo 12.

    Consider systems with other cardinalities (sizes). For example, you can use the common pentatonic scale to describe scale degrees % 5. Now play thirds in this system: dyads of every other scale degree [0,2], [1,3], etc. What do you hear? A lot of perfect fourths despite playing “thirds” in this system. And an Impressionist cliche a la Debussy.

    You can use this with any scale of any size. Many of Messiaen’s planing chordal structures just involve moving a static chord voicing per scale degrees through one of his modes of limited transposition. Listen to a pianist like Craig Taborn and you’ll hear this from time to time.

    All this is to say... I’m not sure why you’d use this approach to learn notes on the guitar but it’s a great way to explore harmony and pan-scalar modality. Go explore the Dorian mode and riff on So What in these ways to generate voicings. Lots of power, lots of fun.


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