Yahoo Tuning Groups Ultimate Backup tuning question about schisma in edo

If we accept fifth of positive systems as 700+(comma/12) or 700+schisma
, we can have for example:

Comma(cent)......edo

1......14400-edo

15.......960-edo

20.......720-edo

25......576-edo

30......480-edo

in 574-edo we have for example fifth as 702.439 and (2.439*12=29.268) as
comma which is 14-degree of system.

in some case we have a general equation , for example:

960=14400/15(14400/comma)

So for comma = 30 we have 960-edo And 480-edo

This rule is also correct for
kleisma(http://tonalsoft.com/enc/c/images/commas.gif) for example :

8.76 cent...........137-edo

10 cent .............1440-edo

Questions :

1-Is it correct to have comma in edos?

2- is it correct to say that edos such as 480 show schisma such as 2.5
cent , although shisma must be rational
(http://tonalsoft.com/enc/s/schisma.aspx)

3- if so can we have <http://tonalsoft.com/default.aspx> Schismic
Temperaments in higher cardinality edo systems?

Shaahin Mohaajeri

Tombak Player & Researcher , Composer

www.geocities.com/acousticsoftombak

My tombak musics : www.rhythmweb.com/gdg

My articles in ''Harmonytalk'':

www.harmonytalk.com/archives/000296.html

www.harmonytalk.com/archives/000288.html

My article in DrumDojo:

www.drumdojo.com/world/persia/tonbak_acoustics.htm

🔗Gene Ward Smith <gwsmith@svpal.org>

🔗Mohajeri Shahin <shahinm@kayson-ir.com>

Dear gene

It would be better for me to say 2.5 as grad.although grad is 1/12 of
pyth.comma but I think it is better to call grad as difference of
positive fifth from 700 cent and so we can have besides comma other
kinds of interval generating grad .

In 425-edo we have some positive fifth :

Degree) cent

248)700.235 cents

249)703.059 cents

250)705.882 cents

251)708.706 cents

For the first we have 2.82

Second we have 36.708

Third ..70.584

Fourth ...104.472

As:

Degree)cent

1)2.824 cents... in the range of schisma

13) 36.706 cents... in the range of small-diesis

25) 70.588 cents... in the range of small-semitone

37)104.471 cents ... in the range of large-semitone
(http://tonalsoft.com/enc/c/images/commas.gif)

You see that we have a range for grads in a system and a range for
source intervals of it. I think that we can consider , according to the
sizes of fifths in for example

425-edo system , source intervals of grads and fifths from schisma to
semitone. In 85-edo as subset of 425-edo we have positive fifth as 50)
705.882 cents and 1/12 of it is 5)70.588 cents.

So we can find the origin of positive fifth of a scale based on an
edo-system , may be schisma , comma ,.......,or semitone.

And also for negative fifth :

In 425-edo we have negative fifths such as 247) 697.412 cents. The
negative grad is 700-697.412=2.588 cent and we have :

2.588*12=31.0588 which is 11)31.059 cents of 425-edo.

So we can have positive grad as 700+(x/12) for positive fifths and
negative grad as 700-(x/12) for negative fifth in which x is degrees of
system due to fifths of system.

And as in ((http://tonalsoft.com/enc/n/negative-system.aspx)) :

If v is the size of the fifth, and a is the size of the octave, then p
= 12v - 7a :

In 425-edo with positive fifth of 249)703.059 cents we have :
p=12*249-7*425=13

And with negative fifth of 247) 697.412 cents we have :
p=12*247-7*425= -11

For edos with fifth of 700 cent we have p=0. It is interesting that in
144-edo the interval of 100 cent produce three different fifths so ,it
acts as positive , edo and negative systems:

83) 691.667 cents

84) 700.000 cents

85)708.333 cents

Shaahin Mohaajeri

Tombak Player & Researcher , Composer

www.geocities.com/acousticsoftombak

My tombak musics : www.rhythmweb.com/gdg

My articles in ''Harmonytalk'':

www.harmonytalk.com/archives/000296.html
<http://www.harmonytalk.com/archives/000296.html>

www.harmonytalk.com/archives/000288.html
<http://www.harmonytalk.com/archives/000288.html>

My article in DrumDojo:

www.drumdojo.com/world/persia/tonbak_acoustics.htm
<http://www.drumdojo.com/world/persia/tonbak_acoustics.htm>

________________________________

From: tuning@yahoogroups.com [mailto:tuning@yahoogroups.com] On Behalf
Of Gene Ward Smith
Sent: Monday, January 09, 2006 12:51 AM
To: tuning@yahoogroups.com
Subject: [tuning] Re: question about schisma in edo

--- In tuning@yahoogroups.com, "Mohajeri Shahin" <shahinm@k...> wrote:

> in 574-edo we have for example fifth as 702.439 and (2.439*12=29.268)
as
> comma which is 14-degree of system.

Is the idea to have a definition for "comma" which could be used in a
general notation scheme?

> Questions :
>
> 1-Is it correct to have comma in edos?

If you have a use for them, sure.

> 2- is it correct to say that edos such as 480 show schisma such as 2.5
> cent , although shisma must be rational
> (http://tonalsoft.com/enc/s/schisma.aspx)

I'd rather say that 480 *maps* the schisma 32805/32768 to 7.5 cents.
Where does 2.5 cents come from?

> 3- if so can we have <http://tonalsoft.com/default.aspx> Schismic
> Temperaments in higher cardinality edo systems?

Absolutely. An excellent schismic temperament is 289-et. 171-et is not
only a very good schismic temperament, it works extremely well in the
7-limit also.

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🔗wallyesterpaulrus <wallyesterpaulrus@yahoo.com>

🔗Yahya Abdal-Aziz <yahya@melbpc.org.au>

On Tue, 10 Jan 2006, "Mohajeri Shahin" wrote:
>
> dear ozan
>
> right ! here is a list for number of fifths (between 690 to 720 cent)
> in different edos :
>
> 5 to 39 .....most edos have 1 degrees as fifth
> 40 to 79 .... most edos have 2(except for example 56edo,....)
> 80 to 119 ...... most edos have 3
> 120 to 159 .... most edos have 4
>
> And so on.
>
> So the intervals generating kinds of fifth are from 0 to 240 cent as
> 0/12 to 240/12.
>
> Shaahin Mohaajeri

Shaahin,

Pardon me for butting in! If you are just counting
the intervals that lie in a particular m-cent range
(eg your fifths lie between 690 and 720 cents,
therefore they lie in a 30-cent range), you have
only to relate the size of the range (m cents) to
the n-EDO step size (1200/n cents). Any m-cent
range that contains the perfect fifth 702 cents
also contains exactly [m/(1200/n)] = [m*n/1200]
steps of n-EDO, where [x] is the integer part of x.

In this example, four different steps intersect
with the given range. For a fixed step size (fixed
n-EDO), all that matters is the size of the range,
except for one detail.

Here the range now intersects one more than
the number of steps given by the formula:
N = [m*n/1200]

In this case, m is just a little larger than a whole
number of steps. You might decide:
a) to include all those steps partly covered;
b) to include only those steps at least half covered;
c) to include only those steps completely covered;
by the range. Depending on your choice, you would
have to adjust the formula up or down by one.

In the example, choice a) leads to 5; b) leads to
3 or 4 depending on just where the range falls
(NOT a good choice for getting a unique answer!);
and c) leads to 3. I think you've chosen a); a good
reason to do this is because you want to ensure
that any EDO, no matter how small, has at least
one tone that approximates your given interval
(in the case you were discussing, a fifth).

So your formula becomes N = [(m*n-1)/1200] + 1.
(The correction -1 ensures that you don't add the
extra one unless m*n is at least a little bit bigger
than an exact multiple of 1200. You could make
it 0.01 instead if you want to be more precise.)

It follows from this formula that the bigger your
range, or the bigger the number of divisions of the
octave, the more matches you will find for a given
target interval. And the formula is almost linear
in n, as you have noticed - adding one more match
for every increase of 40 in the EDO size. It's
also almost linear in the range m. If, instead of
a range 690 to 720 cents for your fifth, you had
stipulated 695 to 710 cents, m would have been
15 cents, only half as much, and the number of
matches would have been (almost) halved.

Regards,
Yahya

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🔗wallyesterpaulrus <wallyesterpaulrus@yahoo.com>

🔗Yahya Abdal-Aziz <yahya@melbpc.org.au>

🔗Mohajeri Shahin <shahinm@kayson-ir.com>

Dear yahya

Many Thanks but have a look at actual number of fifth in the range of
690-710 in 120-140 edo without considering very near intervals to
690(like 988 and so on) with your formula : I think there must be
another logic:

.............actual.....................................................
....your formula

Edo............................fifth...............................edo..
.........................fifth

120 .............. 3 ********** 120
.............. 3

121 .............. 2 ********** 121
.............. 3

122 .............. 2 ********** 122
.............. 3

123 .............. 2 ********** 123
.............. 3

124 .............. 2 ********** 124
.............. 3

125 .............. 2 ********** 125
.............. 3

126 .............. 2 ********** 126
.............. 3

127 .............. 2 ********** 127
.............. 3

128 .............. 2 ********** 128
.............. 3

129 .............. 2 ********** 129
.............. 3

130 .............. 3 ********** 130
.............. 3

131 .............. 2 ********** 131
.............. 3

132 .............. 3 ********** 132
.............. 3

133 .............. 2 ********** 133
.............. 3

134 .............. 2 ********** 134
.............. 3

135 .............. 2 ********** 135
.............. 3

136 .............. 2 ********** 136
.............. 3

137 .............. 3 ********** 137
.............. 3

138 .............. 2 ********** 138
.............. 3

139 .............. 3 ********** 139
.............. 3

140 .............. 2 ********** 140
.............. 3

Shaahin Mohaajeri

Tombak Player & Researcher , Composer

www.geocities.com/acousticsoftombak

My tombak musics : www.rhythmweb.com/gdg

My articles in ''Harmonytalk'':

www.harmonytalk.com/archives/000296.html
<http://www.harmonytalk.com/archives/000296.html>

www.harmonytalk.com/archives/000288.html
<http://www.harmonytalk.com/archives/000288.html>

My article in DrumDojo:

www.drumdojo.com/world/persia/tonbak_acoustics.htm
<http://www.drumdojo.com/world/persia/tonbak_acoustics.htm>

________________________________

From: tuning@yahoogroups.com [mailto:tuning@yahoogroups.com] On Behalf
Of Yahya Abdal-Aziz
Sent: Thursday, January 12, 2006 5:38 PM
To: tuning@yahoogroups.com
Subject: [tuning] Re: question about schisma in edo

Shaahin,

In this example, four different steps intersect
with the given range. For a fixed step size (fixed
n-EDO), all that matters is the size of the range,
except for one detail.

Here the range now intersects one more than
the number of steps given by the formula:
N = [m*n/1200]

Regards,
Yahya

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🔗wallyesterpaulrus <wallyesterpaulrus@yahoo.com>

🔗Yahya Abdal-Aziz <yahya@melbpc.org.au>

Hi all,

I've copied below (slightly edited) some
messages from this thread, including Shaahin
and Paul's replies to my original response to
Shaahin and Ozan's conversation.

My further comments follow Paul's reply.

Regards,
Yahya

________________________________

On Tue, 10 Jan 2006, Shahin Mohajeri wrote:

dear ozan

right ! here is a list for number of fifths (between 690 to 720 cent)
in different edos :

5 to 39 .....most edos have 1 degrees as fifth
40 to 79 .... most edos have 2(except for example 56edo,....)
80 to 119 ...... most edos have 3
120 to 159 .... most edos have 4

And so on.

So the intervals generating kinds of fifth are from 0 to 240 cent as
0/12 to 240/12.

________________________________

On Thu, January 12, Yahya Abdal-Aziz replied:

Shaahin,

In this example, four different steps intersect
with the given range. For a fixed step size (fixed
n-EDO), all that matters is the size of the range,
except for one detail.

Here the range now intersects one more than
the number of steps given by the formula:
N = [m*n/1200]

________________________________

On Mon, 16 Jan 2006 Shaahin Mohaajeri replied:

Many Thanks but have a look at actual number of fifth in the range of
690-710 in 120-140 edo without considering very near intervals to
690(like 988

[YA] presumably you meant 688?

and so on) with your formula : I think there must be
another logic:

.........actual..... . your formula
Edo ..... fifth . edo .........fifth
120 .............. 3 . 120 ................ 3
121 .............. 2 . 121.................. 3
122 .............. 2 . 122 ................ 3
123 .............. 2 . 123 ................ 3
124 .............. 2 . 124 ................ 3
125 .............. 2 . 125 ................ 3
126 .............. 2 . 126 ................ 3
127 .............. 2 . 127 ................ 3
128 .............. 2 . 128 ................ 3
129 .............. 2 . 129 ................ 3
130 .............. 3 . 130 ................ 3
131 .............. 2 . 131 .................. 3
132 .............. 3 . 132 ................ 3
133 .............. 2 . 133................. 3
134 .............. 2 . 134 ................ 3
135 .............. 2 . 135 ................ 3
136 .............. 2 . 136 ................ 3
137 .............. 3 . 137 ................ 3
138 .............. 2 . 138 ................ 3
139 .............. 3 . 139 ................ 3
140 .............. 2 . 140 ................ 3

________________________________

And on Fri, 20 Jan 2006, Paul Erlich replied:

> > > It follows from this formula that the bigger your
> > > range, or the bigger the number of divisions of the
> > > octave, the more matches you will find for a given
> > > target interval.
> >
> > Hmm . . . as far as I can see, if I use a fairly wide but
> > reasonable range, 35-equal has two matches to the
> > perfect fifth, while 36-equal has only one match. So
> > something you're saying isn't quite right . . .
>
> "a fairly wide but reasonable range"?
> Please be more specific!

How about the just fifth plus or minus 20 cents? Or really liberal,
the just fifth plus or minus 30 cents? Either way, what I'm saying
above holds true.

________________________________

Thank you both for your corrections.

I've just created an Excel spreadsheet which
highlights the number of steps of any EDO,
from 1-EDO to 150-EDO, that lie within a
given tolerance of a target interval, both
specified by the user in cents. I intend to post
this file to tuning_files2 shortly.

When you open it, it is centred on 130-EDO,
with a tolerance of 10 cents and a target of
701.955 cents. Reading horizontally for any
EDO in this view, we see that there are either
two or three intervals (coloured green) in the
range between target-tolerance and
target+tolerance. This result is very much like
Shaahin's, except that his range was centred
on a target interval of 700 cents.

My mistake was in thinking that I _could_
"slide the range". But of course, when we are
targetting a specific interval, "near enough" is
not "good enough".

For all practical purposes, this spreadsheet
serves better than a formula. Even though it
is not as compact as the formula I proposed, it
has the undoubted merit of giving the correct
result.

Regards,
Yahya

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question about schisma in edo

🔗Mohajeri Shahin <shahinm@kayson-ir.com>

🔗Gene Ward Smith <gwsmith@svpal.org>

🔗Mohajeri Shahin <shahinm@kayson-ir.com>

🔗Ozan Yarman <ozanyarman@ozanyarman.com>

🔗Mohajeri Shahin <shahinm@kayson-ir.com>

🔗wallyesterpaulrus <wallyesterpaulrus@yahoo.com>

🔗Yahya Abdal-Aziz <yahya@melbpc.org.au>

🔗wallyesterpaulrus <wallyesterpaulrus@yahoo.com>

🔗Yahya Abdal-Aziz <yahya@melbpc.org.au>

🔗Mohajeri Shahin <shahinm@kayson-ir.com>

🔗wallyesterpaulrus <wallyesterpaulrus@yahoo.com>

🔗Yahya Abdal-Aziz <yahya@melbpc.org.au>