The Math of Music
  • dad29
    Posts: 2,232
    Interesting article in the WaPo about "feel good" music. There are a lot of implications for church musicians in this item, as you can imagine, although most of us already knew the gist of the conclusions from the research.

    https://www.washingtonpost.com/news/to-your-health/wp/2015/10/30/the-mathematical-formula-behind-feel-good-songs/

    From the (few) I recognized immediately, it seems that the key of F major is one constant in "feel good."

    Any other thoughts?
  • melofluentmelofluent
    Posts: 4,160
    I've been partial to EbM/Cm most of my life. It's creamy and soothing.
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  • Lots of the songs in the contemporary hymnal we use are in F major, never thought about why, though...
  • CharlesW
    Posts: 11,980
    Since singing is not taught nor encouraged in schools as was once the case, many today have a limited range. I have noticed the older hymns are now in lower keys in newer hymnals. Part of the reason for "F?" Hard to say, but could be.
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  • ryandryand
    Posts: 1,640
    I played a few times in a church where their hymnal had a lot of G hymns in F (St Augustine Hymnal I think). I played them in G and everyone sang them just fine.

    Weren't instruments tuned lower in past centuries? Not a whole step, but could explain why hymns formerly in in Eb are now in D, etc.

  • chonakchonak
    Posts: 9,216
    In some music books, I think keys are selected for the convenience of parish musicians performing them with guitar music.
  • CHGiffenCHGiffen
    Posts: 5,193
    For a melody that ranges from Sol (below Doh) to the La (above Doh), for a range of a major ninth, the key of F major yields a range from middle C to the D a ninth above, which is pretty much regarded as "standard" for today's somewhat untrained congregational voices.

    For a melody that ranges from Ti (below Doh) to the octave above Doh, for range of a minor ninth, the keys of D major or C major tend to be the preferred keys, for the same reason.

    In former times when high E-flat, E-natural, or even high F were within the typical congregational singer's range, the situation was much more fluid vis-a-vis key signatures.
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  • Carl DCarl D
    Posts: 992
    I guess I've assumed that there's several factors with preferences in music these days...

    * Since 4th grade band I noticed that music would avoid lots of flats and sharps, just because it's easier to learn and play for people without high levels of skill. Throughout my band and orchestra years, it seemed like there was a preference for flats rather than sharps. But since I played French Horn, perhaps that already meant I was getting one more flat than the C instruments.

    * In recent centuries, our bodies have gotten larger. It seems to make sense that a slight decline in comfortable pitch might result.

    * People rarely sing these days, so our vocal range hasn't developed as much as people who sang constantly. In my schola, I ended up with a combined vocal range of just about an octave that everyone could sing together. Fortunately, most Gregorian Chant sticks to an octave, and you can pitch it to be comfortable. Win!

    But for myself, it seems that I've always sung harmony because the melody line is either too high, or sometimes ridiculously broad. I have a halfway decent baritone range, but still find it more comfortable to make up harmonies as I go along.
  • Don't forget the emotional-thrill-excitement factor. Most people, I think, have no trouble getting those high notes on the Star Spangled Banner and other songs at sporting events, or certain songs popular around new year's or out camping, or...., or.... 'Can't' nearly always can be translated as 'won't' or 'just don't feel like it because I'm not having fun'. (Make no mistake about it: most people know where those notes are and can sing them if they wish to.)
  • I once had a lady complain to me that the new Gloria we were singing was too high. It's "high" note was a D. The old Gloria we had been singing for years went up to an E-flat.

    Not much difference, I know, but the congregation sang that E-flat with gusto!
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  • Richard MixRichard Mix
    Posts: 2,799
    High notes don't tell the whole story. I am the Bread of life in A major (A-e') at 9:00 AM is not a problem. 6 verses of a narrow tessiatura tune like The Lord hears the cry of the poor (f#-d') is real torture for a low voice.
    Thanked by 2CHGiffen Liam
  • Did I miss something? It looks to me that the article says that up-tempo songs in a major key with 'happy' lyrics make people feel good.
  • dad29
    Posts: 2,232
    No, you didn't miss anything.
  • francis
    Posts: 10,825
    Well I listened to all those songs and I wasn't very happy by the end of it all.
    I can't get no.... Satisfaction!
  • Well I listened to all those songs


    I think you OD'd.
  • MBWMBW
    Posts: 175
    it seems that the key of F major is one constant in "feel good."


    Does this mean that because we are a half step higher now than 18th century pitch, F# must have been the "feel good" key at the time - but those fools just didn't know it?

    This is why all conscientious organists play the Bach "F Major" T and F in E major on instruments tuned to A440. Otherwise, if Bach were alive and heard it, he would be spinning in his grave.

    This is also why good choirs singing unaccompanied, when the pitch for a Renaissance motet is given by a sadly uninformed director, immediately lower the pitch by a half step. This is just plain common sense on their part (and on their part).

  • SalieriSalieri
    Posts: 3,177
    This is why all conscientious organists play the Bach "F Major" T and F in E major on instruments tuned to A440. Otherwise, if Bach were alive and heard it, he would be spinning in his grave.

    Or perhaps G-flat Major if his organs were tuned in Chorton.
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  • doneill
    Posts: 207
    Salieri is right - to say that we are now a 1/2 step higher than 18th c. pitch is a gross generalization. The truth is that pitch was all over the place. A=415Hz is something that modern early instrument players have adopted to approximate the pitch that would have been used in chamber music (and they need a standard - otherwise they would have to own multiple instruments or be breaking strings constantly). Some Italian music, however, would have been at higher pitch. And then there's Chorton. Frankly, I think that the ability to transpose at sight should be a requirement for every full-time music director out there. Forget what's in the hymnal - use what works with your situation, in your space, in your temperament, etc.
  • CHGiffenCHGiffen
    Posts: 5,193
    These pitch (and Chorton vs. Kammerton) issues have been discussed extensively in other threads, for example here and here.
  • CharlesW
    Posts: 11,980
    Salieri is right - to say that we are now a 1/2 step higher than 18th c. pitch is a gross generalization. The truth is that pitch was all over the place.


    Amen to that. Without any instruments to measure pitch retroactively, how could you really know?

    Frankly, I think that the ability to transpose at sight should be a requirement for every full-time music director out there


    It isn't, and is something not generally taught in the ancient days when I studied. When my Schantz console was rebuilt in August, they installed a transposer. Now my wailing divas no longer have key signatures to complain about. LOL.
  • You have a.... a, a, um.... t r ans p p p po ser?!
    Say that you don't.

    As for transposing at sight. That, I believe, is yet (though its days may be numbered) a requirement for FAGO. One would just assume that any degreed musician would be able to transpose. (Having said that, I must admit that some keys give me more trouble than others - which I consider to be a serious shortcoming.)
  • MBWMBW
    Posts: 175
    Good grief everyone! The three things I wrote about pitch were jokes. However, this is not the first time that my sense of humor appeared senseless to others. What is the color for half-witty comments? Lilac, perhaps?
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  • CharlesW
    Posts: 11,980
    You have a.... a, a, um.... t r ans p p p po ser?!
    Say that you don't.

    As for transposing at sight. That, I believe, is yet (though its days may be numbered) a requirement for FAGO. One would just assume that any degreed musician would be able to transpose. (Having said that, I must admit that some keys give me more trouble than others - which I consider to be a serious shortcoming.)


    Yes, transposers are available on pipe organs through the magic of Peterson. I rarely use it, but it is good to have when I need it. My transposing skills are limited to a whole step or two, nothing more. I think transposing is taught more in the piano study days than in organ. I had very little piano and started organ early, so I must have missed some of that. FAGO? I know what it is, but having that after your name would surely set you up as the butt of some very crude jokes. LOL. As a long-time AGO member, I have found the organization grows more irrelevant each year. Locally, it is probably far worse than nationally. I hope that isn't the case everywhere, but I don't know.
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  • SalieriSalieri
    Posts: 3,177
    I know what it is, but having that after your name would surely set you up as the butt of some very crude jokes.

    Its no worse than being a Doctor of Sacred Theology - STD
    Thanked by 1CharlesW
  • Adam WoodAdam Wood
    Posts: 6,482
    The three things I wrote about pitch were jokes.


    I thought "if Bach were alive and heard it, he would be spinning in his grave." was a dead giveaway.
    Thanked by 1MBW
  • melofluentmelofluent
    Posts: 4,160
    With a Rodgers simulacrum, of course we have a transposer. Do we ever use it. Can't, organist has perfect pitch, and I like it like that. Makes me work harder.
    Putting on "Dos Equis" persona....
    "I don't often use the transposition feature....but when I do, I use the large array organ capo. No digital for you!" (Bonus Soup Nazi reference, you can thank me later.)
  • I've worked in a lot of different musical worlds. I find it interesting that most of the musicians that I've encountered who have zero trouble transposing are not classically trained. (I am classically trained, and can transpose easily, so this comment is not at all a dig at classical training!) I wonder why that is?
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  • Wonder why that is?


    Perhaps professional context may be both an inducement and an indicator. In most non-sacred musical circles (I stand to be corrected) I don't think there is really a need to be able to transpose - unless one plays an instrument that is built in other than the key of C and works quite a bit with organists. Why, for instance, would an oboist need to know how to transpose his part in a Mahler symphony into a key different from that in which it was written? So it is, I think, with most instrumentalists. A church organist, on the other hand, is the standard bearer for a centuries-old tradition of improvisation and transposition (the latter, in the form of modulation, being an indispensable requirement for the former). The organist often has need of transposing pieces for soloists, for musicological reasons, for moving an anthem or motet onto a different key, for improvising voluntaries, for congregational singing reasons, and for (as is done in some quarters) transposing certain stanzas of a hymn as an artful and engaging experience for congregations. A degreed person in church music who can't transpose is missing an achievement that makes him fully a church musician (and probably was asleep during music theory and analysis classes). Transposing isn't easy for many - it is not unlike translating into another language at sight, on the spot. This is a talent that does, for most, require studious and determined application. (Leave it to Talon and Codgers, Ltd., makers of fine organ simulacra, to come up with a dial-a-key device which eliminates the need for thought... or knowledge.)
  • CharlesW
    Posts: 11,980
    (Leave it to Talon and Codgers, Ltd., makers of fine organ simulacra, to come up with a dial-a-key device which eliminates the need for thought... or knowledge.)


    Or wasted time learning a skill rarely used and perhaps, not worth the investment of time. So much to study, and so little time... I would rather spend it on something else, like trying to wrap my mind around that Reger piece that is driving me nuts. LOL.
  • dad29
    Posts: 2,232
    Yah, well, one could make the case that transposition skills are about 5th on the list of "necessaries"--after 1) knowing what Catholic church music IS; 2) having a facility with Chant; understanding acoustics enough to NOT use microphones, (etc.).

    In a local parish, the Ph.D. (organ) guy can transpose, so he does his R&B stuff in 3 keys, while shoving the 35-rank output through electronic amplification.

    Whooppeeee!
    Thanked by 1CharlesW
  • Yes, Mr. Osborn, I do think that need drives a lot of it. Perhaps the need is not so often there in most classical contexts, simply because, as you say, classical musicians tend to "play what's written".

    Long ago, I did a stint as a studio accompanist (among other things -- I was far down the hierarchy of the place) for a short while, and singers would come in and request that the accompaniment be taken 'a little down' or 'a little up' (they only occasionally mentioned keys). Paycheck (and not being relegated to errand-boy) demanded instant success...

    Perhaps for this reason, professional jazz pianists tend to be able to transpose.

    I also think it has something to do with how music (I mean individual pieces of music, as well as the discipline overall) is learned outside of a classical context. Much like singing chant (moveable 'do' and all that), many non-classical musicians learn to play in some number of keys, and individual pieces are conceived more in terms of where they lie within the structure of the scale, rather than in terms of absolute pitch, as in "next we go to the 4", not "next we go to B flat". (I did that example in the key of F because I want it to be happy.)

    I think that this way of thinking has merit and value, even for those with no need of transposition.
    Thanked by 1M. Jackson Osborn
  • melofluentmelofluent
    Posts: 4,160
    I can name this tune in two notes: Miles Davis. If a musician cannot intuit intervallic relationship between and half-step/whole step, then s/he's out of the Musician Pool. (As I'm typing I'm listening to Byzantine (Orthodox) Chant, with quartal tones and choral perfection down to micro-cents.
  • SalieriSalieri
    Posts: 3,177
    Maybe part of the problem of transposing is that we learn (figured) music based on C-D-E-F-etc., rather than Do-Re-Mi-Fa (with movable Do).

    I have no difficulty at all in playing/accompanying a chant in any key; if you want Gaudeamus with the final on E-flat, no problem, just make Do D-flat. But figured music, takes a bit more thinking. Putting LASST UNS ERFREUEN up a step is trickier because I have to constantly remind myself that D isn't D, it's E. I personally find transposing figured music easier if I try to think in terms of solfege rather that pitch-names.

    Of course, this doesn't work in places with fixed Do.
  • ryandryand
    Posts: 1,640
    I studied jazz in college and part of our performance exams included being able to play the semester's repertoire in any key. They'd call a tune and a random key, often impractical keys that would never be called on a gig unless there was an annoying jerk sitting in and you wanted to embarrass him.

    I learned to transpose melodies by thinking of them in what I guess you'd call numerical solfege. (1 2 3 not do re mi) and chord progressions as they'd be analyzed in theory classes dealing with functional harmony.

    NICAEA would be 1 1 3 3 5 5 6 6 6 5 5 etc. harmonized I-vi-V-I-IV-I

    If I needed to play it in Gb for some strange reason, its no more difficult than D.
  • ...that Reger piece that's driving me nuts...


    I should think, Charles, that some degree and command of transposition deftness would be quite helpful in grasping the form and structural procedure of something as complex as your Reger. It seems to me that this would be most helpful, and not at all 'wasting time on a skill rarely used'. I am not saying this as a put down, or in a condescending way: surely, all of us here understand to greater and lesser degrees the role of modulation, key relationships, and outright transposition as they are manifest in the structure of musical compositions of any worth. Command of these should be immensely helpful in 'wrapping our minds around' almost anything we might wish to learn. How can one really, truly, 'recite'/present the full essence of a piece to hearers without a thorough comprehension of its structure? Speaking for myself, I know beyond doubt, that I cannot genuinely play any worthy music whose form and tonal procedures I haven't internalised. Transposition and key relationships are foundational for all music. If one doesn't comprehend these, one does not 'know' the music he is presuming to perform. He may be performing the notes - but not the music. (By the way: what daunting Reger are you wrapping your mind around?)
  • Richard MixRichard Mix
    Posts: 2,799
    'wasting time on a skill rarely used'
    I thought he was talking about figuring out the transposer ;-)
  • Maybe he was.
    I'm sure we'll find out.
    Perhaps I over-reacted.
  • Many choirs I have sung with over the years have not merely had the ability to transpose on sight -- they do it without even being asked to change keys, and usually in the middle of the piece. [Please note the lack of purple, although I hope that the point I'm making is clear.]

    You haven't lived until you've sung the Bruckner 3 Graduals with this skill. Starting Locus Iste in C major and finishing it in D-flat major or even D-major is quite the accomplishment.
    Thanked by 1CharlesW
  • CharlesW
    Posts: 11,980
    Jackson, I can transpose a couple of steps in either direction. I am lost beyond that. However, I can count the number of times I have had to transpose in 50 years of playing and there were not very many of them.

    I thought he was talking about figuring out the transposer ;-)


    That did take a few minutes since I wasn't used to having one.

    (By the way: what daunting Reger are you wrapping your mind around?)


    The Fantasy and Fugue on B-A-C-H. It is kind of fun, but I have wanted to pitch the score out the nearest window a few times. LOL.

    Perhaps I over-reacted.


    You over-react? Is the pope Catholic? I used to be certain of the answer on that one. LOL.
    Thanked by 1M. Jackson Osborn