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I'm wondering why was there an emphasis on notes rather than scale numbers in sheet music.

For example mary had a little lamb could be written as: 3 2 1 2 3 3 3 ....

^^^ where the numbers refer to the scale degree.

And a chord underneath it could be written as: 1-3-5 (or the I chord)

so that if someone knows scales they just play the number of that scale degree. an accidental could be written as 2# for example. An octave higher or lower could be written as 3- or 3+. etc.

Because isn't the actual key not really important as we can play the song in any key. but when the notes are explicitly written as they do in sheet music then it makes it harder to transpose.

marked as duplicate by Dom theory May 6 '18 at 20:13

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    I'm sure there has been at least one question similar to this (not music.stackexchange.com/questions/41987/…, which isn't really about focusing on scale degrees) - I can't find it though... maybe someone else can! – topo Reinstate Monica May 6 '18 at 7:30
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    I understand that you want to have control over your question, but this title and the question content don't seem to agree. I don't see how the fact that we use staff notation instead of a number system has anything to do with why sheet music is written in a key, other than possibly that key signatures are communicated via staff notation. Perhaps you can clarify? – ex nihilo May 6 '18 at 8:50
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    @foreyez -- if we didn't allow the community to edit content, the site would be much poorer. So many questions contain spelling errors and grammatical errors, that alone is reason to allow this. Don't forget that the Stack Exchange policy is that once you post content, it belongs to the community to curate and maintain. The idea is not to deform your question, but to hopefully improve it. Don't take it personally. – ex nihilo May 6 '18 at 9:03
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    Can't see anything detrimental in editing of your (or most others') questions. Editing is usually done in the best interests of everyone, especially the OP. If I felt bureaucracy ruled here, I wouldn't be bothering to visit even. For bureaucracy, read betterment ! – Tim May 6 '18 at 10:05
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    @foreyez Making questions searchable is not red tape. The current title does not really indicate what the meat of the question is about so in 2 months when someone askes the same question we won't be able to find this one which isn't good for the site longterm. – Dom May 6 '18 at 15:46
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You are late to the game. Arguably the most-used numerical notation system based on scale degrees is the Chinese system known as Jianpu. Note pitches are represented using their scale degree, lengths by lines and dots, rests by zeros, octaves by additional dots and so on.

It's reasonably workable for writing down melodies but falls apart when trying to notate something as complex as piano music: it's just too linear in nature to make for a good representation of vertical clustering and shifting tonal centers. The graphic nature of common notation just makes for a faster take-in of the structure.

It's like the difference in reading mathematical formulas written in common notation and in FORTRAN.

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Seems like there are a couple of parts to your 'musing' here - one aspect is "why focus on particular notes rather than scale degrees?" Another is "why use dots on a stave rather than numbers?"

I'm not a psychology expert, but think the reason to have a 'graphical' representation of notes is simply that graphs and similar visualisations tend to be faster to read than streams of numbers - the same reason you put graphs in your powerpoint to impress the boss, rather than just the raw numbers! Musical dots also have a very clever and efficient way of representing rhythms, which we'd have to reinvent if we got rid of the dots altogether.

Because isn't the actual key not really important. it's the relation to the scale that's the important part no?

In most specific cases, I don't think that's true. Often, transposing a work a few semitones down might make the notes' timbres mesh differently together and stop the harmony working as well; on a more practical level, many parts might only be playable on some instruments in a limited range of keys (or even only one) - for example, something in E or A is often much easier on a guitar than F or Bb.

Even so, people have recognised that it is valuable to have scale-agnostic ways of notating music - the roman numerals used in Roman numeral analysis are one example, and the idea is also used with Arabic numbers in the Nashville number system. You'll notice that in both cases, the focus is on giving numbers to chords, rather than notating every note with a numeral - notating every note as a number would probably be too dense a stream of information (going back to the idea of why graphs are better).

Both these systems do sometimes hit a practical problem - what do you do when the piece modulates, or when the key of the piece is unclear? That's going to be a problem with any system that explicitly works in relation to a key - in fact, it's already something of a problem with standard notation.

...when the notes are explicitly written as in sheet music then it makes it harder to transpose.

There is some truth in that, although you could argue that when the notes aren't explicitly written, that makes it harder to just play the piece straightforwardly without transposing... ultimately, every system people have come up with for notating music so far involves some compromises.

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You're asking for 'Tonic sol-fa', a peculiarly British system using Anglicised solfege ("Do, a deer, a female deer, Re...") note names and a sort of punctuation notation for rhythms. In its time it was as ubiquitous in British published popular music as chord shapes are now. You still find choral societies etc. using old editions with tonic sol-fa as well as notation, though the ones with ONLY tonic sol-fa are only found now in dusty cupboards.

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I think you've answered this yourself. In your last paragraph. If your player was good enough to be able to play a piece in any key, from your numbers, then given one key, transposition should be just as easy into any other key. They would have to be proficient in any key to do what you suggest in any case. Then you have the problem of extra symbols to signify note length, and when accidentals start coming along...

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