I'm currently reading Henry Cowell's New Musical Resources and On page 98, Section 6,(TEMPO) in part 2 (RHYTHM), is a paragraph of for instances. Directly, I'm grappling with the SECOND FOR INSTANCE ...
"By the correct application of a change of tempo, a change of the rhythmic key of time or metre can be made.
For instance, if a quarter-note at M. M. 96 equals (C), it is evident that if the tempo is changed to M. M. 72, the quarter note will be of different value, namely the equivalent of (G). In this way the key tone of the whole time or metric system can be changed at will, and many simplifications of practice can be made. if, FOR INSTANCE, the rhythmic chord of C (in the the ratio of 4:5:6) has been struck, and it is desired to strike the chord of (F), this can be done in the key of (C) only by the use of three-sixteenths notes against three twentieths notes against eighth notes. If, however the tempo be changed from M. M. 96 to M. M. 64, the chord of (F) can be expressed by quarter notes, since by means of the change of tempo the key will have been changed to that of (F) "
I understand the striking of the Rhythmic (C) Chord and it's ratio (5:6:4) and my grasp of the Whole note Series (3/16 . 3/20 . 2/8) concept is fairly solid. the bit I'm slightly confused by is the striking of the Rhythmic (F) chord in the Rhythmic key of (C).
How is it that the Ratio for the (F)Chord (3:5:2) .. and, I'm assuming this Ratio after a good stare at the Scale Rhythm Chart on Page 99. [C:C-1:1 . C:C#-14:15/(C:Db-15:16) . C:D-8:9 . C:Eb-5:6 . C:E-4:5 . C:F-3:4 . C:Gb-5:7 . C:G-2:3 . C:Ab-5:8 . C:A-3:5 . C:Bb-8:15 . C:C-1:2], . .arrived at using the Overtone Ratios and or the Simple Overtone Ratios?
Also .. in the ratio relationship of (3:5) why , again [according to the chart on p.99], is the (C) given as the (3rd)partial and the (A) as a (5th)partial in regard to the Overtone Series?
The Changing of the Tempo from MM96 to MM64 with the Key change to (F), again out of confusion I'm guessing the Tempos are related by 16 as a base? and the Rhythmic Chord of (F) expressed by quarter-notes, against fifth-notes, against sixth-notes(4:5:6) in the rhythmic key of (F) is now the Tonic key conducted by the tempo MM64?
This Post is mostly Directed at Pat Muchmore, but I will be super grateful to anyone willing to help.