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The mesures of the tones (a theorical study)
Ok... let's work a bit for those who wish to learn the nature of the musical pure tones. The chart I give here has been taken from my works for my opera... so it's not a 'ready thing' to explain... but it will help more than just writing text.
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Briefly... you got two axes starting from a D.
The horizxontal axis shows the cycle of fifths... the position of the cycle has been choosen to work well with the open strings of a string section... you got C, G, D, A, E all in the same chart line.
The vertical axis shows an already more complexe cycle of pure major thirds. Like in Db, F, A, C#, E#.
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For each note appears in descending order : the frequency ratio, the note name and the cent value.
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There a multitude of grids and information to retreive from that chart for I postulate that probably all music (played with intervals) can be understood through that chart... but let me do my post-doctorate on the subhect before going further ! eheh The information shown in that chart is the symetry of twelve pure tones at the distance of one comma (G#(569), G#(590), Ab(610) and Ab(631)). Then again, it's only one information that is read here !
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So the first step here, is to memorize the cent values of all the most centered ratios from D#(25/24 - 71c) to around Eb(27/25 - 133c). Memorizing is helpful for any transpositions... even though I'll teach you some tricks eventually ! eheh
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Second thing to analyse is drawing the shape of the chords (like a major chords D-F#-A making a L for example). You will see that everywhere you draw the same figure, you'll get a major chord... it's a the for anychords... even jazz chords that can be seen as pure as they can be. You'll be able to analyse the uniqueness of the dominant 7 chords with that chart... etc.
Have fun !
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God only brings wars... might music entertains us from it !!
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