FW: [tuning] Re: about range of 12 degrees in EDOs

Ok….dear keenan

I understood!!!!!

150 18

158.3333 19

166.6667 20

But as ± 8.33333333 relates to 144EDO ,155 cent lies between 18 & 19 degrees of 144-EDO and must be n2 . ok?

________________________________

From: Mohajeri Shahin
Sent: Wednesday, August 25, 2004 2:31 PM
To: 'tuning@yahoogroups.com'
Subject: RE: [tuning] Re: about range of 12 degrees in EDOs

Dear keenan

Thanks a lot for your sheet of calculating ratios. It is very useful for me ….

I'm working on intervals and scales in Iranian traditional and folklore music so need to standards for naming intervals.i know that there are different theories but want to know which is useful and practical.

The structure of one you told me to look is systematically good but what about for example 155 cent in :

….

Cent intvl.name note from C ratio

150 N2 Dv 11:12

167 WN2 Dt 10:1

….

Is it n2 or wn2?

________________________________

From: Dave Keenan [mailto:d.keenan@bigpond.net.au]
Sent: Wednesday, August 25, 2004 11:34 AM
To: tuning@yahoogroups.com
Subject: [tuning] Re: about range of 12 degrees in EDOs

--- In tuning@yahoogroups.com, "Mohajeri Shahin" <shahinm@k...>
wrote:
> Hi all
>
> I have a question :
>
> Can anyone help me to know the ranges of degrees like 'major
2nd''minor
> tone' & etc in cent or ratio,
>
> Or the range of any interval in the scale ... has it any role?
What is
> the maximum and minimum value of each degree?

Dear Mahajeri,

These ranges are definitely somewhat fuzzy, but this
http://dkeenan.com/Music/Miracle/MiracleIntervalNam
ing.txt
can be read as suggesting that the ranges can be taken as
approximately +-8.3 cents from the cents given by their nearest
approximations in 72-tone equal temperament. This suits some
purposes but not others. Perhaps if we knew what use you wish to
make of such ranges, we could help you better.

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--- In tuning@yahoogroups.com, "Mohajeri Shahin" <shahinm@k...>
wrote:
> Ok….dear keenan
>
> I understood!!!!!
>
> 150 18
>
> 158.3333 19
>
> 166.6667 20
>
>
>
> But as ± 8.33333333 relates to 144EDO ,155 cent lies between 18 &
19 degrees of 144-EDO and must be n2 . ok?
>

Yes. You got it!

Or putting it another way, 155 cents is closer to 150 than it is to
167.

Instead of using the degrees of 72-EDO, we could use the actual
cents corresponding to the ratios. Using the formula

cents = 1200 * log(large_part_of_ratio/small_part_of_ratio) / log(2)

To one decimal place
11:12 is 150.6 cents (neutral second)
10:11 is 165.0 cents (wide neutral second)

155 cents is closer to 150.6 than it is to 165.0, so we get the same
result, that it is a neutral second.

Consider if you had been asking instead about a 170 cent interval.
This falls clearly in the category of "wide neutral second", however
if your scale (or the set of scales you are considering) did not
have any intervals that fall in the (plain) "neutral second"
category, then you might choose to drop the term "wide" and simply
refer to the 170 cent interval as a "neutral second".

This sort of flexibility is what allows this system to remain
consistent with the common usage in 12-EDO, where for instance 400
cents is simply called a major third.