Remembering The Notes Of On A Fretboard Using Math

If you're quick at basic mental math and you're a beginning guitarist, this lesson might be for you. This may sound pretty nerdy, but I've told other people about it and they some of them quickly learned the notes in the second half of the fretboard (the 12th fret and beyond).

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In math, there is something call congruence modulo n. Congruence is used for sets of numbers that are in some way, related to each other. For example, a clock is the best example of congruence: A familiar use of modular arithmetic is in the 12-hour clock, in which the day is divided into two 12 hour periods. If the time is 7:00 now, then 8 hours later it will be 3:00. Usual addition would suggest that the later time should be 7 + 8 = 15, but this is not the answer because clock time "wraps around" every 12 hours; there is no "15 o'clock". Likewise, if the clock starts at 12:00 (noon) and 21 hours elapse, then the time will be 9:00 the next day, rather than 33:00. Since the hour number starts over after it reaches 12, this is arithmetic modulo 12. 12 is congruent not only to 12 itself, but also to 0, so the time called "12:00" could also be called "0:00", since 12 0 mod 12. In 24 hour time, one uses 0:00 for midnight. 24-hour time uses arithmetic modulo 24. Hope, that didn't bore you too much but it's for a reason. Now, like a clock, the "notes" on the fretboard repeat after 12 notes. That is the first fret of the 6th string is F so, if you were to go up 12 frets, you'd be at the 13th fret and at F again but an octave higher. So, when reading tabs, this might be helpful.(Since there are 12 "notes" in the chromatic scale.)
|---------------|
|---------------|
|---15----------|
|------14-12----|
|-12------------|
|---------------|
Say you wanted to find out what these notes were but you really don't know the fretboard well. Since 12 0 mod 12, that means that 12 is simply the name of the note that is played open on that string,(e.g. 12 on the a string is A, 13 on the a string is A#/Bb, 14 on the a string is B, 15 on the a string is C, etc.) So our first note played in this lick is A. The next note is 15 on the g string. This means that 15 mod 12 = 3 thus, 15 is A#/Bb since this is just three frets higher than the open G, just an octave higher. This may explain it better:
0  1  2  3  4  5  6  7  8  9  10 11 (First octave)
12 13 14 15 16 17 18 19 20 21 21 22 (Second octave)
The number underneath would be the note equivalent, just an octave higher. For example, the E string.
0  1  2  3  4  5  6  7  8  9  10 11 (First octave)
E  F  F# G  G# A  A# B  C  C# D  D# (Chromatic scale)
12 13 14 15 16 17 18 19 20 21 21 22 (Second octave)
so the notes of the riff would be:
|---------------|
|---------------|
|---15----------|
|------14-12----|                
|-12------------|
|---------------|
 
|---------------|
|---------------|
|---A#----------|
|------E-D------|
|-A-------------|
|---------------|

9 comments sorted by best / new / date

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    slowlybilly
    HA...this lesson is a waste of your time...there are only 12 notes that you can hit...they go in order from A to G, with the non-naturals in between...It's really easy...the rest you should be able to figure out on your own in like five minutes, and familiarity will simply come with time...use your cycle of fourths.
    MahiMike
    A bit confusing but I see where you're going. I like starting at 12 from each string and adding up, like the G string + 3 half steps. I also use math to try to find same note on next string (-7) or down 2, over 2.
    krypticguitar87
    FuruiShin wrote: Yeah true 'lol' of the day here- never tried to explain it to myself like that... and it works perfectly. If know the sounds on E strings you will be eventually able to know what sounds are in other places o.O. Gr8 thing to know :]! About this 'problem' geez... are you really like elementary school kid? You should be able to realize that's just a mistake . Why people always try to find bad sides of lessons leaving the good ones outside of their minds...
    it's not really trying to find the 'bad side', its more of corr3ecting the mistakes. right now these mistakes may not effect you, however someone brand new to guitar may see a mistakeand think that it's true, and that can be the difference between them being a decent guitarist and a great guitarist because there foundation is incorrect. if your foundation is not made correctly, then the house will never stand properly.
    krypticguitar87
    small problem here... you have 21 as the octave of bothe the 9th and 10th fret, meaning that it is both C# and D.... the octave of 10 is 22 and the octave off 11 is 23. other than that it makes sense and I'm sure it should help someone.
    FuruiShin
    Yeah true 'lol' of the day here- never tried to explain it to myself like that... and it works perfectly. If know the sounds on E strings you will be eventually able to know what sounds are in other places o.O. Gr8 thing to know :]! About this 'problem' geez... are you really like elementary school kid? You should be able to realize that's just a mistake . Why people always try to find bad sides of lessons leaving the good ones outside of their minds...
    FreekBos
    He, interesting... This really lights up the math behind the fredboard. I'm a math kinda guy so this could help me experiment more with my solo's using math. Thanks a lot. The clock comparison was my 'wow' of the week.