My family members identify themselves as Reform Jews which basically means we go to services on the high holy days, we have a Sedar dinner for Passover, and no one ever discusses what they believe or don't believe. When I was preparing for my Bar Mitzvah I wanted to quit because it was a lot of hard work. The reward of a big party didn't interest me enough so my brother and sister ended up guilting me into doing it. I thank them for that though, the experience itself was quite rewarding. Lessons with an amazing man (with an equally amazing voice) like Cantor David Wisnia plus the Bar Mitzvah day itself was definitely worth the time and effort right there.
More importantly, preparing for the Bar Mitzvah taught me the value of asking questions and learning. After all, this is what my Rabbi told me Reform Judaism is all about. The Torah (The 5 books of Moses) portion I learned about and sang for my Bar Mitzvah was "Ha'azinu" (Hebrew for "listen"), the penultimate Torah portion. Although all Torah portions are sung, this one is in fact a song that Moses sings to the Israelites before he ascends Mount Nebo; where he is allowed to see the land that the Israelites are about to obtain before God kills him (side note: it's not because he smashed the Commandments but because he and his brother Aaron smashed a rock in the wilderness to produce water). I couldn't understand why God would kill a great person like Moses, who did so much, without letting him enter "The Promised Land." Luckily, the Bar Mitzvah process includes sessions with the Rabbi to discuss such issues. The Rabbi helped lead me to the conclusion that God made Moses suffer so that Joshua could more easily succeed Moses as leader of the Israelites. This answer satisfied me for a few years but eventually I began to question this reasoning.
Meanwhile, my Hebrew school teacher at the time mentioned he didn't believe Moses literally split the Sea of Reeds (I just read the book, trust me it says "Sea of Reeds" not "the Red Sea") and that it was a story that got exaggerated over time. Hearing a teacher explicitly say "You can still consider yourself Jewish even if you don't believe these events are literally true" intrigued me greatly. I enjoyed learning and interacting with other Jews, so I continued going to Hebrew school, went through Confirmation, and even entered a Jewish peer mediation program.
I will always consider myself culturally Jewish but at some point I realized I identified myself more as an Atheist. Not that it matters, but my reasoning for this is the same as Epicurus':
"Is God willing to prevent evil, but not able?
Then he is not omnipotent.
Is he able, but not willing?
Then he is malevolent.
Is he both able and willing?
Then whence cometh evil?
Is he neither able nor willing?
Then why call him God?"
However, since Judeo-Christian beliefs impacted history, art, and music so greatly I thought it would be a good idea to familiarize with the stories. So I started with the Tanakh. Next I'm going to read something from Ancient Greece (because those stories greatly impacted history, art, and music as well), and eventually I think I'll read the New Testament and Qu'ran too.
Unfortunately, the process of reading the Tanakh has angered me greatly for the following reasons:
It perpetuates a belief that there is a single right answer, including a single group of "Chosen People" who will prevail because their God is the one true God.
It states that everyone must follow every single law and those who do not will be executed. (At one point, a stranger enters the encampment of Moses and the Israelites. Even though he was never informed that such laws existed, he broke a law by picking up sticks on the Sabbath, the day of rest. Moses asks God what he should do and God tells Moses to stone the man to death)
To make things even worse, it goes on to explain that bad things occur because someone (anyone) isn't obeying every law. This means if things aren't going that well (and imagine how devastating times were thousands of years ago) the only way to make things better is to enforce these laws more efficiently.
The word holocaust is used in the Tanakh to describe what God told the Israelites to do to the former inhabitants of Canaan so the "Chosen People" could claim their "Promised Land". This meant killing every single man, woman, and male child; keeping only the virgin girls alive to become slaves (after all, if you aren't a descendant of Isaac, God doesn't love you.)
It seems so clear to me that such reasoning for so long has had a major negative effect on society (e.g The Crusades, The Spanish Inquisition, The Holocaust). Obviously Hitler took this same idea and just changed the definition of "Chosen People." This reasoning is why it was socially acceptable to own slaves, be racist, demean women, prevent homosexuals from getting married, etc. This is because it perpetuates the notion that the world is black and white; that one belief is more accurate than another. Ironically, using my own reasoning, this means I can't argue that what I believe in is the right thing to believe.
So I'm not going to say that I'm right; all I can say is this is what I believe. Take it or leave it. That being said, I'm going to now expand my complaint even further:
My problem is not with beliefs or Theism but with Fanaticism. Although I am an Atheist, and have my reasons and arguments for being so, it is not my prerogative to persuade people away from their own beliefs. Unfortunately, there are times where I do feel like I am being persecuted for my lack of belief and can get defensive and argumentative in response. This is a trait I try hard to suppress in fear that I will become what I hate. And, to be completely honest, it is hard for me to trust any of the Monotheisms (Judaism, Christianity, and Islam) because they all contain the Tanakh which is full of fanatic ideology. Even though the majority of people aren't fanatics, I still dislike exposing others to a doctrine that can justify behavior I view as backwards and immoral. (Again, this is just what I believe; I don't have to think what you think and you don't have to think what I think.)
Using the same reasoning as before, it is my belief that Capitalism is also bad. Capitalism perpetuates the belief that it is important and better to have more money, neglecting the fact that if some have more, others will have less. As a result, rich people have become the new "Chosen People" who do not care about those who are not.
To make matters worse, Capitalism has effected our products, services, and media through the creation of marketing and advertisement. It's become more important to convince people to buy things they don't need instead of focusing energy and resources towards creating the best products and services. What frustrates me most about this is that art and entertainment suffer too.
Extreme Nationalism is undesirable for similar reasons. It's one thing to be proud of your country, but once you reach the conclusion that your country is the best and that every other country should be just like yours; war becomes the solution (again look at Hitler). And war should never be the solution.
Following this reasoning to the next degree, I also believe sports fanaticism is bad. I've never been interested in sports at all, mostly because I can't understand why it is so important to so many people. In fact, it terrifies me. I grew up and currently live in the Philly area (for God's sake one of our mascots is the Philly Phanatic) and went to school at Penn State. Sport teams have become the new Nationalism, each sporting event its own battle. And don't try arguing "Well, at least nobody gets hurt." because obviously they do. Sports encourage violence and violence should never be the solution.
tl;dr: Christmas is stressful
Wednesday, December 15, 2010
Monday, May 3, 2010
Music: An Imperfect System
Everybody knows about Pythagoras and his theorem. But did you know his studies on music are the origins for Western Music?
Pythagoras was the first to note that mathematics applied to noises created pleasing sounds. He noticed that an anvil being struck in unison with another anvil half its size (2:1), or an anvil 2/3 its size (3:2), produced sounds he enjoyed. The ratio of 2:1 is what we now call an octave (P8) and the 3:2 ratio is what we call a perfect 5th (P5). The simpler the ratio is between two pitches, the more their sound waves overlap, making them more consonant. The P8, P5, and P4 (4:3) are the most consonant intervals (hence the word “perfect” associated with them) and were the main focus for writing music during the Medieval period. Using simple ratios to represent intervals is known as “Just Intonation.” Singers and string players find these simple ratios by using their ears to produce the most consonant sounds. Since other instruments have less control and keyboard instruments can’t be retuned in the middle of a piece of music, tuning systems developed to balance the relationship between just intonation intervals and convenience.
Once again, we have Pythagoras to thank for the first tuning system which we fittingly call “Pythagorean tuning.” This tuning system and the 12-tone scale we all know and love is the result of continually finding the P5 above a given pitch:
C-G-D-A-E-B-F#-C#-G#-D#-A#-F- and then one P5 more and we’re back to C right? Well, not quite (if that were the case this entry would be titled “Music: A Perfect System” instead). The problem is that if you use the 3:2 ratio to get from C back to C, you don’t get exactly the same note. The C you end up with is 23.46 cents sharper than the original, a discrepancy known as the “Pythagorean comma.” In order to fit all 12 pitches into an octave using this Pythagorean tuning system, one of the perfect fifths is lowered by the Pythagorean comma and is known as a “wolf” fifth because of its noticeably out of tune sound which resembles a howl. This wolf fifth can be placed anywhere the player wishes and is placed on a P5 they are unlikely to use.
Starting in the Renaissance period, the major third (M3) became a more desired interval, but using the Pythagorean tuning system its ratio is 81:64. As a result, the tuning system known as “meantone temperament” was developed using justly tuned M3rds (5:4). Since an octave is divided evenly by M3rds (C-E-G#-C) and a M3 is divided evenly into two major 2nds (M2), each M2 serves as the exact halfway point (the mean) between a note and the M3 above it. The P5ths are no longer justly tuned, but 11 of the 12 are only 5.38 cents flat compared to their justly tuned counterparts. This discrepancy is suitable but the remaining P5 is a wolf fifth that is 35.68 cents sharp. In addition to this wolf fifth, meantone temperament also results in 4 wolf M3rds which are 41.06 cents sharp and 3 wolf minor thirds (m3) which are 46.44 cents flat. Meantone temperament allowed M3rds to be an extra consonant (though still considered a lesser consonant than P8, P5, and P4) and allowed keyboard instruments to modulate to other keys for the first time; but only keys with 3 accidentals or less were feasible to use.
During the Baroque period, writing music transitioned from using the various “Church Modes” (Lydian, Dorian, etc), which determine the pattern of ascending intervals for the octave, to the major and minor keys we still frequently use today. This made the keys more important than the intervals themselves. For the first time, being able to use all 12 major keys and all 12 minor keys became important. Any temperament that is irregular and allows this is known as a type of “Well Temperament.” These involve altering the Pythagorean tuning, but instead of having the wolf fifth, the Pythagorean comma is displaced by lowering some of the justly tuned P5 by the same fraction. Organist, composer, and theorist Andreas Werckmeister wrote examples of well temperament. In the one he recommends as being the most efficient, he suggests lowering the P5ths C-G, G-D, D-A and B-F# by 1/4 the Pythagorean comma. Like meantone temperament, the keys with more accidentals are less in tune, but unlike the other tuning systems, these keys still sound in tune. As a result, with well temperament each key has its own distinct sound (key color) which composers liked to explore.
Once all 24 keys became usable, music in the Classical and Romantic periods focused on using, and modulating to, any key. This, combined with the popularity of the piano as an ensemble instrument led to the creation of the tuning system we still use today, “Equal Temperament.” In equal temperament, the octave is divided into exactly 12 equal pitches. This means every interval (M2, M3, P5, etc.) is always the exact same distance regardless of the key. Before equal temperament, a note and its enharmonic equivalent (G#-Ab, D#-Eb, etc.) were considered two different pitches with different frequencies. In fact, enharmonic used to mean “two notes less than a semitone apart” instead of its current meaning of “two equivalent notes (or keys) that are spelled differently.” Equal temperament allows composers to modulate to other keys through enharmonic modulations seamlessly. However, using equal temperament means every interval except the P8 is out of tune in comparison to its just intonation counterpart, with the P4 and P5 only 1.96 cents flat and sharp respectively and the M3 and minor 6th (m6) 13.69 cents flat and sharp respectively. Also, the key colors created from well temperament no longer exist in equal temperament.
Music is an imperfect system, but that’s what has made music so interesting and appealing. As tuning systems developed and changed, composers were able to write music in new and different ways; and as composers aspired to write music in new and different ways, the tuning systems developed and changed. Each tuning system has its own advantages as well as disadvantages. The real problem is not that music is an imperfect system but that we perpetuate the belief that equal temperament is the final (and only) solution in determining what frequencies we use. It is incredibly reliable and should be considered the default system. Without equal temperament, many 20th century music techniques (atonality, serialism, etc.) would have never surfaced. But just like there are an infinite amount of numbers between 1 and 2, there are potentially an infinite number of frequencies to use within an octave. If we only use equal temperament, we limit pitches to precise frequencies that are set in stone; and that would be imperfect.
Note: If you want to read more about tuning systems, I recommend the book “How Equal Temperament Ruined Harmony (And Why You Should Care)” by Russ W. Duffin.
Pythagoras was the first to note that mathematics applied to noises created pleasing sounds. He noticed that an anvil being struck in unison with another anvil half its size (2:1), or an anvil 2/3 its size (3:2), produced sounds he enjoyed. The ratio of 2:1 is what we now call an octave (P8) and the 3:2 ratio is what we call a perfect 5th (P5). The simpler the ratio is between two pitches, the more their sound waves overlap, making them more consonant. The P8, P5, and P4 (4:3) are the most consonant intervals (hence the word “perfect” associated with them) and were the main focus for writing music during the Medieval period. Using simple ratios to represent intervals is known as “Just Intonation.” Singers and string players find these simple ratios by using their ears to produce the most consonant sounds. Since other instruments have less control and keyboard instruments can’t be retuned in the middle of a piece of music, tuning systems developed to balance the relationship between just intonation intervals and convenience.
Once again, we have Pythagoras to thank for the first tuning system which we fittingly call “Pythagorean tuning.” This tuning system and the 12-tone scale we all know and love is the result of continually finding the P5 above a given pitch:
C-G-D-A-E-B-F#-C#-G#-D#-A#-F- and then one P5 more and we’re back to C right? Well, not quite (if that were the case this entry would be titled “Music: A Perfect System” instead). The problem is that if you use the 3:2 ratio to get from C back to C, you don’t get exactly the same note. The C you end up with is 23.46 cents sharper than the original, a discrepancy known as the “Pythagorean comma.” In order to fit all 12 pitches into an octave using this Pythagorean tuning system, one of the perfect fifths is lowered by the Pythagorean comma and is known as a “wolf” fifth because of its noticeably out of tune sound which resembles a howl. This wolf fifth can be placed anywhere the player wishes and is placed on a P5 they are unlikely to use.
Starting in the Renaissance period, the major third (M3) became a more desired interval, but using the Pythagorean tuning system its ratio is 81:64. As a result, the tuning system known as “meantone temperament” was developed using justly tuned M3rds (5:4). Since an octave is divided evenly by M3rds (C-E-G#-C) and a M3 is divided evenly into two major 2nds (M2), each M2 serves as the exact halfway point (the mean) between a note and the M3 above it. The P5ths are no longer justly tuned, but 11 of the 12 are only 5.38 cents flat compared to their justly tuned counterparts. This discrepancy is suitable but the remaining P5 is a wolf fifth that is 35.68 cents sharp. In addition to this wolf fifth, meantone temperament also results in 4 wolf M3rds which are 41.06 cents sharp and 3 wolf minor thirds (m3) which are 46.44 cents flat. Meantone temperament allowed M3rds to be an extra consonant (though still considered a lesser consonant than P8, P5, and P4) and allowed keyboard instruments to modulate to other keys for the first time; but only keys with 3 accidentals or less were feasible to use.
During the Baroque period, writing music transitioned from using the various “Church Modes” (Lydian, Dorian, etc), which determine the pattern of ascending intervals for the octave, to the major and minor keys we still frequently use today. This made the keys more important than the intervals themselves. For the first time, being able to use all 12 major keys and all 12 minor keys became important. Any temperament that is irregular and allows this is known as a type of “Well Temperament.” These involve altering the Pythagorean tuning, but instead of having the wolf fifth, the Pythagorean comma is displaced by lowering some of the justly tuned P5 by the same fraction. Organist, composer, and theorist Andreas Werckmeister wrote examples of well temperament. In the one he recommends as being the most efficient, he suggests lowering the P5ths C-G, G-D, D-A and B-F# by 1/4 the Pythagorean comma. Like meantone temperament, the keys with more accidentals are less in tune, but unlike the other tuning systems, these keys still sound in tune. As a result, with well temperament each key has its own distinct sound (key color) which composers liked to explore.
Once all 24 keys became usable, music in the Classical and Romantic periods focused on using, and modulating to, any key. This, combined with the popularity of the piano as an ensemble instrument led to the creation of the tuning system we still use today, “Equal Temperament.” In equal temperament, the octave is divided into exactly 12 equal pitches. This means every interval (M2, M3, P5, etc.) is always the exact same distance regardless of the key. Before equal temperament, a note and its enharmonic equivalent (G#-Ab, D#-Eb, etc.) were considered two different pitches with different frequencies. In fact, enharmonic used to mean “two notes less than a semitone apart” instead of its current meaning of “two equivalent notes (or keys) that are spelled differently.” Equal temperament allows composers to modulate to other keys through enharmonic modulations seamlessly. However, using equal temperament means every interval except the P8 is out of tune in comparison to its just intonation counterpart, with the P4 and P5 only 1.96 cents flat and sharp respectively and the M3 and minor 6th (m6) 13.69 cents flat and sharp respectively. Also, the key colors created from well temperament no longer exist in equal temperament.
Music is an imperfect system, but that’s what has made music so interesting and appealing. As tuning systems developed and changed, composers were able to write music in new and different ways; and as composers aspired to write music in new and different ways, the tuning systems developed and changed. Each tuning system has its own advantages as well as disadvantages. The real problem is not that music is an imperfect system but that we perpetuate the belief that equal temperament is the final (and only) solution in determining what frequencies we use. It is incredibly reliable and should be considered the default system. Without equal temperament, many 20th century music techniques (atonality, serialism, etc.) would have never surfaced. But just like there are an infinite amount of numbers between 1 and 2, there are potentially an infinite number of frequencies to use within an octave. If we only use equal temperament, we limit pitches to precise frequencies that are set in stone; and that would be imperfect.
Note: If you want to read more about tuning systems, I recommend the book “How Equal Temperament Ruined Harmony (And Why You Should Care)” by Russ W. Duffin.
Wednesday, February 24, 2010
The Taste of Music
As my exposure to music increased (in both amount of time spent listening as well as variety of sounds listened to), I came to realize just how similar our sense of hearing is to our sense of taste. Even though foods are made up of the same basic ingredients, the tastes developed vary from place to place, culture to culture. The basic “ingredients” for music are pitches, timbre, rhythm, meter, tempo, and volume. Different cultures developed their own distinct “flavors” of music using these “ingredients” in various ways. Composers are chefs of music, perfecting tastes, combining flavors, and looking for new tastes in order to create the best recipes.
When you taste something, you do three things whether you notice it or not. First, you identify the taste as best you can by using previous exposures as a reference. Then, you compare this type of taste with different ones, identifying similarities and differences. Finally, you take this new data and store it into the giant computer that is your brain for future reference. The more data you gain, the easier it is to identify these similarities and differences which enhances your sense of taste.
Listening to music works the same way. Genre labels were developed within popular music to better distinguish what “flavor” the music is. Even though metal music developed from rock music, with several similarities, the two genres sound different enough to be in different categories. Throughout western music history, composers were encouraged to write in the style and “flavor” of their time while advancing it to the next stage. Society was continuously too busy developing to pay much attention to the “flavors” of the past. With the creation and improvement of recording technology during the 20th century, the interest and ability to preserve music from the past developed. People were no longer limited to listen to just the most popular music of the time in concert halls, now they could listen to anything they wanted to, as much as they wanted to; all in the comfort of their own home.
When I listen to a piece of music, I identify it the best I can by using my database of categorized sounds. I try to guess what period it is from (and when during that period), what country the composer is from (or in some cases what country’s style the composer is imitating), who the composer is (and when during their life), and finally what piece it is. The more music I listen to, the clearer these “flavors” become, and the clearer these “flavors” become the more in touch I feel with the mentality (historical events, literature, visual arts, etc.) of the time it was composed in too. But “classical” music periods are more than just history lessons; they are the genres of classical music and should be used to describe music with similar “flavors” regardless of when it was composed.
So when it comes to listening to music, don’t get stuck in a rut eating the same foods all the time. Make sure you eat your vegetables (you might not like them but they’re good for you!). And every now and then try something new. You might like it.
When you taste something, you do three things whether you notice it or not. First, you identify the taste as best you can by using previous exposures as a reference. Then, you compare this type of taste with different ones, identifying similarities and differences. Finally, you take this new data and store it into the giant computer that is your brain for future reference. The more data you gain, the easier it is to identify these similarities and differences which enhances your sense of taste.
Listening to music works the same way. Genre labels were developed within popular music to better distinguish what “flavor” the music is. Even though metal music developed from rock music, with several similarities, the two genres sound different enough to be in different categories. Throughout western music history, composers were encouraged to write in the style and “flavor” of their time while advancing it to the next stage. Society was continuously too busy developing to pay much attention to the “flavors” of the past. With the creation and improvement of recording technology during the 20th century, the interest and ability to preserve music from the past developed. People were no longer limited to listen to just the most popular music of the time in concert halls, now they could listen to anything they wanted to, as much as they wanted to; all in the comfort of their own home.
When I listen to a piece of music, I identify it the best I can by using my database of categorized sounds. I try to guess what period it is from (and when during that period), what country the composer is from (or in some cases what country’s style the composer is imitating), who the composer is (and when during their life), and finally what piece it is. The more music I listen to, the clearer these “flavors” become, and the clearer these “flavors” become the more in touch I feel with the mentality (historical events, literature, visual arts, etc.) of the time it was composed in too. But “classical” music periods are more than just history lessons; they are the genres of classical music and should be used to describe music with similar “flavors” regardless of when it was composed.
So when it comes to listening to music, don’t get stuck in a rut eating the same foods all the time. Make sure you eat your vegetables (you might not like them but they’re good for you!). And every now and then try something new. You might like it.
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