I love diminished chords. What would suspense movies do without them? 
Have any of you ever looked at the key change in Elton John’s Funeral for a Friend as it segues into Love Lies Bleeding from C Harmonic Minor to A Major? It basically gets there by dropping from F Minor to E Major (half-steps on the firsts and fifths) and then to A Major. I keep thinking I’ve seen a similar progression before, but where? It seems Beethovian. Much obliged if anyone could enlighten me on this.
That is not really that drastic Lib as it is just a chromatic mediant relationship. Classical music does it all the time. 
At least that is the way you describe it sounds. It is not the most common type of key change being that there are relatively few accidentals but the chromatic mediant modulation is normally something one learns by about the third semester of music theory. I agree that type of progression is pretty cool. I also like non-western tonal harmony played in a classical style but to give that type of analysis is much more difficult.
HUGS!
Sqrl
Thanks, Sqrl! That’s a reasonable assessment since Elton is classically trained. I guess it just jarred me a bit since you don’t see a lot of funeral dirges progressing into heavy metal!
Oh my goodness.
You guys must all be engineers out there in the teeming millions. I have enjoyed reading all of this and, as a musician, follow your reasoning. However, a non-musician is L-O-S-T.
Fortunately, I am a music teacher. Allow me to simplify.
Bach, like many of the aristocrats of his time, was interested in numbers. He found special significance in them. For example, if A=1, B=2, C=3 etc., then B-A-C-H=14. This was Bach’s “favorite” number. He would wear coats with fourteen buttons, for example. He composed melodies of fourteen notes. The notes B (also known as Bb), A, C, and H (aka Bnatural) appear in some of his works.
While the above responses were all wonderful, perhaps a more simple answer is in order. This approach to using numbers as the basis for his melodies may be what OP was referring to.
In an aside, I assume that the nature of this forum causes it to be read by many people in the engineering and mathematics fields. I find it interesting (though not surprising) that so many people are so well-versed in music and it’s terminology. Still, looking over the posts in this thread, I see such a dramatic leaning toward music as a science and less of an emphasis on music as an art. Just a thought.
Drum God, I have a degree in music and formerly tought music. I thought the OP was asking why music is mathematical not really what are the numerical aspects. I thought my post where I explained musical elements and their mathematical counterparts explained quite well what he was asking for. Granted, I know music is art. I also know that music is a form of applied mathematics. You, a drummer I assum by your name, should know that completely simply from the counting elements and polyrhythms that you supposedly play. Have you ever played 5 against 8? The rhythmic breakdown would puzzle most anyone as it is so uneven and crazy sounding. Scriabin wrote an etude for the piano (I believe etude 42 no. 8) that features this in the opening. Vladimir Horowitz played it wonderfully and up to speed but even the Scriabin piano reel that I have heard Scriabin actually playing on had it slowed down considerably. He was more of a composer than a performer, he could mathematically work it out rather than put it into practice. A very skilled performer, such as Horowitz, could basically count the two distinct very differnt rhythms off simultaneously. I know that would make many a mathmetician cringe. Even 2 against 3 is foriegn to a lot of regular people.
I just thought I should point some of this out when discussing math and music. I am in no way an engineer but will take that as a compliment. I meant no offense in my earlier post although I can see how it could come off as snotty.
HUGS!
Sqrl
Whoa there, hold the phone, Sqrl.
I didn’t mean to offend you. I thought your responses to the original post were wonderful. They were dead-on target. I agree that music certainly is mathematical. You’re right – rhythm is mathematical. The sheet-music is a graphical representation of music passing through time. No wonder they’re often called “charts.”
My post only meant to suggest that perhaps the OP was looking for a more simple answer. He seemed to indicate that the discussion of tempered tuning was a bit outside what he meant. I in no way meant to indicate that your responses were incorrect in any way, only that perhaps they went overboard in the vast details.
By the way, my screen name is actually somewhat of a misnomer. I am more of a percussionist than merely a drummer. “Drum God” is actually a bit of conceit that is not entirely warrented. When I chose the name, I actually tried several other names first, but they were taken. I typed in Drum God on a lark, and darn if it didn’t stick.
By profession, I am (as opposed to was) a music teacher. I teach band to middle and high school students in Central Texas. Perhaps my background as a public school teacher caused me to read all of these posts and think “sheesh, let’s simplify a little bit here.” If I explained all of this all at once to my Middle School kids, they’d be totally lost. We do look at mathematical relationships among the pitches and rhythms we play. We learn about intervals, keys, tonality, basic rhythmic counting and pulse, syncopation, and chord structure. That is, of course, in addition to the more affective domains of committment, integrity, perserverence, dedication, cameraderie, and scholarship. Somewhere along the way, we also learn how to play an instrument. And we play it well. My signature quote from Handel fairly sums up my teaching philosophy.
Sqrl, your expertise at explaining the mathematical relationships in music is admirable. In fact, I have already quoted you a bit in my classes. Your not being a music teacher would seem from my perspective to be a loss to our very noble profession. And that, [gender-specific pronoun], is a compliment.
Hey Drum God, you were joking a bit in your first post, right? Bach practicing numerology is almost plausible, but you went over the edge with saying B is also known as Bb and H is B. Why wouldn’t B just be B? I must admit that you still had me going until the part about B, A, C, and Bb appearing in some of his works. That’s like saying Shakespeare liked his initials, so he used the letters “w” and “s” in some of his plays.
So if you were joking, good one! Your deadpan style of humor will fit in well here. If you weren’t joking, and are merely insane, I humbly apologize and ask you not to hunt me down.
Greg, Drum God is correct. Bb in the Baroque period was known as B and B natural was known as an H. You misquoted him wrong when you said, “B, A, C, Bb.” It was really Bb (which was known as B at that time), A, C, H (which is what we know of as a B). It is well documented within music literature. Pick up the Grout Dictionary of music and look up Bach. Or better yet, call your local music department within a college. They will tell you the same.
Thank you for the compliment Drum God. I prefer to teach private lessons as I hate teaching swarms of uncaring children. Sometimes in a classroom setting you get lucky by having a few extremely talented and generally nice students. It has been my experience that most of the kids around that age simply don’t care about school, music, or really anything acedemically related. It really burned me out when I was in college and looking into a teaching degree (my degree is in composition and performance. Big surprise, huh?). I still teach sometimes but recently I have been in a teaching dry spell. I knew what I was saying would sound snooty. I really took no offense to what you said as you added some valuable insight into this topic. Keep up the good work. Hang out in MPSIMS since music topics don’t come up too often.
What type of percussionist are you? I know most percussionists play a large array of instruments but generally specialize in one. Which one? I am particularly fond of the marimba.
HUGS!
Sqrl
A good one, darn it. But seriously, marimba is actually my favorite perc instrument, but I don’t get to work out on it much. Being a teacher, I have to be more of a generallist than a specialist. Our only marimba is at the high school, so I don’t have one to diddle on with my spare (HA!, that’s a good one) time. My truly favorite thing to do as a percussionist is play Broadway-style musicals. I really enjoy getting to be a “one-man-band”, sitting in the pit with all my toys arranged around me.
Thanks for bearing me out in my description of Baroque note-names. I remember in college seeing my first timpani part marked “Pauken en H” and wondering what the heck that meant. I knew Pauken, but H? I thought notes only went up to G.
Another bit of note trivia: Notes used to be known by their Greek letters, beginning with Gamma and ending with Ut. All the notes in this mode were known as gamma-ut. This eventually was shortened to become our English word gammut, meaning all inclusive.
That’s too bad. In my classes, I have students who are really wonderful. They are the leaders in our school: leaders in band, athletes, honors students, student council, local churches, Scouting, Little League, the list goes on. I have the best and brightest students in our school. I just have to be careful to remind the community which came first: Some people say, “All the smart kids are in band.” I remind them that “No, the kids in band GET SMART!”
So if you don’t work in music, what do you do?
I am a government drone, BZZZZ BZZZZ BZZZ, finally getting paid decently. My ex was an elementary music teacher in some very rough neighborhoods. The kids really reflected the neighborhoods that he taught in but he loved them anyway.
You may know that the notes even before the Greek letters came out were identifed by solfaggio that originated in the hymn to St. John the Baptist. Yeah. I see you are in LaGrange. I am originally from San Antonio but now live in DC. It is very different. I may have actually met you when I was a student when I would attend TMEA in San Antonio.
HUGS!
Sqrl
Small world. Where did you go to school? I’m from Austin and went to Southwest Texas State.
I went to the University of the Incarnate Word (San Antonio). My ex got his Master’s Degree in Music at Southwest Texas. Very small world.
HUGS!
Sqrl
Um, Greek letters, gamma to ut? There is no Greek letter ut. The closest I can think of would be either upsilon, tau, or eta. The seventh letter after gamma, inclusive, would be kappa, and the twelfth would be (I think) omicron, neither of which sounds anything like “ut”.
American Heritage Dictionary: (from Greek gamma, gamma; see GAMMA) + ut, first note of the lowest hexachord (after ut, first word in a Latin hymn to Saint John the Baptist, the initial syllables of successive lines of which were sung to the notes of an ascending scale CDEFGA: Ut queant laxis resonare fibris Mira gestorum famuli tuorum, Solve polluti labii reatum, Sancte Iohannes).
It seems like I’m taking a lot of abuse on this thread. Granted, I’m bringing it on myself by misidentifying chords, misspelling “root”, and not knowing that H used to mean B. Let me take a more humble posture and simply ask Drum God what is significant about Bach using Bb, A, C, and B (not B, A, C, and Bb as SqrlCub pointed out) in some of his works? Clearly he used each and every note millions of times. Is there some evidence that he used the ones in his name more often? Or that he used them in some progression unique to himself?
It had always been my impression that it wasn’t Bach specifically who used these letters a lot, but other composers in homage to Bach. I may be wrong though–I always thought B-flat had been H
LL
LL, you are wrong. Bb was named B during Bach’s time and B natural was known as H.
Also, you are correct that many other composers used the BACH theme in their music as an homage to Bach; however, it is also well documented in Groves Dictionary and Grout that Bach did this himself. He was also extremely interested in numerology as was mentioned earlier and their letter and notational equivalents.
According to Dan Long (a well known Bach scholar and leader of the Texas Bach Choir), Bach followed many numerological practices when composing music. He had his favourite number which I believe was 5 and 14 or something like that and many of his themes are either 5 or 14 notes long. 5 notes is awfully short for a theme but for a repeated rhythmic idea it works out pretty well.
HUGS!
Sqrl
It is my understanding that Bach used the pitches B-A-C-H in succession in his works. It doesn’t mean that those pitches were necessarily the motif for the entire melody, but you’ll often find them in there.
Of course he did use the other pitches, too. In fact, his biggest claim to fame, in some respects, is the fact that he composed in all the modern major and minor keys. He is in many ways the father of modern Western music. Bach didn’t invent the rules of modern music, but he was among the first to codify them and employ them in his work. In his time, he was quite the revolutionary.
I imagine that SqrlCub would have more to add. S/He seems to be more of the musicologist than I. This weekend, I’ll do a little research on this issue at home and see what I can come up with. It’s time to blow the dust of the Grout, if you know what I mean.
Chronos, you are absolutely right. I wrote without thinking. Thanks, RM, for clearing up my error.
Sqrl, when was your ex at Southwest? I finished my Bachelor’s in 1991. I’m sure y’all miss Texas: today it’s supposed to get up to 107F, on Sept 1st!!!
Oh, and by the way, Greg, I do have a deadpan style of humor. I tell a joke in class and it falls dead. However, teaching middle school has made me a bit insane. The hunting will begin immediately.
Damn, Sqrl got there while I was on the phone.
Five notes was more than Beethoven needed for a theme: ba-ba-ba-bum. Or would you call that a motif?
Of course, Beethoven’s Fifth was only a Third.
[… ducking, running …]