Degree of difficulty

Hello Carl.
Thanks for the information.
I will follow your advice.
In my website I have used the concept of degree of difficulty to make a comparison between two musical systems, in order to determine which one is easier (or less difficult) to manage. I have adopted this simple principle:
any alteration is a complication.
The first system is generated by the 7 notes 24tET scale, in which both semitonal (# and b) and quarter-tone (^ and v) alterations are used. The second is the system generated by my scale of eight notes, in which I use only the two quarter-tone alterations (^ and v).
If you visit my website and hit the Proposal button, and the the coefficient difficulty button, you'll find a brief explanation on how I calculate this coefficient.
You'll find these two scales close to one another in columns 5 and 6, in the second of three tables in the "tables" section of my site www.ottavanota.info.
The scale of column 5, seven notes, I called it Scala quartitonale articolata, while my eight notes, I called Scala Quartitonale Nuova. They are:
Scala quartitonale articolata: C, C^, C#/Db, Dv, D, D^, D#/Eb, Ev, E, E^/Fv, F, F^, F#/Gb, Gv, G, G^, G#/Ab, Av, A, A^, A#/Bb, Bv, B, B^/Cv, (C)
Scala quartitonale nuova: C, C^, Dv, D, D^, Ev, E, E^, Fv, F, F^, Gv, G, G^, Hv, H, H^, Av, A, A^,Bv, B, B^, Cv, (C)

I hope I was clear and that by visiting my site, you can understand fully how to calculate the coefficient of difficulty. In the coming days I'll apply the same test to the scale you asked about. As soon as I finished it I'll send it to you.

Giancarlo Dalmonte

Giancarlo wrote:

>If you visit my website and hit the Proposal button, and the the
>coefficient difficulty button, you'll find a brief explanation on how I
>calculate this coefficient.

So it is the percentage of tones requiring accidentals in their
notation, out of the tones required to transpose the scale to
every notes of itself?

Like the usual diatonic scale,

C D E F G A B
D E F# G A B C#
E F# G# A B C# D#
F G A Bb C D E
G A B C D E F#
A B C# D E F# G#
B C# D# E F# G# A#

There are 7 x 7 = 49 tones total, 16 with an accidental,
so 33% difficulty? Have I done this right?

>I hope I was clear and that by visiting my site, you can understand
>fully how to calculate the coefficient of difficulty. In the coming days
>I'll apply the same test to the scale you asked about. As soon as I
>finished it I'll send it to you.

Thanks, looking forward to it.

-Carl

I don't think higher number of accidentals means more difficult scale. Maybe for the reading (because there can be also higher number of double accidentals), which is only thing of the experience in reading and sight-reading, and knowledge. Concerning playing the instrument, difficulty depends on other factors.

On fretboard instruments there's no difference in difficulty, just to change position on the fretboard.

Woodwinds - there are biggest differences as tones with accidentals use more difficult fingerings and lowest and highest tones have special fingerings. Probably the most difficult are clarinet (overblowing to 3rd harmonics, not octave) and bassoon (doesn't use Boehm system).

Brass - no difference.

Keyboards - there are small differences, but it can hardly be any problem for skilled performer. Scales with more accidents are even more easily playable, like B major, where naturals (B and E) are played by the first finger and sharps by other fingers. Very comfortable, very ergonomic. Similar with F#/Gb major, C#/Db major, Ab major, Eb major, Bb major... F major is more difficult with its fingering 4-1 between Bb and C notes.

Concert pedal harp - diatonic is no problem, even some enharmonic. Only chromatic is difficult. That's the reason why there are two harps in the orchestra.

Zymbalon - no problem.

And don't forget - there are 15 diatonic scales, not only 7 which you wrote.

Daniel Forro

On 31 Oct 2010, at 6:22 AM, Carl Lumma wrote:

> Like the usual diatonic scale,
>
> C D E F G A B
> D E F# G A B C#
> E F# G# A B C# D#
> F G A Bb C D E
> G A B C D E F#
> A B C# D E F# G#
> B C# D# E F# G# A#
>
> There are 7 x 7 = 49 tones total, 16 with an accidental,
> so 33% difficulty? Have I done this right?

Daniel - first we have to figure out what Giancarlo intends.
I probably got it wrong, so let's not make hasty conclusions.

-Carl

At 06:05 PM 10/30/2010, you wrote:
>I don't think higher number of accidentals means more difficult
>scale. Maybe for the reading (because there can be also higher number
>of double accidentals), which is only thing of the experience in
>reading and sight-reading, and knowledge. Concerning playing the
>instrument, difficulty depends on other factors.

Hello Carl and Daniel.
Carl, the procedure you followed is correct and so it is the result of 33%.
But we must ask: "What is the usefulness of this calculation? It makes sense, in my opinion, only if you make a comparison between the two scales, or better yet, two systems, as I did. I found myself in the situation of wondering if it is harder to manage a 24tET scale of seven notes, or one with eight notes (like mine). So I developed this concept of degree of difficulty, not knowing other ways than to count the accidentals used. My conclusion, as you can see on my site has been that the management of a seven notes system is more complex (76% vs 57%).
From this point of view, therefore, is entirely appropriete the observation of Daniel that the scales are 15, not seven. It is necessary, therefore, to count the accidents for all 15 stairs and then calculate the percentage, with exactly the same procedure. And then do the same thing with another system and then compare coefficients.
Daniel Forrￜ is also correct on the other question, it is certainly true that a greater number of changes does not determine absolutely the greater difficulty. It is, in fact, a relative truth, which I applied in my experience of juvenile bass in pop music, as well as to support the thesis that I learned studying music theory treatises written by teachers of Italian music conservatories.
Remains true to its relativity, so I have no difficulty to give reason to Daniel for all other examples of facilities and / or difficulty with which the musician is forced to operate because of the technical differences between the different instruments (keyboard, brass or whatever). I recognize that in some cases even the opposite may be true.
The criterion I used, ultimately, is just one of many possible tools, which has limited validity to specific circumstances. I felt that, in my specific case it was a parameter to be taken into account.
Do you have another method in mind to make such a calculation?

I will calculate the degree of difficulty as for Carl request.

Thank you and I greet you cordially.
Giancarlo Dalmonte