Violin Scales

Bryan Kelly

April 2023

My daughter decided to take some cello lessons.  I thought that was really cool.  She is an adult now, but did play violin some in elementary school.  She was also a good singer.  There are a few songs, passages of music really, that have always attracted my attention.  If she plays cello, and I play violin, maybe we would play together and sound somewhat acceptable. 

So I have started my attempts to learn a bit of violin.

I have yet to select an instructor so I started working on tuning and playing some scales.  And when I start to play a tune, it would really be helpful to have something to play along with.  A MIDI application is the obvious choice. 

BTW:  MIDI is Musical Instrument Digital Interface.  But MuseScore goes way beyond just the MIDI part. It is a DAW, Digital Audio Workstation.  (Another TLA, Three Letter Acronym.)  The MIDI standard was first put in use in 1983.  I became aware of it in about 1990 and used it to help my daughter learn violin.

Returning to the main point.  I am not a musician, but do know how important scales are.  The notes for the open strings of the violin were set up in MuseScore.  That was followed by a couple of scales to play along with.  The first was the obvious, C Major, no sharps or flats.  Twinkle Little Star came up quickly and the version found is in D Major, two sharps.  So those two were entered into MuseScore first and second.

While playing those scales, over and over, the finger positions for the notes clearly showed up the whole and half steps between the notes of each scale.  As the notes moved up the fingerboard the finger positions become closer together.  That led to wondering about the actual frequencies of each note, and the relationship between each note.  Most people are aware that each octave going up is a doubling of the frequency.  But what about the half steps between the notes?  Do they have a linear relationship?

An internet search for the phrase “frequencies of each musical note in music” returned a couple of sites with charts.  One is here:

Music Note Frequency Chart - Music Frequency Chart | MixButton

From that page the notes for the violin were entered into an Excel workbook.  The next step was to calculate the difference between each half step.  From there, calculate how much each half step incremented from the previous half step.

Each half step is noted in the left column with the frequency of each note to its right.  Moving to the right again is the difference between each half step.  Finally, the amount the frequency changed expressed as the percentage of the previous note.

Since the exact frequency between each half step is always changing, seeing a pattern in the change from each half step to the next is a bit difficult.  The percentage that each half step changes is where the consistency is found.  Take the frequency delta of G to G#, 11.65 Hz, and divide it by the predecessor frequency of G, 196 Hz, and the result is this percentage.  That calculation is repeated for each of the notes in the table.

The change is always 5.94xxx%.  The smallest change is 5.94350% while the largest change is 5.94905%.  The delta between the smallest and largest change is 0.005549%.

Well, how much is that difference?  Take the spread of 0.005549%, the maximum difference found, and multiply it by the lowest violin note, the G at 196 Hz, and the value is 0.010876 Hz. About 1/100 of one cycle per second.  Go to the highest frequency of the range selected and it is about 5/100 of one cycle per second. 

Conclusion:  The frequency spread between each half note is extremely consistent.  Each half note increases the frequency by a very regular interval.

I did not know what to expect, but found this rather interesting.