I have been thinking about how to write this post for a while now. When I think about harmonics and astronomy, all that comes to mind is how beyond me they are. They are the study of the unseen, but there still. How do I even ask questions about these arts? I know I cannot push them aside. Regardless of the fact that I apprehended nothing profound about them. Men and women who have studied longer than I have and have gone before me say great things about the encounter with harmonics and astronomy. So, I trust them and move forward. Choosing to fight for the good, the true, and the beautiful and deciding that it is worth it.
I remembered my resolve today in a wonderful way. I was watching the movie August Rush with my daughter. It is a beautiful story about a boy in the foster care system, and his parents do not know he was still alive. They were told at birth he died. After this tragic news, the parents went on grieving in their separate ways. As the years passed and the boy, Evan- also known as August Rush, grew older it was as if deep called to deep and all began to hear the whispers of music in the air, in the fields, and in all the things all around. The music transfixed Evan, and he choose to follow it in search of his parents. During his journey, he met many people and had some incredible musical encounters. The following clip is from one of those adventures, which beautifully explains the transcendent nature of harmonics and astronomy.
I love that this conversation began by looking at the stars. Throughout history, magnificent things have come to the awareness of humanity through the study of the stars. “In the Old Testament, the Psalms said, ‘The heavens declare the glory of God; the skies proclaim the work of his hands. Day after day they pour forth speech; night after night they display knowledge.’ The ancients believed that the regular pattern of the stars revealed the keys to deep mysteries. They were right.” (Clark & Jain, The Liberal Arts Tradition)
The ancient Astronomers “attempted to understand the actual mathematical relationships among heavenly bodies in terms of size, distance, and geometry.” Overtime “the best astronomers seemed to have given up their nominalism and had started to believe that their calculations represented real bodies –mathematical realism. “These Christians unlike prior generations of Platonists, believed that mathematics predicted something true about nature. Kepler, Galileo, and Newton believed that their calculations represented how the world truly was.” (Clark & Jain, The Liberal Arts Tradition)
This quote gives us a hint regarding why every major scientific discovery has come about as a result of observing and contemplating the heavenly bodies. This microcosmic view of the heavenly bodies also gives us a hint about why astronomy ended up as a liberal art, especially since it was considered a “middle science”, “those sciences which joined mathematics with natural philosophy.” In other words, astronomy helps us to explore the intelligibility of the heavenly bodies, in reference to time and space in the mathematical form. Clark and Jain refer to Astronomy and Harmonics as paradigmatic, which means these arts are a model of something else. This reality became even clearer to me last week at the CiRCE Conference when I had the opportunity to talk with Dr. David Quackenbush from Thomas Aquinas College. He helped open my eyes a little more to the Quadrivium. He said that through the study of astronomy we are presented “a first model of the divine order of the whole world.” We are forever talking about the parts, and the whole and astronomy gives us a first real view of the whole, on a mathematical, almost transcendent level. Just like logic helps us perceive truth through reason, grammar helps us perceive truth through language, astronomy cultivates our ability to perceive truth through the order of the whole.
Harmonics, on the other hand, helps us to “explore the intelligibility of music in mathematical form”. Of harmonics, Dr. Quackenbush also said that harmonics shows us directly, for the first time, that something is beautiful because it is ordered. So maybe we can say that harmonics cultivates our ability to perceive truth through order, or proportional relationships, in time. I love this idea. It helps to shine light on the opening quote in Clark & Jain’s chapter on music. “Nature in the cosmos is harmoniously composed of the limited and the unlimited, both the entire cosmos and everything in it.” (Philolaus the Pythagorean, fifth century BC) The relationship between the limited and the unlimited is present here on earth.
“For millennia scholars thought that above the orbit of the moon, the laws of earthly physics did not apply, and humans could have no conclusive knowledge of that sphere. That was the realm of astronomy. But beginning with the Medievals, tracing through Kepler, and culminating with Newton, this gap between heaven and earth was spanned. Newton claimed that whatever laws God fashioned to apply here on earth apply for all of reality. This joining together of the subject matter of astronomy with the subject matter of music, along with Kepler’s mixing of their methods, forever changed the nature of the Quadrivium.” (Clark & Jain, The Liberal Arts Tradition)
In a sense, Heaven is here, and we can partake in it. We the limited and finite creation created in the image of the unlimited and finite God. This reflects the idea, on an enormous and cosmic level, of two unlike things coming together in a mysterious but proportional relationship. Of course, this includes tension, but without the tension, there could not be harmony. If Charlotte Mason is right, and Education is the science of relations, then harmonics is the crowning jewel of the liberal arts and is one of the most beautiful things we could help our students to feast on.
What it Could Look Like in a Homeschool
So how to we begin? Before we can dive into the depth of astronomy and harmonics we need to have done our best to master arithmetic and geometry. If we or our students are not there, then introducing our students to the wonder of music and astronomy is a great place to begin.
Include some astronomy topics into nature study
Make star gazing a family summer time activity
Focus on arithmetic in mathematics
Listen to harmonious music (the great composers, etc…)
Focus on arithmetic in mathematics
Play an instrument
Note: Even if you do not have money for lessons you can still do this. We play tin whistle and use The Online Academy of Irish Music. There are several free lessons and for $19/month you have access to everything. I like this site because it doesn’t treat tin whistle like a silly instrument that can only be used to play silly kids songs. Tin whistle has its place in history, in culture, and in the orchestra. It is a very worthy endeavor! I use a free online metronome to keep us on count and we use Clark’s Celtic Tin Whistle. I do recommend getting a cleaning stick and a case. We also enjoy learning all the Lord of the Rings tunes on the tin whistle. There are several how-to YouTube videos available for free online.
Middle School Years
Continue to focus on arithmetic in mathematics and begin Euclid’s Geometry when ready.
Continue including star gazing and astronomy in nature study and family life.
Listen to harmonious music and enjoying composer study
Continue Playing an instrument
Continue to focus on arithmetic in mathematics.
High School Years
Take Euclid’s Geometry before Algebra. Here are two great options: Best Option: Polymath Classical Tutorials: Classical Mathematics I or Harold Jacob’s Geometry (just the book) or a coordinating Jacobs geometry DVD course.
After Algebra I & II (Polymath Classical Tutorials has these classes as well) look for a Newtonian Physics class. I have not found one yet, so if you know of one, let us know in the comments section.
Other modern counterparts to advanced astronomy include Experimental Physics and Matrix Mechanics. I am not sure however, if the average student ought to expect to get here in high-school. I could definitely be wrong about this though. One idea out homeschool group had, was to have a series of Senior seminars where we brought in speakers to talk about some of these topics in a way that awakened a sense of wonder and desire to continue the study of these. We are still wrestling through some ideas.
Continue playing an instrument and listening to great music
Take a formal Music Theory class. Our homeschool community plans to use Aaron Copeland’s book What to Listen for In Music along with continued composer study. The Great Courses also has a course that looks good called ‘Understanding the Fundamentals of Music‘
After Algebra I & II take Elementary Calculus along with Newtonian Physics.
Much like Astronomy the other modern counterparts to the liberal art of harmonics make me question how much of it is really attainable in high school. Courses like cosmology, theoretical physics, and theoretical economics seem to be collegiate level courses. We are considering a similar idea for our students using a senior seminar approach to playing with these topics.
“Where do you think it comes from…what I hear?
“I think it comes from all around you really. I mean, it comes through us. Its not like what right in front of you though. Its like the in between. The space. Its invisible. But you feel it.”
“So only some of us can hear it?”
“Only some of us are listening.”
-August Rush, The movie
May we all have the courage to listen, to look, to attend.
Expanding wisdom, extending grace,