The Devil’s interval

by Jimmy Veith

Have you ever been freaked out by a piece of music that sounded evil? Have you heard combinations of notes that were so dissonant that it made you tense and restless, but yet was strangely alluring? Well, you may have been placed under the spell of the Devil’s interval, known in music theory as the augmented 4th or flatted 5th.

Let me explain. Remember when Maria, the good Nun from “The Sound of Music”, taught the children how to sing, with the Do-re-mi-fa-so-la-ti-do song? That was the major scale on which most Western music is based. In the key of C, it would be all the white keys on the piano; ie, C, D, E, F, G, A B and C. Each note of the scale is assigned a number. In the key of C, C is 1, D is 2, E is 3, F is 4, G is 5, A is 6 and B is 7.

For some mysterious reason, the major scale is not symmetrical in its intervals. There are whole steps between C, D, and E, but a half step from E to F. There are whole steps between F, G, A and B, but a half step from B to C. Now, let’s create a more sinister sounding scale by eliminating the half steps and playing only whole steps. If you start with middle C, you would play C, D, E, F# (G flat), G# (A flat), A# (B flat), then C again. You have just played a scale based on the tri-tones, which is a scale of six different notes in equal intervals as opposed to seven notes found in the major scale.

Now this is where it gets freaky. Play the C and F# (or G flat) together. This is the interval known as the augmented 4th or flatted 5th. Play this over and over again. How does it make you feel? Now play C and G flat in alternating order, over and over again, one second apart. Do you recognize the opening guitar riff in Jimi Hendrix’s “Purple Haze”? Play it some more. Have you summoned the devil yet? Ok, that’s enough, Quit Now! Quit Now! Quit Now I say, before it’s too late!

OK. I may be exaggerating. However, this interval has been used by composers when they want to create an atmosphere of evil or dread. It is used extensively by heavy metal groups such as Black Sabbath, and classical compositions such as Wagner’s Gotterdammerung, Beethoven’s Fidelio. Also, it is found in modern compositions such as West Side Story, and the theme song of the Simpson’s.

It has been said that this interval was banned in the middle ages by the clergy. This may be more mythology than fact. Are there any musicologists out there who could shed some light on this issue?

I don’t mean to suggest that artists that use this interval are by any means evil. Great music involves interplay between tension and release, and the use of this interval is one of many tools that a skillful composer can and should use to create tension.

Now here is something for you Lutherans. Consider the great hymn “A Mighty Fortress is Our God,” by Martin Luther himself. The third line of the first verse reads: “For still our ancient foe, doth seek to work us woe.” The third line of the third verse reads: “The Prince of Darkness grim,
we tremble not for him. ” The two lines where Luther refers to the Devil in the text of the hymn, also happens to be when the “devil’s interval” is found in the melody line. Just a coincidence? Or genius?

Big Brother Butts In:  I would add one more thing that Jimmy pointed out to me when he was explaining all of this over the piano.  I had always wondered why it is that musical scales have to have those half-steps.  Wouldn’t it be easier and more consistent and more orderly for a scale to have all whole steps? It would, but now I know that a scale with all whole steps is actually discordant.  Not only that, it has the Devil’s Interval!   Which teaches us that perfect regularity is neither beautiful nor good.   True beauty–whether of music or art or literature or a person–needs its quirks, its inconsistencies, its surprises, even its flaws. Philosophies and ideologies that demand utterly consistent regularity–think of Marxism–become inhuman, tyrannical, and demonic.  As do people when they try to fit their neighbors into some regular pattern of whole notes.  And God, who Himself is unutterably complex and confounding to human reason, designed things this way.  (And if you think such connection between music and other kinds of cosmic order is just made up, the old music theorists, such as Bach–anyone know if he used the Devil’s Interval?–thought and made music in these terms.

  • http://jesus-is-not-irrelevant.blogspot.com/ Mary Johnson

    I remember reading Tolkien’s book The Silmarillion when the Ainu sang the creation work and Melkor broke off into his own version of things, dissonant and discordant. That chapter has always intrigued me and prompted thoughts along the lines of angelic singing and creation itself.

    Music is much more than just pretty sounds, it has the power to transcend language and thought becoming as it were, the seed of each. Who knows exactly the purpose of music in the grand scheme? I do know that the little old folks in nursing homes suffering from various forms of dementia will hold on to song long after verbal skills are lost.

    The use of the devil’s interval is an intentional moment in the story of the piece, just as the use of any and all chords. Music is powerful in it’s own right, no words needed.

  • http://jesus-is-not-irrelevant.blogspot.com/ Mary Johnson

    I remember reading Tolkien’s book The Silmarillion when the Ainu sang the creation work and Melkor broke off into his own version of things, dissonant and discordant. That chapter has always intrigued me and prompted thoughts along the lines of angelic singing and creation itself.

    Music is much more than just pretty sounds, it has the power to transcend language and thought becoming as it were, the seed of each. Who knows exactly the purpose of music in the grand scheme? I do know that the little old folks in nursing homes suffering from various forms of dementia will hold on to song long after verbal skills are lost.

    The use of the devil’s interval is an intentional moment in the story of the piece, just as the use of any and all chords. Music is powerful in it’s own right, no words needed.

  • larry

    Very good article! I’ve always been an amatuer lover of music and music theory. It was one of those ‘fun’ things I took advantage of studying in school in addition to my major, I loved it. Music theory, scales, resolution always fascinated me.

    Like Dr. Veith I always wondered myself when studying always wonder the “why” of the scales (why not symetric and all whole tones or half tones, why sharps and flats on some and not between b and c, e and f, why flats one direction and sharps the other).

    That’s a fascinating insight on Mighty Fortress, I don’t know the answer and I’m not sure which would be more intriguing “coincidence” or “genius”.

    Our pastor was pointing out a signature of all the hymns that Luther himself wrote, I cannot for the life of me recall it right now (perhaps someone can), that one finds in all his hymns. I think it was that 8th note drop in all of them. I’ll have to ask him again.

  • larry

    Very good article! I’ve always been an amatuer lover of music and music theory. It was one of those ‘fun’ things I took advantage of studying in school in addition to my major, I loved it. Music theory, scales, resolution always fascinated me.

    Like Dr. Veith I always wondered myself when studying always wonder the “why” of the scales (why not symetric and all whole tones or half tones, why sharps and flats on some and not between b and c, e and f, why flats one direction and sharps the other).

    That’s a fascinating insight on Mighty Fortress, I don’t know the answer and I’m not sure which would be more intriguing “coincidence” or “genius”.

    Our pastor was pointing out a signature of all the hymns that Luther himself wrote, I cannot for the life of me recall it right now (perhaps someone can), that one finds in all his hymns. I think it was that 8th note drop in all of them. I’ll have to ask him again.

  • Jonathan

    The name “devil’s interval” comes from the Latin phrase “diabolus in musica,” “the devil in music.” The interval in question is the augmented fourth/diminished fifth, also known as the tritone. Harmonically speaking, the tritone is part of the seventh chord built on the dominant, and in that way it’s a part of virtually all tonal music. Melodically, the tritone is less common but by no means infrequent: Bach indeed uses it in the (admittedly rather mysterious) fugue subject of the Kyrie from his B-minor Mass. In his cantata recitatives, the bass line frequently drops by a tritone, not necessarily as an example of word painting, but to support a modulation or tonicization of a new key area (which modulation or tonicization may indeed be an example of word painting).

    Regarding the anecdote that the clergy in the Renaissance banned the tritone in sacred music: I do not know for certain that this happened. A melodic tritone, however, breaks the rules of sixteenth-century counterpoint, and thus it would not have appeared because it was not stylistically proper. This fact, in turn, would create an even more enhanced meaning for any melodic tritone that might be found in this repertoire (I can’t think of a specific example right now; I’m sure it’s exceedingly rare, however—perhaps it appears in the music of Gesualdo, who is known for his particularly dissonant Renaissance polyphony, as well as for being one of the only big-name composers who was also a murderer—likely not a coincidence). In Renaissance polyphony, though, dissonance such as Gesualdo’s is more a consequence of harmonic motion by major thirds (another major component of the whole-tone scale!) than by melodic tritones.

  • Jonathan

    The name “devil’s interval” comes from the Latin phrase “diabolus in musica,” “the devil in music.” The interval in question is the augmented fourth/diminished fifth, also known as the tritone. Harmonically speaking, the tritone is part of the seventh chord built on the dominant, and in that way it’s a part of virtually all tonal music. Melodically, the tritone is less common but by no means infrequent: Bach indeed uses it in the (admittedly rather mysterious) fugue subject of the Kyrie from his B-minor Mass. In his cantata recitatives, the bass line frequently drops by a tritone, not necessarily as an example of word painting, but to support a modulation or tonicization of a new key area (which modulation or tonicization may indeed be an example of word painting).

    Regarding the anecdote that the clergy in the Renaissance banned the tritone in sacred music: I do not know for certain that this happened. A melodic tritone, however, breaks the rules of sixteenth-century counterpoint, and thus it would not have appeared because it was not stylistically proper. This fact, in turn, would create an even more enhanced meaning for any melodic tritone that might be found in this repertoire (I can’t think of a specific example right now; I’m sure it’s exceedingly rare, however—perhaps it appears in the music of Gesualdo, who is known for his particularly dissonant Renaissance polyphony, as well as for being one of the only big-name composers who was also a murderer—likely not a coincidence). In Renaissance polyphony, though, dissonance such as Gesualdo’s is more a consequence of harmonic motion by major thirds (another major component of the whole-tone scale!) than by melodic tritones.

  • Booklover

    I am performing in the wonderfully silly funny musical, “Xanadu,” which contains some good Olivia Newton John and Electric Light Orchestra music, and which pokes fun of the 80′s and leg warmers and roller discos. We sing a tri-tone, which is sometimes difficult to hear, in the title song. The only evil I can think of that the interval might be referring to is the level of artistic achievement in that era. :-)

  • Booklover

    I am performing in the wonderfully silly funny musical, “Xanadu,” which contains some good Olivia Newton John and Electric Light Orchestra music, and which pokes fun of the 80′s and leg warmers and roller discos. We sing a tri-tone, which is sometimes difficult to hear, in the title song. The only evil I can think of that the interval might be referring to is the level of artistic achievement in that era. :-)

  • Booklover

    Welcome to the blogosphere, and may your relationship with your brother, even though you are “opposites,” always be blessed. Thank you for speaking of music.

    I could not find a consecutive or harmonic tri-tone in the third line of “A Mighty Fortress is Our God,” unless you hold the first note until you play the 7th note in the melody. Is this the tri-tone to which you were referring?

  • Booklover

    Welcome to the blogosphere, and may your relationship with your brother, even though you are “opposites,” always be blessed. Thank you for speaking of music.

    I could not find a consecutive or harmonic tri-tone in the third line of “A Mighty Fortress is Our God,” unless you hold the first note until you play the 7th note in the melody. Is this the tri-tone to which you were referring?

  • JH

    Interesting article.

    What blew my mind was in my physics of music class, when we extrapolated tonal frequencies starting at some freq X. Going up by a perfect 5th as discovered by the greeks (2/3rd of root wavelength). And using the circle of 5ths to arrive at an upper harmonic/multiple of the original freq X. IT DIDN’T WORK. The math gives you some freq a few hertz away from the harmonic. We were devastated :)

  • JH

    Interesting article.

    What blew my mind was in my physics of music class, when we extrapolated tonal frequencies starting at some freq X. Going up by a perfect 5th as discovered by the greeks (2/3rd of root wavelength). And using the circle of 5ths to arrive at an upper harmonic/multiple of the original freq X. IT DIDN’T WORK. The math gives you some freq a few hertz away from the harmonic. We were devastated :)

  • http://lutherama.blogspot.com Dr. Luther in the 21st Century

    Oh my, don’t give the anti-rock Luddites more reason to hate good music!!!!! They already convinced its rhythm is from the devil. They don’t need to hear about it containing an interval called the devil’s interval. Interesting article, having played music I knew that some chords were great at creating a sinister feel or indicating chaos, but I never knew the formal name.

  • http://lutherama.blogspot.com Dr. Luther in the 21st Century

    Oh my, don’t give the anti-rock Luddites more reason to hate good music!!!!! They already convinced its rhythm is from the devil. They don’t need to hear about it containing an interval called the devil’s interval. Interesting article, having played music I knew that some chords were great at creating a sinister feel or indicating chaos, but I never knew the formal name.

  • JH

    edit: meant to say “octave multiple” rathern than harmonic multiple. big difference there. one is a subset of the other :)

  • JH

    edit: meant to say “octave multiple” rathern than harmonic multiple. big difference there. one is a subset of the other :)

  • CRB

    So, what do the musicologists on this blog think about rap “music”?
    Does it use the devil’s interval?

  • CRB

    So, what do the musicologists on this blog think about rap “music”?
    Does it use the devil’s interval?

  • Booklover

    CRB, I think that when Elijah called down fire from heaven, in an “in your face” moment, on the Baal worshippers, he may have used rap. :-)

  • Booklover

    CRB, I think that when Elijah called down fire from heaven, in an “in your face” moment, on the Baal worshippers, he may have used rap. :-)

  • http://facebook.com/mesamike Mike Westfall

    What I wonder is how did western music develop a 12 half-step scale?

    It must’ve just sounded good, though other civilizations developed a pentatonic (5-note) scale (which corresponds to just the black keys on a piano).

    At least it developed in a way that is easy to define mathematically. For example, if you take 440 Hz as the note A above middle C on a piano keyboard, you can figure out the frequency of the other notes on the keyboard by applying this formula: F(n) = 440 * 2^(n/12), where n is the distance of the key from the middle A key (negative to the left of middle A).

  • http://facebook.com/mesamike Mike Westfall

    What I wonder is how did western music develop a 12 half-step scale?

    It must’ve just sounded good, though other civilizations developed a pentatonic (5-note) scale (which corresponds to just the black keys on a piano).

    At least it developed in a way that is easy to define mathematically. For example, if you take 440 Hz as the note A above middle C on a piano keyboard, you can figure out the frequency of the other notes on the keyboard by applying this formula: F(n) = 440 * 2^(n/12), where n is the distance of the key from the middle A key (negative to the left of middle A).

  • http://www.newreformationpress.com Patrick Kyle

    Have you ever been freaked out by a piece of music that sounded evil?

    Yes, by a group called The Lords of Acid.
    Even my pagan sister (yes, that is her religion) described the music as having ‘that God-hating edge’ and expressed her hatred for their music.

  • http://www.newreformationpress.com Patrick Kyle

    Have you ever been freaked out by a piece of music that sounded evil?

    Yes, by a group called The Lords of Acid.
    Even my pagan sister (yes, that is her religion) described the music as having ‘that God-hating edge’ and expressed her hatred for their music.

  • http://www.geneveith.com Gene Veith

    I think rap is just poetry. It has no melody at all, except for background samples. All that is left is rhythm.

  • http://www.geneveith.com Gene Veith

    I think rap is just poetry. It has no melody at all, except for background samples. All that is left is rhythm.

  • http://www.toddstadler.com/ tODD

    Jimmy, it’s funny, but when you first mentioned “Maria, the good nun”, I actually thought of “Maria”, the song in West Side Story (which you alluded to later), which contains the tritone interval in the syllables “Ma-ri”.

    However, along with Booklover (@5), I can find no tritone in “A Mighty Fortress”. In order to qualify as an interval, you have to have two notes either played simultaneously (harmonic interval), or consecutively (melodic interval). While the third verse contains notes that, if played simultaneously or consecutively, would constitute a tritone, they are actually several notes apart (in the first verse, they appear in these bolded syllables: “The old E-vil foe”). I don’t think that qualifies. It is the only occurence of an accidental (an augmented fourth relative to the key of the piece) in the melody line, though, which certainly creates tension in the same way a tritone does.

    I think it’s an interesting observation that you make about references to Satan in that song and the accompanying musical tension. Though the observation doesn’t work so much for the other two verses. I’ll go with: coincidence.

  • http://www.toddstadler.com/ tODD

    Jimmy, it’s funny, but when you first mentioned “Maria, the good nun”, I actually thought of “Maria”, the song in West Side Story (which you alluded to later), which contains the tritone interval in the syllables “Ma-ri”.

    However, along with Booklover (@5), I can find no tritone in “A Mighty Fortress”. In order to qualify as an interval, you have to have two notes either played simultaneously (harmonic interval), or consecutively (melodic interval). While the third verse contains notes that, if played simultaneously or consecutively, would constitute a tritone, they are actually several notes apart (in the first verse, they appear in these bolded syllables: “The old E-vil foe”). I don’t think that qualifies. It is the only occurence of an accidental (an augmented fourth relative to the key of the piece) in the melody line, though, which certainly creates tension in the same way a tritone does.

    I think it’s an interesting observation that you make about references to Satan in that song and the accompanying musical tension. Though the observation doesn’t work so much for the other two verses. I’ll go with: coincidence.

  • Martin Winter

    @Mike 17: But didn’t this even-spaced formula develop only fairly late? I think Bach wrote his Well-Tempered Clavier to celebrate the fact that one could finally use all keys equally. There are many other tunings, especially in organs. The even-tempered tuning has only one perfect interval, which is the octave. Every other interval is slightly off, with the benefit of making every key usable.

  • Martin Winter

    @Mike 17: But didn’t this even-spaced formula develop only fairly late? I think Bach wrote his Well-Tempered Clavier to celebrate the fact that one could finally use all keys equally. There are many other tunings, especially in organs. The even-tempered tuning has only one perfect interval, which is the octave. Every other interval is slightly off, with the benefit of making every key usable.

  • Lindsay

    Our major scale is derived from one of the church modes. The modes, which are still used, were formalized by Guido of Arezzo (and other music scholars) in the Middle Ages. They drew heavily from what had been written about Greek music theory. Guido of Arezzo was the first to come up with a system of notation. Before that time all music was passed down orally. That doesn’t answer why we have the pattern of whole and half steps in full, but that’s a start.

    We do know that tritones were avoided in early church music. The first form of polyphony was called organum. There are several types of organum. Parrallel organum was formed by two or more parts singing in parrallel motion at the interval of a perfect 5th. When singing organum at the interval of a 4th, they avoided the tritone at all costs. This style of organum is called mixed parrallel and oblique organum. To our ears, this style of polyphony sounds foreign and discordant, but in the ninth century this was considered consonant and beautiful.

    In any case, the tritone (and all disonance) adds to fullness of music and adds emotion that purely consonant music would lack. One of the most common chords in western music contains a tritone (the major 7th chord). It is found in nearly every song written since 1500. Bach did indeed use the tritone. He loved to prove that he could break the rules of partwriting and still have an amazing work, and I love him for it!

  • Lindsay

    Our major scale is derived from one of the church modes. The modes, which are still used, were formalized by Guido of Arezzo (and other music scholars) in the Middle Ages. They drew heavily from what had been written about Greek music theory. Guido of Arezzo was the first to come up with a system of notation. Before that time all music was passed down orally. That doesn’t answer why we have the pattern of whole and half steps in full, but that’s a start.

    We do know that tritones were avoided in early church music. The first form of polyphony was called organum. There are several types of organum. Parrallel organum was formed by two or more parts singing in parrallel motion at the interval of a perfect 5th. When singing organum at the interval of a 4th, they avoided the tritone at all costs. This style of organum is called mixed parrallel and oblique organum. To our ears, this style of polyphony sounds foreign and discordant, but in the ninth century this was considered consonant and beautiful.

    In any case, the tritone (and all disonance) adds to fullness of music and adds emotion that purely consonant music would lack. One of the most common chords in western music contains a tritone (the major 7th chord). It is found in nearly every song written since 1500. Bach did indeed use the tritone. He loved to prove that he could break the rules of partwriting and still have an amazing work, and I love him for it!

  • Joanne

    I am always impressed by the sharp dissonance I hear in Bach’s St. John’s Passion, at the introductory choral piece. It’s otherwordly and quite modern sounding in its discord. What is Bach doing there to get that awe-full, rue-full sound?

  • Joanne

    I am always impressed by the sharp dissonance I hear in Bach’s St. John’s Passion, at the introductory choral piece. It’s otherwordly and quite modern sounding in its discord. What is Bach doing there to get that awe-full, rue-full sound?

  • Martin Winter

    Joanne, I absolutely agree. I recently had the privilege of hearing St. John’s Passion live in Amsterdam and was very moved by the overture. I am no musical expert, but Bach is repeatedly using seconds (I hope this is the proper English term), which means: He goes up or down a half or whole step while letting the former note continue to play. This causes the unusual dissonance. Also, I think the driving bass line is very modern.

  • Martin Winter

    Joanne, I absolutely agree. I recently had the privilege of hearing St. John’s Passion live in Amsterdam and was very moved by the overture. I am no musical expert, but Bach is repeatedly using seconds (I hope this is the proper English term), which means: He goes up or down a half or whole step while letting the former note continue to play. This causes the unusual dissonance. Also, I think the driving bass line is very modern.

  • http://www.biblegateway.com/versions/Contemporary-English-Version-CEV-Bible/ sg

    Wow, very interesting. Thanks for posting, Jimmy.

  • http://www.biblegateway.com/versions/Contemporary-English-Version-CEV-Bible/ sg

    Wow, very interesting. Thanks for posting, Jimmy.

  • nqb

    Along with the inherent tension, I’ve also heard that the “Devil’s interval” gets its name from the six half-steps that make up the interval, one short of the “Perfect Fifth.”

    I have to take major issue with Dr. Veith’s comment about rap, and I think that when I explicitly state your main assumption you’ll see why: “Music requires melody.”

    The presence of rhythm is really all that is necessary for music. Is a snare drum solo music? Certainly.

    Furthermore, if rap isn’t music, the status of It’s Gonna Rain by Steve Reich is even more in question. That’s one of my favorite pieces.

    Melody is really secondary to rhythm. Though one may say melody is required for good music, but I disagree.

  • nqb

    Along with the inherent tension, I’ve also heard that the “Devil’s interval” gets its name from the six half-steps that make up the interval, one short of the “Perfect Fifth.”

    I have to take major issue with Dr. Veith’s comment about rap, and I think that when I explicitly state your main assumption you’ll see why: “Music requires melody.”

    The presence of rhythm is really all that is necessary for music. Is a snare drum solo music? Certainly.

    Furthermore, if rap isn’t music, the status of It’s Gonna Rain by Steve Reich is even more in question. That’s one of my favorite pieces.

    Melody is really secondary to rhythm. Though one may say melody is required for good music, but I disagree.

  • http://www.toddstadler.com/ tODD

    As to the somewhat parallel discussion of our system of notes, scales, and music … man, that’s a rabbit hole I keep going down, yet not fully grasping. And we all know what a little knowledge is. So begins my attempt to explain, at some length, what I know about musical tuning.

    I’ll start with Mike’s comment (@11). The mathematical formula he gives is correct, but only for more recent centuries (from the 1580s onward, maybe?). It describes what is known as equal temperament*. That is, a system of tuning in which the ratio between the frequencies of any two adjacent notes (notes a half-step apart) is exactly the same. The upshot of this is that you can transpose your music to any key and it sounds the same (other than being higher or lower in frequency, obviously). Ah, but things were not always this way!

    Back in the day, it would seem**, there was a much simpler mathematical system at work in tuning (calculating the twelfth root of something, after all, is a fairly difficult mathematical task). As I understand things (and, again, let me add that I likely do not), before equal temperament, there was Pythagorean tuning (among others). Always bringing it back to the Greeks!

    Pythagorean tuning calculates all its intervals based on the ratio of 3:2 (much simpler to calculate than the 12th root of 2!). Remember that most musical instruments are either based on the vibration of strings or columns of air in pipes. While the ancients may not have been able to calculate the pitch or frequency (in Hertz) of notes, they could, of course, measure the lengths of such strings and pipes — and those lengths are (inversely) proportional to the pitches they generate! So notes whose frequencies are in a 3:2 ratio will also have strings in a 3:2 ratio.

    Well, what would we call this 3:2 pitch ratio today? It’s a perfect fifth! Say, from a C up to a G. Most of us agree that that’s a nice interval. And so mathematically pure! Well, if you keep going up a fifth, you’d get C, G, D, A, E, B, F#, C#, G#, D#, A#, E# (also known as F) … back to C. Hey, whaddya know, 12 notes! Of course, they’d all span several octaves, but as it happens that most of us think that notes an octave apart sound “the same”, you can transpose these notes down varying numbers of octaves to form the chromatic scale we all know and love.

    Except. If you did the math, you realize that the C you ended up on, using this 3:2 ratio, wasn’t a perfect several octaves above the C you started on. Close, but a bit off. That’s one problem (which was solved by simply fudging things back to a perfect octave, which made that particular perfect fifth … less than perfect, also called the “wolf fifth”). Also, this scale you would have constructed wouldn’t really sound like the scale on your modern, equal-tempered piano. If you were so musically attuned, you’d think that such a Pythagorean scale sounded … off on several notes.

    What’s more, though, this Pythagorean tuning doesn’t really produce lots of nice intervals, other than the perfect fifths it’s based on (and their inversion, the perfect fourth). The thirds it produces are fairly dissonant. So people tempered the pitches of some notes and came up with “just intonation”, in which intervals form pleasing simple fractions, as well as more pleasing sounds. The perfect fifth keeps its 3:2 ratio, but the third now has a nicer-sounding 5:4 ratio, as opposed to the Pythagorean 81:64 (do the math — they’re close, but not the same).

    Well, all that’s quite nice, but only in certain keys. By which I mean, both the Pythagorean and “just” systems get some intervals very mathematically perfect, but others, they fudge. So you can’t just go around deciding you’d rather play your song in D instead of C, because it’ll actually sound different, due to those fudged intervals. There were some keys where things just sounded awful! This may explain why older composers picked the keys they did, or why they thought certain keys had different moods from others. Back then, they did. Now, they do not.

    So even if all the musicians using modern (equal) and ancient (Pythagorean, just) tuning wrote their music down the same way, their audiences would’ve heard something (slightly) different than we would on modern (equal-tempered) instruments.

    Anyhow, along came equal temperament, which Mike described, to allow music to be transposed willy-nilly. No more fear of bad keys, or bad intervals. Except. Now all the intervals are all a little bit off from their pure mathematical counterparts! For example, remember the Pythagorean 3:2 ratio (that would be the same as multiplying by 1.5) for a perfect fifth? In our modern system, it’s actually 1.4983! And so on. So in order to make things more perfect overall, we actually had to make the things that were truly perfect and fudge them a bit.

    So, back to Dr. Veith’s addition:

    I had always wondered why it is that musical scales have to have those half-steps. Wouldn’t it be easier and more consistent and more orderly for a scale to have all whole steps?

    I think the more relevant question is: Why does the human brain (apparently? or only in the West?) find such simple ratios as are found in the third, fourth, and fifth so pleasing? It’s that sense of consonance that creates the pattern of steps and half-steps that compose our scale.

    And, finally, to this bit of application from Dr. Veith:

    True beauty–whether of music or art or literature or a person–needs its quirks, its inconsistencies, its surprises, even its flaws. Philosophies and ideologies that demand utterly consistent regularity–think of Marxism–become inhuman, tyrannical, and demonic.

    What’s interesting to me is that any of these tuning systems could be said to be trying too hard to enforce an ideology, as well as containing the fudging necessary to make that ideology work. Ah well.

    *Equal temperament is similar to, but somehow different from, well temperament, as made most famous by Bach with his Well-Tempered Clavier. Don’t ask me about the differences, I don’t get them myself.

    **Obviously, we don’t have recordings of how things sounded back then, so we can only go off of what people wrote about how they tuned their instruments.

  • http://www.toddstadler.com/ tODD

    As to the somewhat parallel discussion of our system of notes, scales, and music … man, that’s a rabbit hole I keep going down, yet not fully grasping. And we all know what a little knowledge is. So begins my attempt to explain, at some length, what I know about musical tuning.

    I’ll start with Mike’s comment (@11). The mathematical formula he gives is correct, but only for more recent centuries (from the 1580s onward, maybe?). It describes what is known as equal temperament*. That is, a system of tuning in which the ratio between the frequencies of any two adjacent notes (notes a half-step apart) is exactly the same. The upshot of this is that you can transpose your music to any key and it sounds the same (other than being higher or lower in frequency, obviously). Ah, but things were not always this way!

    Back in the day, it would seem**, there was a much simpler mathematical system at work in tuning (calculating the twelfth root of something, after all, is a fairly difficult mathematical task). As I understand things (and, again, let me add that I likely do not), before equal temperament, there was Pythagorean tuning (among others). Always bringing it back to the Greeks!

    Pythagorean tuning calculates all its intervals based on the ratio of 3:2 (much simpler to calculate than the 12th root of 2!). Remember that most musical instruments are either based on the vibration of strings or columns of air in pipes. While the ancients may not have been able to calculate the pitch or frequency (in Hertz) of notes, they could, of course, measure the lengths of such strings and pipes — and those lengths are (inversely) proportional to the pitches they generate! So notes whose frequencies are in a 3:2 ratio will also have strings in a 3:2 ratio.

    Well, what would we call this 3:2 pitch ratio today? It’s a perfect fifth! Say, from a C up to a G. Most of us agree that that’s a nice interval. And so mathematically pure! Well, if you keep going up a fifth, you’d get C, G, D, A, E, B, F#, C#, G#, D#, A#, E# (also known as F) … back to C. Hey, whaddya know, 12 notes! Of course, they’d all span several octaves, but as it happens that most of us think that notes an octave apart sound “the same”, you can transpose these notes down varying numbers of octaves to form the chromatic scale we all know and love.

    Except. If you did the math, you realize that the C you ended up on, using this 3:2 ratio, wasn’t a perfect several octaves above the C you started on. Close, but a bit off. That’s one problem (which was solved by simply fudging things back to a perfect octave, which made that particular perfect fifth … less than perfect, also called the “wolf fifth”). Also, this scale you would have constructed wouldn’t really sound like the scale on your modern, equal-tempered piano. If you were so musically attuned, you’d think that such a Pythagorean scale sounded … off on several notes.

    What’s more, though, this Pythagorean tuning doesn’t really produce lots of nice intervals, other than the perfect fifths it’s based on (and their inversion, the perfect fourth). The thirds it produces are fairly dissonant. So people tempered the pitches of some notes and came up with “just intonation”, in which intervals form pleasing simple fractions, as well as more pleasing sounds. The perfect fifth keeps its 3:2 ratio, but the third now has a nicer-sounding 5:4 ratio, as opposed to the Pythagorean 81:64 (do the math — they’re close, but not the same).

    Well, all that’s quite nice, but only in certain keys. By which I mean, both the Pythagorean and “just” systems get some intervals very mathematically perfect, but others, they fudge. So you can’t just go around deciding you’d rather play your song in D instead of C, because it’ll actually sound different, due to those fudged intervals. There were some keys where things just sounded awful! This may explain why older composers picked the keys they did, or why they thought certain keys had different moods from others. Back then, they did. Now, they do not.

    So even if all the musicians using modern (equal) and ancient (Pythagorean, just) tuning wrote their music down the same way, their audiences would’ve heard something (slightly) different than we would on modern (equal-tempered) instruments.

    Anyhow, along came equal temperament, which Mike described, to allow music to be transposed willy-nilly. No more fear of bad keys, or bad intervals. Except. Now all the intervals are all a little bit off from their pure mathematical counterparts! For example, remember the Pythagorean 3:2 ratio (that would be the same as multiplying by 1.5) for a perfect fifth? In our modern system, it’s actually 1.4983! And so on. So in order to make things more perfect overall, we actually had to make the things that were truly perfect and fudge them a bit.

    So, back to Dr. Veith’s addition:

    I had always wondered why it is that musical scales have to have those half-steps. Wouldn’t it be easier and more consistent and more orderly for a scale to have all whole steps?

    I think the more relevant question is: Why does the human brain (apparently? or only in the West?) find such simple ratios as are found in the third, fourth, and fifth so pleasing? It’s that sense of consonance that creates the pattern of steps and half-steps that compose our scale.

    And, finally, to this bit of application from Dr. Veith:

    True beauty–whether of music or art or literature or a person–needs its quirks, its inconsistencies, its surprises, even its flaws. Philosophies and ideologies that demand utterly consistent regularity–think of Marxism–become inhuman, tyrannical, and demonic.

    What’s interesting to me is that any of these tuning systems could be said to be trying too hard to enforce an ideology, as well as containing the fudging necessary to make that ideology work. Ah well.

    *Equal temperament is similar to, but somehow different from, well temperament, as made most famous by Bach with his Well-Tempered Clavier. Don’t ask me about the differences, I don’t get them myself.

    **Obviously, we don’t have recordings of how things sounded back then, so we can only go off of what people wrote about how they tuned their instruments.

  • http://www.geneveith.com Gene Veith

    Man, you guys are knowledgable! I’ve learned a lot from these discussions already. And Lindsay, I believe you deserve a hat tip for teaching your father about this interval!

  • http://www.geneveith.com Gene Veith

    Man, you guys are knowledgable! I’ve learned a lot from these discussions already. And Lindsay, I believe you deserve a hat tip for teaching your father about this interval!

  • http://www.toddstadler.com/ tODD

    Technically, Dr. Veith is right when he says (@13) that “rap is just poetry”. But that’s because the word “rap” more often refers to the vocal styling, rather than the musical genre itself (which is more often called hip-hop). These days, at least.

    That said, it’s really hard to come by a hip-hop song that doesn’t have tonality in it. And rappers are not indifferent to the music they’re rapping over. It’s all of a piece.

    But some hip-hop songs do come close. The best example that leaps to mind is Dizzee Rascal’s “I Luv U” (all the caveats you’d expect in a link to such a video), which I find remarkably different from most hip-hop.

    And NQB (@20), as a percussionist who was in marching band, I’ve heard more than my fair share of snare solos, and while I won’t claim they’re not music, I will say that they’re really, really boring. Almost pure technique. Now make it a drum-set solo, and you can really start making things interesting, if still largely lacking in distinguishable pitches.

  • http://www.toddstadler.com/ tODD

    Technically, Dr. Veith is right when he says (@13) that “rap is just poetry”. But that’s because the word “rap” more often refers to the vocal styling, rather than the musical genre itself (which is more often called hip-hop). These days, at least.

    That said, it’s really hard to come by a hip-hop song that doesn’t have tonality in it. And rappers are not indifferent to the music they’re rapping over. It’s all of a piece.

    But some hip-hop songs do come close. The best example that leaps to mind is Dizzee Rascal’s “I Luv U” (all the caveats you’d expect in a link to such a video), which I find remarkably different from most hip-hop.

    And NQB (@20), as a percussionist who was in marching band, I’ve heard more than my fair share of snare solos, and while I won’t claim they’re not music, I will say that they’re really, really boring. Almost pure technique. Now make it a drum-set solo, and you can really start making things interesting, if still largely lacking in distinguishable pitches.

  • bikegal

    It’s all too easy to oversimplify when we consider the role of the tritone in music. Bach, for example, used the tritone in many different ways, sometimes in harmony or compound line (implying harmony within a melody), sometimes by strategically violating standard conventions in search of a larger goal, sometimes by using the tritone as rhetorical figure or gesture (yes, German Baroque theorists and composers imitated Aristotle and Cicero by categorizing and using musical figures).

    A helpful way to think about dissonance in music generally is to contrast the prima practica of the Renaissance with the seconda practica of the Baroque. This is difficult to summarize concisely, especially if it has been five years since your last music history seminar, but I’ll try (even at the risk of oversimplifying) because I just love this part of music history. At the turn of the 17th-c. there was a big battle between one group of musicians who wanted to adhere strictly to the rules of counterpoint and structure typified by Palestrina and another group of musicians who chose to occasionally break those rules in service of text or affect. My personal take on this is that it is a continuation of a long, slow change that just happens to parallel the Reformation, namely the shift of music from the mathematical realm, the quadrivium, into the grammatical realm. Renaissance composers were concerned about text and its meaning, but they handled it in a very different way than the Baroque composers did. Fun stuff.

    If you play and sing a wide variety of music from the medieval period until today, you can sense that the conventions for using the tritone evolved as composers found different ways to exploit its possibilities within their own places in history. Eventually, 1500 years of changing conventions culminated in a crisis, “the crisis in tonality.” Composers had pushed the bounds of traditional composition so far, that they felt they could no longer innovate unless they fundamentally rethought musical structure. This is one reason why 20th-c. classical music is so difficult to define; the various composers went scurrying off in all different directions. Some, like Rachmaninoff, found a way to continue with traditional structures. Arnold Schönberg, for example, argued for “the emancipation of the dissonance” and said that all intervals could be used equally. Still other composers tried to manipulate texture, rhythm, and timbre (musical color).

    The point of all this is that the successful use of the tritone, or any other interval or compositional device for that matter, is context-specific. To be fair to the tritone and to all the composers, you must glance at several hundred years of repertoire. “Diabolus in musica” is, in that sense, a double-edged sword. It is dangerous if we toss it about only as an amusing and impish catchphrase, but it is also a very useful term if we allow it to draws us in to consider music history and theory from a very early point. The tritone is a bit like alcohol: it’s easy to see how to misuse it or cause damage with it but there are countless, countless ways to use it well to contribute to your musical meal.

    On symmetry: I was once singing in a choir that was rehearsing a section of music based on the octatonic scale. We were being led by a music theory professor and he could have told us any number of things about the octatonic scales, for example, how there are only three of them, how they are common in jazz and in various non-Western musical traditions, how they consist of two interlocking fully-diminished seventh-chords, how they’re crammed full of tritone intervals. Instead, he showed us how the alternating half and whole steps create a scale that is symmetrical in four places within the octave. (You can only cut a major scale in half. If you’ve had piano lessons you may remember how some of the elementary books keep talking about the two tetrachords.) Because the octatonic scale is so symmetrical composers can easily exploit it, and its four identical building blocks, to create a sense of stasis.

    In that spirit, I suggest (in answer to Dr. Veith’s question above) that the major and minor scales endure because they offer a good balance between symmetry and asymmetry, stasis and propulsion.

    This symmetry/asymmetry thread leads us back to the Well-Tempered Clavier and the difference between “well-tempered” and and our modern standard of “even temperament.” Think of this as set and subset, rectangle and square. There were many systems of temperament that could allow composers like Bach to play in all of the different keys. Depending on which of the Pythagorean ratios were more or less preserved close to perfection and which were more or less adjusted to accommodate the others, the different systems gave the different tonalities different colors relative to each other. If a keyboard is well-tempered you can play tastefully in all different keys, but the different tonalities (or scales) do not have to sound identical. So, there are many ways to make a keyboard well-tempered. Eventually even-temperament became standard because all the tonalities sound the same, but that’s another story. Scholars of early Baroque keyboard music research the temperaments extensively because there are advantages to the ways that different tunings can make the same piece sound completely different.

  • bikegal

    It’s all too easy to oversimplify when we consider the role of the tritone in music. Bach, for example, used the tritone in many different ways, sometimes in harmony or compound line (implying harmony within a melody), sometimes by strategically violating standard conventions in search of a larger goal, sometimes by using the tritone as rhetorical figure or gesture (yes, German Baroque theorists and composers imitated Aristotle and Cicero by categorizing and using musical figures).

    A helpful way to think about dissonance in music generally is to contrast the prima practica of the Renaissance with the seconda practica of the Baroque. This is difficult to summarize concisely, especially if it has been five years since your last music history seminar, but I’ll try (even at the risk of oversimplifying) because I just love this part of music history. At the turn of the 17th-c. there was a big battle between one group of musicians who wanted to adhere strictly to the rules of counterpoint and structure typified by Palestrina and another group of musicians who chose to occasionally break those rules in service of text or affect. My personal take on this is that it is a continuation of a long, slow change that just happens to parallel the Reformation, namely the shift of music from the mathematical realm, the quadrivium, into the grammatical realm. Renaissance composers were concerned about text and its meaning, but they handled it in a very different way than the Baroque composers did. Fun stuff.

    If you play and sing a wide variety of music from the medieval period until today, you can sense that the conventions for using the tritone evolved as composers found different ways to exploit its possibilities within their own places in history. Eventually, 1500 years of changing conventions culminated in a crisis, “the crisis in tonality.” Composers had pushed the bounds of traditional composition so far, that they felt they could no longer innovate unless they fundamentally rethought musical structure. This is one reason why 20th-c. classical music is so difficult to define; the various composers went scurrying off in all different directions. Some, like Rachmaninoff, found a way to continue with traditional structures. Arnold Schönberg, for example, argued for “the emancipation of the dissonance” and said that all intervals could be used equally. Still other composers tried to manipulate texture, rhythm, and timbre (musical color).

    The point of all this is that the successful use of the tritone, or any other interval or compositional device for that matter, is context-specific. To be fair to the tritone and to all the composers, you must glance at several hundred years of repertoire. “Diabolus in musica” is, in that sense, a double-edged sword. It is dangerous if we toss it about only as an amusing and impish catchphrase, but it is also a very useful term if we allow it to draws us in to consider music history and theory from a very early point. The tritone is a bit like alcohol: it’s easy to see how to misuse it or cause damage with it but there are countless, countless ways to use it well to contribute to your musical meal.

    On symmetry: I was once singing in a choir that was rehearsing a section of music based on the octatonic scale. We were being led by a music theory professor and he could have told us any number of things about the octatonic scales, for example, how there are only three of them, how they are common in jazz and in various non-Western musical traditions, how they consist of two interlocking fully-diminished seventh-chords, how they’re crammed full of tritone intervals. Instead, he showed us how the alternating half and whole steps create a scale that is symmetrical in four places within the octave. (You can only cut a major scale in half. If you’ve had piano lessons you may remember how some of the elementary books keep talking about the two tetrachords.) Because the octatonic scale is so symmetrical composers can easily exploit it, and its four identical building blocks, to create a sense of stasis.

    In that spirit, I suggest (in answer to Dr. Veith’s question above) that the major and minor scales endure because they offer a good balance between symmetry and asymmetry, stasis and propulsion.

    This symmetry/asymmetry thread leads us back to the Well-Tempered Clavier and the difference between “well-tempered” and and our modern standard of “even temperament.” Think of this as set and subset, rectangle and square. There were many systems of temperament that could allow composers like Bach to play in all of the different keys. Depending on which of the Pythagorean ratios were more or less preserved close to perfection and which were more or less adjusted to accommodate the others, the different systems gave the different tonalities different colors relative to each other. If a keyboard is well-tempered you can play tastefully in all different keys, but the different tonalities (or scales) do not have to sound identical. So, there are many ways to make a keyboard well-tempered. Eventually even-temperament became standard because all the tonalities sound the same, but that’s another story. Scholars of early Baroque keyboard music research the temperaments extensively because there are advantages to the ways that different tunings can make the same piece sound completely different.

  • Artist formerly known as Stephen

    bikegal

    “Eventually even-temperament became standard because all the tonalities sound the same, but that’s another story.”

    Which leads me to a thought. I was reading recently about equal temprament, what we hear now in all music based on A-440 (do I have that right?). It seemed that it did not actually “arrive” completely until the 19th c. I also read that Steinway practically began inventing the piano as we know it in the US sometime soon after that, in the mid- 19th c. So, Bach and Mozart do not or may not actually sound like the way we hear that music today, even if musicians play on 17th and 18th c. instruments. For all you way geekier musicians, is that true? Interpretations aside, can we know or hear the music previous to that time with any kind of accuracy? If so, any suggestions on recordings?

    I guess interpretation is always part of the mix, but I was listening to Hilary Hahn play Bach and it got me wondering as to how much music is a training thing for the ear and how much is “natural” to the human brain. Was I hearing Bach? Is that fair question? Do we like equal temprament (in the West at least) because we have always heard music that way? I had a friend once with perfect pitch who could tell the notes on the dial tone. She hated the dial tone because it was so dissonant.

    But as for flat 5s, I’m confused because that is actually a sweet chord to play for the IV in a jazz/blues progression. It sounds almost like a dom 7 (neither major or minor – spooky!) . What’s up with that? Both are based on tritones as I understand it. Is that it?

    I knew an old black man once who used to come into the guitar shop where I worked and play blues ont he rattiest, cheapest guitar he could find. One day he came in with his wife. I’d never seen her before. I asked him if he was going to entertain us with some blues. He said he didn’t play that music any more. That’s the devil’s music. Seems he’d found Jesus. No more flat 5 and dom 7 chords for him.

  • Artist formerly known as Stephen

    bikegal

    “Eventually even-temperament became standard because all the tonalities sound the same, but that’s another story.”

    Which leads me to a thought. I was reading recently about equal temprament, what we hear now in all music based on A-440 (do I have that right?). It seemed that it did not actually “arrive” completely until the 19th c. I also read that Steinway practically began inventing the piano as we know it in the US sometime soon after that, in the mid- 19th c. So, Bach and Mozart do not or may not actually sound like the way we hear that music today, even if musicians play on 17th and 18th c. instruments. For all you way geekier musicians, is that true? Interpretations aside, can we know or hear the music previous to that time with any kind of accuracy? If so, any suggestions on recordings?

    I guess interpretation is always part of the mix, but I was listening to Hilary Hahn play Bach and it got me wondering as to how much music is a training thing for the ear and how much is “natural” to the human brain. Was I hearing Bach? Is that fair question? Do we like equal temprament (in the West at least) because we have always heard music that way? I had a friend once with perfect pitch who could tell the notes on the dial tone. She hated the dial tone because it was so dissonant.

    But as for flat 5s, I’m confused because that is actually a sweet chord to play for the IV in a jazz/blues progression. It sounds almost like a dom 7 (neither major or minor – spooky!) . What’s up with that? Both are based on tritones as I understand it. Is that it?

    I knew an old black man once who used to come into the guitar shop where I worked and play blues ont he rattiest, cheapest guitar he could find. One day he came in with his wife. I’d never seen her before. I asked him if he was going to entertain us with some blues. He said he didn’t play that music any more. That’s the devil’s music. Seems he’d found Jesus. No more flat 5 and dom 7 chords for him.

  • Artist formerly known as Stephen

    Isn’t the Purple Haze chord a 9th? E, G#, C#,G (# 3rd and #6) if it is in E Minor. Hmmm, 5th, 7th, 9th (11?). 11 chords are cool – they’re in a lot of Bossa Nova music as are Major 7 and 6th chords. Is it simply that they sound like they need to be resolved? Then what about suspended 4ths, like G in D Major that wants to go to F#? Why is that so pretty? Wait! I suddenly know why!

    I don’t know what I’m talking about. :)

  • Artist formerly known as Stephen

    Isn’t the Purple Haze chord a 9th? E, G#, C#,G (# 3rd and #6) if it is in E Minor. Hmmm, 5th, 7th, 9th (11?). 11 chords are cool – they’re in a lot of Bossa Nova music as are Major 7 and 6th chords. Is it simply that they sound like they need to be resolved? Then what about suspended 4ths, like G in D Major that wants to go to F#? Why is that so pretty? Wait! I suddenly know why!

    I don’t know what I’m talking about. :)

  • Lindsay

    @25
    Ahh, we have stumbled into the great performance practice debate! Lots of very learned folks have lots of very different opinions on what music actually sounded like then. We can guess what it was meant to sound like, and we can get close on period instruments tuned accordingly. But even back then one performance would vary greatly from the next, as musicians would add improvisational cadenzas that might go on for a while, especially in the Baroque era. One of my very favorite recordings is Jean-Christophe Spinosi’s recording of La verita in cimiento, a Vivaldi opera. It will blow your mind! Is it historically acurate? We can only hope, of course some things we know are different (such as the castrato role is sung by a countertenor, and I’m sure he is thankful). There are so many Baroque groups out there with wonderful, and possibly accurate recordings. Anyone else have a favorite?

  • Lindsay

    @25
    Ahh, we have stumbled into the great performance practice debate! Lots of very learned folks have lots of very different opinions on what music actually sounded like then. We can guess what it was meant to sound like, and we can get close on period instruments tuned accordingly. But even back then one performance would vary greatly from the next, as musicians would add improvisational cadenzas that might go on for a while, especially in the Baroque era. One of my very favorite recordings is Jean-Christophe Spinosi’s recording of La verita in cimiento, a Vivaldi opera. It will blow your mind! Is it historically acurate? We can only hope, of course some things we know are different (such as the castrato role is sung by a countertenor, and I’m sure he is thankful). There are so many Baroque groups out there with wonderful, and possibly accurate recordings. Anyone else have a favorite?

  • http://www.biblegateway.com/versions/Contemporary-English-Version-CEV-Bible/ sg

    @6, @16, and @21

    deja vu

    I was just reading about this the other day, and found this Greek musical scale.

    http://members.cox.net/mathmistakes/music.htm

    http://members.cox.net/mathmistakes/greek.mid

  • http://www.biblegateway.com/versions/Contemporary-English-Version-CEV-Bible/ sg

    @6, @16, and @21

    deja vu

    I was just reading about this the other day, and found this Greek musical scale.

    http://members.cox.net/mathmistakes/music.htm

    http://members.cox.net/mathmistakes/greek.mid

  • bikegal

    Artist formerly known as Stephen,

    Excellent question:

    “Interpretations aside, can we know or hear the music previous to that time with any kind of accuracy?”

    Allow me to happily refer you to the eminently readable book, “Hearing Bach’s Passions,” by Daniel Melamed. Dr. Melamed is one of the world’s foremost Bach scholars, yet he wrote this book for the general reader and he addresses this question quite reasonably. It is one of my favorite books. If you can recreate the exact acoustic, find a historically accurate instrument, and hire a knowledgeable musician who understands the conventions latent within the original score, can you have a historically accurate performance? What would it take?

    Much ink has been spilled over the question of music and the brain. I think that we are wired for music the way that we are wired for language. Recent research shows that the two are linked. Having not studied this in any great depth, I will simply observe all humans have a capacity and a drive for language that is universal, even though the specific languages are different. Music seems to be analogous. In some languages, double negatives intensify or emphasize the negativity. In English, double negatives are a no-no and they undermine or confuse the point. So the inclusion of the 5th above the bass of a V7 is fairly standard in common practice partwriting and continuo playing (think Baroque-style comping) because it can strengthen the sonority. But if you comp in jazz you leave the 5th out in case someone who is improvising wants to raise or lower it. Listeners exposed to both languages can still comprehend and be satisfied by them, even without knowing how or why the grammatical or rhetorical conventions are different.

    If, by flat 5, you mean F, A-flat, C-flat, E-flat, you are talking about what classical theorists call half-diminished seventh chord. It typically functions as a pre-dominant or a subdominant, but the diminished triad at the bottom implies some dominant color. You are correct, and that is a good observation. In classical theory, this is sometimes used as a borrowed chord. If you’re playing in C major and you want a ii7 (DFAC) as your pre-dominant, then you have a fully-minor seventh chord. If you ask C major to put in a call to his good friend C minor, then you can use iiø7 by taking the A-flat from the minor scale to make the half-diminished (a.k.a. diminished-minor) seventh chord. Often these half-diminished chords are used in places where a standard dominant or subdominant would provide too much contrast within the phrase. In Baroque music the composers would indicate flat-5 in the figures under the bassline. If there was no figure, the keyboardist or lute player included the perfect fifth.

    I’m not familiar with the Purple Haze chord myself. But 9th, 11th, and 13th chords are called extended tertian sonorities and even classical composers used them, depending on the context…

  • bikegal

    Artist formerly known as Stephen,

    Excellent question:

    “Interpretations aside, can we know or hear the music previous to that time with any kind of accuracy?”

    Allow me to happily refer you to the eminently readable book, “Hearing Bach’s Passions,” by Daniel Melamed. Dr. Melamed is one of the world’s foremost Bach scholars, yet he wrote this book for the general reader and he addresses this question quite reasonably. It is one of my favorite books. If you can recreate the exact acoustic, find a historically accurate instrument, and hire a knowledgeable musician who understands the conventions latent within the original score, can you have a historically accurate performance? What would it take?

    Much ink has been spilled over the question of music and the brain. I think that we are wired for music the way that we are wired for language. Recent research shows that the two are linked. Having not studied this in any great depth, I will simply observe all humans have a capacity and a drive for language that is universal, even though the specific languages are different. Music seems to be analogous. In some languages, double negatives intensify or emphasize the negativity. In English, double negatives are a no-no and they undermine or confuse the point. So the inclusion of the 5th above the bass of a V7 is fairly standard in common practice partwriting and continuo playing (think Baroque-style comping) because it can strengthen the sonority. But if you comp in jazz you leave the 5th out in case someone who is improvising wants to raise or lower it. Listeners exposed to both languages can still comprehend and be satisfied by them, even without knowing how or why the grammatical or rhetorical conventions are different.

    If, by flat 5, you mean F, A-flat, C-flat, E-flat, you are talking about what classical theorists call half-diminished seventh chord. It typically functions as a pre-dominant or a subdominant, but the diminished triad at the bottom implies some dominant color. You are correct, and that is a good observation. In classical theory, this is sometimes used as a borrowed chord. If you’re playing in C major and you want a ii7 (DFAC) as your pre-dominant, then you have a fully-minor seventh chord. If you ask C major to put in a call to his good friend C minor, then you can use iiø7 by taking the A-flat from the minor scale to make the half-diminished (a.k.a. diminished-minor) seventh chord. Often these half-diminished chords are used in places where a standard dominant or subdominant would provide too much contrast within the phrase. In Baroque music the composers would indicate flat-5 in the figures under the bassline. If there was no figure, the keyboardist or lute player included the perfect fifth.

    I’m not familiar with the Purple Haze chord myself. But 9th, 11th, and 13th chords are called extended tertian sonorities and even classical composers used them, depending on the context…

  • http://www.biblegateway.com/versions/Contemporary-English-Version-CEV-Bible/ sg

    “Philosophies and ideologies that demand utterly consistent regularity–think of Marxism–become inhuman, tyrannical, and demonic.”

    Curiously this sentiment/view has the same flavor as the recently much discussed observations of William Lind:

    As Russell Kirk wrote, one of conservatism’s most important insights is that all ideologies are wrong. Ideology takes an intellectual system, a product of one or more philosophers, and says, “This system must be true.” Inevitably, reality ends up contradicting the system, usually on a growing number of points. But the ideology, by its nature, cannot adjust to reality; to do so would be to abandon the system.

    http://www.isegoria.net/2011/07/all-ideologies-are-wrong/

  • http://www.biblegateway.com/versions/Contemporary-English-Version-CEV-Bible/ sg

    “Philosophies and ideologies that demand utterly consistent regularity–think of Marxism–become inhuman, tyrannical, and demonic.”

    Curiously this sentiment/view has the same flavor as the recently much discussed observations of William Lind:

    As Russell Kirk wrote, one of conservatism’s most important insights is that all ideologies are wrong. Ideology takes an intellectual system, a product of one or more philosophers, and says, “This system must be true.” Inevitably, reality ends up contradicting the system, usually on a growing number of points. But the ideology, by its nature, cannot adjust to reality; to do so would be to abandon the system.

    http://www.isegoria.net/2011/07/all-ideologies-are-wrong/

  • Jimmy Veith

    To Booklover at #5 and tODD @ 14, who could not find a tritone interval in “A Mighty Fortress“.

    Technically you may be correct in the sense that an interval is defined as the distance between two notes. You only get the dissonant sound when the flatted fifth is played with the root note or the 1 of the scale. For example, in the key of C, you would have to play C with F# (or G flat) to get the devilish sound like in Jim Hendrix‘s “Purple Haze”.
    .
    In “A Mighty Fortress”, the flatted 5th is used in the melody line. In the key of C, it would be F#. In most arrangements of “A Mighty Fortress”, when the flatted 5th is sung, it is accompanied by the II major chord, which in the key of C, it would be D, F# (the flatted 5th) and A. When the flatted 5th is played with these other notes, it is not very dissonant at all, but leads naturally to the V chord, (In the key of C, that would be G.)

    When Martin Luther wrote the parts to “A Mighty Fortress”, he most likely used the II major chord when the melody line went to the flatted 5th , this would make it less dissonant and easier to sing. Is it possible to find the original arrangement of this song to see what chords he actually used?

    I was wondering if anyone knew of any instrumental or organ arrangements of “A Mighty Fortress” where the composer deliberately stayed on the root note when the flatted 5th was played to obtain the kind of dissonance that one would expect when one “speaks of the devil”? If there is no such arrangement, there needs to be.

    I have greatly enjoyed all the other comments. I have learned a lot.

  • Jimmy Veith

    To Booklover at #5 and tODD @ 14, who could not find a tritone interval in “A Mighty Fortress“.

    Technically you may be correct in the sense that an interval is defined as the distance between two notes. You only get the dissonant sound when the flatted fifth is played with the root note or the 1 of the scale. For example, in the key of C, you would have to play C with F# (or G flat) to get the devilish sound like in Jim Hendrix‘s “Purple Haze”.
    .
    In “A Mighty Fortress”, the flatted 5th is used in the melody line. In the key of C, it would be F#. In most arrangements of “A Mighty Fortress”, when the flatted 5th is sung, it is accompanied by the II major chord, which in the key of C, it would be D, F# (the flatted 5th) and A. When the flatted 5th is played with these other notes, it is not very dissonant at all, but leads naturally to the V chord, (In the key of C, that would be G.)

    When Martin Luther wrote the parts to “A Mighty Fortress”, he most likely used the II major chord when the melody line went to the flatted 5th , this would make it less dissonant and easier to sing. Is it possible to find the original arrangement of this song to see what chords he actually used?

    I was wondering if anyone knew of any instrumental or organ arrangements of “A Mighty Fortress” where the composer deliberately stayed on the root note when the flatted 5th was played to obtain the kind of dissonance that one would expect when one “speaks of the devil”? If there is no such arrangement, there needs to be.

    I have greatly enjoyed all the other comments. I have learned a lot.

  • Jonathan

    @31
    Re. Luther’s original arrangement of “A Mighty Fortress:” I’ve done some study of early Lutheran liturgy and music. To my knowledge, Luther did not harmonize his melodies. That is, he wrote only the melody, and did not provide any chords. This would be in keeping with the information we have regarding the very earliest Lutheran hymn singing: it was a cappella, and it appears to have been quite brisk in tempo.

    The most recent German-language edition of Luther’s liturgical writings works edited by Markus Jenny includes a full-size color facsimile of Luther’s working manuscript for “Vater unser in Himmelreich” (“Our Father, Who in Heaven Above,” his catechism hymn on the Lord’s Prayer). It’s absolutely fascinating to see him revise and edit the text: lines and words are crossed out and replaced, arrows are drawn, textual notes are written in the margins. The tune is also present in the manuscript, and it also has the same kind of revisions as the text. (Particularly interesting is that the text and tune are not written together; i.e., they are on the same paper, but the tune is down in the lower right corner while the text occupies the rest of the page—it seems to me he first worked on the text with a specific metrical structure in mind and then started playing around with notes separately.)

    Anyway, my point is that there is no indication of harmony in this particular manuscript of Luther with regard to the tune—he plays around with various melodic figures, but doesn’t seem to be concerned with note-to-note harmony. (Of course, this doesn’t count out the possibility that he wrote harmony for other tunes such as “A Mighty Fortress,” or even that he wrote harmony for this particular tune later, on a different manuscript.) “A Mighty Fortress” postdates Johann Walter’s 1524 Gesangbuch, which contains what I think are the first harmonic treatments of many Lutheran chorales. Walter’s 1524 arrangements are not hymnal-style harmonizations, but rather motet-like four- and five-part compositions for choir with the melody in the tenor voice. Lucas Osiander’s cantional hymnal of 1586 likely provides the earliest period harmonization of “A Mighty Fortress” with the melody in the soprano voice. I checked Eugene Schuler’s dissertation on the Osiander cantional, which includes a transcription of the complete volume: Osiander does indeed harmonize the F-sharp in question with a major chord built on D. At any rate, I don’t know exactly where one would find the absolute earliest harmonization of “A Mighty Fortress.” But we can at least substantiate that someone was harmonizing that F-sharp with a D major chord at least from 1586.

  • Jonathan

    @31
    Re. Luther’s original arrangement of “A Mighty Fortress:” I’ve done some study of early Lutheran liturgy and music. To my knowledge, Luther did not harmonize his melodies. That is, he wrote only the melody, and did not provide any chords. This would be in keeping with the information we have regarding the very earliest Lutheran hymn singing: it was a cappella, and it appears to have been quite brisk in tempo.

    The most recent German-language edition of Luther’s liturgical writings works edited by Markus Jenny includes a full-size color facsimile of Luther’s working manuscript for “Vater unser in Himmelreich” (“Our Father, Who in Heaven Above,” his catechism hymn on the Lord’s Prayer). It’s absolutely fascinating to see him revise and edit the text: lines and words are crossed out and replaced, arrows are drawn, textual notes are written in the margins. The tune is also present in the manuscript, and it also has the same kind of revisions as the text. (Particularly interesting is that the text and tune are not written together; i.e., they are on the same paper, but the tune is down in the lower right corner while the text occupies the rest of the page—it seems to me he first worked on the text with a specific metrical structure in mind and then started playing around with notes separately.)

    Anyway, my point is that there is no indication of harmony in this particular manuscript of Luther with regard to the tune—he plays around with various melodic figures, but doesn’t seem to be concerned with note-to-note harmony. (Of course, this doesn’t count out the possibility that he wrote harmony for other tunes such as “A Mighty Fortress,” or even that he wrote harmony for this particular tune later, on a different manuscript.) “A Mighty Fortress” postdates Johann Walter’s 1524 Gesangbuch, which contains what I think are the first harmonic treatments of many Lutheran chorales. Walter’s 1524 arrangements are not hymnal-style harmonizations, but rather motet-like four- and five-part compositions for choir with the melody in the tenor voice. Lucas Osiander’s cantional hymnal of 1586 likely provides the earliest period harmonization of “A Mighty Fortress” with the melody in the soprano voice. I checked Eugene Schuler’s dissertation on the Osiander cantional, which includes a transcription of the complete volume: Osiander does indeed harmonize the F-sharp in question with a major chord built on D. At any rate, I don’t know exactly where one would find the absolute earliest harmonization of “A Mighty Fortress.” But we can at least substantiate that someone was harmonizing that F-sharp with a D major chord at least from 1586.

  • Jimmy Veith

    Thank you SG @ 28 for pointing us to the article which you cited.

    After reading about overtones, it occurred to me why a flatted 5th played with the root note may produce such a dissonant sound compared to all the other notes in the chromatic scale. In the key of C, the F# is the flatted 5th. The overtones for F# is a F# major chord which consists of F#, A# and C#. None of these overtone notes are found in the C major scale, whereas all the other black keys (in the key of C), contain at least one overtone that is found in the C major scale.

    That may be a more scientific explanation. Although I prefer to just blame the devil.

    To the “Artist formerly known as Stephen” @25. Thank you for the story about the black man who played blues in the guitar shop where you worked. I’m glad he found Jesus. But I’m wondering if maybe Jesus also sang the blues. I like to think so.

  • Jimmy Veith

    Thank you SG @ 28 for pointing us to the article which you cited.

    After reading about overtones, it occurred to me why a flatted 5th played with the root note may produce such a dissonant sound compared to all the other notes in the chromatic scale. In the key of C, the F# is the flatted 5th. The overtones for F# is a F# major chord which consists of F#, A# and C#. None of these overtone notes are found in the C major scale, whereas all the other black keys (in the key of C), contain at least one overtone that is found in the C major scale.

    That may be a more scientific explanation. Although I prefer to just blame the devil.

    To the “Artist formerly known as Stephen” @25. Thank you for the story about the black man who played blues in the guitar shop where you worked. I’m glad he found Jesus. But I’m wondering if maybe Jesus also sang the blues. I like to think so.

  • bikegal

    The Episcopal hymnal (Hymnbook 1982, No. 687) has Luther’s original rhythm but with the Hassler harmonization. The F-sharp in question is not a flatted fifth. It is a raised fourth with respect to the C, but even that terminology is highly misleading because there is no need to include a C in the counterpoint.

    Instead, the F-sharp is functioning as a lower neighbor to the G. This was a common figure in Renaissance music, especially at cadences. It is so common, in fact, that it was customary for the performers of polyphonic works to raise a lower neighbor to within a half-step of the primary tone even in the absence of notation indicating that the note should be raised. This was called musica ficta, and performing editions of Renaissance music often have tiny sharps and flats above some notes so modern singers can see what the composer actually wrote and still know which notes should be altered. Casting the F-sharp as a dissonance or a diabolus in musica misses the point entirely and implies the opposite of what’s really going on: the F-sharp is more aesthetically pleasing here at the end of the phrase than an F-natural would be. Try singing the melody with an F-natural instead of an F-sharp. It’s harder. The F-sharp is melodically cadencing to G according to standard Renaissance convention.

    Can I say definitively that Luther didn’t have that vertical tritone relationship in mind when setting “der alt’ böse Feind?” No, but given all that we know about Renaissance composition, I think it highly unlikely that he would have intended any average listeners or congregants to catch any kind of symbolism there because the gesture itself is so ordinary.

  • bikegal

    The Episcopal hymnal (Hymnbook 1982, No. 687) has Luther’s original rhythm but with the Hassler harmonization. The F-sharp in question is not a flatted fifth. It is a raised fourth with respect to the C, but even that terminology is highly misleading because there is no need to include a C in the counterpoint.

    Instead, the F-sharp is functioning as a lower neighbor to the G. This was a common figure in Renaissance music, especially at cadences. It is so common, in fact, that it was customary for the performers of polyphonic works to raise a lower neighbor to within a half-step of the primary tone even in the absence of notation indicating that the note should be raised. This was called musica ficta, and performing editions of Renaissance music often have tiny sharps and flats above some notes so modern singers can see what the composer actually wrote and still know which notes should be altered. Casting the F-sharp as a dissonance or a diabolus in musica misses the point entirely and implies the opposite of what’s really going on: the F-sharp is more aesthetically pleasing here at the end of the phrase than an F-natural would be. Try singing the melody with an F-natural instead of an F-sharp. It’s harder. The F-sharp is melodically cadencing to G according to standard Renaissance convention.

    Can I say definitively that Luther didn’t have that vertical tritone relationship in mind when setting “der alt’ böse Feind?” No, but given all that we know about Renaissance composition, I think it highly unlikely that he would have intended any average listeners or congregants to catch any kind of symbolism there because the gesture itself is so ordinary.

  • Artist formerly known as Stephen

    Thanks bikegal.

    I think I followed about 1/3 of it. I’ll cut and paste and look for the book. I have been studying the history of Western music lately, sort of floundering around listening to all kinds of stuff. I listen to all kinds of stuff, but what I know of playing music comes from being self-taught on the guitar. Basically, that means learning whatever I can on my own, asking someone who knows more than I do, jamming, and being in awe of those who understand the grammar in all its complexity (jazz and classical players).

    Every rock guitar player from my generation learned Purple Haze. I think it is an E7#9 (or Em7#9). Hendrix used it a lot. F# becomes G in the E major scale. I guess that’s the demonic interval. The notes are heavy E in the bass, G#,D(a minor 7, right?), G (#9?). Had to have a guitar in my hands to figure it out. Does that make sense? With F# instead of G it is an E9 I think – E, G#,D, F#. I still don’t understand completely how chords are named.

    Thanks for the post Jimmy.

  • Artist formerly known as Stephen

    Thanks bikegal.

    I think I followed about 1/3 of it. I’ll cut and paste and look for the book. I have been studying the history of Western music lately, sort of floundering around listening to all kinds of stuff. I listen to all kinds of stuff, but what I know of playing music comes from being self-taught on the guitar. Basically, that means learning whatever I can on my own, asking someone who knows more than I do, jamming, and being in awe of those who understand the grammar in all its complexity (jazz and classical players).

    Every rock guitar player from my generation learned Purple Haze. I think it is an E7#9 (or Em7#9). Hendrix used it a lot. F# becomes G in the E major scale. I guess that’s the demonic interval. The notes are heavy E in the bass, G#,D(a minor 7, right?), G (#9?). Had to have a guitar in my hands to figure it out. Does that make sense? With F# instead of G it is an E9 I think – E, G#,D, F#. I still don’t understand completely how chords are named.

    Thanks for the post Jimmy.

  • bikegal

    Regarding the C Major / F-sharp Major dichotomy in Comment 33, that is correct. Modulations between keys separated by a tritone are very rare in classical music. Dominant, common. Subdominant, common. Mediants, common. Chromatic mediants, common. Tritones, rare. I am sure I could think of a few pieces where the composer actually gets to or passes through a tritone key (for lack of a better term), but that’s usually accomplished by modulating through intermediary keys. I can’t think of anything that goes directly from, say, C to F-sharp. Does anyone know of any works that feature a tritone modulation without intervening tonalities?

  • bikegal

    Regarding the C Major / F-sharp Major dichotomy in Comment 33, that is correct. Modulations between keys separated by a tritone are very rare in classical music. Dominant, common. Subdominant, common. Mediants, common. Chromatic mediants, common. Tritones, rare. I am sure I could think of a few pieces where the composer actually gets to or passes through a tritone key (for lack of a better term), but that’s usually accomplished by modulating through intermediary keys. I can’t think of anything that goes directly from, say, C to F-sharp. Does anyone know of any works that feature a tritone modulation without intervening tonalities?

  • Artist formerly known as Stephen

    Well, I just read all the other posts I missed since I started writing. I will now sit quietly and absorb.

  • Artist formerly known as Stephen

    Well, I just read all the other posts I missed since I started writing. I will now sit quietly and absorb.

  • Artist formerly known as Stephen

    @36

    Ever heard Messiaen’s “Concert A Quatre.” More than a few places where he really stabs the air with that interval in the Vocalise. It seems to be the structure of the Cadenza. Anyway, mesmerizing music, like some fusion without mixture of light and dark.

  • Artist formerly known as Stephen

    @36

    Ever heard Messiaen’s “Concert A Quatre.” More than a few places where he really stabs the air with that interval in the Vocalise. It seems to be the structure of the Cadenza. Anyway, mesmerizing music, like some fusion without mixture of light and dark.

  • bikegal

    Artist formerly known as Stephen,

    Yes, that makes sense.

    Here it is notated! http://en.wikipedia.org/wiki/Hendrix_chord

    Note that classically-trained music majors don’t study chords like this until fourth- or fifth-semester core music theory classes. So you shouldn’t feel overwhelmed. Although, I admit to feeling overwhelmed if I try to play jazz. I know only a few very basic fundamentals.

    The best thing you can do is trust your ear. You’ve already said some perceptive things. So have confidence in yourself, keep listening, and don’t worry so much about the order in which you try to learn things.

    Have you listened to any Renaissance or Baroque lute music? If you like to feel things out on the guitar, you may be intrigued by lute tablature…

  • bikegal

    Artist formerly known as Stephen,

    Yes, that makes sense.

    Here it is notated! http://en.wikipedia.org/wiki/Hendrix_chord

    Note that classically-trained music majors don’t study chords like this until fourth- or fifth-semester core music theory classes. So you shouldn’t feel overwhelmed. Although, I admit to feeling overwhelmed if I try to play jazz. I know only a few very basic fundamentals.

    The best thing you can do is trust your ear. You’ve already said some perceptive things. So have confidence in yourself, keep listening, and don’t worry so much about the order in which you try to learn things.

    Have you listened to any Renaissance or Baroque lute music? If you like to feel things out on the guitar, you may be intrigued by lute tablature…

  • Martin Winter

    Regarding historical temperaments: My brother is an organ builder in the city of Dresden. He tells me that there are occasional disputes about whihch temperament to choose for an organ that is built for a historical building or when restoring one. Such was the case for the rebuilt Dresden Frauenkirche. Since everything else was recreated faithfully as it used to be before 1945, why change the organ, so the fans of historic performance practice argued. The proponents of a modern temperament replied that it would be impossible to play music composed after the Baroque era; a major flaw when trying to attract tourists rather than musical experts. As a compromise, the organ can be switched to play with A at 415 Hz instead of 440 Hz.

    Here is an interesting treatment of Bach’s personal temperament, which he apprently encoded in a number of flourishes at the top of a page:

    http://www.larips.com/

    Since the topic of dissonances and not being able to stand certain intervals came up: I am the kind of nerd who adjusts the power of his vacuum cleaner so the lower and higher pitched sounds are tuned to be a major third, which makes cleaning the apartment just a bit nicer.

  • Martin Winter

    Regarding historical temperaments: My brother is an organ builder in the city of Dresden. He tells me that there are occasional disputes about whihch temperament to choose for an organ that is built for a historical building or when restoring one. Such was the case for the rebuilt Dresden Frauenkirche. Since everything else was recreated faithfully as it used to be before 1945, why change the organ, so the fans of historic performance practice argued. The proponents of a modern temperament replied that it would be impossible to play music composed after the Baroque era; a major flaw when trying to attract tourists rather than musical experts. As a compromise, the organ can be switched to play with A at 415 Hz instead of 440 Hz.

    Here is an interesting treatment of Bach’s personal temperament, which he apprently encoded in a number of flourishes at the top of a page:

    http://www.larips.com/

    Since the topic of dissonances and not being able to stand certain intervals came up: I am the kind of nerd who adjusts the power of his vacuum cleaner so the lower and higher pitched sounds are tuned to be a major third, which makes cleaning the apartment just a bit nicer.

  • Artist formerly known as Stephen

    Martin @40 – Ha! Isn’t that funny. Why is it my 3 year old loves to screech at the top of her lungs, bang on the piano, listen to Bach and Mozart (not sure about Wagner!) but runs in terror from the vacuum, the coffee grinder, the garbage truck, or when I go falsetto like Curly of the Three Stooges and sing to her when she’s taking a bath (“Daaa-deeee stop it!!!”)? It’s like she wants to be in control of all sounds.

    So, if an instrument can be tuned to 417hz, then what does “perfect pitch” mean? After 10 years in a guitar shop tuning instruments every day I got to where I could “feel” EADGBE and just tune a guitar to A440. I also tuned violins, mandolins, harpsichords, and just about anything with strings. I still haven’t lost it after 20 years of only intermittent playing, though I can go a smidgen sharp. It seems I learned to hear or recognize pitch that way, along with music being around me growing up in the church (we had the local Bach Society at my little congregation!).

    But I guess I am still wondering if we are hardwired for certain frequencies (like A440), or is that more about what we’ve become used to? It seems it isn’t the actual pitch that matters for making music, but the intervals themselves. That’s what I’m getting from this conversation. That would make sense when thinking about things like tempo and meter too – it’s not so much the sound/pitch itself but the distance between the sounds. That gets into things like the heartbeat and a innate sense of time which is fundamental having consciousness itself. If I think about music like tap dancing or a drumming, it’s all timbre and rhythm without a discernible pitch, at least not one that another instrument could tune itself to – or could it? And even in that can be a dissonance.

    Okay, now I’m really flaking out. Thanks for the encouragement bikegal. I’ll look for lute music too. I read that Martin Luther was a lute player who could whip out a tune at a party and entertain everyone. I’m kind of like that with a guitar. And I love to sing. Stick a quarter in me (or a beer) and we’ll sing all night.

  • Artist formerly known as Stephen

    Martin @40 – Ha! Isn’t that funny. Why is it my 3 year old loves to screech at the top of her lungs, bang on the piano, listen to Bach and Mozart (not sure about Wagner!) but runs in terror from the vacuum, the coffee grinder, the garbage truck, or when I go falsetto like Curly of the Three Stooges and sing to her when she’s taking a bath (“Daaa-deeee stop it!!!”)? It’s like she wants to be in control of all sounds.

    So, if an instrument can be tuned to 417hz, then what does “perfect pitch” mean? After 10 years in a guitar shop tuning instruments every day I got to where I could “feel” EADGBE and just tune a guitar to A440. I also tuned violins, mandolins, harpsichords, and just about anything with strings. I still haven’t lost it after 20 years of only intermittent playing, though I can go a smidgen sharp. It seems I learned to hear or recognize pitch that way, along with music being around me growing up in the church (we had the local Bach Society at my little congregation!).

    But I guess I am still wondering if we are hardwired for certain frequencies (like A440), or is that more about what we’ve become used to? It seems it isn’t the actual pitch that matters for making music, but the intervals themselves. That’s what I’m getting from this conversation. That would make sense when thinking about things like tempo and meter too – it’s not so much the sound/pitch itself but the distance between the sounds. That gets into things like the heartbeat and a innate sense of time which is fundamental having consciousness itself. If I think about music like tap dancing or a drumming, it’s all timbre and rhythm without a discernible pitch, at least not one that another instrument could tune itself to – or could it? And even in that can be a dissonance.

    Okay, now I’m really flaking out. Thanks for the encouragement bikegal. I’ll look for lute music too. I read that Martin Luther was a lute player who could whip out a tune at a party and entertain everyone. I’m kind of like that with a guitar. And I love to sing. Stick a quarter in me (or a beer) and we’ll sing all night.

  • Artist formerly known as Stephen

    Did I say harpsichords? I meant Autoharps, ya know – zithers and dulcimers and all those sorts of things. I’m listening to Bach right now. Guess it rubbed off. I did have an art professor many years ago who painted the scenes on handmade harpsichords. Wow!

  • Artist formerly known as Stephen

    Did I say harpsichords? I meant Autoharps, ya know – zithers and dulcimers and all those sorts of things. I’m listening to Bach right now. Guess it rubbed off. I did have an art professor many years ago who painted the scenes on handmade harpsichords. Wow!

  • Jimmy Veith

    To the Artist formerly known as Stephen @ 35. The demonic interval in Purple Haze is contained in the first four beats of the introduction to the song. The E7#9 chord is played when he starts singing.

    The E7#9 is a very cool chord but it does not contain a flatted 5th. But thinks for bringing this to our attention. It is a great example of how dissonance can be used with great effect.

  • Jimmy Veith

    To the Artist formerly known as Stephen @ 35. The demonic interval in Purple Haze is contained in the first four beats of the introduction to the song. The E7#9 chord is played when he starts singing.

    The E7#9 is a very cool chord but it does not contain a flatted 5th. But thinks for bringing this to our attention. It is a great example of how dissonance can be used with great effect.

  • Jimmy Veith

    Oops, I made a typo. Should be “Thanks”.

  • Jimmy Veith

    Oops, I made a typo. Should be “Thanks”.

  • Artist formerly known as Stephen

    Oh, now I get it. Sorry. Sometimes it takes me a while. You were talking about the lick he plays right at the beginning. E, Bb, E, A (rest) G, E, D,E (I think).

    Thanks right back at you. I learned a lot.

  • Artist formerly known as Stephen

    Oh, now I get it. Sorry. Sometimes it takes me a while. You were talking about the lick he plays right at the beginning. E, Bb, E, A (rest) G, E, D,E (I think).

    Thanks right back at you. I learned a lot.

  • http://www.youtube.com/watch?v=50qfUOYjrf8 Makes69

    I made a song to my band , song is called: World of Mystery, Devil´s Intervalis in the middle, i used it back and forward and cross a like, here incluted straight to the website riff strarting at 2:43

  • http://www.youtube.com/watch?v=50qfUOYjrf8 Makes69

    I made a song to my band , song is called: World of Mystery, Devil´s Intervalis in the middle, i used it back and forward and cross a like, here incluted straight to the website riff strarting at 2:43

  • http://paris.com venice paris

    I WAS BANNED FROM THE U.S. I KNOW WHAT IT FEELS LIKE TO BE BANNED. I DON’T CARE ‘CAUSE U.S SUCKS. PARIS IS SO MUCH BETTER. MY LAST NAME IS PARIS. MY FIRST NAME IS A CITY IN PARIS.

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