Jon-Petr

< Jon,

< All audiences listen musical works through musical scales. An important part of the world does it through the equal < tempered. No doubt that you know that this arithmetical scale is imperfect so I won´t mention its slight but < detectable imperfections. I transcribe here the opinions of some composers and musicians:

---------------------------------

W.T. Bartholomew "Acoustics of Music" (Page 183)

"Although musicians often repeat glibly that tempered scale is imperfect, few understand the necessary cause of that imperfection, even with such works available as those of Helmholtz, Ellis, and many others. The cause lies in the mathematical relations of the ratios involved".

(Page 184)

"In other words, a twelve-tone division of the octave is necessarily imperfect because of the nature of the number series itself".

(Page 185)

"Equal temperament enables us to play equally well, or perhaps we should say equally badly, in all keys".

(Page 193)

"Thus the "tuning" of a tempered instrument is in reality a process of controlled mistuning".

Joaquín Zamacois "Teoría de la Música" (Pages 155-156)

Difficulties in the Tempered System

- "Scientifically, it has no basis"

- "When considering practical inconveniences, there are none in fixed sound instruments, since even its harshest critics recognize that there is no substitute and accept it as the lesser evil".

----------------------------------------------

< When I clearly wrote that my purpose is to resolve a problem that has existed since music was born, this phrase < definitely separates two concepts: the problem "and" the time when music was born. The problem is the presence < of small discordances, inexistance of perfect fifths and fourths and other negative aspects introduced by the equal < tempered scale into the music world. Most audiences do not detect the scale imperfections; if they have not heard < better chords there is no reason to complain or to expect harmonious ones. I hope that you agree that the better < the scale is, the more pleasant the music is listened. Two separate although complementary concepts.

< Who said that I found a tuning that can improve certain kinds of music. Nobody said that nonsense because poor < and good scales are unable to select the kind of music they work better.

< I suggest you to stop your idea that Music itself has a problem. I alredy stressed the fact that I am only interested in < the perfecting or replacing the equal tempered by another better scale.

Mario,> The Piagui Musical Scale is not an invention, it is a discovery based on years of research on micro-consonance to resolve a problemthat has existed since music was born.Music does not have a problem. Maybe some tunings do, but the best music transcends this. Balinese and Javanese gamelans don't have aproblem. Georgian liturgical singing does not have a problem. North and South Indian musics do not have a problem.I'm glad you've found a tuning that *you* find can improve certain kinds of music, but please stop with the idea that Music itself has aproblem. Because, in fact, music is more than tuning.-----------------------------------------------------

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De:
"Petr Parízek" <p.parizek@...>

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Fecha:
19 Jul 2008, 08:27:27 AM

Asunto:
Re: [tuning] The roots

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Mario wrote:xml:namespace prefix = o ns = "urn:schemas-microsoft-com:office:office" /

> ZC = Zarlino comma = (81/80) = 1.0125

> ZS = Zarlino semitone = (16/15) = 1.06666666..

> D = Pythagorean and Just Intonation note D = (9/8) = 1.125

> EAZ = Note E of the Aristoxenus-Zarlino scale = (5/4) = 1.25

#1. It's not good to say that "5/4 is E" and "9/8 is D" and so on. Why can't you just say "major second" or "major third"? If you want to label 5/4 as E, then you have to also specify the pitch of the 1/1 as C, which is what you probably meant but didn't say.

#2. Why are you still writing the factors as decimal numbers? It would be much better understandable for most of us if you said "5/4 = ~386.314 cents" instead of "5/4 = 1.25". Decimal numbers are not of much use here.

#3. I still don't understand what is the interval that you call "the new comma U".

Petr

............................................................................................................................

< Petr,

< I cannot escape from decimal figures which are referred to Do = 1. Since the Piagui scales were derived thanks < to the features and information given by the Progression of Musical Cells where 612 cells covered the range Do = < 1 up to 2Do = 2, 612 products were succesively required. This demanded the use of decimal cell frequencies < whose values compeled the use of twelve digits like 1.00112915039 in order to reduce the error and thanks to this < the octave 2 was round.

< Have you ever tried to get 612 products which form a geometric progression by only using common fractions? < Practically impossible.

< The relative frequencies of notes D, E, F, G, .....with respect to Do of the Just Intonation Scale: 9/8, 5/4, 4/3, < 3/2 ..... (Most of this fractions are also used in the Pythagoras scale as you know) are normally used when < necessary.

< Since there are various "major second" or "major third" depending on the scale, some times I have to precise < their values.

< To deduce and discern about the Piagui system the only numeric system that can be used is the fractional < decimal; the cents system cannot be applied.

< When developing the 612 cells progression, the first 22 cells were determined by using the schisma < 1.00112915039 and the comma J = 1.001131379911. Cell Nº 23 required a different comma; it was deduced and < found U = 1.00121369651...

< If you want, I can send you the six pages of the progression, just request it.

MARIO PIZARRO

piagui@...

Lima, July 19, 2008

Mario,

I certainly understand how you are framing your argument, and I also
want to stress that I realize English is not your native language, and
possibly some of this may be just misunderstanding.

Nonetheless, you are posting this to a list that is not strictly based
on, or interested in, Western classical music. That may form a big
part of it, but there are many, many other musical cultures in this
world that not only have nothing to do with 12tet, but have an entire
culture and repertoire based around their own tunings. Therefore, it
really comes across wrongly when you simply say "music has a problem".

Because music is a very, very big ocean.

Mario wrote:

> < I cannot escape from decimal figures which are referred to Do = 1. Since the Piagui scales were derived thanks < to the features and information given by the Progression of Musical Cells where 612 cells covered the range Do = < 1 up to 2Do = 2, 612 products were succesively required. This demanded the use of decimal cell frequencies < whose values compeled the use of twelve digits like 1.00112915039 in order to reduce the error and thanks to this < the octave 2 was round.

> < Have you ever tried to get 612 products which form a geometric progression by only using common fractions? < Practically impossible.

I was not speaking about common fractions, I was speaking about logarithmic conversions. If you want to divide the octave into 612 steps, then one step is ~1.9607843 cents, which makes, when multiplied by 612, 1200 cents, which is the octave. Similarly as the 612-equal scale divides the 12-equal semitone into exactly 51 steps, so do cents divide it into exactly 100 steps. You can read more here: http://tonalsoft.com/enc/c/cent.aspx

> < The relative frequencies of notes D, E, F, G, .....with respect to Do of the Just Intonation Scale: 9/8, 5/4, 4/3, < 3/2 ..... (Most of this fractions are also used in the Pythagoras scale as you know) are normally used when < necessary.

> < Since there are various "major second" or "major third" depending on the scale, some times I have to precise < their values.

Calling an interval by a note name does not specify it any further than calling it by an interval name.

> < To deduce and discern about the Piagui system the only numeric system that can be used is the fractional < decimal; the cents system cannot be applied.

Why not?

Petr

--- In tuning@yahoogroups.com, Petr Parízek <p.parizek@...> wrote:
>
> Mario wrote:
>
> > < I cannot escape from decimal figures which are referred to Do =
1. Since the Piagui scales were derived thanks < to the features and
information given by the Progression of Musical Cells where 612 cells
covered the range Do = < 1 up to 2Do = 2, 612 products were
succesively required. This demanded the use of decimal cell
frequencies < whose values compeled the use of twelve digits like
1.00112915039 in order to reduce the error and thanks to this < the
octave 2 was round.
>
> > < Have you ever tried to get 612 products which form a geometric
progression by only using common fractions? < Practically
impossible.
>
> I was not speaking about common fractions, I was speaking about
logarithmic conversions. If you want to divide the octave into 612
steps, then one step is ~1.9607843 cents, which makes, when
multiplied by 612, 1200 cents, which is the octave. Similarly as the
612-equal scale divides the 12-equal semitone into exactly 51 steps,
so do cents divide it into exactly 100 steps. You can read more here:
http://tonalsoft.com/enc/c/cent.aspx
>
> > < The relative frequencies of notes D, E, F, G, .....with respect
to Do of the Just Intonation Scale: 9/8, 5/4, 4/3, < 3/2 .....
(Most of this fractions are also used in the Pythagoras scale as you
know) are normally used when < necessary.
>
> > < Since there are various "major second" or "major third"
depending on the scale, some times I have to precise < their
values.
>
> Calling an interval by a note name does not specify it any further
than calling it by an interval name.
>
> > < To deduce and discern about the Piagui system the only numeric
system that can be used is the fractional < decimal; the
cents system cannot be applied.
>
> Why not?
>
> Petr
>
From Robert: 100 steps scaled to 100tet is interesting. I am
actually carrying out sound harmonic experiments in 100tet at
the moment. The results are so far very promising.

> From Robert: 100 steps scaled to 100tet is interesting. I am
> actually carrying out sound harmonic experiments in 100tet at
> the moment. The results are so far very promising.

What is that better than 50?

Petr

--- In tuning@yahoogroups.com, Petr Parízek <p.parizek@...> wrote:
>
> > From Robert: 100 steps scaled to 100tet is interesting. I am
> > actually carrying out sound harmonic experiments in 100tet at
> > the moment. The results are so far very promising.
>
> What is that better than 50?
>
> Petr
>
From Robert. It is easy to work with. All the notes are separated
by 12cents. The meantone 5th is 696cents. The just third is 384cents.
And being decimal it can be adapted to all sorts of numerical
prestidigitations and jugglings. And no decimal points to fiddle
about with. All in all it's a reasonable way to approach microtonality
from a scientific view.