"2. Learn your intervals, and learn Solfege. If you're a musician, you already know these things in principal, even if you don't know the words or the terminology. In particular, you should be able to "hear" the distance between Do-Mi-Sol without too much difficulty, because you hear those distances in music a lot."
I believe the Solfege named intervals (Do-Re-Mi-Fa-So-La-Ti-Do) are only taught as a historical oddity these days (or maybe used more in classical training?). All of my musical instruction, at the high school and college level, used numeric interval names (1-2-3-4-5-6-7-8). Most of the serious musicians I've played with also used the numeric scale rather than Do-Re-Mi. We learned how to sing Do-Re-Mi, "Just in case", but we never used it.
Were you taught in the US, or somewhere else? Maybe it is a regional thing.
I was taught in the US, and Solfege was used prominently in my voice classes, but rarely in my theory and piano classes. I think it's a system that works well when you don't have to think about the actual note name that you're singing, as it describes intervals very well, but relates somewhat poorly to pitch.
I grew up attending a Church of Christ, which used full congregational singing with four part harmony. Our songbooks used a variation on music notation that used shape notes, and the shapes corresponded to Solfege. If you knew your musical intervals, you could completley ignore the key signature, because a Do was always drawn as a triangle, a Sol was a circle, a La was a square, etc etc. This was especially handy because the song leaders were always men, and could not always sing as high as the written music required. They picked whatever key they could sing comfortably, and the congregation adjusted to them. Drove the music majors in the audience nuts. :D
Growing up with that system meant that Solfege was simply the easiest system I had to understand music. To this day, I struggle with pieces in unusual modes, and with passages that modulate their key and make use of unusual progressions, because it breaks down my innate understanding of music and requires me to think in a different way.
Shape note seems really clever! But, I can also see where it would break down in many cases. I learned music predominantly in a Jazz context. That'd be very tricky to use for jazz...especially the various modal types of jazz.
Solfege/solfège is still used prominently in France, or at least it was ~25 years ago. I took music lessons when I lived in France as a teenager. My piano instructor was very confused by the fact that I spoke good French, was at a solid intermediate level at the piano, and yet I could not at all follow his solfège commands (like you say, I had only used numeric intervals back home, although teachers usually called the note by its alphabetic name, like most here I think).
I tried reviewing in my head each week before class what I remembered from the Sound of Music, but made the mistake of thinking that Do-Re-Mi etc. was a static C-D-E instead of realizing that my music instructor was simply describing intervals depending on the key we were in.
In the present day, I would just look it up online, but back in 1991, in a small city in northern France, I didn't have that privilege. It took me several months of twice-weekly instruction before I finally figured out that he was using solfège for intervals, I'm embarrassed to say (to my instructor's frustration and confusion). I'm wincing even now when I think of it.
I asked around at the time and was told it was pretty universal to use solfège there.
I do think using solfège to indicate notes is a much better system for students, since it emphasizes the importance of intervals and keys. It's probably harder at the beginning that just learning static A-B-etc., but worth it.
Solfege is definitely still in strong use, especially in public school choirs. They are convinced that it helps in sight-reading competitions (yes, sight reading is one of several areas in which a choir can compete).
Having said that, I absolutely hate solfege. But my bachelor's was in piano performance, not vocal.
Interesting note: quite a few countries use a "fixed Do" system rather than "A-B-C". It is quite confusing (and humorous to observe) when a solfege disciple tries to sing with a fixed Do native.
Fixed Do sounds awful! I just spent some bit of time reading the wiki on Solfege, as I realized I have a limited view of it. Interestingly, there are additional syllables beyond the 7 I learned! There are also syllables for flattened and raised notes, which is really nice. I have always been bugged by saying "flat three" or "minor three" when singing intervals, and it's hard to make the voice actually make it minor (for me) because of the muscle memory for three being so firmly set.
So, I may have to somewhat rethink my dismissal of the solfege, at least for singing intervals. Unless there's a secret system for singing with intervals by number that accommodates accidentals.
As a computery person, what bothers me the most is the 1-based indexing of intervals. I get that music theory predates zero, but it makes it incredibly frustrating to work with (e.g. add a third to a fourth and you get a... sixth).
When do you need to do math like that with intervals?
As a computer nerd myself, I can understand the argument for 0-based indexing in this case, but I don't recall ever being stumped by it being 1-based. When would you need to add a 3rd and a 4th to get a 6th? Harmonic theory doesn't use addition like that. e.g., playing a 6th is not the same as playing a third and a fourth. So, why do that kind of math with intervals?
Whenever you play three notes in sequence, no? I'll read a passage and think "tonic, up a third, up a fifth so that puts me up to the tonic again... nope."
Huh. That's interesting. In a "people's brains think surprisingly differently sometimes and we rarely think about those differences when the resulting behaviors look the same" kinda way.
I mean, I guess that's not so foreign...But, I tend to think of it as pulling out the notes I need from the scale, and not actually counting up to them. e.g. in my brain I'm grabbing the third and the octave (well 7th, if you've got a third and then the fifth of that third, which I guess is why you're preferring 0-based) that are already there...not climbing up them to find there's the tonic there. I mean, I can see that it's a fifth interval if I go from E to B (in C), but unless I'm building a chord on E, I don't care..it's either the 7 in C, and I'm not so much thinking of its relation to E as I play it, and it's a phrase in C, with maybe an Em chord (either implicit or explicit) underneath; or I'm playing jazz, or some other very chord-based music, and I want my phrase to be relative to the chord we're currently playing (so we're inside that Em, and the key is less relevant).
Sight reading is different, as well, in my brain, but, I think it even bypasses the intervals to some degree and is just distances and shapes and an awareness of the key I'm in. I don't read much these days, but I recall it working best (or at least fastest and most accurately) when most of the theory was turned off in my brain and I just let the shape of the notes (their distance from each other) guide me. But, I feel like it's only in improvising and composition where one would be doing any sort of interval math. But, maybe I'm wrong.
When are you doing this kind of math? When reading, improvising, playing memorized pieces, or composing?
The main context I was thinking of was learning a new piece, particularly the initial read-through of something I haven't heard - I sometimes try to think what it "should" sound like ahead of playing it.
Yes, I know. But having the log base 2^(1/7)-ish built in is useful. If we could just subtract 1 from all the numbers (i.e. what we call a fifth should be 4) then we would have a measure that actually made sense.
Eh. Calling it a “fifth” is making it clear that the label is an ordinal number: first second third fourth fifth ...
You need to think of it as “if the bottom note was the first note of a scale, where in the scale would the top note be?”
As with many questions of indexing, off by one errors are tricky.
It’s a system that confuses names for notes in a scale with names for intervals between notes. You’d rather they called them by cardinal numbers representing some kind of “distance”, instead of a count starting at one.
But that would be applying a later mathematical understanding on the earlier system. If that’s what you want, you should just use a log scale and count twelfth roots of two.
Ideally we’d switch all our indexing to start at zero, and use half-open intervals everywhere. Start at 0 AD, call the ground floor of a building “0”, start spreadsheets with row 0, switch Matlab to index from 0, et cetera. This is pretty unlikely to happen though.
The intervals in a 7-note scale inherently don’t add up like that, because they’re not based on even divisions. So regardless we need to have 12 different named intervals for various numbers of semitones:
Reducing all those ordinal numbers by one really doesn’t help all that much. You still have to remember how the “minor” and “major” labels interact for every interval in the scale, and remember that sometimes the interval between the same two notes is given multiple names depending on the key, etc., which is all horribly confusing mess.
> Reducing all those ordinal numbers by one really doesn’t help all that much. You still have to remember how the “minor” and “major” labels interact for every interval in the scale, which is a horribly confusing mess.
Those interactions are pretty intuitive. Where defined, major + minor = perfect (considering an octave as perfect), perfect + major/minor = major/minor. As long as you remember which notes exist, you can't get it wrong, so you'll never get confused by a piece of arithmetic in an actual piece.
The “perfect” intervals are just ±5 (ratios very close to 3:2 and 4:3). The “major” intervals are –3, –1, 2, 4 (approx. ratios of 5:3, 15:8, 9:8, 5:4). The “minor” intervals are –4, –2, 1, 3 (approx. ratios of 8:5, 16:9, 16:15, 6:5).
Then it’s easy to see that your “major + minor = perfect” formula only works for some intervals, Etc. Overall the simple heuristics are more obfuscatory than helpful IMO.
> Then it’s easy to see that your “major + minor = perfect” formula only works for some intervals, Etc.
Where does it go wrong? Do those cases come up in practice?
Counting up and down the scale is a core use case for a notation for intervals. It absolutely needs to be well-supported. A 12-semitone approach is never going to match the usability of even the existing system.
Nearly all aural skills classes (learning to hear/sing music) for music majors use solfege or something like it. Some people use scale degree numbers instead (so a IV chord in a major key is "4-6-1" rather than "fa-la-do"), but the concept is still very useful.
What I'm questioning is the popularity of Solfege vs numeric interval names.
My music classes of ~20 years ago treated Solfege as being of historic interest, but not particularly common. While numeric intervals were used daily. It came up somewhat more in sight singing and vocal training than in any of the instrument or theory oriented classes. But, I think it was mostly students who were used to it using it rather than instructors teaching it.
But, maybe I just so strongly preferred numbers that I immediately discarded any instruction involving Solfege as being silly and a waste of my time.
Still, I can only recall seeing numbers (and Roman numerals) in writings on theory and such.
Fair enough. It's still pretty common...it's hard to pin down any numbers exactly, but I'd guess it's probably half and half for solfege vs. other systems. We teach solfege at my school (although I prefer numbers myself). And you're right that it's used mostly in sight-singing/aural-skills classes; I mention solfege much less often in my written theory classes.
Exact opposite for me. I learned do-re-me as a kid and then ever saw it again, until I started reading about music theory recently. Then I saw it a lot - e.g. voice leading rules saying that a voice must start from Do and end on a ti-do step, etc.
Well, sure, but what's that got to do with actual music instruction and how musicians talk about music? Movies aren't always entirely accurate representations of the world, particularly on highly technical topics.
Knowing solfege because you heard it in a movie and using it on a daily basis in the process of teaching or making music are independent concepts.
Anyway, conversation here has brought it to my attention that it is still pretty common, there are some areas where it is useful (maybe even better than numbers, as in the singing and vocal training area; I personally have recognized the limitation of numbers when singing minor notes, for example), and that my own experience was only partly representative of music pedagogy in the US and elsewhere. That said, when I'm teaching people about music, I still plan to only use numbers...the areas where solfege would be useful are pretty advanced, and require more than watching Sound of Music to understand.
I believe the Solfege named intervals (Do-Re-Mi-Fa-So-La-Ti-Do) are only taught as a historical oddity these days (or maybe used more in classical training?). All of my musical instruction, at the high school and college level, used numeric interval names (1-2-3-4-5-6-7-8). Most of the serious musicians I've played with also used the numeric scale rather than Do-Re-Mi. We learned how to sing Do-Re-Mi, "Just in case", but we never used it.
Were you taught in the US, or somewhere else? Maybe it is a regional thing.