Common fractions and MJ commas

Recently I realized that when M and J progression commas are used as factors or dividers and applied to the apropriate common fraction like those shown below, we get good scales directly. For instance if 135/128 is multiplied by the product MMMJ we get C#.

(135/128)*MMMJ = Cents 99.997 1.05946152764 ----C#

---------------(9/8)/J =

201.952

1.12372864590

----D
Interval 101.955 1.06066017178
(32/27)*MMMMJ = Cents 303.907 1.19189421859 ----Eb
100.001 1.05946387772
--------(81/64)/MJ = 403.909 1.26276887067 ----E
100.001 1.05946387772
--------(4/3)*MMJ =. 503.910 1.33785800439 ----F
100.001 1.05946387772
((729/512)/MMMJ) = 603.911 1.41741222917 ----F#
100.001 1.05946387772
---------------(3/2)*J = 703.913 1.50169705665 ----G
99.997 1.05946152763
---(8/5)/(MMJJM) = 803.910 1.59099025767 ----Ab
100.001 1.05946387772
--------(27/16)/ M) = 903.911 1.68559670781 ----A
101.955 1.06066017178
----(16/9)*(MMJJ) = 1005.866 1.78784529366 ----Bb
101.955 1.06066017178
-------(243/128)/M = 1107.821 1.89629629628 ----B
Interval 100.001 1.05946387772
----------2*(MMJJ) = Cents 1207.823 2.00905742741 Toctave

(MMJJMM) = 1.00679852243
(MMJJM) = 1.00566297768
(MMJJ) = 1.00452871371
(MMMJ) = 1.00452648545
(MMJ) = 1.00339350328
(MJ) = 1.00226179898
(MM) = 1.00225957576
M = 1.00112915039
J = 1.00113137110

Mario

September, 02