At first, music and mathematics may seem like completely different fields of study. Making music can be the epitome of human artistic expression, while mathematics represents the pinnacle of abstract logical thought. However, the internal logic of musical organization has many similarities to mathematics.
It is true that there is not always a clear connection between taking piano lessons in Pasadena and improving your math skills. Do not expect studying music with the Altadena Academy of Music in Pasadena to directly improve your ability to do algebra, for example! However, numerical relationships are embedded in all levels of musical structure and organization. While you can successfully learn to play the piano in Pasadena without studying musical structure in much detail, studying music theory is invaluable in understanding how music is constructed, which can help you approach new pieces, and to help you see how they relate to what you’ve already learned.
Almost any element of musical structure can be described numerically. For example, within each octave are twelve tones before pitches repeat. Most scales are made up of seven notes out of these twelve, each with a selection of notes that have a unique set of distances between the chosen notes. If you are studying piano in Pasadena, you will notice that you will need to cover these seven notes with five fingers while playing scales as well, so you will break things up into repeating patterns of three and four fingers, or two and five fingers, depending on which note you start on and how this works with the piano’s irregular grouping of white and black keys. Moreover, the distance between any two notes on a piano can be described numerically in a few ways. You can count the number of musical tones between notes either by counting all the piano keys in between, or you can count the number of notes in the current scale between the chosen notes. For example, between the first and fifth notes of any major scale is called a perfect fifth, and there are seven total notes possible between these notes. The more you analyze music, the more you will see such arithmetic relationships between notes.
Another area where music is most clearly connected to mathematics is in the rhythmic structure of music. A common quip is that as long as you can count to four, you can play music. The reality is much more complicated. In the majority of music, there are clear repeating patterns of four beats that can be heard and counted, called measures, and the lengths of all of the individual notes that make up each of these measures must actually add up to four. The notes can have a wide variety of lengths, many of them fractional. The names of the notes even refer to fractions of these four-beat measures. An eighth note, for example, takes up one eighth of a four-beat measure, or one half of one of these four beats. There is even some rhythmic notation that requires calculation, such a dot after any note will extend its length by an additional half. In order to figure out the rhythms of what you are studying during your music lessons in Pasadena, you will almost certainly need to do some arithmetic with fractions. Your music teacher in Pasadena will help you do these calculations at first, but as you practice, you will become more adept adding together different rhythms into complete measures and phrases.
As you continue to play more complicated music, you will continue to encounter more complicated mathematical relationships. For example, not all music is arranged in four-note units, so both the number of beats and how those beats are subdivided can change, and as a player, you must adjust your calculations and how you count the music accordingly. Also, if you study certain genres in your music lessons in Pasadena, jazz in particular, you will likely use mathematical relationships to move music to new keys, and to figure out which notes you can play while improvising according to chord symbols, which often include numbers to indicate added notes.
Finally, studying piano in Pasadena can be a jumping off point for the study of musical acoustics, and how particular notes relate to vibrational frequencies and string lengths. For example we usually use A440 as a tuning standard, meaning something producing the note A will be vibrating 440 times per second. For each octave, the vibration will be twice as fast, so the next A up will vibrate at 880 times per second, and the string will be twice as short. Similarly, a string that is two thirds as long as another will vibrate 1.5 times faster, and will produce a note a perfect fifth (or seven semitones) higher. This sort of calculation may seem esoteric, but if you use what you learn in piano lessons in Pasadena to become involved in electronic music, you can use synthesizers and computers to produce new notes and scales. Your piano lessons in Pasadena will already help greatly with electronic music, as the large majority of electronic instruments have piano-like keyboard interfaces. However, once you learn some of the mathematical physical relationships that underpin music, you can use electronic instruments to experiment with whatever new ways of organizing music that you can calculate.
Although the connections between music and mathematics may seem distant at first, the more you study music theory in piano lessons in Pasadena, the more you will understand the mathematical architecture that underpins music at all levels.