Text: Subject: Re: [svpvril] Non-Physical Neutral Center Date: Sun, 13 Jan 2002 19:22:46 +0000 From: "Luigi Di Martino" Reply-To: svpvril@yahoogroups.com To: svpvril@yahoogroups.com Ok! Someone else has offered to help me get this together and I hope we begin working on it quite soon. In the mean time the following grid can help some people 'get it' straight away. This grid is to be taken as something to help understand the equal temperament system within music scales. What is a scale? It is a series of ratios. It has a starting point called a root note. We can call this position 1. For arguments sake we can call this first position the note C. This is a favorite place to start for most people because the Major scale starting on that note produces only the white notes on a piano. When the note C is found then the other notes of the C Major scale are found by using ratios. What is important at the moment is not the ratios themselves but the knowledge that when we double a number we produce the SAME note. So by doubling the number 1 we produce a C note one octave higher. This ratio is the 1:2 In the equal temperament system there are 12 notes that make up an Octave. Have you ever wondered what the black notes on a piano are for? They come in blocks of twos and threes. Finding one C note means we can easily find the other C notes on the piano, because they will be at the same relative position all the way up and down the piano. We need to find the first C. It lives just before the grouping of two black notes. The next C above that will again live just before the next clump of two black notes and so forth. This means we can succesfully count 12 steps between the two C notes. These are our twelve SEMITONES which go to make up an octave within the equal temperament scale. C Csharp/D flat The Csharp is a black note as well as the Db. They are represented by the same black note. It is one step forward from the note C. Another step forward brings us to the note D. So, we are using letters of the alphabet for all the white notes and adding the word 'sharp' or 'flat' to any of the black notes. Why? C Cs/Db D It all depends on context. Generally speaking if we are going up one step from C then that C has been sharpened (augmented). If we are taking a step down from the note D then the D has been flatted (diminished). This logic applies between all white and black notes. So here is the grid and the way to easily work out INVERSIONS. w b w b w w b w b w b w w C Cs/Db D Ds/Eb E F Fs/Gb G Gs/Ab A As/Bb B C this is how the piano is laid out with white (w) and black (b) notes. There are 12 different notes. Let's call the first move from C to Cs/Db 1/12 (which is the same as saying one semitone), then from C to D 2/12 etc. C C to Cs/Db = 1/12 = minor second = 16:15 C to D = 2/12 = Major 2nd = 9:8 etc C to Ds/Eb = 3/12 = minor 3rd C to E = 4/12 = Major 3rd C to F = 5/12 = 4th C to Fs/Gb = 6/12 = sharp (dim) 4th C to G = 7/12 = 5th C to Gs/Ab = 8/12 = minor 6th C to A = 9/12 = Major 6th C to As/Bb = 10/12 = minor 7th C to B = 11/12 = Major 7th C to C = 12/12 = Octave >From this grid any inversion can be worked out. So what is an Inversion? C to E, for example, is a Major 3rd (4/12). To invert this relationship we take the higher of the two notes and drop it below the first note so it reads E to C. This is not a Major 3rd but an INVERSION of it. With the above grid you can instantly know what the inversion of a Major 3rd is. All you do is add up the missing ?/12 in order to make 12/12. SO, a Major 3rd is 4/12. There is a difference of 8/12. Look at the grid and see what 8/12 is interval wise. It is a minor 6th. So the inversion of a Major 3rd is a Minor 6th. Notice that the interval numbers add up to 9 (3rd and 6th). This is true for all inversions, they always add up to 9. ALL INVERSIONS ADD UP TO 9 A MAJOR INTERVAL BECOMES A MINOR INTERVAL WHEN INVERTED. C to D = a Majopr 2nd (2/12). So we find the interval for 10/12 which is a minor 7th. So the inversion of a Major 2nd is a minor 7th and vice versa. So, E to C is as much a minor 6th in distance as C to Ab is. C d e f g Ab = minor 6th E f g a b C = minor 6th There are 6 letters in the count. Anybody care to guess what the inversion of the sharp (dim) 4th is?! If anyone can think of ways of further simplifying this it would be great for you to share your thoughts. You should remember that with a little practice most children and adults learn these sorts of things. It is only hard with no practice! in Keely's time this sort of theory was to be expected from all musicians.....and even the listeners who were well clued up on keys and modulations.

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