Re: Tuning systems and relative / perfect pitch "My Experiment"

OOPs, I didn't mention my experience, let's go...

I made an algorythm that made the following sequence
by calculations;

num den ratio
1 1 1
2 1 2
3 2 1,5
4 3 1,33333333333333
5 3 1,66666666666667
5 4 1,25
7 4 1,75
6 5 1,2
7 5 1,4
8 5 1,6
9 5 1,8
ETC.....

I used and created a databse, I said that the division
of my two terms shouldn�t be more than 2, and if a
ratio value wasn�t in the database it should be
inserted there. The denominator would increase in
value up to where I wanted... etc... etc... I also
created a column for the value in cents, and names if
there were any (I got the name from a couple of lists
on the net).

Anyway, by that algorythm I coud easily calculate all
these intervals and I chose to do that up to a
denominator of 1024, wich gave me all the integer
ratio intervals in an octave up to 2047/1024!!! That
gave me 318.965 numbers of intervals in na octave.

I was first doing that to convert a value in cents to
a ratio proportion, I guess the only way should be a
database convertion. But I realized that in these
samples of intervals that I've got so far, there are
many small differences ( obviously, there are about
320 thousand, damn it ). For exemple, from 699.5 and
700.5 cents, this universe of 1 cent arround the 12EQ
fifth, I have 288 Intervals from 1411/942
(699.50282758137712 cents ) to 1187/792
(700.49711947475646 cents).

So at this point I started wondering about the
practical use of a bigger database, and even wonder
about the use of big interval ratios. I know that
there are famous tempraments that user higher number
ratios [ Pythagorean for Exemple ( C# = 2187/2048 =
113,685 cents ) ].

But in my database I have 2 intervals between 113.68
and 113.69;

1007/943 = 113.68080879802572 cents &
236/221 = 113.6885879644916 cents

Now 236/221 is much simpler than 2187/2048 and the
difference is only 0.0035... cents

Wich makes me believe that in this dimension, ( about
less than a cent ) a lot of big integer ratio
proportions are more theoretical than practical.
That�s when I mentioned my accoustic teacher, wich
told me about the DLO effect, and the William�s
syndrom. The DLO effect tells us about the smallest
intervals (played simoutaneously) that we can listen
without the �beating effect� (is that how you say
it?). And he also agreed when I mentioned the C#
pythagorean example, but he reminded me that a
temperament is characterized by other parameters that
make it special than the possible similarity of a
simpler integer ratio.

That�s when I felt like bringing this discussion to
the group, I hope you can all help me figuring out how
to categorize these samll differences... anyway, I�ll
save the rest for a reply...

Cheers
Alex

Ps. Would anyone like to get the database?

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Hi Eric,

Nice work with the database, which could be a useful thing to have.
One of my college projects was to build a monochord and go through the motions of doing the relationsships like you did, but obviously you took it far further than I did and in a database as well. I just wrote the results down while attempting to describe the interval produced in relationship with equal temperment, which has translated to playing synths and use of the pitch to get the note tempered where I want it to be.

If I may use an analogy with amplitude, the "db" ia known as "the least significant difference". While that MAY be true when listening to two different distinct tones sounding at different times, I've found while mixing that a 1dB resolution on a console is not sufficient, that sometimes even a 1/2 or 1/4 of a dB when mixing two sounds together IS necessary to get that "perfect' balance between the sounds. Does this mean that the validity of getting 1/8dB increments may be necessary resolution for amplitudes? To give sufficient resolution to resolve amplitude.

Bonnie *:>

Eric Viking <decuritiba@...> wrote:
OOPs, I didn't mention my experience, let's go...

I made an algorythm that made the following sequence
by calculations;

num den ratio
1 1 1
2 1 2
3 2 1,5
4 3 1,33333333333333
5 3 1,66666666666667
5 4 1,25
7 4 1,75
6 5 1,2
7 5 1,4
8 5 1,6
9 5 1,8
ETC.....

I used and created a databse, I said that the division
of my two terms shouldn�t be more than 2, and if a
ratio value wasn�t in the database it should be
inserted there. The denominator would increase in
value up to where I wanted... etc... etc... I also
created a column for the value in cents, and names if
there were any (I got the name from a couple of lists
on the net).

Anyway, by that algorythm I coud easily calculate all
these intervals and I chose to do that up to a
denominator of 1024, wich gave me all the integer
ratio intervals in an octave up to 2047/1024!!! That
gave me 318.965 numbers of intervals in na octave.

I was first doing that to convert a value in cents to
a ratio proportion, I guess the only way should be a
database convertion. But I realized that in these
samples of intervals that I've got so far, there are
many small differences ( obviously, there are about
320 thousand, damn it ). For exemple, from 699.5 and
700.5 cents, this universe of 1 cent arround the 12EQ
fifth, I have 288 Intervals from 1411/942
(699.50282758137712 cents ) to 1187/792
(700.49711947475646 cents).

So at this point I started wondering about the
practical use of a bigger database, and even wonder
about the use of big interval ratios. I know that
there are famous tempraments that user higher number
ratios [ Pythagorean for Exemple ( C# = 2187/2048 =
113,685 cents ) ].

But in my database I have 2 intervals between 113.68
and 113.69;

1007/943 = 113.68080879802572 cents &
236/221 = 113.6885879644916 cents

Now 236/221 is much simpler than 2187/2048 and the
difference is only 0.0035... cents

Wich makes me believe that in this dimension, ( about
less than a cent ) a lot of big integer ratio
proportions are more theoretical than practical.
That�s when I mentioned my accoustic teacher, wich
told me about the DLO effect, and the William�s
syndrom. The DLO effect tells us about the smallest
intervals (played simoutaneously) that we can listen
without the �beating effect� (is that how you say
it?). And he also agreed when I mentioned the C#
pythagorean example, but he reminded me that a
temperament is characterized by other parameters that
make it special than the possible similarity of a
simpler integer ratio.

That�s when I felt like bringing this discussion to
the group, I hope you can all help me figuring out how
to categorize these samll differences... anyway, I�ll
save the rest for a reply...

Cheers
Alex

Ps. Would anyone like to get the database?

__________________________________
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Yahoo! Calendar - Free online calendar with sync to Outlook(TM).
http://calendar.yahoo.com

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--- In MakeMicroMusic@yahoogroups.com, Bonnie Goodwin
<goodwinbonnie@y...> wrote:
> Hi Eric,
>
> Nice work with the database, which could be a useful thing to have.

Cool, that's what I'd like to hear, actually I'd like to hear some
options as to what it may be useful, Ha ha...

> which has translated to playing synths and use of the pitch to get
the note tempered where I want it to be. >

Don't know if I got that, but one use for that databse that I thought
of could be a tuning assigment, or I could link it to a software,
something like that

> If I may use an analogy with amplitude, the "db" ia known as "the
least significant difference". While that MAY be true when listening
to two different distinct tones sounding at different times, I've
found while mixing that a 1dB resolution on a console is not
sufficient, that sometimes even a 1/2 or 1/4 of a dB when mixing two
sounds together IS necessary to get that "perfect' balance between
the sounds. Does this mean that the validity of getting 1/8dB
increments may be necessary resolution for amplitudes? To give
sufficient resolution to resolve amplitude.
>

Geeee , I could catch up with you, and I couldn't figure the relation
of pitch and amplitude, I guess I'm to raw for all this... could you
try to explain this issue again?

Cheers
Alex

(I'm sorry that my nick name comes as "Eric" when I'm using my
mailbox, I don't know how to get rid of that, I come as "Porres" when
I use the forum site, and I wish I could stay like that0

Hi Alex,

I was comparing the "least significant difference" in pitch with the same thing in amplitude of sound. What does it have to do with the price of noodles in China? Probably not much. I've been almost totally immersed in the world of recording studio acoustics for the past few months, probably looking for colloraries to my current plights. I am making considerable progress in my efforts, however, but then that is well outside the scope of this message area.

Discussion here seems to make the "least significant difference" to be about two cents, the thought of ear training to the point where this might be debatable has been discussed and it is now something I am considering doing just to see where my ear can percieve these noticable differences as opposed to the "accepted", since I've found out that at least in mixing two sounds together that 1 dB is NOT the "least significant differenc as I had been led to believe, with 3 dB being about the usual difference in musical volume steps.

When it comes to playing "in the cracks", on synthesizer, I go to the nearest semitone and bend up to the desired pitch, kind of the way trombonists temper the pitch to where it should be from one of the 7 positions on the slide. Having watched them carefully, I have noted minute changes from those "stock" slide positions based on what the note is in relationship to the root of the chord as they temper the tuning and string players, as they run scales up and down, then to go sharp on the ascending scale, and a little flat on the way down.

Does this make a little more sense to you?

Bonnie *:>

Porres <decuritiba@...> wrote:
--- In MakeMicroMusic@yahoogroups.com, Bonnie Goodwin
<goodwinbonnie@y...> wrote:
> Hi Eric,
>
> Nice work with the database, which could be a useful thing to have.

Cool, that's what I'd like to hear, actually I'd like to hear some
options as to what it may be useful, Ha ha...

> which has translated to playing synths and use of the pitch to get
the note tempered where I want it to be. >

Don't know if I got that, but one use for that databse that I thought
of could be a tuning assigment, or I could link it to a software,
something like that

> If I may use an analogy with amplitude, the "db" ia known as "the
least significant difference". While that MAY be true when listening
to two different distinct tones sounding at different times, I've
found while mixing that a 1dB resolution on a console is not
sufficient, that sometimes even a 1/2 or 1/4 of a dB when mixing two
sounds together IS necessary to get that "perfect' balance between
the sounds. Does this mean that the validity of getting 1/8dB
increments may be necessary resolution for amplitudes? To give
sufficient resolution to resolve amplitude.
>

Geeee , I could catch up with you, and I couldn't figure the relation
of pitch and amplitude, I guess I'm to raw for all this... could you
try to explain this issue again?

Cheers
Alex

(I'm sorry that my nick name comes as "Eric" when I'm using my
mailbox, I don't know how to get rid of that, I come as "Porres" when
I use the forum site, and I wish I could stay like that0

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[MMM info]------------------------------------------------------
More MMM music files are at http://www.microtonal.org/music.html
------------------------------------------------------[MMM info]

Your use of Yahoo! Groups is subject to the Yahoo! Terms of Service.

---------------------------------
Do you Yahoo!?
Free online calendar with sync to Outlook(TM).

[Non-text portions of this message have been removed]