wesleyan – Page 3 – Les said, the better II

First the Bad News

This in the mail this morning:

Public Safety would like to notify the community that this morning Saturday, November 22,
2003 at approximately 2:50am a male student reported he was assaulted on High Street near
Huber Ave.

The male student was walking by himself when he was approached by a male who made a
homophobic comment and struck him. The student continuing walking a short distance and
then was approached by the same suspect and four others who began punching and kicking
him. The suspects then left the area on foot and headed north on High St. The student was
brought to Middlesex Hospital for treatment.

that’s the opposite side of campus from where I live, about a 5 minute walk from the CFA. I have walked home from the CFA by myself at such an ungodly hour. In the future, I’m going to either bicycle (it’s downhill going home) or take Xena with the hope that she might intimidate somebody. High Street is a major enough street that I would have thought it was “safe.”

and

I will not be going home during winter break. A mis-reading of schedules lead me to beleive that there would be time for christi and i to spend a week at home. but this was in error. i won’t be home for thanksgiving either. my thansgiving day tickets are non-refundable, so i’m not going to be able to change them, even in the unlikely event that i could book a flight home at this late date.
however, I have a two week spring break, at least one week of which will be spent in California. Possibly (hopefully) both weeks.

Good news

the good news is not as good as the bad news was bad, but i felt that if i just said “bad news” and “other news,” that would come off as too pessimistic.
I went to the Music in Sacred Spaces symposium and head many lectures about church architecture and a little bit about music. Nothing came up that was useful for my paper, aside fromthe notion that processions create a sort of temporary sacred space, through the music used and the objects carried. but my paper, while it involves processions, is a bit more secular.
Went to a concert of 17th cenutry sacred chamber works afterwards. the program notes seem to be very interresting. i’ll read them later. the trio used a 17th centure tuning system, which was not meantone. it was closer to equal temperment, so more keys sound better, but was period appropriate.
after the concert, several symposium participants and grad students went to the organizer’s (prof Jane Alden)’s house for drinks. The party didn’t break up till like 2:00 am. she served some sort of apple brandy. it’s two nights in a row that i’ve perhaps gotten a bit loopy in a social setting, but rest assured, a trend is not starting.
One interresting thing is that all the musicologists there can look at a score and hear how the harmonies work. none of the composers there (grad students) have that skill, although aaron can read rhythms very well, as he’s a percussionist.
I think I’m missing a fundamental musical skill.

Concert

Tonight was the Graduate Composition Seminar concert, officially titled Five Minute Wonders. We all wrote five minute pieces. A lot of people came to hear them. Really a lot. I was impressed.

We started setting up at noon. I finally left the building at about 11:30 pm, after striking. (Striking as in, striking the stage, not as in doing a walkout to protest long hours).
My piece seemed to be well-received. I’ll have a recoding of it to post later. I would like to hear it again, perhaps played by a pianist who had more time to practice it.
the second half of the concert was a performance of John Cage’s songbooks. It is an extremely silly collection of “songs.” I can probably be burned at the stake at Wesleyan for calling it silly. For one of my songs, I was to attack a microphone to my throat and drink cognac. I got concerned about drking cognac without eating immediately beforehand. Fortunately, one of the songs in songs books says eat or drink three things. Jascha made an arrangement with a local pizza place, so that they would deliver pizza during the performance. the pizza delivery guy was actually Neely (the professor in charge)’s grandson.
when the pizza guy came on stage and I handed him cash, the audience was luaghing like crazy. I could barely stop giggling. So I ate some slices of pizza and then sipped my cognac. I had been practicing drinking cognac the last few evenings, with the idea that it would be good to know how to pace myself and build up my tolerance a bit before the concert so as to not be drunk by the end of the performance. So at the end of the performance tonight, I was disturbingly sober.
this problem has sicne been fixed.
tomorrow is a symposium about sacred spaces. Most about medieval christian music. so i’m going to most of it. hopefully it will somehow aid my paper.
speaking of my paper, i realized last night that the dissertation-copy of the play (the one I’m writing about) that I have is in medieval french, instead of modern french. I don’t speak modern french either, but i really don’t stand a chance with old french. But I have a book out of the library which has it in side-by-side translation into modern french. joy! but that book was due today with no renewals. I knew I had no time to do anything about this. with a heavy heart, I went to plead with the Inter Library Loan office.
I am dedicating my next piece to the ILL office, especially Kate. She told me just to hang onto the book. I’ve never had a librarian tell me to just let something get overdue. So Sunday, I’ll be photocopying all the pages with musical pauses. Fortunately, this is only about 400 pages or so. arg.
I couldn’t get a paper today, so i dunno if they printed my letter. i wonder how i would find out?

Alaxander Nevsky Paper

Celeste Hutchins
Proseminar
Nevsky Paper

I read Eisenstein’s explanation of how the Nevsky images and sound work together and I remain unconvinced. However, what was clear both in his writing and his film were strong issues of Russian identity.
These were very obvious in the film, where the characters openly discuss what it means to be Russian and the importance of the homeland. This was contrasted with the German other. Today’s Colloquium speaker noted that the music used for the Russian themes in the film were based on Russian folk modes. Thus it is somewhat similar to Stravinsky’s Svadebka, as they both use folk elements to re-imagine folk life.
I recognized other things common to Svadebka including that the female love interest had her hair parted into two braids, thus indicating her status as an unmarried woman. However, at the end of the film when the two couples pair off, neither woman starts singing a platch, but instead look happy with their future husbands. However, the matchmaker (mentioned early in the movie) has not yet been sent, so perhaps the platch would be premature and might interfere with the happy ending.
Russian identity is obvious in Eisenstein’s writings as he quotes Pushkin. Pushkin’s poetry is strongly linked to Russian identity. He is widely quoted and revered.
Despite the obvious and strong Russian identity in the film, certain American film conventions were used. For example, as one of the Germans fell through the ice and slowly slipped in and drowned, there was a Mickey Mousing downward trombone slide matching his action. Eisenstein goes so far as to claim that all of the score in the waiting scene is Mickey Moused, drawing diagrams and making claims of eye motion. Some scenes had music pre-written for them and Mickey Moused in reverse, so that the action was made to mirror the score.
This type of Mickey Mousing however, goes far beyond anything that would be found in an American film. The score, with it’s folk modes and choral works is distinctly Russian. These Russian identities in the film are contrasted with the film’s portrayal of German otherness. The creepy bucket-style helmets make the Germans look like aliens. Issues of religion also figure in very prominently.
The Germans have crosses on their uniforms. They have crosses on their shoulders. Even the eye holes in their helmets are cross shaped. Many scenes show the German holy leaders raising crucifixes. The religious leader goes so far as to say that there is only one world emperor and he must bow to the Pope. The Germans are in Russia on a religious crusade to impose Catholicism.
In contrast, there was only one scene showing Russian Orthodoxy. It was a short shot of some people standing, one of them holding an icon. The Germans are evil Catholics and the Russians are practically atheists by comparison, but they do have this other religion, which they get to keep, at least until the revolution.
Musically, Catholicism is represented by the organ that the priest plays. Also, since the trumpets are first blown at a church service, they also represent catholicism as much as they represent the threat of the knights. It is hard to draw a distinction between Catholicism and the Teutonic threat as Catholicism is the Teutonic threat. It is their motivation for coming to Rus and their justification for committing atrocities. Religious baiting is a tired old form of propaganda, but probably useful in a legally atheist society, as it helps build national religious (or irreligious) unity.
There is also a single character who was probably supposed to be a Jew. This character tells the angry nationalist mob that nationalism is not as important as money. Some nobel character kicks the Jewish man and calls him a cur. Because of the diasporic nature of Jewish peoples, they were viewed as stateless. In the Soviet era, Jews were not considered Russian citizens, but rather resident aliens. Their legal nationality was Jewish.
This possible Jewish character does not get a musical theme. He has about the same amount of screen time as the Russian Orthodox church, maybe a bit more. He is represented by stereotypes and carries no iconography. Thus religions in Russia are barely present in the film, whereas German religion is threatening, gets a lot of screen time and has musical themes and instruments associated with it.
Russian identity is thus defined, both as what it is and what it is not. Russian identity uses folks modes, quotes Pushkin and is forever optimistic. Enemy identity is religious, faceless and threatening, with odd instrumentation of bassoons and strange trumpets. Most horrible of all is the traitor to Russia who gets killed by an angry mob. Real Russians – the ones not kicked to death by the proletariat – love their country and will fight for it.

I am going insane

Ok, I’m not really going insane.

what do grad students do when they’re not studying?

I go to endless classes. I played a gamelan concert on friday at a posh private elementary school in West Hartford. It had a shadow puppet play, which went over ectremely well, but I couldn’t really see it, because I was playing the kempul, a set of the second-largest gongs. There are five of them and I sit in the back, so I couldn’t really see the puppets around the gongs, but even if I could, I get lost in the music when I look at them.
I write papers, but of course, that’s also studying. and I eat and i sleep and often I talk to other grad students about classes or homework or concerts or music or professors or whatever. but mostly grad students talk about sex. Everytime I go out to have beers with folks, they end up talking the whole time about sex. Long angsty conversations about sex.
It’s starting to stress me out. I keep having this dream that I get so stressed about classes and homework and my angsty interactions with other highly angst grad students, that my hair falls out. Almost all the men here are balding. There’s only a couple of guys here that have all their hair. Is their hair falling out because they are angsty grad students or are they angsty grad students because their hair is falling out? Could this happen to me? I’ve been checking in the mirror and so far so good. But really, the angst around here is so palpable that I can feel my hair follicles start to tingle.
I am so glad that the semester is almost over. My desire for a break has actually become greater than my near-certainty that I’m not going to get all my projects and papers finished.

Sleep is a new religion

Those of you who have talked to me lately may have noticed that i sound kind of . . um . . . angsty. Those who have not talked to me may have noticed that I haven’t posted much to my blog. So I got somewhat behind on school work and decided that I should spend more time being social, because I like to be social and at the same time I decided that coffee was the Best Thing Ever. Yeah, so I didn’t sleep very much the last week or two. I’m not sure.

Yesturday I slept 12 hours. I feel mellow again. I’m quitting coffee as it is EVIL, since it temporarily allows one to go without sleep, when one should not go with out sleep.
So I think I’m more or less up to date on my school work. Everyone is still talking to me. I have memories of angst that don’t make sense, but that’s ok I guess; I think I didn’t fling too much drama around, or not everyone would be talking to me. Um, and I have a purple mohawk. Well, it’s clairol burgundy color, which is like a subtle brownish purple. I woke up from a strange dream and my pillow was missing. No, my hair was changed.
My advisor says that first year grads push themselves to the edge of a nervous break down and then become apathetic and stay that way for the remainder of their program. Maybe apathy is like a form of composer student nirvana? I don’t actually care. Sleeping makes me feel so much better that I’m considering taking a nap.
Sorry if I dumped angst on you. Next time (godess help me if there is a next time), just tell me to sleep it off.

Kids say the darndest things

Alvin likes to tell folks about his undergrad seminar that he teaches on Esxperimental music. His goal is to inundate the kids with thousands of musical examples and not much discussion. he wants them to understand structure and not talk about emotional reactions to music.
this stance has led to speculation on the part of the grad student population as to what motivated him to limit discourse in this way. One of the vetran students said that the undergrads here will say bizarre things trying to describe their reaction to a pice. really, really strange, he said.
Today, in the class I TA, the students were playing their midterm projects and the class was discussing them a bit. One of the students played a really good project. Very nice. Very tonal (as in, it used them, verses being musique concrete), very thoughtful. It was lovely. Ron gave some feedback and then the class was asked if they had comments. they’re a quiet bunch. half the time, they won’t say anything. But this one kid, who was very impressed, started speaking, kind of slowly about it. “The beginning sounded like robots who were in love, but who were fighting, like, on top of a carribean restaurant . . .” [pause] “that was full of aliens.”

took the words right out of my mouth

Lovely Day

Not only was it a Wednesday, a relatively happy day during the week, since I don’t have too many stressful classes, but the weather was so nice that it felt like home. I could walk around with only a shirt and light swearer and feel nice.

I gave my presentation about tuning during class today. It was a bit of a disaster. Aaron said it was ok and that people were just scared of math, but I think maybe he was just being nice. Nobody knows what it means to be out of tune. I said, “out of tune notes beat. Beating is out of tune. the paino beats, so therefore it is out of tune.” I didn’t help that I was showing them a Pythagorean Tuning Lattice. That lattice has really nice fifths, fourths and octaves and horrible thirds, so it’s very very similar to Equal Temperment. I was on the way to talking about 5 limit intonation (which has wonderful thirds), when I played an example of the 7th and said, “that’s a terrible 7th.” and then I said something about how it didn’t matter that thirds were terrible because they weren’t considered consonant. And then the ethno types wanted to argue with me about consonance and dissonance. The ancient greeks thought it was consonant!! No, only string players would have used this tuning because it’s horribly out of tune. No, it’s in tune according to what they thought. Tuning is culturally constructed!
tuning is based on the overtone series. It is not socially constructed because it is centered around a physical fact. some notes are out of tune. the piano is out of tune and you’re wrong, because not everything is culturally constructed.
uh yeah

the to-do list of doom

old items

pedagogy things is done, now i need to write a syllabus for an intro to harmony class, due in 2 weeks
i now owe six instrument definitions, and i’ve done none of them.
still the world’s most clueless TA. I think we might be doing a realization of I am Sitting in a Room
I’m on the ITS comittee of the OtherMinds Board now. they didn’t ask me to run for secretary. (If you are a potential donor and want to go to a party wihtout me, let me know, and I’ll get you onto the list)
listened to Krystalnacht by John Zorn. Too many issues on top of the piece to say much about it, really. If you try to look at it abstractly and not as a programatic work, some of the tracks do not stand up on their own. the second track could never have been written about a non-programatic topic.
so, this morning, i thought i should put the JJICalc on Aaron’s computer before I left for school, to see if it would be loud enough. the program wouldn’t run. I ran out the door and charged off to school. got to the bike rack and realized that I left my keys sitting on my porch railing. Went back for my keys. Went back to school, now late for class and printed my handouts. Walked late into class. at the break went to try to find a key to the room where the Mac Truck is kept, so I could grab a laptop from it. the secretaries say that it’s very strictly against the rules and this is exactly why the mac truck is kept locked (and why grad students don’t get keys). then they let me have one anyway and it runs JJICalc just fine. The problem is that I compiled the calc on a new version of java and some macs are running older version of java and apparently there’s no backwards compatibility. I need to compile the program on an old machine so that it can run on other old machines. Write once, compile everywhere.
Haven’t touched OSC, but my perl script can get themes off of moo objects
emailed music prof about Joan of Arc mystery play. this prof doesn’t send prompt replies, so i may have to drop the research.
I’m going to analyze Turtle Dreams by Meredith Monk for my composition seminar. I don’t know if a score exists. Neely seems to think that a score is unnecessary.
The five minute piece is for piano. It’s started. Only god knows when it’s due.
none of the other composers know what’s going on either

new things

Must read inch-thick handout about Stravinsky by next wednesday
Aaron has organized a house concert where all the composition students will present five minutes worth of stuff. I must figure out what to do, as it is this saturday, I don’t think I can make people learn my SolReSol duet
Must return overdue library books and enquire as to the status of the books that i requested via inter-library loan
Must find and speak with a bell maker, but first, must find out how to find and speak with a bell maker.

Celeste hutchins
Graduate Pedagogy

I attended ARHA 213: Monastic Utopias. The class topic is architecture of Christian monastic buildings before 1300. to talk about this, the teacher uses two slide projectors which show pictures of architectural drawings and photographs of extant buildings or ruins or woodcuts of what the buildings used to look like or art from said buildings. He uses a laser pointer to point out whatever features that he is discussing. This class takes place early in the morning in a dark classroom, but when I was there, all the students appeared to be awake.

The use of slides leads to students facing away from the professor, since he sits at the back of the classroom by the slide projectors and the slides are projected onto the front wall.

Periodically, the professor will stop lecturing and ask the class leading questions, either ones that they know the answer to or ones that the only know part of the answer to. He will use their answers to fill in gaps in discussed material or to go on to new topics. Sometimes he asks questions which they can only guess at and when someone makes an obvious answer, he will say something like, “I would completely agree, but other evidence says it’s exactly the opposite.” His initial agreement acts as praise to the student and his subsequent disagreement gets the other students attention and helps point out that answers are not obvious. He may then explicitly discuss pedagogy and talk to students about how to reason from evidence. I talked to him after class and he said that his highest hope was that students learn to ask the right sort of historically relevant questions.

When the professor makes an important point, he may highlight it by spelling out the vocabulary word that he just used, thus cueing students to write it down. He uses the history of architecture to explain trends in Christianity, for instance that pointing out that one church’s crypt is an exact replica of another church’s crypt, because the second church was gaining power and the first church wanted to ally themselves with the power and legitimacy of the first church. Thus, he talks about political developments through architecture and architectural copying. this is like a music history class, which also touches on politics and how it affects written music.

The teacher will break up the class a bit. He spends a while lecturing from the slides and then will pause to take or ask questions. He might then return to the slides or lecture without the aid of pictures. When he’s taking questions, he may quietly advance the slide, thus cueing students that he’s ready to move on when they are. when he’s giving the lecture he may signal important points through spelling, or stress in his voice. He occasionally will make a joke about the material, lightening the mood and perhaps signaling a change in importance in the material. for instance, he mentioned something in passing about St Cruddedon and made a remark that the saint’s parents must not have liked him very much, or they would have named him David or Bill. The students only laughed a little at this (it only deserves a little laugh), but it did relax them a bit.

arg

didn’t do any work all weekend and slept in today and now i’m behind behind behind. a mountain of stuff is about to fall on me.

I can’t get supercollider to record my stupid sound samples. all the time spent on that is wasted
Just talked to a second year masters guy who talked about how his relationship of 8 years completely fell apart while he went to wesleyan last year because they were seperated and he was too busy to call frequently or write frequently and they became completely estranged. this was during gamelan. i’m blaming this conversation for why i cannot play any of the music. weeks of practcing and i have not gotten better. i still get lost all the time. i have no idea how to play the instrument i was on tonight. it’s only the first piece of music that he gave us. i should have done intro gamelan instead.

To do

attend a class on medival monastic architecture and then write up a report on the pedagological methods employed by the teacher. (class is 9:00-10:20. paper is due at 5:00)
write an instrument definition for supercollider and mail it to TA (due asap. class is at noon)
I have no idea what i should have prepared for the class I TA tomorrow. I haven’t done any of the reading in ages. I don’t know what I’m supossed to be doing. Maybe my job as a TA is too look decorative so that the students beleive that the tution must be worth it. that class is at 2:30
8:30 PM must call in the OtherMinds Board Meeting
Must listen to enough John Zorn to be able to talk intelligently about it (due for class 9:00 AM wed)
Need sound samples and handouts for 15 minute talk on just intonation also due for 9:00 am wed class. think i will have to generate them very slowly in the CFA lab with some program that the undergrads in my TA class thing are taking. I actually have no idea how to use the software, but somehow I’ve been giving them advice on it. No wonder the TA-A is more popular than I am.
midterm SuperCollider project is due sometime in the future. need to be able to have SC talk to MOO. For this I need to open an OSC socket in perl. OSC support for Perl is alpha. documentation does not exist.
Must talk to early music prof about Joan of Arc mystery play. Must find out if written music exists before fall break
compositon seminar wants to know what major work i’m going to analyze. i have no idea. can it be a really old work?
Compositon seminar may also require that I have to write a five minute piece. For what instruments? due when?
what the heck else is due for that class? I’m so confused. i think an avelanche is looming overhead. the syllabus is no help. I must corner other composers and get the to explain.

i’m supossed to be sleeping right now so i get up on time to look at slides of medival ruins.

Talking about Tuning

I’m scheduled to teach “anything” to my seminar on Wednesday. I though I should tackle tuning. This talk is just written and the sound samples and diagrams have not yet been generated.

what is Just Intonation?

Lou Harrison said that “Just Intonation is the best intonation.” An intonation is a type of tuning. Just tuning is a tuning that uses fractions. In just intonation, pitches are set using whole number ratios. To understand this, let’s look at the harmonic series.

Harmonic Series

The fundamental is the base frequency. (sound sample)
The first overtone is twice the base frequency. It’s relationship to the base frequency is 2/1. In other words, the base frequency * 2 = the first overtone. this makes a perfect (or just) octave. (sound sample)
The second overtone is 3 times the base frequency. It makes an octave plus a fifth. this fifth is perfectly in tune with the base frequency and the first overtone. (sound sample) but is an octave too high to use in a scale between those two notes. We can divide it by 2 to make it an octave lower. this new pitch, the fifth between the base frequency and the octave, is related to the base frequency by a ratio of 3/2. (sound sample) The three comes from it’s place in the harmonic series. The two comes from dividing it down to be in the first octave.

2’s and octaves

All notes in the first octave, will be between the ratios of the base frequency, which is 1/1 and the octave, which is 2/1. If something is too small, it is below 1/1, and if it’s too large it’s over 2/1. We can transpose it to the correct octave by multiplying or dividing by 2.

Therefore 2’s are very important for transposition, but they don’t change a pitch, except by octave. If the base frequency is C and we multiply it by 3, we get a G. If we multiply it by 3/2s, we also get a G, but in the first octave. so 2’s are “for free” you can multiply and divide by them any time you need to change the octave and you will still have the same note as before, just an octave higher or lower.

Inversion

the inversion of a fifth is a fourth. So we can invert the fifth fraction to get a fourth. the inversion of 3/2 is 2/3. But 2/3 is too small. It is not between 1/1 and 2/1. We can multiply it by 2, to get 4/3, a perfect just fourth. (sound sample)

You can do this with any tuning fraction. Invert it to find the inversion, then multiply or divide it by 2 to put it in the correct octave.

Pythagoras

3/2, the perfect, just fifth is a ratio made up of small, whole numbers. Small numbers sound more in tune because they are lower in the harmonic series. 3/2 is the most in-tune sounding note that you can get aside from the perfect octave.

There’s a story that pythagoras was walking by blacksmith shop and heard very harmonius sounds. After experimenting with the smiths, he discovered two excellent intervals, 3/2 and 9/8.

9/8 is a major second and since it still has small numbers, it sounds really good. (sound sample)

From this, he hypothesized that good rations were made up of powers of 3 over powers of 2 and their inversions. You know that the circle of fifths will eventually take you through all 11 notes in an octave. According to pythagoras, you can use this to tune all the notes. First, turn the first two strings as a perfect 3/2 fifth. Then tune from the 3/2 to the next fifth, a 9/8. then tune from the 9/8 to the next fifth, the 27/16. Notice that everyone of these ratios is a power of 3 over a power of 2.

Lattices

You can create a chart of these (pass out handout) called a tuning lattice. a lattice of powers of 3 over powers of 2 is called a Pythagorean tuning lattice. The line on your handouts at the top is a pythagorean tuning lattice. Below that, is chart of them in oder of the notes in the scale. Notice that E, the third is not a small number ratio. It is 81/64. This was considered ok at the time because thirds weren’t considered consonant. Notice also, that the octaves don’t line up. The octave, instead of being 2/1 is 243/128.

this is a sound sample of the tuning lattice going around the circle of fifths. (sound sample). This is a sound sample of it climbing the scale diatonically and then chromatically (sound sample). And this sound sample shows the difference between 243/128 and a 2/1 octave.

N-limit tuning

That last example demonstrates why mixing in other numbers than just three is a good idea. People often use 5’s, 7’s and sometimes higher prime numbers like 11’s. Your tuning system draws it’s name from the largest prime number that you use. A tuning that used 2’s and 3’s is a 3-limit tuning. One that uses 2’3, 3’s and 5’s is a 5-limit tuning.

(if I have time)

5-limit tuning

(Draw on blackboard) this is a tuning lattice of 5’s. This note 5/4 is a just third. The ratio has much smaller numbers than the pythagorean third. This is the pythagorean third (sound sample). This is the 5-limit third (sound sample). there’s almost a quarter-tone difference between them (sound sample).

N-limit lattices

When you are drawing lattices, every new prime number gets a new axis. so a tuning lattice could be thought of as an N-dimensional array, where N is the number of prime numbers. this one, with 5’s and 3’s is a two dimensional array. If we added 7’s, we’d need a new axis and we’d have a three dimensional array.

We can add notes to our lattice that are multiples of 5’s and 3’s. (draw on blackboard) All of these notes are the note right below it multiplied by 3/2s. Remember before, that multiplying fractions was raising them. Like 3/2 * 3/2 makes a note a fifth above. So because all of these notes are multiplies by 3/2s, they are all a fifth higher than the notes below them.

this is useful for two reasons. One is that 6/5 is the smallest numbers ratio we’ve yet seen for d#, the minor third. (sound sample). So adding lines like this helps us find extra ratios. the other thing that it’s good for is transposing. All of these notes are the same as the ones right below it, but raised by a fifth. So you might use this when you modulate to a new key.

Uses of Lattices

composers use lattices like these to figure out what tunings they want to use in their piece and then manipulate them for key changes and transpositions. they then use this to give instructions to instrumentalists or to program them into synthesizers.

One composer that uses tuning lattices to figure out how to tune her instrument is Ellen Fullman. She uses larger prime numbers to tune the many strings of her Long String Instrument. This track is based on a sweep of the harmonics of a C chord. (sound sample)