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Sunday, January 17, 2016

7. Mathematically more correct and simpler terminlogy, symbolism and writting of music compared to the traditional method . Piano roll software to write it.


Some disadvantages of that classical musical notation system

1) Has names of the notes, only for 7 -tone scales and has to use, flats , sharps and scale keys for the pentagram, which also results in  many alternative ways to write a  score of the same melody. The "key"and single tonality scale in which a songs is written is misleading as most often a song has many tonalities. An if one tries to follow all the modulations (that still are not unique) more complications is introduced in the writing of music. 

2) The terminology of the intervals, does not refer to the real distance in semitones or steps in the scale, but includes, the ends of the interval, a habit that mathematics and all other sciences carefully avoid. 

3) The time duration of the notes (as divisions by powers of 2) has redundant graphical notation with tails on the notes, that may take much space when writing music.

4) The rhythm is not notated with sufficient information but with very little information only by two only numbers , referring to the mutual relation of the duration of a measure and the basic time unit of the notes.

Al the above disadvantages can be easily corrected, and some this has been done by the designers and programmers of musical interface, when e.g. are utilize the interface of "Piano roll editor". 

We will show in the next how simple modifications of the tarditional musical notation system, eliminate the above disadvantages. 

We present one way which does use a pentagram (5 parallel lines) and still a simpler and more compact way that is using only letters, without a pentagram. 

HOW TO WRITE FAST MUSIC WITHOUT A PENTAGRAM

1) At first in order to do it we must notate a note with its absolute scientific pitch, with the usual standard scientific notation, where we add at the end of the letter the number of the octave (in  the piano). By adding the information about the octave of each note, we get the exact pitch e.g. C3, C4, C5 etc


2) In addition we can to eliminate the use of sharps and flats.
Here are names of all 12 notes , that eliminate the need for flats or sharps and can be pronounced  with the human voice.
(Do , Di=D#, Re, Ri=R#, Mi, Fa, Fil=Fa#, Sol, Sil=Sol#, La, Li=La# , Si , Do) 
In the Latin letters notation we may keep only the symbol of sharp (eliminate the symbol of flat which may be confused with the note b), or utilize instead of the non-letter symbol #, the letter h.
So here are the 12 notes sai in the octave 3.
c3, ch3=c3#, d3, dh3=d3#, e3, f3, fh3=f3#, g3, gh3=g3#, a3, ah3=a3#, b3, c4.

3) For the time we may keep the classical conventions for notation, and just put the numbered letter (e.g. g4, c3 etc) inside the round body of the symbol of the note. As this will eliminate the discrimination of full black notes (1/4, 1/8, 1/16 etc) and white hollow ones (1/2, 1) we just put a different sign at the top of the vertical line of 1/2 e.g. the Swedish or Danish o.
Alternatively for the duration we use as usually in musical notation divisions by powers of 2, of the full duration. 
So (c3 /2^0), means a whole duration of the note c3, (c3,/2^1) means a half duration of the note c3, (c3,/2^2) means a quarter of the duration of the note c3 , (c3,/2^3) means an eighth  of the duration of the note c3, (c3,/2^4) means an 16nth  of the duration of the note c3, etc. Other duration is derived by  denoting the divisor of the full duration. E.g. (c3,/3) means that the note c3 sounds 1/3 of the full duration. Multiples of the full duration are denoted without the slash. E.g. (c3,2) means that c3 sounds two full durations etc. 

4) Some melodies do not have rhythm,in which case the writing of the melody does not require separation of the notes in to measures. But some melodies do have rhythm, especially with percussion, in which case the separation of the melody in to measures is necessary.  The full duration must be linked with the duration of the basic measure of the rhythm, and contrary to the traditional conventions in the musical pentagram symbolism, here it is preferred to be identical with the duration of the measure of the rhythm. In this way, we fix a single way to write the timing and not many equivalent ways. So in writing a  melody which in the classical musical notation has rhythm number 3/4, in the current symbolism would be notes of the type e.g. (c4, /3*2^y). We separate the measures with vertical lines, between the symbols of the notes.



5) For the pause and non-sounding we use of course the usuall mathematical symbol of empty set that is ø, so with the duration of the pause it could be like (ø, /3*(2^2)).



So with the current notation the notes of a melody may seem like this

|(c3,/2^0)| (d3, /2^1) (d3, /2^1)|  (f3,/2^0) |etc

Parallel melodies are written one above the other.

There is an even better simplification of the writing of a measure, without using the numbers of time duration, which gives an even better image of the timing of the melody. 
E.g.Instead of writing a measure of melody like this
|(d4,/2^2),(g4,/2^4),(g4,/2^4),(g4,/2^4),(ø,/2^4),(g4,/2^2),(f#4,/2^4),(f#4,/2^4),(f#4,/2^4),(ø,/2^4),(f#4,/2^2),(e4,/2^4),(b3,/2^4)|

We write without numbers as 
|(d4-d4),(g4),(g4,),(g4,),(ø,),(g4-g4),(f#4),(f#4),(f#4),(ø),(f#4-f#4),(e4),(b3)|

In other words we write the full measure with a Greatest Common divisor of equal duration, and we put the notes on this grid, as if it was a rhythm. (see also post 10 about how to write rhythm ). The occurrence of a note is assumed in this minimal duration unit for the measure, while notes with longer duration are denoted by linking dashes, as it is always an integral multiple of this minimal duration.. 


HOW TO WRITE FAST MUSIC WITH A SIMPLIFIED PENTAGRAM NOTATION.


1) At first for the duration we utilize the same rules of notation In other words  we use as usually in musical notation divisions by powers of 2, of the full duration. 
So (x /2^0), means a whole duration of the note x, (x,/2^1) means a half duration of the note x, (x,/2^2) means a quarter of the duration of the note x , (x,/2^3) means an eighth  of the duration of the note x, (x,/2^4) means an 16nth  of the duration of the note x, etc. Other duration is derived by  denoting the divisor of the full duration e.g. (x,/3) means that the note x sounds 1/3 ofthe full duration. Multiples of the full duration are denoted without the slash. E.g. (x,2) means that x sounds two full duration etc.


2) Next we utilize the pentagram so that we do not use sharps and flats, neither keys. Instead of a key we write a number denoting the number of the octave that the pentagram refers. In other words a note centered at the first line of the pentagram with initial number 3 (put where usually a scale  key was put) is a c3. A note centered at the space between the first and the second line is a c3#. A note centered at the the second line is a d3, etc. A note centered at the c3# , etc. All notes are hollow circles (like a whole duration classical notation note) so that we save ink, and the duration written as in 1) is set next to the right of it. 

(See for example such pentagram  notation, which is one step away from the simplification we suggest that would make it actually a simplified piano Roll in the free midi editor here
https://www.youtube.com/watch?v=X8M1FP2AOQE )

   


For the Common Octaves symbolism see

https://en.wikipedia.org/wiki/Octave#/media/File:Common_Octave_Naming_Systems.png


For betyer keyboard designs cmpared to the classical of piano see the Lippens Keyboard

https://www.youtube.com/watch?v=MHfG20HvPHA


Pitch symbols by octave

https://www.thoughtco.com/pitch-notation-and-octave-naming-2701389

(The post has not been written yet completely)