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Thread: Ask me about music theory

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    Confused Box Guy fachverwirrt's avatar
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    Default Ask me about music theory

    I had a bit of a conversation in chat about some music theory stuff, and Inner Stickler suggested I make a thread. So here it is.

    Disclaimer: my training is in performance, not music theory. so I don't have the knowledge base of a PhD in music theory. However, I do have six semesters of theory, a graduate semester of analysis, and several years of experience in the industry.

    Ask away.

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    Oliphaunt The Original An Gadaí's avatar
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    Are there such thing as complimentary keys in a structured theory sense. I mean if I am playing a melody in the key of F and decide I want to change key is there some system for ascertaining what would be the best key to change to? This probably sounds stupid but I've wondered about it before. I can write, sing a passable melody in one key but when it comes to changing key mid-song I never seem to do it right, nor the transitions back to the original key.

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    The Apostabulous Inner Stickler's avatar
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    A) Your sig makes me laugh.

    B) You and exy were talking about temperaments in chat, specifically even tempered and I think, mean tempered? What does this mean? I feel like it refers to how evenly spaced the notes are from one another but I have no idea.

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    Confused Box Guy fachverwirrt's avatar
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    Quote Originally posted by The Original An Gadaí
    Are there such thing as complimentary keys in a structured theory sense. I mean if I am playing a melody in the key of F and decide I want to change key is there some system for ascertaining what would be the best key to change to? This probably sounds stupid but I've wondered about it before. I can write, sing a passable melody in one key but when it comes to changing key mid-song I never seem to do it right, nor the transitions back to the original key.
    Generally, transitions to keys that are one or two accidentals away (in terms of key signature) are going to sound the smoothest. In the "classical" world, major keys generally modulate to the dominant key (the fifth), and minor keys to the relative major. So F would usually modulate to C, although B-flat is also possible. Getting to B-flat is actually pretty straightforward; add an E-flat to the F chord and you have an F-dom7 which slides right into B-flat.

    Basically, the farther away the new key (in key signature) the more jarring the transition.
    Last edited by fachverwirrt; 30 Jul 2010 at 04:38 PM. Reason: Added quote tags so you'd know whom I'm responding to

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    Confused Box Guy fachverwirrt's avatar
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    Quote Originally posted by Inner Stickler View post
    A) Your sig makes me laugh.

    B) You and exy were talking about temperaments in chat, specifically even tempered and I think, mean tempered? What does this mean? I feel like it refers to how evenly spaced the notes are from one another but I have no idea.
    This gets complicated. Even this will be simplified.

    I'm sure you've heard an out-of-tune piano or guitar (or singer). What makes some notes out of tune and others in-tune?

    Our perception of what sounds "in-tune" can be traced back to the harmonic series. A vibrating body vibrates along its whole length at what's called the "fundamental". This is the note you hear. At the same time, it vibrates along half it's length at two times the fundamental, along a third of its length at three times the fundamental, and so on to (theoretically) infinity. That creates overtones. The relative amplitude of the overtones, incidentally, is what imparts timbre on a tone.

    Those overtones--or partials--define the harmonic series. Terminology aside: the only difference between the term "overtone" and "partial" is that "partials" include the fundamental. So the first partial is the fundamental, while the second partial is the first overtone. For our purposes, it's more useful to talk about partials.

    The partials consist of the frequencies X, 2X, 3X and so on, where X is the fundamental. As you move up the harmonic series, the intervals between partials gets progressively smaller. So, for instance, the difference between the first and second partial is an octave, the second and third is a fifth, and the third and fourth is a fourth. The difference between the first and fourth partial, therefore is two octave: notice that as you continue up, every power of two will correlate to an octave. The ratios between partials defines what we perceive as "in tune" intervals. So 3/2 (the ratio between the second and third partial) we hear as an in-tune fifth.

    Pythagoras is generally credited with discovering and defining the relationship between string length and interval. Take a string of a certain length and tension, stop it halfway down its length, and you get an octave (if you have a guitar, notice that the twelfth fret (the octave fret) is about halfway between the bridge and the nut). This principle is pretty much exactly the same idea.

    This gives rise to the tuning system known as “just intonation”. This involves taking a note, say C, and tuning every note of the octave using these whole note ratios. Strictly speaking, just intonation is any system of intonation that uses whole not ratios, but traditionally it refers to a system using specific intervals, i.e. 9/8 for a whole step (C-D), 5/4 for a third (C-E), 4/3 for the fourth (C-F), 3/2 for the fifth (C-G) and so on. An instrument tuned this way will yield very sweet sounding intervals, as long as one of the notes is C.

    The problem is, they don’t add up. Just look at C-D-E: C-D is 9/8, and C-E is 5/4. That means the interval from D-E is 10/9, not 9/8: they’re two different sized whole steps. They even have names: 9/8 is a major tone while 10/9 is a minor tone (not to be confused with major and minor seconds). Because the internal intervals don’t all add up, chords other than those involving C (and even some that do) can be out of tune: e.g. D-F-A is a particularly bad one. Further, if you want to play in another key, they will get progressively more out of tune the more remote the keys get. F# is pretty much unlistenable.

    So, in order to accommodate more complex music, you need to introduce “temperament”. Temperament is the practice of slightly detuning some intervals in order to mitigate the out-of-tuneness of others. There are many different temperaments: mean-tone was a popular one a few hundred years ago. This involved the “syntonic comma” which is the difference between the third you get if you go up four pure fifths and the one you get if you go up two pure octaves and a pure third. By lowering the fifth by one quarter of the syntonic comma, mean tone yielded a third which was closer to pure, rather than the rather noticeably sharp third of Pythagorean tuning (which involved simply tuning things using the pure fifth).

    But mean tone, while better than just intonation, still suffers the same problem; it gets more and more out of tune the farther you get from C (or whatever your base tuning note was). Various solutions were proposed and tried over the years, but the one that won out is equal temperament. This involves breaking the pure octave into twelve equal half steps logarithmically. This has the advantage of having every key be identical, with the disadvantage of having only one pure interval: the octave.

    In general, musicians are unsatisfied with equal temperament for various reasons (Mozart hated it). So while it is a necessity on some instruments like piano and guitar, any instrument that allows for minor pitch variation (like voice or un-fretted strings) will make micro adjustments to compensate for the fundamental deficiencies in equal temperament.

    And that, friends, is the simplified version. Don't get me started on stretched octaves.

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    So for instruments that are even-tempered, is there any difference between different keys? My music training is limited to a few years of piano lessons but I always had the impression some types of music tended to be in some keys, and some in other keys. But if each interval is the same, what difference does it make what key I play a piece of piano music in -- beyond, say, accommodating a singer I'm accompanying.

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    Confused Box Guy fachverwirrt's avatar
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    Quote Originally posted by Exy View post
    So for instruments that are even-tempered, is there any difference between different keys? My music training is limited to a few years of piano lessons but I always had the impression some types of music tended to be in some keys, and some in other keys. But if each interval is the same, what difference does it make what key I play a piece of piano music in -- beyond, say, accommodating a singer I'm accompanying.
    Theoretically, no. Brass players tend to like to play in flat keys and strings in sharp keys, but how strictly equal-tempered they are is situational (actually, basic brass acoustics sort of preclude them from being strictly equal tempered anyway). I don't really know why they have those preferences.

    But, at least in terms of the intervals, all keys are identical on a piano. Transposing a piece up will, however, result in a brighter sound since the notes are higher, and dropping it will darken it. But that's a function of absolute pitch, not the intervals themselves.

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    The Queen Zuul's avatar
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    I caught a reference to this glancing in chat earlier, but didn't stick around long enough to find out more, so: can you explain modes in music a little?

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    Confused Box Guy fachverwirrt's avatar
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    Quote Originally posted by Zuul View post
    I caught a reference to this glancing in chat earlier, but didn't stick around long enough to find out more, so: can you explain modes in music a little?
    A mode is a scale. The technical definition I learned was "a repeating interval set" or words to that effect. Basically, if you play a bunch of notes from one note up to its octave then repeat them, you have a mode. There are seven basic "named" modes, although you could make up others if you wanted. The seven modes are Ionian, Dorian, Phrygian, Lydian, Mixolydian, Aeolian, and Locrian. You can hear what each of these sounds like by going to a piano and playing the white notes up one octave from the appropriate starting note. Ionian starts on C, Dorian on D, and so on. Note that that doesn't mean that Dorian always starts on D; that's just a convenient way to hear the Dorian scale (once upon a time, Dorian did always start on D--at least notationally. In performance it would depend entirely on the pitch given.).

    To understand what is meant by "modal music" requires a little bit of history. For the last four hundred years or so, Western music has been largely based on the idea of "tonality". Tonality refers to the "tonic" which is the home note of a key. What makes the tonic feel like "home" is the strong directional feel of the leading tone (a half step below the tonic) leading into the tonic, and even stronger, the scale degrees 5-6-7-8 (where 8 is also 1--the tonic). This is a natural feature of the Ionian mode, which is also known as "major". No other mode has this movement leading to its base note. "Minor" derives from Aeolian (also known as "natural minor"), but when it is adapted for tonality, the sixth and seventh scale degrees are raised in the ascending scale (lowered to their "natural" pitch when descending).

    Essentially, music is "modal" if it stays within a mode without chromatic alteration, and without that strong drive to the tonic. So, it's minor if you have a raised seventh, but modal (Aeolian) if the seventh stays flatted. Modal music is common in traditional folk music. A well-known song in Dorian is "Parsley, Sage, Rosemary and Thyme". The key there is that the note on "-ry" of Rosemary is a half step higher than it would be if it were in Aeolian. The three most common modes are Aeolian, Dorian and Mixolydian. Lydian and Phrygian are pretty rare, and Locrian more so, although it's popular in jazz.

    Note that music in Ionian will never really sound modal to our modern ears, as we're so used to tonality that anything in major will naturally sound tonal.

    There's more to the history: modes are an important aspect of plainchant, for instance, but this is probably enough to start off with. I can talk about that more if anyone's interested.

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    Happy New Year! Trojan Man's avatar
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    Facher, where were you when I was starting out?!

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    The Apostabulous Inner Stickler's avatar
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    I would love for you to expand on modes in plainchant.
    I don't think so, therefore I'm probably not.

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    Confused Box Guy fachverwirrt's avatar
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    Modes in plainchant:

    Mostly, there are eight modes in plainchant. This might seem strange, since I only listed seven before, but the modes are defined a little differently in chant. Modes come in pairs in plainchant, divided into the authentic modes and the plagal modes. The difference between them is the range; authentic modes range from the final (the base note) to an octave above, with perhaps one step below the final, while plagal modes extend from a fourth below the final to a fifth above. The eight modes are Dorian, Hypodorian, Phrygian, Hypophrygian, Lydian, Hypolydian, Mixolydian, and Hypomixolydian. Hypo- indicates a plagal mode.

    The critical features of a church mode are the final the ambitus and the recitation tone. The final, as I mentioned, is the base note--what became known as the tonic in tonal music. The ambitus is the range, and the recitation tone is the tone that most of the melody centers around. In the authentic modes, the recitation tone is a fifth above the final, while in plagal modes it's a third above the final.

    You might notice the absence of the Aeolian, Locrian and Ionian modes. These were not used by name in plainchant. However, notice that the ambitus of Hypodorian actually covers the scale of the Aeolian mode, Hypophrygian that of Locrian, and Hypoliydian that of Ionian. So while, for instance, Hypodorian is theoretically centered around the Dorian interval set and based on D, in practice it sounds very much like Aeolian.

    These modes are all based on the naturals (the white notes): so Dorian always starts on D, Phrygian on E, etc. I've already mentioned that modes don't have chromatic notes. I also mentioned that things are never that simple. In reality, B-flat often appears in plainchant, particularly in Dorian and Lydian. The reason for this is that the tri-tone (the interval between F and B) was considered unacceptable (the devil in music), so the B-flat was introduced to avoid direct tri-tones. Thus was born the concept of chromatacism. Note also that Dorian with a B-flat is identical to Aeolian, and Lydian with a B-flat is identical to Ionian. I'd say that this is one of the seeds of the later development of tonality, but that's getting into PhD theory or musicology stuff and I don't have the knowledge base for that.

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    The Apostabulous Inner Stickler's avatar
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    I'm sure we've all seen Rob Pavaronian's bit on Pachelbel, specifically his contention that "all songs use the same damn chords". I imagine you could tell us quite a bit about chord progression. What chord progression is Rob talking about, why is that one so popular in western music and is it specific to tonal music or is it also present in modal?

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    This isn't really music theory, but I was wondering about this today and figured you were the person to ask: do opera singers learn the languages they sing in? Do you have to speak Italian and German and French to at least some degree to sing opera? Or do singers just memorize the words phonetically and get coached on pronunciation? Is reading a translation of the lyric enough to insert the right emotion in the right spot when performing? Do singers eventually pick up on the languages? Do they study them formally?

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    Confused Box Guy fachverwirrt's avatar
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    Quote Originally posted by Inner Stickler View post
    I'm sure we've all seen Rob Pavaronian's bit on Pachelbel, specifically his contention that "all songs use the same damn chords". I imagine you could tell us quite a bit about chord progression. What chord progression is Rob talking about, why is that one so popular in western music and is it specific to tonal music or is it also present in modal?
    Answered in three part:

    I: Chord progressions
    II: Pachelbel's canon
    III: Rob Paravonian's rant

    N.B.: Symbols. Chords in tonal music are identified using Roman numerals. The numeral itself identifies the scale degree of the root of the chord. Upper case numerals (e.g. IV) indicate a major triad. Lower case (e.g. iii) indicate a minor triad. Lower case with a small superscript "O" (e.g. viio) indicates a diminished triad, and upper case with a superscript + (e.g. VI+) indicates an augmented triad.

    Part I: Chord progressions.

    Tonality is ultimately based on the following chord progression: I-V-I. That's it. Move from the tonic (the I chord) to the dominant (the V chord) and back. Obviously that's not terribly interesting, so two things happen: music is broken into phrases, and other chords are added in to make things more interesting. This turns the structure into I-y-V-I, where y is everything that happens between the first I and the last V. This can be viewed both in the context of individual phrases, and the piece as a whole.

    This is not to say that every phrase takes the same form. Phrases can (and often do) begin and end on other chords. There are four basic types of cadences (endings) that phrases can use. The authentic or full cadence (V-I), the half cadence (y-V), the deceptive cadence (usually V-vi) and the plagal cadence (IV-I). The last is most commonly used as a tag at the end of a piece or section, especially in hymns; it's colloquially known as the "amen cadence".

    We'll talk about phrases that end in full cadences. These are the I-y-V-I phrases. The y part can include any number of chords, although their sequences are governed by some rules (and by "rules" I mean "conventions"). The most common movements are to chords a fifth below (or a fourth above) the preceding chord. So I often goes to IV, vi goes to ii, ii goes to V, iii goes to vi, etc. Those aren't hard and fast; you can play around with those relationships quite a bit. There are a few moves that are not going to happen often if at all, like iii-V, but there's a lot of freedom. Movement by fifths is the strongest movement, though, so you'll see it a lot.

    The most common chords immediately before V are ii, IV and vi. These are the "pre-dominants".

    In baroque and classical music, things tend to come in sets of four and eight: so phrases are often four bars or eight bars, or, in the case of Pachelbel, two bars of four beats. That brings us to Pachelbel.

    II Pachelbel's canon.

    Pachelbel's canon in D is based on the chord progression I-V-vi-iii-IV-I-IV-V (back to I to start the next iteration). It's a perfectly logical sequence: down a fourth (not as strong as down a fifth, but still a strong move), weak deceptive cadence (weak because it's in the middle of a phrase), down a fourth, up a step (similar motion as from V-vi), down a fourth, then down a fifth to the predominant IV, then V, then back to I.

    It's not unusual, but neither is it that common. Here's the key point, though: while it's the only harmonic scheme that makes sense given the bass line, it is not the only way to harmonize the melody. There are other perfectly logical ways to do so, Pachelbel just didn't choose to do so.

    This brings us to Paravonian.

    III: Rob Paravionian.

    I love the Pachelbel Rant; don't get me wrong.

    However, there are a few things to realize. First of all, when he starts demonstrating how various songs use the same chords as Pachelbel's canon, he only uses half the progression: I-V-vi-iii. It's a lot more likely that four chords are going to be the same between any given songs than eight. Further, after a while he starts fudging it completely and just going I-vi-V-I. That's a sequence that doesn't even appear in the canon, although it can be used to accompany the melody.

    And that's the thing; there are always going to be different ways to harmonize a melody. Not every melody can be harmonized the same way as the canon, but the canon has a fairly simple melody, as do a lot of popular songs, and it's not terribly surprising that you can find a bunch of songs that can be harmonized the same way.

    As to the last question, the things that fundamentally separates tonal music from modal music is the universality of V-I in tonal music. Most modes don't have a V chord: Dorian, Mixolydian and Aeolian have v chords (that is, minor), Phrygian has vo and Locrian's V chord is a tri-tone away, not a fifth. Only Ionian and Lydian have a V chord, and only Ionian (i.e. major), has the major-minor V7, which imparts even more directional strength to the dominant-tonic movement. Lydian's V7 is major-major, which is much weaker.

    Long story short, V-I just isn't as important in modal music as tonal.

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    Confused Box Guy fachverwirrt's avatar
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    Quote Originally posted by Exy View post
    This isn't really music theory, but I was wondering about this today and figured you were the person to ask: do opera singers learn the languages they sing in? Do you have to speak Italian and German and French to at least some degree to sing opera? Or do singers just memorize the words phonetically and get coached on pronunciation? Is reading a translation of the lyric enough to insert the right emotion in the right spot when performing? Do singers eventually pick up on the languages? Do they study them formally?
    You need to know what you're singing, certainly. But you don't need to be fluent. As long as you are aware of what you (and everyone else on stage) is talking about, and know how to pronounce it, you'll be fine. That said, opera singers tend to pick up quite a bit of various language simply through exposure.

    Some people study languages formally, but it's by no means a requirement. My degrees required diction training and I had to pass a reading test in one language (I chose German) for my master's, but that was a requirement of the academic side of things to establish that I could successfully perform research in another language.

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    Happy New Year! Trojan Man's avatar
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    Facher, how do you explain the similarities, in chord structure, between Pachebel's Canon in D, and Green Day's 'Basket Case'?

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    Confused Box Guy fachverwirrt's avatar
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    Quote Originally posted by spitz View post
    Facher, how do you explain the similarities, in chord structure, between Pachebel's Canon in D, and Green Day's 'Basket Case'?
    See post 15.

    The answer, ultimately, is that Green Day chose the same chord structure as Pachelbel. Nothing more complicated than that.

    I-V-vi is a particularly popular chord progression. See: O Canada.

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    I've played guitar since I was 15 and I've learned more about music theory reading this thread than I've learned in the last 45 years. This is fascinating!
    Political correctness will be the death of our country.

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    * Do you know, if one exists, the order of dissonance between intervals? Eg, in C Major, the least dissonant is obviously C. Then I believe it's G (the 5th interval).

    * Do you know the names/intervals of the scales used to make drony, 'oriental/middle eastern' sounding music? (Eg, Bb notes in D Major, etc).

    * Is there a proper musical term for starting a song on a dominant 7th chord?

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    Confused Box Guy fachverwirrt's avatar
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    Quote Originally posted by spitz View post
    * Do you know, if one exists, the order of dissonance between intervals? Eg, in C Major, the least dissonant is obviously C. Then I believe it's G (the 5th interval).
    A proper answer involves a rather in depth exploration of music history which I'm not prepared to give right now (ask me 12 years ago). But basically, you could order things within the octave thus (least to most dissonant): perfect unison, perfect octave, perfect fifth, perfect fourth, major third/minor sixth, minor third/major sixth, minor seventh, major second, major seventh, minor second, augmented fourth (diminished fifth, tritone, whatever you want to call it). I would call the tritone the most dissonant because it has the most tendency to resolve; that is, it sets up the highest degree of tension.

    * Do you know the names/intervals of the scales used to make drony, 'oriental/middle eastern' sounding music? (Eg, Bb notes in D Major, etc).
    Not really. The vast majority of my training is in western music.

    * Is there a proper musical term for starting a song on a dominant 7th chord?
    Not that I know of. You can start a song on pretty much any chord you want to. Relevant terminology tends to refer to the last chord, not the first.

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    Why do some songs or jingles get stuck in my head, while others are easily forgotten?

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