Music Box and Music Theory Lesson

For Friendsmas, Michaelyn gave me a music box.  Not just any music box, but one for which I could write my own music!  I have elected to write her a waltz and give the music box back to her (if you want to hear what I come up with, you’ll have to bug her :P).

There are a few stipulations.  The music box is in the key of C major, does not allow for accidentals, and has a two octave range (from C3 to C5).  What this translates to in non-music nerd is that writing a song for this music box that isn’t boring will be a challenge.  It’s ok – I’m on vacation and have nothing but time, and I do love a good challenge.  If you think you are up to the challenge, feel free to write your own.  Mine will be about 15 measures long.

This reminded me of a series of posts I did way back in the day when I was on xanga over music in an effort to acquaint people with the basics.  Below the fold is a reprint of the introductory post about music theory.  Enjoy!  Let me know if you guys like it and, if you do, I’ll write more on music theory/vocal technique.

Also, feel free to ask any questions you might have in the comments.  I will answer all theory-related questions.

Intro to Music Theory

Let me first say that from the moment I was introduced to it, I’ve always loved music theory.  I loved it even though it was difficult for me to grasp at first (and boy was I slow at it compared to all the other students who had been musicians since they were two years-old), but I soon found it to be a very challenging and enjoyable synthesis of my analytical and artistic sides.

The more you learn about theory, particularly as you get into moderately complex stuff like twelve-tone serialism, the more mathematical it becomes.  It’s like a puzzle with an infinite number of variations.  It’s beautiful, and I encourage you to take the time to get the basics down – once you do, they open a whole world of possibilities that you must never go near an instrument or sing a note in order to enjoy.  And once you understand the construction of music, you will find that there is a whole other level on which you can appreciate the music you already listen to aside from the fact that it sounds nice – once you understand theory, you can also revel in the chess-like mentality, the cleverness of the composer as they created those sounds.  Like everything else, music is more beautiful, more awe-inspiring, the more you understand it.

My early entries in this series on music will be to set up my final entry in the educational blog series, four weeks from now, which will be over music history.  In order for that one to make sense we will all need to be on the same page with basic theory first.  Here’s how I think my entries will work:

Entry #1:  Intro to theory.  Note values, intervals, major/minor chords.
Entry #2:  Intro to vocal technique.
Entry #3:  More intro to theory.  Diminished/dominant7 chords, progressive/regressive motion.  Bonus entry on modal music.
Entry #4:  History.

Today there’s going to be a lot to cover.  You may want to take it in sections.  Also, if you’re already familiar with note values and what not, you may want to skip ahead.  :D  To start off with, we need to be familiar with notes.

When you look at a piano, you will see this pattern repeated over and over.  So once you learn what notes these keys represent, you will know what note every key on the piano represents.  :D

Starting from the far left and just going along the white keys (ignore the black keys for now), the notes are C, D, E, F, G, A, and B.  And if you were to put the same pattern after this…

…then the pattern starts over again on C.  Easy, right?  Every time you see the two black keys together, you know that the white key to their left is a C.

Now for the black keys.  You can describe them using either sharps (#) or flats (looks like a lower-case b).  For instance, the black key to the right of C and to he left of D can be described as C# or as Db.  To make a note sharp you simply take it up to the next note to the right.  Likewise to make it flat, you take it to the neighboring key to the left.

Real quick!

1.  Find F#
2.  Find Bb
3.  (Tricky, tricky…)  Find E#

Now we need to learn distance terminology.  Between every two notes is a particular distance.  The smallest distance between any two notes is what’s called a minor 2nd (m2).  You achieve a minor 2nd by moving one key in either direction on our virtual keyboard.  From D -> Eb, that’s a minor 2nd.  From B -> C (and also C -> B), also a minor 2nd.  If you want to know what a minor 2nd sounds like, think the theme from Jaws.

Real quick!

Moving along the white keys on our virtual keyboard (starting at C and ending on the C above it), there are two minor 2nds that occur naturally.  Where are they?

A minor second can also be called a “half-step”.  All other intervals are composed of a different number of half-steps.  A major 2nd (M2), or a “full-step” is just two minor 2nds stacked on top of each other.  So an example of a major 2nd would be from C -> D or from F# -> G#.  Here are the rest of the intervals:

Minor 3rd (m3) – Three half steps.
Major 3rd (M3) – Four half steps.
Perfect 4th (P4) – Five half steps.
Perfect 5th (P5) – Six half steps.
Minor 6th (m6) – Seven half steps.
Major 6th (M6) – Eight half steps.
Minor 7th (m7) – Nine half steps.
Major 7th (M7) – Ten half steps.
Octave or and 8th – Eleven half steps.Real quick!

1.  Give one example of a perfect 4th.  (example: E -> A)
2.  Give one example of a major 3rd
3.  Give one example of a minor 7th

Rather than counting all the half steps for 6ths and 7ths, there’s an easier way to go about it.  From D to B is a major 6th if you’re going up the keyboard.  However, if you go down the scale it’s only a minor 3rd, which is much easier to count.  Well, 3rds and 6ths are inversions of each other, as are 2nds and 7ths.  In other words, as you go up the keyboard for one, it is the opposite if you go down the keyboard using the same notes.  If you modify the prefix, then you have the correct interval in an inversion.  A major 7th going up the keyboard is just a minor 2nd going down.  An example of this would be from C to B.

Now for chords.  Chords are built on these intervals.  Chords require at least three notes (three-note chords are called tertian chords) played simultaneously.  We’re going to start with some standard tertian chords.

Major chords:  A major chord is composed of two intervals, which means we’ll need three different notes.  The intervals in a major chord are a major 3rd on the bottom and a minor third on top, both of which are built above the chord’s “root” note (in a C major chord, that note would be C.  Easy, right?  :D).

So, to make a C major chord we start on C and add the major third above it, E.  Then we go a minor third above that E to G.

We refer to the notes in their chord by their position above the root.  So in a C major chord, the E would be the third, and the G would be the fifth of the chord.

Real quick!

1.  What notes would you use in an F major chord?
2.  What notes would you use in a G major chord?
3.  What notes would you use in an Eb major chord?
4.  What notes would you use in an A major chord?

Minor chords:  Minor chords are the exact opposite of a major chord.  Minor chords start with their root note, and then have a minor third on the bottom and a major third on top.  So a C minor chord would be made up of a C, an Eb, and a G.

You’ll notice that the only note that changes between a C major and a C minor chord is the middle note (the 3rd of the chord).  This goes for any minor chord.  If you take it’s major chord brother and lower the middle note a half step, you will have a minor chord.

Real quick!

1.  What notes would you use for an E minor chord?
2.  What notes would you use for an F# minor chord?
3.  What notes would you use for a D minor chord?
4.  What notes would you use for a Bb minor chord?

I think that’s enough for today.  In the next theory post, we’re going to be dealing with the chords that allow the tonal system to exist: diminished and dominant chords.  It is an understanding of these chords that will be necessary for my post on music history.  Stick with it!  We’re just building the frame right now, and the frame is never as aesthetically pleasing as the completed house.  

  • feralboy12

    Cool. I hope some people get something out of this.
    For me, though, it’s all review–I majored in comp & theory about 20 years at the University of Oregon.
    My only criticism would be to point out that I regard 12-tone serialsim as an historical event, and nothing more.
    Really, a paint-by-numbers approach that sounds like beep beep boop, one of the reasons why encyclopedias often divide music up into “popular” and “classical.” (Classical thus being defined as “music that is not popular.”
    Also, I’ve written music box pieces before–but I had to simulate the music box effect by slowing down on the third or so repeat and stopping in an arbitrary place. Always thought it was a cool little form.

  • Rob L

    I absolutely agree on the beauty and mathematiciness (?) of music theory. I’ve just spent a term at a conservatoire studying jazz (unfortunately I won’t be able to continue my studies, but don’t get me started) and it gave me a new lease on life. Years ago I used to lie awake at night, unable to sleep because I was too busy transposing melodies and thinking about chord inversions.

    It struck me that music theory could be a good way of arguing against the ‘evolution is only a theory’ argument. Music theory is the explanation of why music works; the music would exist with or without our explanation of it. Someone more wordy and better at multi-tasking (I have Tinariwen playing as I type) can probably expound on this better than I can (I nominate Ben Goren, who I see comment around FTB and WEIT).

    One thing that bugs me terribly is this idea that knowledge of music theory stifles creativity, which is extremely common in popular music and comes up in magazine interviews all the time. I think it’s correct to a point – too much reliance on not enough theory tends to result in stilted music, and many people without a great musical education are able to create precisely because they don’t have the trees obscuring their view of the wood. But I also believe that enough knowledge can be attained to make this a moot point.

    Case in point: the first thing my guitar teacher at conservatoire had me do was play only the 3rd and 7th of chords, dropping the 1 and 5, the point being that the notes remaining were the ones to most strongly define the chord, and in fact are probably the most important notes in a melody written above that chord. This got me thinking about punk guitarists who only ever seem to play ‘power chords’ comprising the 1st and 5th. I thought of the song ‘All the Small Things’ by Blink 182 (disclaimer: not to my tastes!) and realised that the melody uses the thirds all the time. The same goes for a lot of very popular songs. With this in mind, I’ve been able to improve my own composition by writing melodies that hit these strong notes more often, whereas before I was hitting the 1s and 5s a lot more.

    Anyway, sorry to wax lyrical…you hit upon a passion of mine here!

  • Ibis3, denizen of a spiteful ghetto

    Too fast for me to follow. For example:

    The smallest distance between any two notes is what’s called a minor 2nd

    Why? What does that mean? Why doesn’t it start at a 1st? What makes an interval a minor vs. a major? Why are 4th and 5th called Perfect?

    The intervals in a major chord are a major 3rd on the bottom and a minor third on top

    I have no idea what you mean by “on the bottom” or “on top”. Stopped reading at this point because I felt too lost.

    I feel like if I had more explanation, I’d follow along better. This is something I’ve always wanted to learn, but it’s really like a foreign language.

    • Rob L

      I wrote a reply below, forgetting that we can reply directly below comments on here.

    • consciousness razor
      The smallest distance between any two notes is what’s called a minor 2nd

      Why? What does that mean? Why doesn’t it start at a 1st?

      Well, actually, it does. If you have two instruments playing the same note, they are “in unison” and have an interval of zero. So, a minor second is equivalent to what is called an “augmented unison.” Technically, the interval from C to C-sharp is an augmented unison, but (in equal temperament) it’s the same two notes as the interval from C to D-flat, which is a minor second.

      Originally, theorists were identifying them according to the corresponding degree of the scale or mode they belonged in. Basically, the second degree of the C major scale is D, so intervals going from some kind of C to some kind of D were a “second.” C and D are adjacent degrees of a scale — there aren’t any letters between them. Let’s say you have the interval from Cb to D#. You have to call that an “augmented second” or else respell the Cb as a B, which would make it a major third. You can avoid this by using numbers rather than letter names, but the letter names are so useful and easier to remember that we’ll probably never get rid of the alphabetic notation entirely.

      What makes an interval a minor vs. a major? Why are 4th and 5th called Perfect?

      For seconds and sevenths, the reason is very convoluted. Remember, a lot of this stuff was sorted out centuries ago, and it’s partly just a matter of convention now.

      It’s easier to understand in terms of thirds or sixths. C major and C minor triad have different thirds but everything else is the same: C major is C-E-G, C minor is C-Eb-G. Thus, the note which identifies it as major or minor triad is the third. If it’s the E, it’s a major third from C. If it’s the Eb, it’s a minor third.

      Fourths, fifths, octaves and unisons are “perfect,” because centuries ago people thought those were the consonant harmonies. Think Gregorian chant and even earlier music. They thought that sound was “perfect,” so a fourth (for example) didn’t need to resolve to a third to release any of the tension you or I would probably hear in it, because basically they thought fourths sounded perfect just as they were. Apparently tonality, which hadn’t yet been invented, would’ve been of the devil. Part of it had to do with religious or numerological rationalizations involving the trinity and nonsense like that. Anyway, we’re stuck with it.

      The intervals in a major chord are a major 3rd on the bottom and a minor third on top

      I have no idea what you mean by “on the bottom” or “on top”. Stopped reading at this point because I felt too lost.

      Notes which are “higher” or “lower” are ones which are higher in frequency or lower in frequency, respectively. C is the root of a C major chord, meaning that C major in root position has C “on the bottom,” with the lowest frequency, then it goes “up” to an E, then “up” to a G. The major third from C to E is therefore “on the bottom,” compared to the minor third from E to G.

      • Ibis3, denizen of a spiteful ghetto

        Thanks! Between you and Rob and JT, I think I’m finally learning something. Maybe my nephew or niece has a keyboard or other instrument I could listen to so as to hear what the tones and intervals and chords actually sound like…

        (I played clarinet, not very well, in high school for two years, but the little bit of music theory we were taught did not sink in at all.)

        • consciousness razor


          Sure. Any more questions, ask away.

          A correction:

          Let’s say you have the interval from Cb to D#. You have to call that an “augmented second” or else respell the Cb as a B, which would make it a major third.

          I should’ve said a “doubly-augmented second,” which is a bit ridiculous, but an augmented second is the same as a minor third. Also, just for the sake of completeness, you could also respell the D# as an Eb. So the options are Cb-D#, B-D#, or Cb-Eb. They’re all the same, as long as they’re in equal temperament.

          If it is in some other temperament, all hell breaks loose. Human sacrifice, dogs and cats living together, mass hysteria. Immediately locate your time machine and go back from whence you came. Or put down the bong. Or just keep having a good time. It doesn’t matter.

  • vltava

    12-tone serialism is more than a historical curiosity. A vast and diverse array of important and beautiful works influenced by Schoenberg’s idea have been written in the last ninety years. It is also interesting to note the opening bars of the development of the last moment of Mozart’s symphony number 40 in G minor, which nearly form a tone row, and strikingly, the only note omitted is G natural itself! I doubt Mozart did this by accident. It is a powerful idea in both conception and how it makes its impact on the listener, whether she understands the music theory involved or not; it is no mere idiosyncrasy.

  • Rob L


    If we use the key of C as our example, the second note in the scale is D. The interval between C and D is one step (or, if you’re a limey like me, one tone). D is the major second of C. Flatten it (so you’re one half-step, or one semitone, above C) and you’re playing the minor second. I personally find it a lot easier to understand than to explain!

    When creating a chord of C major, the three notes are C, E and G. E is a major third (two full tones/steps) above C. G is a minor third (three semitones/half-steps) above E. So C major is made up of a major third interval (C->E) and a minor third above that (E-> G). C minor, on the other hand, is comprised of C, Eb and G. That’s a minor third (C-.Eb) with a major third (Eb->G) atop it.

    Hope that clarifies!

  • kaorunegisa

    Thanks for posting. Been working with a friend to teach her theory and this will be a great addition to the lessons if you don’t mind my printing and using it, giving appropriate credit?

    I do have a question, but it’s more related to ear training. Do you have any exercises other than listening and comparing to known songs in order to get better at listening for pitches? I’m learning the mandolin for the SCA and a lot of the songs I want to learn are difficult to find music for, so I’ve been trying to work on training my ear better. Any suggestions you have would be wonderful, and I hope this isn’t so far off the topic as to offend.

    • lowspark13

      I second this request. It would bring back a lot of the confidence that was sapped from me when I realized I couldn’t recognoze any notes by ear, and that this would be a major hindrance if I ever join a group. I don’t have any musical friends and can’t afford classes ATM, so any suggestions would be super-duper appreciated :)

      • HP

        Music theory can be a big help with ear-training, with the following caveat: There is no single universal music theory, and you have to know the specific theoretical underpinnings of the music you’re trying to aurally transcribe. So, assuming you’re trying to learn Renaissance music for SCA, that would mean learning Renaissance music theory and performance practice — species counterpoint, dance forms, figured bass and basso continuo, etc.

        The point of this is that, when you’re trying to pick something up by ear, it’s much easier to hear and remember, say, a 4-3 suspension resolving to a Picardy third, than it is to try to pick out each and every individual note.

        You’ll probably also want to read and hear everything you can get your hands on regarding 16th-18th c. Spanish music for fretted instruments. The Spanish really developed music for fretted strings to a high degree, and there’s tons of information out there (much of it in tablature, which I can’t read).

        For just general ear-training, the basic thing is to learn the sound of all the intervals, rather than focussing on individual pitches. There are tons of mnemonics for this (e.g., the first interval in the theme to Star Trek (TOS) is a minor 7th; Happy Birthday starts with a major 2nd. There are some pretty good free ear-training websites out there (or at least there were the last time I looked, which was probably 8-9 years ago).

        • kaorunegisa

          Thank you very much! Just got back from celebrating my New Years at an SCA event (and premiering some of my mandolin playing in public at Bardic Circle, which went decently well), and this answer was incredibly helpful and a great topper to a fantastic 2012 so far. Really appreciate the suggestions, now to start working on both the ear training and acquainting myself with the new theory. Here’s to finding primary source documentation!

  • Kat

    This is so great! Just this single post explains so many things I sort-of was aware of during my years of learning piano and flute as a child. I wish my teachers had made even an attempt at music theory. More please!!

  • Phledge

    I’ve played classical piano for over thirty years, played the violin for ten years, and studied classical voice for four…and I am ashamed to admit that I don’t really have a strong background in theory at all! Very excited to get a primer here. Keep it coming, please!

  • Drakk

    Explain that, musician! ;)

    JT, have you ever watched Vihart’s videos on youtube?

  • HP

    Introductory music theory is tough to teach — you wind up basically taking a “lying to children” approach, with the caveat that “If you keep this up, in ten years you’ll know why everything I taught you is wrong.” In that respect, it’s just like math or physics!

    One minor [!] correction: A chord made up of three notes comprising two stacked thirds is called a triad. A tertian chord is any chord made up of stacked thirds. So, C9 (C-E-G-Bb-D) is a tertian chord, but it’s not a triad. Tertian chords are defined in opposition to chords based on other intervals (such as fourths or seconds).

    Tertian harmony describes > 99% of the music most people ever get to hear, so it’s not a term I would introduce until you start to cover the theoretical structure of non-tertian music (e.g., plainchant and early polyphony, non-Western music, pandiatonicism, panchromaticism, musique concrete, etc.).

    Music theory has a lot of highly specialized jargon, which is frequently used incorrectly (especially by music critics*), but is one of those things you gotta learn if you’re going to communicate precisely.

    *If I had a nickel for every critic who uses crescendo as a synonym for “climax” . . ..

    • consciousness razor

      Tertian harmony describes > 99% of the music most people ever get to hear

      This figure has been verified by 84.7% of music statisticians, and they are all wrong.

      Exaggeration and sarcasm aside, part of my (minor, quibbling) problem with it is that many sonorities can be interpreted as tertian harmonies or as something else functioning in some other system. So, it seems a chord’s quality or function isn’t always inherent to the structure itself, but to the chord’s context in the rest of a work. For example, a C13 chord like C-E-G-Bb-D-F#-A could instead be interpreted as a quartal/quintal harmony (of stacked fourths/fifths), like so: Bb-E-A-D-G-C-F#. There are other ambiguities like that, but I would also add that a lot of film music uses non-tertian or non-tonal harmony (at least as a device or a sort of special effect), especially more recent film scores. So people’s exposure to that sort of thing is greater than what most probably realize.

      • HP

        I agree with everything you say, actually.

        Or to put it another way, there’s really no such thing as “music theory” as such. There are many, many music theories, with each music theory being specific to a specific set of performance praxes and a specific time and place. Or, music theory is like grammar — when most (English-speaking) people talk about “grammar,” they mean something like “grammatical features, plus style, usage, and orthography specific to written English.” All of which is pretty useless for learning Mandarin or Swahili, and often confusing as hell when learning a closely related language like Spanish.

        Music has no equivalent to scientific linguistics. We’re still sort of stuck at the philology stage of discipline development. And the cognitive scientists who study music cognition have yet to abandon their “music appreciation 101″ assumptions.

        So, music theory is not one thing that you can learn. The great thing about that, however, is that you’re never done.

        (I would quibble about the phrase “recent film scores,” however. Most recent film scores I’ve heard are largely repurposed pop songs, with the occasional sentimental rehash of late-Romantic music [Howard Shore, how could you?]. Now, if you want to talk classic Morricone* scores from 40 years ago . . . .)

        *I was trying to describe Morricone’s score for Danger: Diabolik to a musically literate friend of mine, and I said, “Imagine that Miles Davis and Burt Bacharach had a love child, and it was adopted by Penderewski who named Stockhausen to be its godmother.”

        This is a topic about which it is difficult for me to shut up.

        • consciousness razor

          Music has no equivalent to scientific linguistics. We’re still sort of stuck at the philology stage of discipline development. And the cognitive scientists who study music cognition have yet to abandon their “music appreciation 101″ assumptions.

          Which is just plain sad, for a discipline that’s been around for, what? Well over a thousand years no matter how you reckon it, arguably 2,500 if you go back to the Pythagoreans. But cognitive science is very young. I guess there are more important issues that have to be given priority.

          Have you read Musicophilia, This is Your Brain on Music, or The Art Instinct, perchance? Some of it was nice, but some of it made me want to rip the pages out. Garbage.

          I would quibble about the phrase “recent film scores,” however.

          Oh, sure, I would too. Accepted. Generally speaking, everything is terrible, but there are a few gems now and then.

          • HP

            Well, in defense of Humanity, “music” is huuuuuuuuuuge. I can’t even imagine a sound theoretical description that would encompass Bach’s Magnificat in D, the shakuhachi tradition in Japan, 20th c. Native American pow-wow music, the Charleston, and Central Asian epic poetry performance. Let alone all the music that has ever existed since prehistory that was born and died without ever being recorded.

            Back in the Olden Days of Usenet, I argued on that any universal theory of music would have to be sociological/anthropological, and not acoustic or architectonic. It’s all about reinforcing group identities through shared experience, isn’t it?

            I’ve not read the books you mentioned, mostly because my specialty since I left academia is early 20th c. jazz and pop performance practice. But even then, I think the last book I read was Gidden’s Blue: The Murder of Jazz. The Internet has been an amazing resource for students of early 20th c. music, especially since the Internet Archive has been digitizing and sharing early radio broadcasts, which are a goldmine of source material.

          • HP

            I’ve not read the books you mentioned

            Adding, I’ve read the reviews, and whenever feasible, I’ve read the peer-reviewed papers on which they’re based. And there are still only 24 hours in a day to parcel out, and so much music to learn.

            When I hear about a music cognition study that’s not based on passive listening in relation to 19th c. Western expectations about emotion and meaning, I’ll certainly follow up.

            (Someone needs to take a living-roomful of amateur folk musicians and wire those fuckers up. That shouldn’t be too hard to do on a typical college campus. “Salty Dog” in G!)

            I always loved Stravinsky’s famous remark that “music is incapable of expressing anything.”

          • consciousness razor

            I always loved Stravinsky’s famous remark that “music is incapable of expressing anything.”

            If it were, neither he nor anyone listening to it has any idea what’s being expressed. You know, except for useless mush like “minor keys are sad.” The day I stop hearing people equate music with lyrics, or claim music is about some band’s political agenda or whatever, I will seriously doubt whether I’m still on the same planet.

            I’m curious about JT’s thoughts on this, as a vocalist.

            PS — Are you sure you aren’t me?

          • HP

            PS — Are you sure you aren’t me?

            Not quite. But I’m sure you’re a handsome devil with many attractive qualities.

  • Mike

    I loved these posts on your xanga and would like more. I don’t know music at all but I love theory.

    I have one question though, about how a major 6th upward is equivalent to a minor 3rd downward, etc. The math doesn’t seem to add up, even in the example given. Correct me if I’m wrong but from D to B is nine half steps up the keyboard, not eight, which would make it a minor 7th up equivalent to a minor 3rd down.

    Actually, on closer inspection JT says an octave is eleven half steps, but isn’t it twelve?

    I must be missing something here. Something to do with the E-F and B-C gaps, maybe? Is one of those considered an honorary full step, or something?

    • consciousness razor

      I have one question though, about how a major 6th upward is equivalent to a minor 3rd downward, etc. The math doesn’t seem to add up, even in the example given. Correct me if I’m wrong but from D to B is nine half steps up the keyboard, not eight, which would make it a minor 7th up equivalent to a minor 3rd down.

      Actually, on closer inspection JT says an octave is eleven half steps, but isn’t it twelve?

      Yes, it’s twelve. He skipped the tritone. The list should look like this:

      Minor 3rd (m3) – Three half steps.
      Major 3rd (M3) – Four half steps.
      Perfect 4th (P4) – Five half steps.
      [Tritone (TT) -- Six half steps. (aka Augmented 4th (A4)/Diminished 5th (D5)]
      Perfect 5th (P5) – Seven half steps.
      Minor 6th (m6) – Eight half steps.
      Major 6th (M6) – Nine half steps.
      Minor 7th (m7) – Ten half steps.
      Major 7th (M7) – Eleven half steps.
      Octave or and 8th – Twelve half steps.

      It’s useful to remember inverted intervals add up to twelve (though if an interval is larger than an octave, reduce it by an octave). To take your example, a major sixth plus a minor third is an octave, which is another way of saying 9+3=12. So if you go from D to B, then from B to the next D, you’ll be going an octave from D to D (up or down, doesn’t matter) and you’ll be covering a major sixth and a minor third.

      • HP

        So, consciousness razor, where do you stand on equal temperament? :)

        (Personally I can’t stand it. I avoid cheap digital keyboards whenever possible, and tolerate real pianos only after they’ve had a chance to “settle.”)

        • consciousness razor

          So, consciousness razor, where do you stand on equal temperament? :)

          I think of it as the lesser of two evils sometimes. There is at least a place to stand. A lot of people can’t discriminate small pitch differences well enough to perform them with a precise intonation anyway. Equal temperament is an extremely useful shorthand most of the time. As a composer I don’t write anything with the intention of it being played with an exact intonation (of whatever temperament). I expect the performers to do figure that out for themselves. As an added benefit, this guarantees that I can always claimed they’ve screwed it up. But when I venture into writing electronic music, that’s something I’ll often fiddle with.

  • Paul

    Hi JT,

    Thanks! I’ve admired your blog anyway, and I love this.

    I’ve returned to playing guitar after taking 25 years off to obtain a divorce. The guitar is different, in that you don’t need theory, especially when you’re a kid. I wanted to be an improvisational rock and roll guitarist like Jerry Garcia, and I just banged around on it. We didn’t even worry about, you know “songs” or anything. We’d find a couple of chords to that we thought we were grooving on, and I’m sure it sounded horrible about 98 percent of the time.

    I’m wiser now. I’m learning actual songs and learning some theory. I’ve written a bunch of tunes too, but I’m finding it difficult to become a singer/songwriter at age 50 because I’ve never sung before. I take lessons from a wonderful musician and I’m already working on (extremely) rudimentary breathing and vocal exercises. At this point I’m just trying match pitch and to find my range.

    I hope you continue, especially with posts on vocal training. My instructor and I were talking the other day about how our culture thinks that a person singing during the course of a day is something odd, when it should be an ordinary joy. One of my true regrets now is not having learned music theory and how to sing when I was young.

    I could answer your theory questions pretty well, I’m happy to say, but I still always relate the intervals to a fretboard instead of a keyboard.

    Thanks again, and please continue.


  • Bill

    I’m not a musician…I’ve found that actually playing an instrument requires both coordination and good taste.

    But I have a couple of sixteen-bar saccharine love melodies running around in my head; and I once thought that I could get rid of them if I gave them away. It didn’t work.

    One recipient was a former girl friend who plays second clarinet in a symphony orchestra. She really loves the E-flat clarinet, so I wrote down one piece for E-flat clarinet and harp. She was supposed to giggle (she has a really adorable giggle) and make my day; and that was supposed to be the end of it. Instead, she studied it and said, “You did this right!” It turned out that she was impressed that I had correctly transposed the E-flat clarinet part…I guess she hadn’t thought that I could count to three.

    A violinist friend, who would sometimes give my ramblings more credit than they were worth, received Motivo in si diesis maggiore per Dana che mi prende troppo in serio (tune in B-sharp major for Dana who takes me too seriously). Yes, the key signature was F-C-G-D-A double-sharp, E-B sharp…twelve sharps. She took it seriously.

    Oh, well…