I wonder why they called notes by names like A..G. Wouldn't it be better to give them numbers? Could this be troublesome or better?

E.g., I have numbered notes on my guitar neck in standard tuning as below, with 0 being the very lowest note (6th string open) and up from that. E.g., open 5th string gets number 5, same as the note on the 6th string, 5th fret.

     5| 6| 7| 8| 9|10|...  
     0| 1| 2| 3| 4| 5|...  

Now a chord is a set of numbers and by subtracting them I can immediately see note intervals in terms of half-steps, because a difference of 1 equates to 1 half-step. E.g., the C-major chord would be [8,12,15,20,24]. Between the lowest C (8) and following E (12) there are 12-8=4 semitones, that is 2 tones.

Moreover I can easily found barre positions for open chords, because it is just a matter of finding out the same chord numbers. E.g., I immediately see C-major can be also played by fully barring fret 5 with a capo and playing note 8 on the 6th string, note 12 on the 5th and note 32 on the 1st string (this is a C with a G-shape). So [3,7,27] is G and by adding 5 to each number of this vector we get [8,12,32] which is a high-pitched C. Indeed C and G are 5 frets apart, because 3+5=8.

Inversions of triads are also easy to work out. Eg in [8,12,15] (C-E-G) I do not play the 8, add 12 to it and stick the result to the end. I get [12,15,20], which is E-G-C.

If for convenience we do not want to represent each note as a frequency number and work only with a finite number of frequencies in a geometric progression (with the common ration being the 12th square root of 2), it makes sense to me to locate each progression element with its sequence number, which is a natural number.

Maybe I am not the first to have thought of an integer notation for music. If this is so, why didn't it take?

  • Comments are not for extended discussion; this conversation has been moved to chat. – Matthew Read Feb 18 '16 at 3:26
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    typically not numbers because octaves repeat! =) You are right though, the numbers help clarify a lot of what's going on, especially with something with a visible frequency-of-oscillation like a guitar. Here is a cool question... why not split the octave into more than 12 slices? Fretless everything -> get wavy – sova Feb 18 '16 at 7:25
  • I would like to share this resource about alternative ways to represent music, including numbers and number sequences, which is very related my question: learningideas.me.uk/musictheory – Antonio Bonifati 'Farmboy' Mar 5 '16 at 15:52
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    Wouldn't it be better to give them numbers? Would you feel more comfortable having a number instead of a name? See @MattPutnam 's answer. – Stinkfoot Mar 16 '18 at 17:33
  • @sova - There are musical systems that divide the octave into more than 12 notes. Indian classical music divides it into 22 notes. However, the chromatic octave is based in physics: The circle of 5ths/overtone series. Every violinist and good lead guitarist "gets wavy" - but music which is nothing but 'wavy' will become likely become boring, if not incoherent, quite quickly: Different instruments have different roles - some, such as the bass cannot/should not be 'wavy' - just the opposite. – Stinkfoot Mar 16 '18 at 19:31

I would like to construct and algebric theory of Western music.

It's been done.

Up until now I have seen no problem in my notation, I would be happy if some expert could find some.

For purely theoretical work, it's fine, but it suffers immensely when it comes to actually playing music. Which is what the vast majority of musicians do. I object greatly to your assertion that a set of numbers is clearly identifiable as a chord. And we lose all sense of the diatonic scale, and all of the symmetry of the octave.

I can immediately see note intervals in terms of half-steps

But this is not how most people think of intervals. For Western music it's much more common to think of steps of the scale. We don't think of a minor 7th as 10 half steps, we think of it as the seventh scale degree of a minor scale (perhaps more accurately, it's the major seventh, flattened).

Between the lowest C (8) and following E (12) there are 12-8=4 semitones, that is 2 tones.

Nobody should have a problem recognizing that C to E is a major third.

isn't a note just a dominant frequency in the spectrum after all?

How is this useful?

  • For Western music it's much more common to think of steps of the scale... - but maybe part of the OP's purpose is that he wants a way to get away from that? One of the drawbacks of the 7 note / 7 letter system is that it implies a diatonic way of thinking that for some music may not be helpful. Losing all sense of the diatonic scale might be a good thing, sometimes! – topo morto Feb 17 '16 at 18:09
  • Nobody should have a problem recognizing that C to E is a major third. - " OK, so B to D must be a major third too, 'cos that's also two letters' difference. Oh wait, it isn't? Whaaaaaa...?" – topo morto Feb 17 '16 at 18:16
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    @topomorto Most people go their entire careers without ever encountering non-diatonic music. And yes, you're very cute with your B-D example. I repeat myself, nobody should have a problem recognizing that B-D is a minor third. It's just basic musical literacy. – MattPutnam Feb 17 '16 at 18:33
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    @topo morto: yep, I invent tunes in my mind and can hum an whistle them. If I measure note frequencies, they do not form a scale as in Western music, so it's non-diatonic music, yet they are pleasant. I can't compose on a musical instrument, I find it difficult and limitating. – Antonio Bonifati 'Farmboy' Feb 17 '16 at 22:19
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    If you want to come up with a new system that serves some non-Western system of music, then go for it. But the tone of this question is "wouldn't it be better to replace all of standard notation with this number thing?", and the answer to that is unequivocally "no". – MattPutnam Feb 17 '16 at 22:38

There is nothing wrong with your idea from a mathematical point of view. However from a practical musicians point of view it would be very confusing and cumbersome and less informative.

You see with only seven letters to deal with in a given diatonic piece (may be altered by sharps or flats) it's easy for me to get my head around how any given note relates to the overall scale of the key I am playing in. For example I know that a note that translates to C4 and a note that translates to C6 both belong in the key of C. I immediately know where to find those notes on the piano keyboard and I can immediately (without a calculator) see that they are the same note - two octaves apart.

If those two notes are represented by numbers - say 8 and 32, I can't tell what key 8 and 32 are in (you may argue it's unimportant - but it is important to a musician), and I have to get out my calculator or worse - do math in my brain, to see that they are exactly two octaves apart (math is not my strong suit).

If I learned to play an instrument simply by knowing what number key or what number string/fret to play, then I would lose any sense of tonality and how each note relates to the key or mode I am playing in. I would simply be robotically finding numbers and pressing them. And while I could replicate a song in that manner, I would lose understanding of how those notes relate to the key and not learn any useful information that might help me compose my own music.

To me, trying to see the relationship between two numbers between 1 and 88 (or 0 and 87) for piano would require more brain power than if I only have to deal with 7 letters (plus sharps/flats) which repeat at each higher octave.

Where your system is most useful is when a computer will be able to instantly do the math and see the relation. That's why it's very useful for MIDI applications which involve computer processing of the information. But for musicians, a number based system is far too cumbersome and less informative for understanding a notes relation to the key and impractical because if I have to use a calculator to play my instrument .... well it's just not going to work.

And for composing, it's easier to only have to think about the 7 letters in the diatonic scale as my pitch class set from which I will build my melody and harmony. I can move those seven notes up and down the keyboard (or fretboard) to choose notes from the scale in various octaves, because to move up or down an octave only requires me to shift position on my instrument. Using numbers that are the sum of a particular note plus 12 or 24 or 36 (ie 3 vs 15 vs 27) do not immediately stand out as the same note shifted up the keyboard.

Again, a system that assigns a number to each note would be very useful for telling a computer how to play a particular musical composition, but not so useful for composing a piece of music.

  • There is nothing wrong with your idea from a mathematical point of view. However from a practical musicians point of view... - We get many questions along these lines - all of them are covered by this well stated objection: Math != Music . – Stinkfoot Mar 18 '18 at 14:37

Pitch-class sets are perhaps the most common integer notation you'll come across in a 'theory' setting. The usage of sets isn't restricted to pitches either, but can also be used to indicate points in time.

As Andy points out, MIDI note numbers are another integer representation (which is quite similar to the system you outline for guitar) that is commonly used - and don't ignore guitar tablature, which represents the fret to be played on each string as a number.

So you can see that to some extent, number systems have 'taken'. However, people who are very familiar with standard note names and notation may not feel the need for them, as they will be comfortable enough with converting the note and chord names to intervals in their head, and sometimes seem to quite enjoy the mental exercise - although as people tend to divide the scale into octaves, and there are only 12 notes in an octave, it's not that hard!

As an aside, you may also be interested in the Nashville Number System - a way of using numbers to notate a chord progression in a way that is independent of key.


Letter names do indicate the (almost) identity of octave transpositions. Numbers require a different modulo operation depending on how many notes one has to the octave. Of course, octave transposition may not be important in all styles or applications.

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    @AntonioBonifati some people might point out that there's nothing stopping you from using the chromatic scale and still calling the notes A, B, C... and using flats/sharps where necessary. Personally I agree with you and I find that system messy and inconvenient. but it's clear that others don't have a problem with it and that's great for them. Ultimately a big part of being creative is to have the confidence to find what works for you and go with it. One thing I would say is that using the chromatic scale 'freely' could be considered to be something that is enabled by equal temperament, – topo morto Feb 18 '16 at 1:39
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    but equal temperament has its own compromises. So although abandoning the diatonic and embracing the chromatic is a valid choice, and may be better for what you want to achieve, it's not really a 'better' choice in absolute terms, just a different choice. – topo morto Feb 18 '16 at 1:42
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    @topo morto: I agree, but since I was to play my music on common fretted instruments and they are physically based on the chromatic scale, I have no other choice. Anyway I also want to make some electronic music and there I will choose frequencies freely, just like birds do when they sing :-) – Antonio Bonifati 'Farmboy' Feb 18 '16 at 8:55
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    @topomorto there's nothing stopping you from using the chromatic scale... Bingo. We all use the chromatic scale. A-Bb-B.... – Stinkfoot Mar 16 '18 at 17:29
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    @AntonioBonifati'Farmboy' - the chromatic scales has no alterations. It's 12 equal, unqualified generic tones. You are just imposing your own variations/conventions/'alterations' on the chromatic scale. The nice thing about the diatonic system is it does that work for you - you just use it. IMO you are deluding yourself . You are reinventing the wheel. When you learn and use the diatonic system, you can immediately leverage the knowledge of centuries of great composers and musicians. You don't have that with your 'system' unless you learn the diatonic system and then transpose. – Stinkfoot Mar 16 '18 at 21:02

Notes DO have numbers in the world of MIDI and computer music. Middle C is note number 60. If you find this system useful in your method of approaching music, feel free to use it! enter image description here


It's a bit moot since when playing, you don't have the time to do calculations anyway. It turns out that scale steps are usually the proper way to think about tonal Western music and normal music notation reflects that, and it maps well to piano keyboards. It doesn't map all that great to "naturally played" string instruments without keyboard access (on contrast to a piano or harpsichord or hurdygurdy, take a violin or guitar) and other instruments with diatonic arrangement (like most wind instruments with flap systems).

Stuff like "walking thirds" don't make a whole lot of sense as numbers: there is some willy-nilly system of major and minor thirds that is a result rather than a determination of the scale step arrangement.

So basically note names are sort-of arbitrary and you have to learn to associate them with positions, but so would be numbers on their own. When they are being used in tablatures, they aren't used for expressing musical relations but playing instructions. They are more related to what your fingers rather than your head are doing.

  • It doesn't map all that great to "naturally played" string instruments without keyboard access - not exactly. Don't forget that stringed instrument are tuned to particular, special notes in the scale and the strings are tuned to 4ths or 5ths of each other - so they also reflect the diatonic system. – Stinkfoot Mar 16 '18 at 23:01

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