My first encounter with ear training

I have not studied music professionally, so one area that baffled me revolved around the key of a song. I would come across sheet-music of the same song writtin in different keys, and wonder why this was so. I would play a song in the key that it was written, and it did not sound like the record. I would be taught a song in a different key than it was written, but it sounded like the record. I learned the concept of changing keys, but to what key do I change it to? That was a question I could only guess the answer to. Whatever key I could sing along with was fine with me. And of course the best songs are the ones that don't need any change in key.
My first encounter with "Ear Training" came about when I went in to Boston Music Company to buy some sheet-music. While there, I saw a book by Mel Bay which brought back some old memories. I started out learnng guitar with Mel Bay books, many years before. This book, "Mel Bay's Guitar Workbook. Learning Guitar Fingerboard Theory, Mel Bay Productions, Robert Andrew Phelps, 1990" was a workbook for learning the entire fingerboard. I tend to go no higher than the 5th fret, so I bought this book also. Once I began reading it, he went into theories of ear-training which was all new to me. He explains that the concept is very abstract, that it seems like a lot of information being presented at once in the beginning but then it all falls into place eventually. I asked my brother if he was familiar with ear training. He's been playing guitar for over 40 years. But he didn't know what I was talkng about. I asked my nephew who had only been playing for about five years or so, but who had been taking lessons recently (maybe they teach it these days??), but no, he had no idea what I was talking about. So I was on my own, which was another reason I decided to write these pages.
The idea behind the ear-training, hearing two notes and being able to name them, seemed impossible. I tried to hear two notes, C-D, and at first in my mind, they could have been any two consecutive notes on the scale, but after a while I began to hear C-D. Still I could only hear it on my guitar, not in any song. I also had trouble hearing it on a higher octave. Still I thought that if I could learn the C scale I'd know when I was hearing something that wasn't the C scale. At least I hoped I would, considering that all songs use the same 12 notes but in a different way, a different tone. It was like learning the alphabet all over again. And then using that alphabet to write different words. But we're using music scales to write different songs. Some people compare it to different "colors". But I can't wrap my mind around the key of red or the key of green. And the blues can be written in many keys.
I'd like to begin with the basics that I learned from this book, which the author claims is a "mental vision" that gives the student access to the fingerboard in higher positions. I got sidetracked however. I lost site of the fingerboard and began to concentrate more on the scales, began to concentrate more on chord arrangements as they relate to intervals, and on music signatures and how they relate to the keys. But these things could be part of those things that are hitting me all at once.
First things first. So first I will give a synopsis of the intervals as written by Phelps, for the beginner. After a series of exercises that involve writing out scales in different positions and playing them, he introduces ear training theory. The building blocks of ear training are called Intervals. An Interval is the distance between two notes. They are measured by number and quality, with the number being where the note appears in a natural scale of 8 notes as in C to C, and the quality being whether that note is sharp or flat or natural. He begins with the C scale since all the notes are natural. In the ascending order C-D-E-F-G-A-B-C are equal to numbers 1-8, but the numbers also have a quality that is equal throughout all scales. 1-4-5-8 are called Perfect (P) and 2-3-6-7 are called Major (M). Taking the C scale at two notes at a time you get: C-C (low C played twice)=P1. C-D=M2. C-E=M3. C-F=P4. C-G=P5. C-A=M6. C-B=M7. C-C=P8. Descending intervals are called Inversions. In the descending order C-B-A-G-F-E-D-C, 1-4-5-8 remain Perfect (P) and 2-3-6-7 become minor (m). There is a formula for Inversions derived from the original numbers. If those numbers are subtracted from 9 you will obtain the inversion of the ascending interval. For example: C-D=M2. 9-2=7 The inversion C-D descending=m7. It always happens that a P=P and M=m. However note that C-F=P4 9-4=5. C-F descending=P5.

I took this information and tried to put it all out in a table where I could get a better look at the intervals in each key. This table is based on key signatures. It begins with the key of C which has no sharps or flats and then goes to the key of G which has 1 sharp, then to D which has 2 sharps and so on. It can be found in section 4 on the side bar.
The next thing to be aware of in Chromatic ear training are sharps and flats. When an interval is enlarged or reduced by 1/2 step it is either Augmented (A) or diminished (d). In the Inversion formula an A becomes d. I am still confused on this point because the examples he uses in his book utilizes A and d when dealing with sharps and M and m when dealing with flats (to avoid confusion--since a C# and Db, for example, are the same pitch). What confuses me however is how to distinguish between a naturally occurring sharp and flat as dictated by the key signature, and an accidental sharp and flat as indicated by the song-writer. I have written my table for the sake of moving forward using A and d when it is an interval that is deviating from the key signature in a # or b direction. For example the key of Eb to Ab (notes) are the same signature so I called it a P4. But the key of F to Bb I called a d4 since the second note was flat and the first note natural. I am looking at the intervals at this point from the mind set that I don't know what key I'm in. If I heard those two notes being played, and if I wanted a perfect pitch interval I would call it a diminished interval. I have also repeated the table using compound intervals which cover the notes higher than one octave. These are useful in building chords, but I am concentrating more on simple intervals on these pages. The compound interval table can be found in Section 5 in the side bar.
Perhaps in the end it is all relative, that all do-re-mi intervals are perfect pitch whether sharped or flatted and only accidentals are A or d. But these are questions I hope to have answered along the way and refuse to be stopped by some setback that is only an abstraction. I know for sure it is a 4. And if the author can juggle his m and M's I guess I can juggle my A and d's. This will prove to have no validity in building chords but as far as dealing with two single notes, it is enough to know the number and whether one or both notes are sharped or flat or natural.

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