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 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
https://en.wikipedia.org/wiki/Shape_note
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.
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.
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.
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 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?
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?
Better:
In equal temperament, log base two: add 4/12 to 5/12 and you get 9/12.
In ratios (depending on tuning, these could be loose approximations): multiply 5/4 by 4/3 and you get 5/3.
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.
I don't want to count in twelfths, I want to count up the scale.
> call the ground floor of a building “0”
I'm a Brit, we do that here already.
For instance, “minor second”, “major second”, “minor third”, “major third”, “perfect fourth”, “augmented fourth”, “perfect fifth”, “minor sixth”, “major sixth”, “minor seventh”, “major seventh”, “octave”.
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.
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.
If instead you used digits from –5 to 6, using arithmetic mod 12, it becomes obvious that e.g.:
-2 + -3 = -5
4 + 3 = -5
5 + 5 = -2
-5 + -1 = 6
4 + -3 = 1
etc.
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.
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.
I am obliged to point out that a 12-semitone approach is in fact part of the "existing system" (see: pitch-class set theory).
(Mind you, I of course think its usefulness is overrated, because I think the "atonal" repertory is tonal.)
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.
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.
> 4c. Get a good feel for common jumps
i think that's why the current system works so well. most musicians have intervals burned into their muscles. to use an excel reference, reading R1C1 from the staves is much faster than reading A1, because you can read R1C1 from any line in the staves.
1. Find Do. This is the first note of the Major scale in the key which you are playing. Find it on the page, and burn it into your mind; everything you're about to do centers on the location of Do. In the key of C (white keys on a piano) Do is right in the middle of the grand staves, keeping things simple. If you know where Do is, you don't have to care about the key signature for like 97% of the notes you're going to read, and you can make educated guesses about what the sharps and flats do by using your musical intuition. Once you've found Do on the page, figure out where Do is musically, and keep it in your head. Make sure that when you're singing or playing any other note, you know where you are relative to Do, and can jump back there without losing your place.
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.
3. When you're sight reading the first note in a passage, find the note, then step it off visually to the nearest Do. If you're good, you can also step it off to the nearest Sol. I usually root myself on Do and Sol both in a given passage, as it gives me less visual separation between any note I need to find in a hurry.
4. For every note after that first note, pay mind to the spacing on the page:
4a. Moving up and down the scale should be easy; you're a musician, you already know what a scale sounds like, just sing along.
4b. Moving up or down from one line to the next line is a third. Most often you'll hear these relative to Do-Mi-So-Ti in major keys, and La-Do-Mi in minor keys. You'll hear these a lot, so get used to reading them quickly.
4c. Get a good feel for common jumps while you're at it. As a Bass singer, I got really good at reading jumps between Do-Fa and Do-So, because those chord progressions exist in everything, and their sole purpose in life is to make bass singers bored out of their mind. You're a human, in addition to a musician, so you'll pick up on the patterns in any given composition and have the common tricks down before you even realize what your brain is doing. Don't question that, let your brain be awesome all on its own.
That sounds like a lot of steps, until you realize that you're performing most of them already to make sense of any piece of music that you play. Don't worry about the names or the terminology, you can use numbers (1-3-5) if that's easier, or just "hear" it if you don't feel like you need an aide. Remember, the goal is to drop the aide and be able to just perform these steps on your own eventually.
I'm analytical in nature, so I'm always thinking about these things. I suspect the reason most musicians can't describe this process very well is because the process of analyzing our craft detracts from the quality of its output. The more you can commit to "muscle memory" as a musician, the more you can pull your analytical mind out of the process of a performance, the easier it becomes. Your body's built in reflexes are faster than your analytical brain will ever be, and good musicians tap into that biological strength through loads of practice.