Scale I and Scale II

Dear fellows,

In Scale I, ratios 19/16 and 57/32 are Eb and Bb tone frequencies and the relation 2/Bb = (64/57) gives D frequency. The quotient between contiguous Eb/D produces the "m" interval factor (m = 1083/1024) while "p" resulted from the quotient D/(1083/1024), Both factors work alternatively and determine the scale tones. So C# is the product of C = 1 by "a" interval factor, D frequency equals the product of C# frequency and "b" interval factor; next "a" applied on D frequency to get Eb and so forth.

The table given below contains the main information of both scales. Scale I was evaluated, its exceptional chords listened on the piano are supposed to be similar to those of Scale II since their tone frequencies are about the same, some of them differ only 0.5 cents. Both new scales clearly differ from 12 Tet.

* Major thirds.

* * Fifths

I----------------------------SCALE II------------------------I...I-----------SCALE I --------------I

------------------------------------CENTS ..(*)..(* *).......HZ .....................CENTS..(*)..(* *)....HZ

C = 1 ..............-3 .....(401).(702)..261.2133 ...... -2.5...(401).(702)..261.25

(13447/12718) = "m" ..........................( 1083 / 1024 ) = "r"

C# = (13447/12718) ...94.....(401).(702)..276.1862 ..... 94.5..(401).(702)...276.3025

(20340/19151) = "p" .........................(65536 / 61731) = "s"

D = (2000 / 1781) .....198...(401).(702)..293.3333 ......198..(399.5).(702)..293.3333

(13447/12718) = m.............................. ( 1083 / 1024 ) = "r"

Eb = (1781 / 1500) ......294.5..(401)..(702)..310.1473 ......295....(404.4)..(702)..310.2344

1.0620855300 = p.................................(65536 / 61731) = "s"

E = (50872/40341) .......399...(401)..(702)..329.4030 .....398.6..(398)....(702).329.3567

(13447/12718) = m..............................( 1083 / 1024 ) = "r"

F = (4/3) ..........495...(401)...(702)..348.2844 ......495.6.(404.4)...(702).348.3333

q = (9/8)^(1/2).....................................q = (9/8)^(1/2)

F# = (2^0.5) ........597...(401)...(702)..369.4114 ......597.5..(402).....(697)...369.4633

q = (9/8)^(1/2)..................................... q = (9/8)^(1/2)

G = (3/2) ..........699...(401)..(702)...391.82 ..........699.5...(401)..(698.5)..391.875

(13447/12718) = m..................................( 1083 / 1024 ) = "r"

Ab =(40341/25436) .....796...(401)..(702)...414.2793 ........796.5..(401)...(698.5)..414.4537

1.0620855300 = p.....................................(65536 / 61731) = "s"

A = (3000 / 1781) ....900...(401)..(702)..440 ..............900..(394.5)...(699)..440

(13447/12718) = m...................................( 1083 / 1024 ) = "r"

Bb = (1781/ 1000) .....997...(401)..(702)..465.2209 ........997....(401)..(699)...465.3516

1.0620855300 = p.....................................(65536 / 61731) = "s"

B = (25436/13447) ....1099....(401)..(702)...494.1044 ........1100.5..(394.5)...(697)..494.0351

(13447/12718) = m..................................... ( 1083 / 1024 ) = "r"

2C=.2...........1197...(401)..(702)....522.4267 Hz ....1197.5...(401)...(702)...522.5

Thanks

Mario