Am I the only one who thinks that the classic music notation is 3x harder to learn than the basic music theory (without the rules of notation)?
I think that you can learn music theory (to play an instrument or to compose music e.g. in a "piano roll tool" / MIDI editor) much faster if you skip the classic notation. And I think that it is even better to learn the notation AFTER you understand the music theory.
This is a bit off topic, but since you mentioned your guide:
I hope this doesn't come off as hostile, but the guide you linked contains a number of inaccuracies and oversimplifications - it's kind of naive in an endearing way, but also leaves the reader with the impression that it covers all there is to music. I guess what I'm saying is it's fine to restrict yourself in what you include in the guide, or even simplify things, but it should be clear that the topic (i.e. music) is far richer and more complex.
Yeah, I think a good discussion on music theory is starting from first principles, explaining Pythagorean tuning, then explaining 5-limit just intonation, the explaining we compromised on 12-tone equal temperament because it made tuning and changing keys a lot simpler, at the expenses of some notes being slightly out of tune (e.g. the minor and major thirds deviate by about 15 cents from their 5-limit just intonated “ideal” tunings).
Aside from that not being what was said (the parent’s pull-quote is wrong in multiple ways), it is in fact not possible to tune a piano to any arbitrary set of 88 pitches without changing the design so dramatically and fundamentally that it would no longer be a piano. The triangular shape of a grand determined by the strings lengths, the placement of the pins, the use of double/triple strings in some frequency ranges, and design of the sound board, all permit only a very limited range of frequencies for each key on the keyboard. You very obviously cannot take an existing piano and tune it to 88 keys of A0, nor to 88 keys of C9.
Of course you can, but that's not what's implied by the quote.
In addition to microtonality, many instruments (and the human voice) are capable of infinite tuning, and musicians will deviate from the "correct" note (as played by an even-tempered instrument) based on chord structure, voice leading, etc.
That's not what "tuning" means. Yes, fretless string instruments, the human voice, instruments like the trombone are all capable of being played with arbitrary or semi-arbitrary pitch. But they are still either tuned in some way, or never tuned at all. Performance is not tuning.
Since an "arbitrary piano" is tuned by turning screws, like simpler string instruments, the only pitches that it cannot be tuned to are those that fall outside the range of each string. Departing from the usual inharmonically tempered 12-EDO tuning would just sound strange, possibly outside some piano tuner's professional comfort zone.
And that isn't a nuanced opinion; a common one among rigid materialists. Its not the best piano for a stage, but I am sure it could fool your ears in a recording. Morpheus would think it was a piano too. "What is real? ..."
It kind of reminds me of the periodic declaration someone makes on HN that textual programming sucks and we all need to switch to something else, usually visual programming in this case.
If someone takes time to deeply understand the advantages of the textual approach and then builds an alternative, I'll listen.
But at this point, anyone who is doing this and their criticism of the original approach is shallow and uninsightful, where it's basically just "it's old and it must therefore suck", is unlikely to produce a good answer.
I think that applies to the music notation case too. "Conventional" music notation isn't just a staff and a couple of types of notes. By the time you handle all the use cases that conventional notation handles, or even just a solid subset of it, your brand new notation is probably a lot less elegant than it started out as in someone's head.
Exactly. Music theory is a programming language for musical composition and performance.
Unlike most languages it's inherently two dimensional because music includes both horizontal (time, rhythm) and vertical pitches (chords/colours, harmony) information.
And - especially important - melody is an element that needs both.
You can't represent the same information with text without losing a lot of important content, which is why toys like Sonic Pi are more limited than they seem.
You can kinda sorta represent the same information on a piano roll, but it's not any easier to read than dots - in some ways harder, because you're not going to see the relationship between a bass line and chords as clearly.
Is it a good programming language? It's quite dense, but not denser than some code idioms. The 2D element is unique, and hard to represent in other ways.
The learning curve is steep, but it's probably as good as it can be given the requirements and constraints.
I know neither is about music notation per se (but about fixing the piano), but it is analogous: Music notation has exactly the same problem as the piano -> it defaults to C, which makes everything else relative to C and overly complicated.
For the record, I don't think this means we should switch to a new system, but it is usefull to recognize that it is suboptimal, if only to be able to accept it and continue (because nobody is going to translate everything to some new notation)
I think the discussion around changing the piano keyboard is somewhat more obvious and less subtle. It's pretty obvious that the main thing keeping the current piano keyboard alive is the same thing keeping QWERTY alive. Now, the current piano keyboard is not as bad as QWERTY, which is all but an objectively bad layout, whereas the current piano keyboard is one with pros and cons.
I am typing this comment in Dvorak on a split keyboard so split that the two halves are literally on one side each of my chair's armrests, separated by about two feet, so I am no stranger to heterodox opinions about keyboards and putting them in action, and have a track record of not defending the status quo just because it's the status quo.
The current piano keyboard, while it does require you to learn the 12 keys separately, is something that is demonstrably possible for a normal human being, and the advantage is then that you are in fact in those 12 keys separately. You can not be playing in D major and then, for any period of time, accidentally slide into D# major and be confused, which Terpstra makes very easy to do. Of course, recovery is then not difficult either, but it might take a moment.
But other than that, the debate around the piano layout is really a matter of just trying it out and seeing what works.
For notation, I see a lot of people trying to replace the current notation without realizing how many subtleties are in it. It's not just about single quarter notes being banged out in a regular rhythm. It's about many different instruments. It's about dynamics, how the notes are struck, it's about subtle details in how the notes are horizontally spaced, it's about how the notes are played, even things like vibrato can be indicated as starting halfway through the note, and it's about a lot of other things. It's about having a representation for the conductor, it's about working for percussion, it's about guitars and other things. The usual "notation sucks, let's use X" is "let's just use piano roll notation", but if you make a full inventory of what conventional notation has and compare it to "piano roll notation", piano roll notation isn't even close to filling the gaps.
A more fully-fleshed out proposal could. A more fully-fleshed proposal to break up the proposal based on instrument (classical notation does some of this anyhow) might get closer. But that's not what people propose. They generally propose that piano roll notation is already what we need. But it isn't even close to fitting the bill. I don't even have to start asking questions about how exactly one distinguishes between a minor and major 10th interval with their notation (a huge problem generally left unsolved) because they haven't even developed their supposed notation far enough to be a serious competitor. Maybe there's a solution to that too, if someone puts the work in. I wouldn't care to try to categorically exclude it... but I've never seen anyone demonstrate it or answer the question. Conventional music notation doesn't necessarily even have the final word on that question, it certainly has issues if you go too far above or below a clef, but it has an answer to that question. Proposals based around something other than piano roll notation are generally even less fleshed out than piano roll notation, which at least does have some decades of prior use in computer software, which I've also clocked some years with, I used to compose music for fun. Even whackier proposals are generally complete nonstarters even on their own terms.
I think if someone is going to come up with a new, useful notation, it is going to have to retain the non-representationality that the current notation has, where we are not trying to directly encode pitch changes into a literal, 1-to-1 geometry on the page, and especially not a direct 1-to-1 representation of time. Current notation is correlated to those things, but it's not even close to a 1-to-1 map (for example also 8ve block notation for jumping up and down). I have no problem with the idea that there could be something much better if it was worked out, but I doubt that much better thing is going to have those characteristics either.
Personally I think musical notation should be optimized for ease of playing first and foremost - and I think that would be best achieved with a 1-to-1 mapping to the pitch. I.e. if I just want to play a piece in an orchestra, it's easiest if it just literally says the notes. Having to parse what a note with a double flat actually is on the fly is just unnecessary mental labour, when the information you need as a player is just 'what note do I need to play'.
I also imagine that transposing is a lot easier if I was reading piano roll notation - just play the note but X down.
It's easy enough to extend piano roll notation or something like it with hints regarding what interval it is etc, so you have both benefits.
For the rithm though I always found the existing notation intuitive, piano roll probably would be hard to parse in that regard.
love that video, it made me lol so hard the first time I saw it :D
Classical composer and software engineer here. One of my goals is to help update score notation. I use something called "harmonic coloring" which is like a reduced MIDI notation: You color a note by its functional role (harmonic value) rather than an arbitrary hue in 0-11.
What this view shares with MIDI: Long rectangles representing the applied durations.
How it is different: Occupies a minimal amount vertical space.
The color palette I'm using is intended to support people with colorblindness. The shades/hues of a color encodes the functional harmony. The root key signature (origin) is always the same color; and chords some distance r away on the circle of fifths is the shade/hue at that offset r.
There is a similar concept described in the Tantacruel video towards the end.
You can explore it here on Monic Theory.
(mobile view should be fixed within 48 hours)
Note that in historical Byzantine musical culture, there are no absolute pitches at all. Their notational form is entirely intervals from some arbitrary root note.
Similarly, in Carnatic and Hindustani classical traditions, the note names (Sa, Re, Pa etc) do not denote pitches - Sa is always the root, whatever it is, and the rest have a somewhat well defined intervallic relationship to it.
I personally would not use "harmonic value" to describe this, since it occurs in music that (broadly speaking) lacks harmony. The key point, IMO, is that what matters are sets of intervals (ratios, if you prefer) rather than actual pitches (as frequencies).
Hindustani (and Carnatic) music indeed do not denote pitches for a very sound (pun intended) reason: They let singers choose the root note (Sa), and thereupon the melody is built. Most (all?) of Hindustani music is melody-based, not harmonic based (like Western music). And the melodies are themselves created within the Raga framework. Raga is like a mode (but not exactly that), and is hard to explain within the constraints of Western music theory precisely because that concept does not exist in western music per se. Which is why most Indian classical theorists call a raga a "melodic framework", and leave it at that (or expound on it, as the case may be).
A great reference for Indian classical music is [1] and and more recent one [2]
Actual frequencies matter in bass-focused dance music. You want a root note around 40Hz to 60Hz, which is high enough that it's easily heard and reproduced, but not so high that it loses the tactile body-shaking effect.
As a semi-professional trombonist, C clefs are very important to me. Alto and tenor as-written, tenor as a means of transposing Bb treble, mezzo-soprano as a means of transposing F parts… they are not obsolete.
My favorite genre of hacker news comment is when someone lacks sufficient imagination to wonder why something that’s commonly used by many people is still in use
FWIW, there's no real need for imagination here. The comment says "mostly", and added a parenthetical comment that was simply meant to name the viola as a prominent remaining use.
In particular, trombones have almost entirely stopped using the tenor clef in jazz.
It's true that jazz charts are unlikely to use tenor clef. Nonetheless, it remains career limiting for a trombonist to be unable to read clefs.
Commercial players are likely to use the skill for transposing Bb treble lead sheets, or playing in a pit. Tenor clef shows up in modern musicals regularly.
Not to mention being shunned from quartet or choir opportunities that are the basis of networking in the industry.
I suppose it makes historical sense, and even ingeniously designed.
But it, and the piano black keys with it, are definitely not optimal. It makes playing in C easy, and playing in anything else hard. I've picked up a new instrument since ~2 months, and 1 month in I could already play all scales by by deliberately staying away from music notation, learning the raw distances/steps that make up a scale and how to play them, rather than the 'delta from C', which is how classical training taught me to think. (Same story for chords etc)
But it, and the piano black keys with it, are definitely not optimal. It makes playing in C easy, and playing in anything else hard.
I don't think this is true—I was under the impression that, at least on piano, keys other than C major are sometimes chosen specifically to make things easier on the fingers.
Easier on the fingers - maybe (I don't know what you reference), but not easier on the mind: Instead of learning each chord once, you have to learn it 12 times (for each key).
It's all about the integers modulo 12. Classical notation obscures that (while making it easier to figure out which of the integers modulo 12 you're using, minus being able to assign them to integers in an obvious way).
24, 128, approach infinity -- I know there are microtonal systems, but if you want to understand them, choose the nearest multiple-of-twelve (or really, choose whatever TET contains the closest approximations to the exact notes) TET and look where their intervals land with respect to the symmetries (factors) within that TET, and where those symmetries are broken by a note moving by a perceptual 'slide' (one note 'moves' into the other position) rather than sounding like a new distinct voice.
More like, only if you're playing Schoenberg it's about modulo 12.
Almost all sheet music that you play uses 5 or 7 unequal subdivisions of the octave, and occasionally the rest. Sure, sometimes you'll have one or two of the rest on a regular basis (blues, harmonic/melodic minor), but still most music won't use all twelve.
Isn't modulo-twelve (if we ignore microtonal) the core underlying structure, and then you pick scale (like 2 2 1 2 2 2 1) and a key as a mapping, and then use degree as an 1-based index into the scale?
I don't really know a thing about music, so I could be wrong here - but that mental model at least made some sense to me when I tried to map all the concepts I've heard about into some sort of a mental system.
The point is that to a player the mapping is more important than the core 12-note structure, because highly chromatic (12-note) passages happen but they are the exception.
At least in western music you pick the seven basic notes on the scale, and that gives you the sharps and flats you place at the beginning of each line. That choice, from the point of view of notation, is even more important than the exact scale. And the choice is constrained to 15 sets of sharps and flats because it implicitly tells the player (veeeery roughly) to expect some patterns that probably will occur.
It doesn't always work great, for example if you want to write the Simpsons theme the set of notes in the scale doesn't fit any of those 15 sets. But it uses an unfamiliar scale in any case, so there's not much to gain and as a player you just deal with it.
I fun little exercise is to work out what would be different if we found aliens that also used 12 tone equal temperament, and also used a subset of 7 of those 12 notes to make their major scale, and also followed the same convention that we do of naming the notes of the major scale C, D, E, F, G, A, B like we do and naming the other 5 by naming a major scale note and adding modifier to tell how far away the not is from that like our # and b modifiers, and we both have the convention that when naming the notes of a transposed major scale we use each letter exactly once--except they picked a different 7 notes to be their major scale.
Our 12 tone scale with the major scale note names and notes not in the major scale marked with dots looks like this:
C.D.EF.G.A.B
Suppose the aliens have a very different idea of what makes a good sounding major scale, and their system is:
CDE.FGAB....
Suppose we transpose ours up 7 tones. We can represent this graphically by drawing out major pattern for two octaves, and below that drawing our major scale pattern with names replaced by X (X.X.XX.X.X.X) shifted over by 7, then look above to see how to name the notes (remembering we can only use each letter once):
C.D.EF.G.A.BC.D.EF.G.A.B
X.X.XX.X.X.X
Our major scale transposed up 7 is G A B C D E F#.
Let's do the same 7 tone transposition for the aliens. Their major scale pattern is XXX.XXXX..., so we get
CDE.FGAB....CDE.FGAB....
XXX.XXXX...
That's B Cbbbb Dbbbb Ebbb Fbbbb Gbbbb Abbbb.
At first that seems very different from our 7 tone transposition. We only need one sharp and they need 23 flats! But wait...mod 12 we have -23 = 1.
It turns out for all transpositions if you count sharps in your key signature as +1 and flats as -1, the key signature for a transposition by N tones will have 7N sharps or flats mod 12 in both our systems.
In general if you have a T note equal temperament scale with an M note subset major scale, transposing the major scale up N tones gives a key signature with NM mod T sharps/flats.
I'll leave it as an exercise to prove that. Hint: you can think of a transposition as a two step operation: (1) a shift that keeps the same letters and just adds sharps or flats to move the notes, and (2) a renaming that changed the name you use to name the first note of the transposed scale. Think about what each of those operations does to the number of sharps and flats needed.
Comments
Am I the only one who thinks that the classic music notation is 3x harder to learn than the basic music theory (without the rules of notation)?
I think that you can learn music theory (to play an instrument or to compose music e.g. in a "piano roll tool" / MIDI editor) much faster if you skip the classic notation. And I think that it is even better to learn the notation AFTER you understand the music theory.
I even made my own guide to music :D https://www.jampea.com/learn
This is a bit off topic, but since you mentioned your guide: I hope this doesn't come off as hostile, but the guide you linked contains a number of inaccuracies and oversimplifications - it's kind of naive in an endearing way, but also leaves the reader with the impression that it covers all there is to music. I guess what I'm saying is it's fine to restrict yourself in what you include in the guide, or even simplify things, but it should be clear that the topic (i.e. music) is far richer and more complex.
To give an example, this it of course not true:
Yeah, I think a good discussion on music theory is starting from first principles, explaining Pythagorean tuning, then explaining 5-limit just intonation, the explaining we compromised on 12-tone equal temperament because it made tuning and changing keys a lot simpler, at the expenses of some notes being slightly out of tune (e.g. the minor and major thirds deviate by about 15 cents from their 5-limit just intonated “ideal” tunings).
You're saying its not possible to tune a piano to an arbitrary set of 88 pitches?
Aside from that not being what was said (the parent’s pull-quote is wrong in multiple ways), it is in fact not possible to tune a piano to any arbitrary set of 88 pitches without changing the design so dramatically and fundamentally that it would no longer be a piano. The triangular shape of a grand determined by the strings lengths, the placement of the pins, the use of double/triple strings in some frequency ranges, and design of the sound board, all permit only a very limited range of frequencies for each key on the keyboard. You very obviously cannot take an existing piano and tune it to 88 keys of A0, nor to 88 keys of C9.
That's clearly not what was meant, even without the context of this following bit:
(This is not to mention that at a 1.06x increase per half step you're going to be sharp by 1 cent / octave which starts to add up).
Of course you can, but that's not what's implied by the quote.
In addition to microtonality, many instruments (and the human voice) are capable of infinite tuning, and musicians will deviate from the "correct" note (as played by an even-tempered instrument) based on chord structure, voice leading, etc.
That's not what "tuning" means. Yes, fretless string instruments, the human voice, instruments like the trombone are all capable of being played with arbitrary or semi-arbitrary pitch. But they are still either tuned in some way, or never tuned at all. Performance is not tuning.
Also quarter step bends in guitar and vibrato in general.
there are absolutely pitches that an arbitrary piano cannot be tuned to. it is also non-trivial to tune a piano.
Since an "arbitrary piano" is tuned by turning screws, like simpler string instruments, the only pitches that it cannot be tuned to are those that fall outside the range of each string. Departing from the usual inharmonically tempered 12-EDO tuning would just sound strange, possibly outside some piano tuner's professional comfort zone.
https://www.modartt.com/pianoteq_overview :) Very high quality and affordable software modeled piano. It is rather easy to tune via Scala KBD formatted files.
Not a piano, and not relevant to the parent remark.
And that isn't a nuanced opinion; a common one among rigid materialists. Its not the best piano for a stage, but I am sure it could fool your ears in a recording. Morpheus would think it was a piano too. "What is real? ..."
https://youtu.be/Eq3bUFgEcb4 explains why music notation is the way it is. There are very good reasons for it.
The parts that are really weird (like the C clef) have mostly been obsoleted, unless you play the viola I guess.
It kind of reminds me of the periodic declaration someone makes on HN that textual programming sucks and we all need to switch to something else, usually visual programming in this case.
If someone takes time to deeply understand the advantages of the textual approach and then builds an alternative, I'll listen.
But at this point, anyone who is doing this and their criticism of the original approach is shallow and uninsightful, where it's basically just "it's old and it must therefore suck", is unlikely to produce a good answer.
I think that applies to the music notation case too. "Conventional" music notation isn't just a staff and a couple of types of notes. By the time you handle all the use cases that conventional notation handles, or even just a solid subset of it, your brand new notation is probably a lot less elegant than it started out as in someone's head.
Exactly. Music theory is a programming language for musical composition and performance.
Unlike most languages it's inherently two dimensional because music includes both horizontal (time, rhythm) and vertical pitches (chords/colours, harmony) information.
And - especially important - melody is an element that needs both.
You can't represent the same information with text without losing a lot of important content, which is why toys like Sonic Pi are more limited than they seem.
You can kinda sorta represent the same information on a piano roll, but it's not any easier to read than dots - in some ways harder, because you're not going to see the relationship between a bass line and chords as clearly.
Is it a good programming language? It's quite dense, but not denser than some code idioms. The 2D element is unique, and hard to represent in other ways.
The learning curve is steep, but it's probably as good as it can be given the requirements and constraints.
Don't forget about the dynamics (loud or soft) dimension of music.
Not really. Here in the 21st century people mostly use DAWs, and there's a piano roll inside that thing instead of staff notation.
Have a look at http://terpstrakeyboard.com/about/ and the janko keyboard
I know neither is about music notation per se (but about fixing the piano), but it is analogous: Music notation has exactly the same problem as the piano -> it defaults to C, which makes everything else relative to C and overly complicated.
For the record, I don't think this means we should switch to a new system, but it is usefull to recognize that it is suboptimal, if only to be able to accept it and continue (because nobody is going to translate everything to some new notation)
Context: I played piano for about 15 years.
I think the discussion around changing the piano keyboard is somewhat more obvious and less subtle. It's pretty obvious that the main thing keeping the current piano keyboard alive is the same thing keeping QWERTY alive. Now, the current piano keyboard is not as bad as QWERTY, which is all but an objectively bad layout, whereas the current piano keyboard is one with pros and cons.
I am typing this comment in Dvorak on a split keyboard so split that the two halves are literally on one side each of my chair's armrests, separated by about two feet, so I am no stranger to heterodox opinions about keyboards and putting them in action, and have a track record of not defending the status quo just because it's the status quo.
The current piano keyboard, while it does require you to learn the 12 keys separately, is something that is demonstrably possible for a normal human being, and the advantage is then that you are in fact in those 12 keys separately. You can not be playing in D major and then, for any period of time, accidentally slide into D# major and be confused, which Terpstra makes very easy to do. Of course, recovery is then not difficult either, but it might take a moment.
But other than that, the debate around the piano layout is really a matter of just trying it out and seeing what works.
For notation, I see a lot of people trying to replace the current notation without realizing how many subtleties are in it. It's not just about single quarter notes being banged out in a regular rhythm. It's about many different instruments. It's about dynamics, how the notes are struck, it's about subtle details in how the notes are horizontally spaced, it's about how the notes are played, even things like vibrato can be indicated as starting halfway through the note, and it's about a lot of other things. It's about having a representation for the conductor, it's about working for percussion, it's about guitars and other things. The usual "notation sucks, let's use X" is "let's just use piano roll notation", but if you make a full inventory of what conventional notation has and compare it to "piano roll notation", piano roll notation isn't even close to filling the gaps.
A more fully-fleshed out proposal could. A more fully-fleshed proposal to break up the proposal based on instrument (classical notation does some of this anyhow) might get closer. But that's not what people propose. They generally propose that piano roll notation is already what we need. But it isn't even close to fitting the bill. I don't even have to start asking questions about how exactly one distinguishes between a minor and major 10th interval with their notation (a huge problem generally left unsolved) because they haven't even developed their supposed notation far enough to be a serious competitor. Maybe there's a solution to that too, if someone puts the work in. I wouldn't care to try to categorically exclude it... but I've never seen anyone demonstrate it or answer the question. Conventional music notation doesn't necessarily even have the final word on that question, it certainly has issues if you go too far above or below a clef, but it has an answer to that question. Proposals based around something other than piano roll notation are generally even less fleshed out than piano roll notation, which at least does have some decades of prior use in computer software, which I've also clocked some years with, I used to compose music for fun. Even whackier proposals are generally complete nonstarters even on their own terms.
I think if someone is going to come up with a new, useful notation, it is going to have to retain the non-representationality that the current notation has, where we are not trying to directly encode pitch changes into a literal, 1-to-1 geometry on the page, and especially not a direct 1-to-1 representation of time. Current notation is correlated to those things, but it's not even close to a 1-to-1 map (for example also 8ve block notation for jumping up and down). I have no problem with the idea that there could be something much better if it was worked out, but I doubt that much better thing is going to have those characteristics either.
Thanks for your writeup! Nice insightful read.
Personally I think musical notation should be optimized for ease of playing first and foremost - and I think that would be best achieved with a 1-to-1 mapping to the pitch. I.e. if I just want to play a piece in an orchestra, it's easiest if it just literally says the notes. Having to parse what a note with a double flat actually is on the fly is just unnecessary mental labour, when the information you need as a player is just 'what note do I need to play'.
I also imagine that transposing is a lot easier if I was reading piano roll notation - just play the note but X down.
It's easy enough to extend piano roll notation or something like it with hints regarding what interval it is etc, so you have both benefits.
For the rithm though I always found the existing notation intuitive, piano roll probably would be hard to parse in that regard.
love that video, it made me lol so hard the first time I saw it :D
Classical composer and software engineer here. One of my goals is to help update score notation. I use something called "harmonic coloring" which is like a reduced MIDI notation: You color a note by its functional role (harmonic value) rather than an arbitrary hue in 0-11.
What this view shares with MIDI: Long rectangles representing the applied durations. How it is different: Occupies a minimal amount vertical space.
The color palette I'm using is intended to support people with colorblindness. The shades/hues of a color encodes the functional harmony. The root key signature (origin) is always the same color; and chords some distance r away on the circle of fifths is the shade/hue at that offset r.
There is a similar concept described in the Tantacruel video towards the end.
You can explore it here on Monic Theory. (mobile view should be fixed within 48 hours)
https://monictheory.com/project-templates
Note that in historical Byzantine musical culture, there are no absolute pitches at all. Their notational form is entirely intervals from some arbitrary root note.
Similarly, in Carnatic and Hindustani classical traditions, the note names (Sa, Re, Pa etc) do not denote pitches - Sa is always the root, whatever it is, and the rest have a somewhat well defined intervallic relationship to it.
I personally would not use "harmonic value" to describe this, since it occurs in music that (broadly speaking) lacks harmony. The key point, IMO, is that what matters are sets of intervals (ratios, if you prefer) rather than actual pitches (as frequencies).
^^ THIS
Hindustani (and Carnatic) music indeed do not denote pitches for a very sound (pun intended) reason: They let singers choose the root note (Sa), and thereupon the melody is built. Most (all?) of Hindustani music is melody-based, not harmonic based (like Western music). And the melodies are themselves created within the Raga framework. Raga is like a mode (but not exactly that), and is hard to explain within the constraints of Western music theory precisely because that concept does not exist in western music per se. Which is why most Indian classical theorists call a raga a "melodic framework", and leave it at that (or expound on it, as the case may be).
A great reference for Indian classical music is [1] and and more recent one [2]
[1] The Ragas of North Indian Music, N.A. Jairazbhoy, https://archive.org/details/dli.ministry.26725
[2] Rāgs Around the Clock, A Handbook for North Indian Classical Music, with Online Recordings in the Khayāl Style, https://www.openbookpublishers.com/books/10.11647/obp.0313#r...
much love for the Just Intonation in the house
Actual frequencies matter in bass-focused dance music. You want a root note around 40Hz to 60Hz, which is high enough that it's easily heard and reproduced, but not so high that it loses the tactile body-shaking effect.
As a semi-professional trombonist, C clefs are very important to me. Alto and tenor as-written, tenor as a means of transposing Bb treble, mezzo-soprano as a means of transposing F parts… they are not obsolete.
Yes, I did write "mostly". Sometimes the bassoon uses the C clef as well. Still, overall it can be safely ignored in most cases.
My favorite genre of hacker news comment is when someone lacks sufficient imagination to wonder why something that’s commonly used by many people is still in use
FWIW, there's no real need for imagination here. The comment says "mostly", and added a parenthetical comment that was simply meant to name the viola as a prominent remaining use.
In particular, trombones have almost entirely stopped using the tenor clef in jazz.
It's true that jazz charts are unlikely to use tenor clef. Nonetheless, it remains career limiting for a trombonist to be unable to read clefs.
Commercial players are likely to use the skill for transposing Bb treble lead sheets, or playing in a pit. Tenor clef shows up in modern musicals regularly.
Not to mention being shunned from quartet or choir opportunities that are the basis of networking in the industry.
I suppose it makes historical sense, and even ingeniously designed.
But it, and the piano black keys with it, are definitely not optimal. It makes playing in C easy, and playing in anything else hard. I've picked up a new instrument since ~2 months, and 1 month in I could already play all scales by by deliberately staying away from music notation, learning the raw distances/steps that make up a scale and how to play them, rather than the 'delta from C', which is how classical training taught me to think. (Same story for chords etc)
I don't think this is true—I was under the impression that, at least on piano, keys other than C major are sometimes chosen specifically to make things easier on the fingers.
Easier on the fingers - maybe (I don't know what you reference), but not easier on the mind: Instead of learning each chord once, you have to learn it 12 times (for each key).
See http://terpstrakeyboard.com/about/
I have some great news: you're a nerd ! :))
... or is it geek, i can never remember the difference ...
It's all about the integers modulo 12. Classical notation obscures that (while making it easier to figure out which of the integers modulo 12 you're using, minus being able to assign them to integers in an obvious way).
Only in 12TET.
24, 128, approach infinity -- I know there are microtonal systems, but if you want to understand them, choose the nearest multiple-of-twelve (or really, choose whatever TET contains the closest approximations to the exact notes) TET and look where their intervals land with respect to the symmetries (factors) within that TET, and where those symmetries are broken by a note moving by a perceptual 'slide' (one note 'moves' into the other position) rather than sounding like a new distinct voice.
More like, only if you're playing Schoenberg it's about modulo 12.
Almost all sheet music that you play uses 5 or 7 unequal subdivisions of the octave, and occasionally the rest. Sure, sometimes you'll have one or two of the rest on a regular basis (blues, harmonic/melodic minor), but still most music won't use all twelve.
Isn't modulo-twelve (if we ignore microtonal) the core underlying structure, and then you pick scale (like 2 2 1 2 2 2 1) and a key as a mapping, and then use degree as an 1-based index into the scale?
I don't really know a thing about music, so I could be wrong here - but that mental model at least made some sense to me when I tried to map all the concepts I've heard about into some sort of a mental system.
The point is that to a player the mapping is more important than the core 12-note structure, because highly chromatic (12-note) passages happen but they are the exception.
At least in western music you pick the seven basic notes on the scale, and that gives you the sharps and flats you place at the beginning of each line. That choice, from the point of view of notation, is even more important than the exact scale. And the choice is constrained to 15 sets of sharps and flats because it implicitly tells the player (veeeery roughly) to expect some patterns that probably will occur.
It doesn't always work great, for example if you want to write the Simpsons theme the set of notes in the scale doesn't fit any of those 15 sets. But it uses an unfamiliar scale in any case, so there's not much to gain and as a player you just deal with it.
See around 32:30 in https://youtu.be/Eq3bUFgEcb4?t=1950
I fun little exercise is to work out what would be different if we found aliens that also used 12 tone equal temperament, and also used a subset of 7 of those 12 notes to make their major scale, and also followed the same convention that we do of naming the notes of the major scale C, D, E, F, G, A, B like we do and naming the other 5 by naming a major scale note and adding modifier to tell how far away the not is from that like our # and b modifiers, and we both have the convention that when naming the notes of a transposed major scale we use each letter exactly once--except they picked a different 7 notes to be their major scale.
Our 12 tone scale with the major scale note names and notes not in the major scale marked with dots looks like this:
Suppose the aliens have a very different idea of what makes a good sounding major scale, and their system is: Suppose we transpose ours up 7 tones. We can represent this graphically by drawing out major pattern for two octaves, and below that drawing our major scale pattern with names replaced by X (X.X.XX.X.X.X) shifted over by 7, then look above to see how to name the notes (remembering we can only use each letter once): Our major scale transposed up 7 is G A B C D E F#.Let's do the same 7 tone transposition for the aliens. Their major scale pattern is XXX.XXXX..., so we get
That's B Cbbbb Dbbbb Ebbb Fbbbb Gbbbb Abbbb.At first that seems very different from our 7 tone transposition. We only need one sharp and they need 23 flats! But wait...mod 12 we have -23 = 1.
It turns out for all transpositions if you count sharps in your key signature as +1 and flats as -1, the key signature for a transposition by N tones will have 7N sharps or flats mod 12 in both our systems.
In general if you have a T note equal temperament scale with an M note subset major scale, transposing the major scale up N tones gives a key signature with NM mod T sharps/flats.
I'll leave it as an exercise to prove that. Hint: you can think of a transposition as a two step operation: (1) a shift that keeps the same letters and just adds sharps or flats to move the notes, and (2) a renaming that changed the name you use to name the first note of the transposed scale. Think about what each of those operations does to the number of sharps and flats needed.