Music, Math, and Revelation

Most historical/traditional western music is composed from a series of tones we call scales. Scales are defined by the number of notes they use, and the relative distance of those notes from their adjacent notes. For example, the major scale is defined by seven pitches, with each note either a half step or a whole step higher than the one before it. A minor scale is also defined by seven pitches, but the sequence of whole and half steps has been modified to create a different set of pitches and intervals (the distance between pitches) to work with.

To create melodies, a composer generally picks a scale and then uses the pitches in the scale to create her melody. To create harmony, a composer arranges the notes from the scale into vertical stacks called chords. The movement from one chord to another is what creates the effect of harmony, or harmonic progression.

The mystery of harmony, however, is that some chords sound naturally pleasing to the ear, while others sound unfinished, jarring, or otherwise unpleasant. Additionally, if the instrument or choir playing a chord is out of tune, the chord doesn't lock into place, and the harmony sounds wrong. Most people who've attended a junior high school choir concert or youth recital can tell the difference immediately: while the players may have nominally played all the right notes, their collective tuning could have been off just enough to make people notice that something wasn't quite right.

Most music lovers and players have at some point had the experience of learning to play or sing in tune. But what does it mean for the player and listener to be "in tune" or "out of tune", and why does it matter?

When humans hear a certain pitch, we aren't hearing just that single frequency. This is because when strings or air in pipes vibrate, they don't vibrate at a single frequency. Instead, they vibrate primarily at the frequency that equals the length of the string/pipe, but simultaneously, they also vibrate in a sine wave along each whole-integer division of the length of the string. Each of those vibrations creates its own pitch. The volume of these pitches corresponds to their intensity relative to the other pitches being played. Because the longest vibration on the string is usually the most intense, the lowest pitch is the loudest pitch. In fact, all of the other pitches are quiet enough that we hear the whole array of vibrations as one pitch. Any pitches other than the fundamental (lowest) note are called overtones. The practical consequence of their existence is that they give nuance to the sound quality of a pitch.

For example, if you play the A on the middle of a piano (or on any other instrument, you'll hear the conglomeration of the following notes:

* The fundamental pitch, which happens to be 440Hz. This is the only one you'll probably notice. Everything else will blend into the sound of this tone.

* The first overtone, at 880Hz (or, vibrating twice as fast as the fundamental tone). This creates the sound of A an octave higher.

* The second overtone, at 1320Hz. This creates the sound of an E.

* The third overtone, at 1760Hz, sounds like a high A (again).

* The fourth overtone, at 2200Hz, sounds like a C#.

Again, while all of these notes (and further) are playing at once, the overtones are so much higher and quieter that their sound blends into the fundamental pitch.

The trick about the overtone series comes in the construction of harmony. Harmonies are generally built out of chords, or, multiple notes played at the same time. In most western music, chords are built by stacking the notes from the overtone series of the bottom note of the chord. So, an A major chord consists of the notes, A, C#, and E. The reason these notes sound good together, is that they are all present in the note A. When the C# and E are played on the piano, they are amplifying the sounds that are already present when just the single note A is played. A chord sounds harmonious or 'in tune' when the frequencies of the notes in the chord match the frequency of the overtones in the bottom note. This causes the sound waves to come into phase with each other. When sounds waves come into phase, the sounds amplifies, creating both more volume, and more overtones. (Thus, the volume of the in-tune chord is measurably greater than the sum of the individual notes if they were played separately).

However, to create this effect the notes of the chord have to be perfectly in tune. If the instrument is out of tune, the notes won't match the overtone series, the sound waves don't come into phase, no sound is amplified, and the chord sounds wrong, or out of place.

The way in-tune harmonies create and amplify overtones is metaphorical of some of my experiences with revelation. When the notes move into phase with each other, the effect is that everything about the sound and our experience of it is amplified. Revelation does the same thing: it can amplify and clarify our experiences, make them easier to digest or understand, and introduce us to a higher plane of ideas, insight, or living. Though we can go through life making the same motions, or playing the same chords, making the effort to tune them properly for me introduces a more complete, enjoyable, comprehensible, and rewarding way of living.

There are a lot of ways to connect these concepts; this is one I have been thinking about for some time. If you are interested in the connection between music and heaven, you might be interested in is the Musica Universalis theory of Pythagoras. It's related to this overtone schpeel, because it was Pythagoras who discovered that the relationship between pitches matched mathematical proportions, and those same proportions compose the overtone series. (For example, a 2-foot string and a 1-foot string will play notes exactly an octave apart, given that they are under the same tension). He further theorized that the planets were organized according to these proportions, and that each of them had a pitch associated with them. Bringing the pitches of the planets into harmony was then part of what made the universe a more perfect place to live, or opened a clearer conduit between man and the universal creator. It's all more complicated than that of course, but Pythagoras is credited with the general idea that musical harmonies house certain knowledge or energies. 

Some thoughts on 'Mormon' Music - a review of Jeremy Grimshaw's "Mormon Music After the Mormon Moment" on NewMusicBox

This blog post is a response to an invitation to comment on Jeremy Grimshaw's "Mormon Music After the 'Mormon Moment'" article posted today on NewMusicBox. It's in the form of a letter, and still rough, but I thought I would post it here rather than on a facebook wall. Would love further thoughtful comments.

Hi Kevin and Charity Sunshine Tillemann-Dick and the public world - thanks for bringing me in on this! In the spirit of Jeremy's full disclosure, I know him somewhat and have worked with nearly all of the composers he mentioned, either through their music or personally.

Some thoughts which I would be happy to expand upon more formally. Firstly, I think Jeremy handled extremely well the question of Mormon as an ethnicity - canonized into academia by Harold Bloom - what exactly, is Mormon, is a complicated, though much younger question - than what it is to be Jewish, Muslim, Hindu, etc. etc. There is also of course, some racial element to that from a historical standpoint. Walking the countryside of New England, and the strikingly-British-Looking-for-an-arid-desert streets of Much of Utah and Idaho will confirm the ideals and influence from the UK that this ethnic map of the US shows: http://thelede.blogs.nytimes.com/2010/04/05/bloggers-discuss-race-and-the-census/?_php=true&_type=blogs&_r=0

But what it means to be Mormon, and even Mormon history, is just as complex as is any other faith, tribe, or nation. Jeremy has dealt with this by casting a rather wide net of Mormonism - it includes those raised in Mormon families, practicing and not-practicing, or perhaps never-practiced, to recently-began-practicing. Given that, Jeremy's idea of what 'influence' is - from Mr. Young's yes-I-am to no-I'm-not to Ms. Tian's training far from the influences of what is generally referred to as mainstream or historical Mormon ideas - obviously changes depending on who he is talking about.

One question I have had for a long time (and have done a little work in trying to answer, but bow to Jared Oaks for the deeper research) is what was the style of many of the composers who wrote music for the institution and about Mormon stories when they weren't doing that? E.g., Leroy Robertson, Crawford Gates, Merrill Bradshaw, even Mack Wilberg, maybe others like Marie Bennett. I don't know the answer on the whole, but the things I have seen indicate that their ideas waxed a little more experimental in wider realms, just like those of Prokofiev, Shostakovich, Mozart, and others who wrote music for institutions at some point in their careers. It so happens that the church started commissioning a lot of music during the time when neoromantic styles were the conservative style to write in, and in many cases, that has stuck as a church 'style' not so much because it is somehow indicative of a deeper Mormon aesthetic, but because that was the music that got people hired, and that was popular at the time.

Jeremy's points about normalcy also entice. The idea of Mormons as a culture striving for peculiarity and normalcy – sometimes at the simultaneously – is something I have experienced, but also a common trope in academia not just about Mormon Studies, but about many minority religions and cultures – even, in broad strokes, the impetus for much of the Counter-reformationists’ raison-de-etre, and the long history of Catholic Bishops spending huge amounts of time discovering whether miracles reported to their offices were bona-fide miracles, or simply a function of natural law/natural causes. From Mormon and American historical standpoint, yes, Mormons stood out from a crowd in some respects, but not all – they were perhaps the most populous and long-running of the religions that sprang from the hills of New York (and the 200-mile radius of Palmyra) in the early 1900s, but certainly not the only ones interested in finding old sacred texts and objects, seeing deified beings, experimenting with/changing/codifying non-monogamous marriage, family and sexual practices on religious, political, or ‘need-based’ grounds, etc. (As a commercial break, it only takes a short jaunt into American Colonial-Era history to realize that Western Americans were not, by and large, sexually monogamous, nor were they abstinent before marriage – there is a noticeable number of 5/6-month intervals between marriage and baby christenings in Puritan American vital records, not to mention the well-known practice of keeping mistresses. Ugh.)  Mormon persecution was of course severe and all-encompassing – but so was that of other faiths, often in proportion to their size/population concentration/propensity to show up on voting day.

All of that is to say, that it’s interesting that so many of the singular things about Mormons and Mormonism are surprisingly normal – migrations toward the west coast in the 1840s, forming religious and political blocs, temperance movements, family structure debates – was yes, peculiar in many ways, and arguably in magnitude and longevity – but also deeply culturally normal. Even the ‘outsized’ Mormon Tabernacle Choir didn’t start with even 100 of the 300+ choir so well-known today. It grew, I would assert, much in the style of other British and American mega-choirs that became icons of musical power much like surround-sound or big subwoofers does in today’s pop culture. Again, the Tabernacle choir has outlasted many other of the large-scale choirs, but its roots are quite secular and quite ‘normal’. So perhaps even the Tabernacle choir is an exercise in the church as an institution queuing up in American pop culture-land. (In the spirit of a review, I don’t think Jeremy would disagree with me on this, though I could stand to be corrected by the same Michael Hicks that Jeremy cites – maybe guru to all of us in the realm of Mormon Music History).

So it is that, in general, I am very pleased that this article has been published, and that some interesting, diverse, and talented composers have gotten some air time for it. Also, within the realm of composers identified by religion, I would be very curious to see how other groupings would compare. I’ve looked as far as Judeo-Christian liturgical music, hymnals, and a little bit of the radio-world. In the ‘Sabbath-day morning’ contexts Mormonism seems a little behind some, and right with others. The large number of Mormons in the Christian-pop radio sound-world, supported heavily by Deseret Book placements, and what they would call their demand curve, skews what many would see as the Mormon musical style largely in what is actually the pop-culture arm of musicians, which I see is the largest arm of music making in most cultures/ethnicities. Saying that Mormon film composers or pop musicians define Mormon music-making is a little like saying Kay Perry defines singers. It’s a little more complicated, of course, when a huge amount of music by Mormon pop artists about Mormon subjects is bought and sold through Deseret Book and subsidiaries – an institution owned by the Church Corporation – but not much more complicated than the existence of gatekeepers across the recording and music making industry.

Two other conversations I think are interesting points in this discussion are economics, and a revisitation of Mormon identity and the need for innovative culture within a cultural/ethnic/political group. I have many, many artist colleagues, not just Mormons, but many Mormons, who choose certain pathways for their work-lives out of considerations of supporting a family in a 9 to 5, middle-class way. This is a tangible contributing factor to the outsize number of film composers, media music artists, commercial-makers, arts administrators, and frankly, businesspeople in general that I am fascinated to gather more opinions/stories about for my own collection. But again, in the spirit of a Mormon claiming the comforting cloak of normalcy, I would wonder how this compares to society at large. My guess is that there are a lot of aspiring-artists-turned-consultants out there. It is worth noting that many of the composers Jeremy brought up in the end of his article (and, again, he admits this) are BYU faculty. I.e., a their salaries are being paid by a combination of tuition and Church-appropriated funds, which indicates a tacit approval/appreciation for their work and the need for it; it also indicates that they are composers for a living and still can support a family from it – perhaps they are part of a sadly small list of composers who have interesting voices and managed to ‘make it’.

I would add to the list of interesting ‘Mormon’ voices: Murray Boren, Ethan Wickman, up-and-coming composers Joseph Sowa, Curtis Smith (and at this point I proceed to name the composers in my BYU Music classes…) I’d be interested to know what they would say/what others would say about the influence question Kevin brought up.

The second thought that I’m interested in considering is other’s opinions on the idea of culture- or nation-building. For example, I have been to very inspiring lectures on the need for a ‘Mormon Shakespeare’ – great artists to help the culture (and perhaps the institution as an art-advocate) reach intellectual and aesthetic greatness on the proportion of game-changing household names like Shakespeare. Part of this mission, for some, is also to help bring to their fullness Mormon ideas (whatever those are) and their exploration through art forms. Another camp says ‘why bother with a Mormon Shakespeare when we already have Shakespeare’? (We=humanity and also we=Mormons). 

A deeply poignant thought in many ways, and a terrible place to stop the discussion.

So, I'll write a PS - Also, there is a wide world of Non-American culture based Mormonism, and Mormon Music, also barely touched on by Jeremy or here. 

Ruth's spring travels part 1: Jo and Daniel's wedding

Here's the first in a series of vignettes from my last 6 weeks of travels: a choir tour, two holidays, and a wedding at the end. For faster info on the tour, see singers.byu.edu

26 May 2012 was spent at the wedding of Joanna Rusby and David Scamman. Joanna and I were colleagues from the Musicology MSt at Oxford and I was honored to be invited to her wedding and pleased even more to have been able to attend. It was a distinct pleasure to play the organ on the occasion. (The music, for those who must know, was a baroque mixture: a piece of the Watermusic as processional, which I had to learn in the day before the service, the second movement of the second trio sonata as the registry music, and an abridged (by me) version of the Piece d’orgue, BWV 572, as recessional. the hymns were standard and some of my favorites: Love Divine, All Loves Excelling, The King of Love My Shepherd Is, Be Thou My Vision.)

As with most weddings, the lead-up to the big day was, well, big, and at least from my perch as a guest at Charlotte’s (Joanna’s sister’s) house, along with Hilary the florist and Katherine the maid of honor, well-orchestrated and smooth from beginning to end. We had the normal rehearsal and dinner on Friday evening, went to bed early that evening, and were up (relatively) early Saturday morning to start the real wedding-making. Hilary and Joe (Charlotte’s husband) left early to decorate the reception venue, leaving Katherine, Charlotte and me to take the train from Ascot to Richmond carrying our dresses (luckily of the wrinkle-free variety that fit nicely into backpacks) and the rest of the wedding flowers, which amounted to six bouquets, about 20 boutonnières, button-holes (which I now know are small boutonnières), and corsages, and a hair-piece. (Picture forthcoming). Needless to say, we attracted some attention on the train, but everything made it safely to the church.

The ceremony and reception were really nothing short of delightful and included a list of my favorite things: great families, great music, sincere vows, beautiful weather, yummy food, heartfelt and pithy speeches, new friends, and a ceilidh dance to top it all off. By my accounting everyone ages 4 and up danced at least once, including Joanna’s great-aunt and the little sons of the best man.

Thanks, Jo and Daniel, for such a wonderful day, and congratulations on beginning your new lives together!

Women in Education interview

Last week, my friend Monica interviewed me for the BYU Women's Services blog. Here's an advance look at the edited version. It's a little raw, that's what blogs are for, right?


This week’s interview is with my good friend Ruth Eldredge, an organ performance graduate student in the School of Music. Ruth grew up in Colorado, the ninth of ten children. She received her bachelor’s degree in organ performance, and went on to study musicology at Oxford. But for as long as I’ve known Ruth, I never knew that when she started college, she had very different plans for her life! I’ll let her tell the story. The following is a truncated version. You can read the full interview on my blog: (link to full interview also forthcoming.)

MHR: When you first started college, what was your plan, for your education, career, family?

RE: Oh, I had everything planned. Down to the T. I was going to come to BYU, major in linguistics, then go to medical school, because I wanted to run pediatric neuro-surgery clinics in Central America. I figured I’d start learning the languages, and then go to medical school, and spend a lot of time overseas building clinics, maybe even a medical school in Central America. And I had every expectation of being married by the time I was twenty… partly so I wouldn’t have to decide whether to go on a mission!

Anyway, I was going to drive a gold SUV, and be a neurosurgeon. I worked in a doctor’s office my freshman year and I remember driving home and pretending that I was in my SUV—I was actually in this really ugly two-toned truck. So, I was pretending that I was calling my kids on my cell phone and telling them I was on my way to pick them up from school.

MHR: So how did you get from this well-rehearsed plan to majoring in organ performance?

RE: It came on gradually… (for full interview go to LINK)

MHR: How do you feel that your time at Oxford changed you?

RE: I feel like I am responsible for everything I know, everything I’d learned in the past, and
for everything else people expected me to know. Now I understand that while the first two may be true, I also have a responsibility to admit what I don’t know, and keep learning and using the information I get. I feel very responsible for that. I think this is the important part: We have a responsibility for the opportunities we have, for the education we receive, for the wisdom bestowed on us through our life experiences. It would be like learning to drive, and then refusing to drive well. In that way, the whole experience of living abroad and forming an opinion about the world, learning things that I find important, I feel like I have a responsibility to reflect those things in my character and personality, and to contribute those things to my society.

If anything, having had the educational advancement that I’ve had has made me more committed to a domestic life. I love to cook and clean more now than I ever did before I went to graduate school. They are creative processes that are important to life.
More than choosing what we’re going to do, is choosing how we’re going to do what we need to do. And one thing feeds on another. If we do one thing well, we’ll do another thing well. The only thing that’s going to hold you back and really disqualify you is stopping doing things, not thinking or creating. But being creative in one way, facilitates our ability to create in other ways.

If you’re a good student, you’ll be a good mother. You engage the same mental, spiritual, and physical, faculties. And it works in the opposite direction. That’s why there are so many curve-breaking mothers on campus! Have you ever had a class with a 40-year-old mother who’s raised five kids? They get good grades! If you can learn to engage your mind in something, you’ll pick up the skills you need to get a good job, start your business, run a household, anything.

MHR: If you were to give advice to yourself as a freshman, what would you say?

RE: I would say, do not be afraid of anything. It just slows you down. Don’t be afraid that one choice will exclude other choices. Rarely is that the case. Fear takes away the opportunities you’re afraid you won’t get. The only thing that’s going to hold you back and really disqualify you is stopping doing things, not thinking or creating.

Things learned

Every family needs a chef in the mix to spice up conversation. (Apologies for the double pun.) Last Sunday I learned from brother-in-law Big A, our family chef, that green onion roots will re-sprout in a jar of water with a water source. I'm looking forward to trying this one at home.

On friends

As the end of the year and the holiday season parties, cards, presents, vacations, and so on come upon us, my thoughts occasionally turn to what constitutes a friend.

I have two best

friends. Luckily for me, both of them have two best friends as well - me and the one of my best friends that isn't them. Growing up we lived in three different areas of the greater Denver area. We met as 12-year-old campers at our church's annual girls camp and forged a rather querky (as all the best ones are) friendship over six years of camping trips, youth outings, lunches, sleepovers, shopping trips, and parties. By 18 two of us showed up at BYU, while the third continued her studies in Denver, then in Hungary.

In those early years of college we had everything figured out: friends K and C would both serve LDS missions, K would go directly to graduate school, and C would pursue her career in music, and I would finish college, go to medical school, become a surgeon-super-mommy, and build clinics in Guatemala with my also-doctor husband. Irony struck early and often in the coming years: by age 20 I had left medicine for a music career of my own, and the day I received my mission call, K called to say she was engaged and was putting off graduate school plans. The flip-flopping of lives came full circle when, in the weeks surrounding the beginning of my mission and K's wedding, both C and K's brother underwent life-changing medical emergencies that have made both K and C into medical experts in their own rites over the years of hospitalizations and other treatments that have followed for both families. And to top it all off, I went to grad school and took on the life of the academic musician.

In the seven years since those turning points, I have seen K and C on several occasions - though each meeting has been in a different city, and we still haven't succeeded in getting the three of us together in one place. Other communication has been sporadic at best, and just last week I found myself thinking about them and wondering if what we had still constituted best friends, or if even that notion was a thing of the past.

Then it came: on Christmas Eve I received an email saying that C was back in the hospital, awaiting a second operation, and could we please send our prayers in her behalf. Suddenly everything came back - all the love, the memories, the pure hope for one another - came rushing out from the shelf it had been stored on. Even as my heart burned and tears welled at the news, I was relieved to know no matter who or what else came into our lives, our friendship is as current as it ever has been. And so I send my continued prayers for dearest C, and send an extra word of thanks for the longevity of friendship.

on Mormons and their Music

When the subjects of Mormons and their music comes up it's not uncommon to hear gripes from the Mormon musicians themselves: Mormon musicians are all amateurs, the aesthetic is sullied by the absence (outside the few tabernacle organists and choir conductors, etc.) of paid positions for musicians ( a similar argument could, and probably is, made about clergy, activities coordinators, teachers, and virtually all of the day-to-day functioning of the church community). Often, musicians complain about 'tin-eared' leaders who have jurisdiction over their musical decisions, that the church music market is being flooded by pop music, or the amorphous and either loved or disdained genre of 'inspirational' music... and so the musings go. The one common string amongst many of the conversations I hear about Mormon and their Music is that it could be much better, and that most people want it to be better. (Speaking of which, there will soon be an electronic version of David Warner's BYU Arts Alumni lecture asking for LDS innovators in the arts - watch this space).

With this on my mind, I had a conversation today with the choirmaster and organist from a 6,000-member Methodist Church in Plano, Texas, who have been coming to BYU regularly for two years now to work with some of our choral musicians here. I was more than a little worried when the choirmaster began a sentence saying 'The Mormon Musical tradition is...'

Long pause...

'A very singing tradition. Mormons are a singing people. We want more of that in our church.'

And so, in the midst of introspection about what the state of Mormon music is, where it is going, and what it could be, let's take a moment to enjoy the fact that the average LDS congregation sings its hymns with envied gusto and fluency.