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Ramsay - PLATE XXVII - The Mathematical Scale of Thirty two notes in Commas, Sharps and Flats

PLATE XXVII



page 151


PLATE XXVII.


This plate, in the outer stave, has the 32 notes which arise with mathematical development of twelve scales in advancing fifths. The notes are marked with sharps, flats, and commas. The flats and commas of lowering are placed on the left of the notes, in the order in which they arise, reading them from the note downward; the sharps and commas of rising on the right, also reading from the note upward. The whole of these 32 notes are brought within the compass of an octave. [Scientific Basis and Build of Music, page 119]

The inner stave contains the chromatic scale of twelve notes as played on keyed instruments. The flat and sharp phase of the intermediate notes are both given to indicate their relation to each other; the sharpened note being always the higher one, although seemingly on the stave the lower one. The two notes are the apotome minor apart overlapping each other by so much; ?D is the apotome lower than C#; ?E the apotome lower than D#; F# the apotome higher than ?G; G# the apotome higher than ?A; and A# the apotome higher than ?B. The figures for the chromatic scale are only given for the notes and their sharps; but in the mathematical series of notes the numbers are all given. [Scientific Basis and Build of Music, page 120]

See Also


chromatic scale
chromatic
flat
Law of Mathematical Ratios
mathematical intonation
Mathematical Relations are Constant - page 125
mathematical scales
mathematical system
On the Partial Differential Equations of Mathematical Physics
Ramsay - PLATE VIII - The Mathematical Table of Majors and Minors and their Ratio Numbers
Ramsay - PLATE XXII - Mathematical Table of the Twelve Major Scales and their relative Minors
Ramsay - PLATE XXIII - The Mathematical and Tempered Scales
Ramsay - PLATE XXVII - The Mathematical Scale of Thirty two notes in Commas, Sharps and Flats
scale of mathematical intonation
semitone
semitonic progression
sharp
tempered key
tempered scale
tempered system
three mathematical primes

Created by Dale Pond. Last Modification: Wednesday January 6, 2021 03:14:48 MST by Dale Pond.