Just try to get the general picture. When you double the number of vibrations per second, you get the same note one octave higher. You already know what an octave is. Think about it for a minute. Sing a note. Now sing it an octave higher. Western music has divided this interval the octave by twelve. The other side of this argument is that the overtone series is a naturally occurring phenomenon and it clearly defines a set of intervals which, taken to their logical mathematical conclusion, give us a scale which divides the octave by twelve and, therefore, twelve is the ideal and correct number to divide an octave by that is my position.
Trust me on this. Twelve is actually a fantastic number to base a system on. If we had evolved with twelve fingers instead of ten, we would almost certainly have developed our mathematical system based on it. The beauty of twelve is that it can be evenly divided by two, three, four, and six. Ten can only be evenly divided by two and five. Divide it by 3 and you get an augmented chord.Prolog and natural-language analysis">
Tech Stuff - Frequency Ranges
Divide it by four and you get a diminished 7th chord. They could have picked You have to pick somewhere to start. Double the number of vibrations per second and you get the same note one octave higher. These 12 divisions are called notes and they can each be designated as the key to any piece of western music. They are:. I could have. You can start anywhere you want. You should also be able to see why there is no E F flat or B C flat. All that was an attempt to show you that you have twelve choices when picking a key. An octave is divided by twelve.
Twelve is plenty. Everyone has a vocal range which we can define as the distance between the lowest note they can sing and the highest. You can easily determine yours. Do it now.
Sing the lowest note you can sing 2. Now sing that same note up one octave 3. Repeat number 2 4. Repeat number 3. A pretty standard vocal range is about an octave and a half to two octaves. A few of you will have a greater range. This is only an advantage if you are attempting to sing a song with a very wide range. Most songs have a range of between one and two octaves. Many of you will also notice that a certain point, you changed the way that you were singing in order to go higher.
You had to apply more energy and you engaged your vocal muscles in a different way. The tambour of your voice changed. The higher notes in a song generally convey more emotion and intensity.
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The same is true for a voice. When picking a key for a given song, two of the things you might want to consider are:. Is the song relaxed and easy going use your lower register or is it more emotional and intense consider using the higher part of your register? One of the ideas many novice singers have is that there is a specific key which is the best one for them regardless of which song they are trying to sing.
The reason why this misunderstanding persists is that there is some very small amount of truth to it. This idea should be abandoned. It is, however, a good place to start — particularly if you are a male with a relatively average vocal range. If you are a female with a relatively average vocal range, you might want to start with a wild guess that a reasonable key for you to try might be about half an octave above standard key.
The musicians who are accompanying you will be most comfortable with it and are more likely to be able to give you their best performance. Interestingly enough, they are also, on some levels, less likely to be especially creative with it. When you have played a song more or less the same way hundreds of times, it is hard to keep from repeating yourself.
There are great musicians out there — all with different skill sets and talents.
- Enharmonic Keys and Scales.
- Choosing A Key | Bob Smith Musical Services!
Not all of them are equally proficient in all keys. In fact, few of them are Bob Smith is an exception to this generalization. Some keys are easier for the rest of us mortals than others. This varies a little depending on the instrument. Rock guitar players like E, A, D, and G. Horn players like F, B flat, and E flat. Piano players often like C, F, and G.
Tech Stuff - Frequency Ranges
There are a few keys that are not used often generally the ones that have the most of those pesky black notes with two names each and because they are not often used, many musicians are less familiar and less comfortable in them. Different instruments playing the same note also play the same overtones, but emphasize or de-emphasize them differently; some overtones are stronger in a violin than in a flute, for example. It is by putting in carefully engineered overtones that a synthesizer imitates instruments. I have put apostrophes to indicate higher octaves. C' is the C above middle-C, and so on.
The notes in brackets are not part of our musical scales at all, so the note [Bb] is only very approximately our B Flat. If you select the overtones that are multiples of 3, you get the overtone series for the note G. If you take the overtones that are multiples of 5, you get the overtone series for the note E, and so on. What we have here is a sort of fractal, a kind of self-similarity. Fractals are mathematical diagrams or objects that contain, within themselves, scale models of themselves.
Examples are Heighway's Dragon and Sierpinski's Gasket.
Why not tune pianos and harpsichords in such a way that the ratio of a note to the next note on the keyboard was exactly the same for every pair of neighbors? The pitches would be different, but the ratio of one pitch to the next would be fixed. What did this ratio have to be? Let's call it s, for semitone ratio. One thing that nobody would give up, of course, was that the ratio of a note to its octave had to be 2. This is the origin of the famous "equal-tempered scale.
Bach called the Well-Tempered Scale, which he celebrated by writing 48 preludes and 48 fugues, four for each note of the scale, two in the major key, two in the minor which you music maniacs will understand, I'm sure. On the other hand, there were improved-Just-Intonation scales that were called Well-Tempered Scales also, and to go into this question will get me in trouble with music experts.
The idea of affine transformation is present in fugues. A fugue pronounced "fyoog" is a piece of music with several "voices. In fact, the fugue usually simply drips with the subject. Suppose we consider the fugue to be a plane. This is easy when you think of music written on paper. Time goes from left to right, and the notes go from high to low, top to bottom.
Then most of the occurrences of the subject will be just time-translations: left-to-right. Sometimes the fugues are moved to different pitches, often at the octave, sometimes at other intervals; so that's a frequency-translation up-down. Then, sometimes, the subject is stretched out, doubled in length. This is a scaling composed with a translation. In extreme cases, the subject is turned upside-down, called inversion, and occasionally reversed, back-to-front, called retrograde motion.
The first three bars of a Bach fugue can be found at: I have colored three portions of it. The portion in purple is the subject. Even if you don't know music notation, you can sort of imagine the melody from the rise and fall of the notes. The portion colored blue is the same melody, but inverted.
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