rational result from ED :Re: [tuning-math] 24-edo 36-EDO , 48-edo FROM CHAINs OF tritone , PYTHAGOREAN THIRD and .....

Hi all

Reference to my previous mails and considering definition of "schisma" by Philolaus <http://tonalsoft.com/enc/s/schisma.aspx> as (Pythagorean comma)^(1/2) , we can have (2*(531441/524288))^(1/2)=729/512 or Pythagorean tritone.

So, each degree of 12-ED(729/512) is equal to ((2*(531441/524288))^(1/2))^(1/12) or

by considering Grad <http://tonalsoft.com/enc/g/grad.aspx> as (Pythagorean comma)^(1/12)) we have (2^(1/24)*(grad)^(1/2))

we can see the importance of philolaus schisma .

now , in 3-ED(729/512) we have ratios :

1/1..........9/8:..........81/64:..........729/512

Which shows a rational result from equally dividing an interval.

By extending it to 2/1 we have 6-ED(1223.46)

0:..........1/1..........0.000 ..........unison, perfect prime:..........

1:..........9/8 ..........203.910 ..........major whole tone:.......... 200+2 grad

2:..........81/64..........407.820 ..........Pythagorean major third:.......... 400+4 grad

3:..........729/512.......... 611.730.......... Pythagorean tritone:.......... 600+6 grad(or 600+philolaus schisma)

4:..........6561/4096.......... 815.640..........Pythagorean augmented fifth:.......... 800+8 grad

5:..........59049/32768..........1019.550 ..........Pythagorean augmented sixth:.......... 1000+10 grad

6:..........531441/262144..........1223.460..........Pythagorean augmented seventh:.......... 1200+12 grad

Tempering it will result 6-EDO.

So it is another way to have 12, 24, 36,48-EDO.

Shaahin Mohajeri

Tombak Player & Researcher , Microtonal Composer

My web siteوب سايت شاهين مهاجري <http://240edo.tripod.com/>

My farsi page in Harmonytalkصفحه اختصاصي در هارموني تاك <http://www.harmonytalk.com/mohajeri>

Shaahin Mohajeri in Wikipedia شاهين مهاجري دردائره المعارف ويكي پديا <http://en.wikipedia.org/wiki/Shaahin_mohajeri> <http://www.harmonytalk.com/id/908>

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