Pianos (keys) are badly designed!

PASHKULI · 2025-01-10T22:16:32+00:00

Hello, PianoTell members and readers! TL; DR (please scroll down for the links to my 'Google Drive' repository and my YouTube channel) I design pianos (...

MRC

PASHKULI If we agree to use 12TET then naming only 7 notes out of 12 is by definition a special case

But we don't agree. Tuning 12 tones in an equal temperament is only a compromise that works well, happily, for many styles of music, and is suited to the modern piano. It's less suited to the harpsichord, or the string or wind families.

An orchestra does not play in equal temperament. The musicians are constantly adjusting the tuning, based on the tonalities of the piece they are playing. They need a notation system that gives them information about the harmonies they need to produce; they understand that there are many more than just 12 notes equally spaced, that this particular written C will not be at the same height as this particular written B#. It's true that the fine tuning is essentially done by ear, but the written harmonies give essential evidence as to what to listen for.

Even if you're only playing a piano tuned to equal temperament, giving a separate, unique name to each of the keys of the chromatic scale is a hindrance, not a help, for correctly interpreting tonal music. In the traditional system, any key of the piano (not just the black ones) can have different names depending on its harmonic function. At first this may seem over-complicated, but once you have grasped the way the tonal system works, you will understand the power of this notation system.

Anyway, please do show how your PMN system notates the few bars I posted above.

PASHKULI

MRC But we don't agree. Tuning 12 tones in an equal temperament is only a compromise that works well, happily, for many styles of music, and is suited to the modern piano. It's less suited to the harpsichord, or the string or wind families.

I beg to differ, although I do understand your wish. But I would also like to see you building such an instrument which could encompass all the perfect ratios from at least every single note off of a 4 renova ("octave") ranges.
Do not werry too much about the lowest 12 and the highest 12 notes from a 88 keys piano. They can be hardly ever recognised regardless of tuning.

What you call Just or Perfect tuning is perfect only on paper though or… I will write it yet once again… for a very special case of a single note reference… until the sequence of notes crosses the renova (what you call "octave") of that single tone. You change that root note… you'll need a new set of notes (and you need at least 12 such root notes). It has nothing to do with Music application. It has more to do with ratios where one "note" is derived from a 'root' one up to an extent ("octave").

In the real physical world though things can not be mathematically perfect. Because… time and forces → utilisation. amortisation, environment changes and so on. With a physical instrument you can never play the same note twice perfectly (because of The River of Time… you can not enter in the same river twice… if you remember tho old saying).

We, on the other hand strive for perfectly build instruments, again because of amortisation: we want the strings to stay fresh and protected from the emefents, the keys, buttons, you name it, proportions.

I would like to see your perfectly intonated instrumfent with 200+ notes\strings\pipes (as bare minimum) stay in tune! Good luck with that! Imagine the maintainance of a full blown church organ but in a smaller (hopefully) scale.

Yes, non-fret instruments can play off of non descrete tuning – the player choses – and that is why they offten adjust on the go with a 'pivot slide' movement of the fingers to mask it as a form of vibrato. With fretted instruments it is the same – you can use vibrato and it is quite important technique so you do not sound mechanical in perfect notes as a digital sampler would (with a small library of samples). Again, ggood luck keeping your 'perfectly tuned' instrument to stay in that 'perfect' tune.

In 12TET the word 'equally' is misleading though. It does not refer to space or physical property at all. It is a common ratio coeficient that is 'equal' for the chosen n‑tonal division.

I would like to differ again regarding the special case of 7 notes out of 12. It is an ongoing debate since the time of Aristoxenus but also Pythagoras made it so cumbersome for the next generations of music thorists and explorers. Trust me, the common folk musicians could not care less about this. They played ages before Pythagoras tried to explain notes with math. ratios.
Diatonic vs Chromatic genera. Which one is the best one. Diatonic is popular as it is easy from a modal point of veiw for tha case of staying in a mode. The problem again was that 'perfectly' tuned modes worked for about in a renova ("octave") – above that the higher notes had to be 'adjusted' including the renova (octave).
That is what led to the enharmonic genera, which was a consequence of such rational discrepancies and later debates which higher ratios of numbers fit best to the imperfect notes. With those higher numbers they simply were icreasing the resolution (as we would say today). That is why there are multiple thirds, sixths… and endless debates over enharmonics.

There are enharmonic (we call them 'microtonal' which is a pathetic word) instruments but good luck building, maintaining and learning one such instrument. Violin, cello trombone can be played microtonally – getting it right on the "perfect" ratios though… I doubt any human being can do that every time\tone!
The medieval music notation system (alleged as "standard") is only somewhat suited for the "standard" (Halberstadt) keyboard (piano\organ). Going with key signatures and the rules in the bar for 'accidental' symbols or double‑accidentals and so one is why it is "somewhat" suited. It is only 'perfectly' suitable for diatonic genera modes and big 'white' keys.

MRC

PASHKULI I would like to see your perfectly intonated instrumfent with 200+ notes\strings\pipes (as bare minimum) stay in tune!

Who said anything about an instrument with more than 200 notes? Not me!

I already explained: the twelve tone equal temperament system is a compromise. It, or some sort of well temperament near to it, is certainly the best compromise for a modern piano, for playing the vast majority of works written for that instrument. For other instruments and repertoire, other compromises are more appropriate.

For baroque music played on a harpsichord, it's usually much better to choose a temperament suited to a narrower range of keys. I am lucky enough to have worked with top specialists of baroque music, who bring a refinement to the art of tuning that most pianists (who do not tune their own instruments) are unaware of. There's a special joy in adjusting to pure perfect 5ths, perfect 4ths and major/minor 3rds. This isn't just a theoretical, mathematical game: it's something you can experience through hearing.

The downside for the harpsichord is that if you want pure intervals you are limited to just a few tonalities, but if the pieces you are playing do not stray from a small subset of all the possible tonalities (which is often the case in renaissance or baroque music), you can tune the harpsichord to just these ones.

And, as I also already said, even if you're a pianist playing on a modern piano, the standard notation system gives you essential information about the harmonic structure of the music, information which is lacking in chromatic systems.

Nearly all western music is tonal, based on major and minor scales. Studies have shown that we experience tonality even in music that is considered to be atonal. Our notation system makes tonality visible. I have yet to see an alternate system that achieves this.

PASHKULI

MRC
Perfect intonation works only for ⅔ (you call that "fifth" from diatonic 'geocentric' view) and ¾ ("fourth"), both inversions to each other, hence titled as "perfect". That is all. Three notes including the root. The renova (you call that "octave") won't work so great with those ⅔ and ¾ though – it will be slightly 'sharper' (higher) or flatter if you use the reverse ratios ³/₂ and ⁴/₃ respectively.
But logic says 1 (root note) ×2 = 2 or 1÷2 is ½ hence 'renovas' ("octaves"). This is the real 'perfect' ratio and also the first timbral harmonic. Then are ⅔ and ¾ as mutual inversions, inversions because ⅔ × ¾ = ½ (gives us the 'renova'\"octave" of our root note). That is it. All the other anticipated "perfect" ratios fail: ⅘, ⁵/₆ are debatable, ⁶/₇ and ⁷/₈ are non-diatonic, then ⁸/₉ is debated as diatonic. All other fractions are adjusted as high numbers to suit, for example ¹⁵/₁₆ vs ²⁴³/₂₅₆ as some will say one is better (more perfect) than the other. Therefore none is.

That is why Pythagoras relied solely on ⅔ or its reverse renova ("octave") ³/₂ for length as the ratio to stack upon and find all the other "higher resolution" ones.
Thus (³/₂)¹² = ³/₂ × ³/₂ × ³/₂… and so on 12 iterations gave him a number (129.746337…) very close to the real perfect multiplication = 1×2×2×2… and so on till = 2⁷ = 128. Seems like the 'root' note's 'twins' would not sound great with ⅔ nor with its reverse ³/₂ tone, but the base one with length 1.
That is why modal music was just that – modal. It reffered to a base note. And old greek modes were moving down to that note (known as cadence today).

But, hey… musicians (thankfully) did not care much about ratios. They tuned and played whatever seemed great sounding. And to be hones adjusted tuning by stretching the strings or bending pipes. That is actually how sharp\and flat were born – sharper meant more sharp endge, flat – more rounded (molle) edge to increase slightly the travel of airflow.
This what bow instruments do and some of brass\pipe ones such as trombones and simple horns.

The diatonic genera prevailed because of the church chants but it was already etablished around Alypius' time (just when the Roman empire declined and split, adopting Christianity as Catholicism and Orthodoxy to the East).
Go and listen to some common folks music and diatonics are gone, well at least in some parts of Eurone. It is actually the Pentatonic which is more widely spread combined with chromatic notes here and there. Diatonic modes are church invention, but since Church dominated education ever since the 9th 10 century (even earlier) it is normal that most music (written on score by educated scholars) up until Baroque music was mostly diatonic. It served the Church. Folk music was still taught (developed and memorised) from hand to hand and by ear\example.

Music is not about perfectly matching two or three waves (harmony, simple chord) by themselves as examples of good matching harmony. It is much, much more than that. As one conductor used to say to his musicians: "Ladies and gentlemen, no need to tune it perfectly. Let's sound more rich!"

This is not music. Music is not clean sinesoidal waves. This is special cases of tone combinations.

PASHKULI

MRC Who said anything about an instrument with more than 200 notes?

Ok, so how many notes an intstrument tuned to "perfect" ratios will have?
Can you name the perfect ratios (how many and which exact ratios) and tune the physical instrument that way?
You can't. Because it is not physically possible. At most, you will end up with lots of enharmonic sequences (microtonal notes) which have to be ordered somehow in order to be playable by human hands\fingers… and\or feet.
Non-modal (modern) music sounds terrible in Just intonation. It is not possible. It is not intended for it. Only for simple modal music with root note and maybe a few more notes as song\voicing and that is it (Medieval church chants).

The inherited drawback of the curent "standard" music notation is that it refers to modal order of notes – hence the usual key signatures are placed next to the clef – and you need them in order to recognise the notes (all as ovals) on the staff lines (and ledger lines). Maybe worked ok up untill the 14 to 15 century. And most certainly did not work for common folk music but the church chants and the such educated musicians – usually bound to the Church.

"Johann Sebastian Bach studied music at St. Michael's School in Lüneburg (in Germany).
St. Michaelis is one of the main church schools in Lüneburg, Lower Saxony, Germany. It was first an abbey church of the former monastery of Benedictines who repurposed it as a school in the 11th century.
Bach was a chorister at St Michael's School in Lüneburg and a pupil of Georg Böhm. He then attended classes with teacher Johann Adam Reincken in Hamburg where studied the church organ."

Quite similar to Vivaldi in Italy (who is seven years older than Bach) when at the age of fifteen, he began studying to become a catholic church priest as a pupil to the maestro di cappella at St Mark's Basilica (local church institution in Venice) and at the age of 24 began to teach Music at Ospedale della Pietà and its boys choir.

Both musicians though wrote musical pieces which were more suitable for a chromatic music than strictly diatonic.
Otherwise Bach would have never wrote the "Well tempered klavier\keyboard" which used intonation similar to the then quite modern invention of 12TET but not exatly as we use it today because they did not have modern state om the art in sound recording and producing of exact pitches.

Maybe this is more like it (but how they tuned ratios in Bach's time before 12TET is not really known):

MRC

Well, those three examples are ghastly. They have nothing to do with the beautiful intonation that a fine baroque group or a top barbershop quartet can produce.

I think we've gone far enough down the rabbit-hole of pure intonation. I'd just like, once again, to stress this: you don't have to delve into different temperaments to appreciate why the current notation is so well-adapted to conveying the essence of tonal music.

Let's take the example I posted above. I'll post it again for convenience:

The key signature immediately tells me that:

the piece is tonal.
the tonality is either A major or F# minor; glancing at the first bar I see it's F# minor.

Knowing the key of the piece already gives me important information. I know that, as long as no accidentals appear, I will be limited to the 7 notes of the natural F# minor scale. This makes life easier: I'm only dealing with 7 notes instead of 12.

But that's not all: I have the information that F# minor is the home key. As I read the first few bars, I see the harmonies in relation to this key. Before I even play the music, I hear it in my head and I understand it. I immediately see the first turning point, when an accidental appears in bar 6 to create an F#9 chord.

The notation isn't just telling me which notes to play when, it's giving me information about the harmonic structure of the piece and the composer's concept. Other notation systems may do a reasonable job of telling me which keys to press at what time, but none of the ones I have encountered manage to combine this with imparting all the harmonic information that is part of the piece.

PASHKULI

MRC
You have learnt how to read it. Do not forget about that. Ever. Remember the hours, days, weeks.
Also it starts in Ne³ (what you call F♯ min) but later at bar 7 it becomes Ne⁴˙¹⁰ (what you would call F♯ maj but it is actually 'dominant' chord… which is the ⁴˙¹⁰ in how I will write it between the bars to show a tonality change… because it is quite characteristic in the sounding of the piece).

Ok, it is going pretty good as I started transcribing it… but I need your help to tell me what is going on here:

here is how it is on the MIDI, yet, as I watched real pianist play it (on Youtube) it was difficult to see which fingers press that as it is quite fast and hands overlap more or less.

• this MIDI roll also gives you the legend for the mapping of the noteheads (symbols)

So, what does it mean this 'doubled' note? Some of the same 'doubling' appear later as well. How is it possible to play the same note or is it with two different fingers at the same time – but that would be redundant on a piano. I do not get it! So, I placed the ¹/₃₂ pauses there (in my notation) as it looks more logical (to me at least) for the voices in line.

Please, note that if you do not want (to use) the noteheads you can always write just the noteletters for each note instead – especially when hand writing it – is much more convenient like writing words (but only with consonants).
Here is the map of all symbols with the rests:

At a glance, on PMN (Plain Music Notation) system I can see the renovas ("octaves") in the piece and how simple it is actually in terms of notes variety. I do not get distracted by busy lines and accidentals. I just can see how it is, without any need to remember key signature in order to know which notes on the score are actually 'altered'.

Also, and I think it is plainly (pun!) obvious, in the Plain system I can change the clef note for the other hand yet the notes will have the same meaning, where on the "standard" score their meaning\pitch will change (so called F clef or movable treble C clef). So…

MRC

PASHKULI You have learnt how to read it. Do not forget about that. Ever. Remember the hours, days, weeks.

Yes, of course I have learnt to read it! That's the normal thing to do if you want to understand a language. And it's normal that learning a language takes time.

Let's say you move to a country where the language is totally unfamiliar to you. Do you:

Do your best to learn the language as well as possible, so you can speak it, read it, and write it, up to a point where you have a deep understanding of the way the language works and are capable of appreciating the literature written in it.

or:

Learn it superficially without fully understanding it, tell the people of the country where you are now living that their written language is the result of "1000 years of… indoctrination" and "a work of ignorance", and that you have created a simpler one.

You pose this question:

PASHKULI So, what does it mean this 'doubled' note? Some of the same 'doubling' appear later as well. How is it possible to play the same note or is it with two different fingers at the same time – but that would be redundant on a piano. I do not get it!

That makes it clear that you do not understand a very basic feature of voice writing in standard musical notation. Before you try to create a new notation system, you might begin by learning the current one correctly.

MRC

PASHKULI This is very well known as the stems sort of separate the voices – usually up to 4 – two for each stave.

Strange, just a few posts ago, confronted with an example of such voice writing, you wrote:

PASHKULI . How is it possible to play the same note or is it with two different fingers at the same time – but that would be redundant on a piano. I do not get it!

I took the trouble to explain it to you, and now you claim it's "very well known". Yes, indeed it is well known, but before I posted my explanation, you clearly didn't know what was going on.

PASHKULI

MRC

I want to learn from you and your understanding on the question I asked with regards to those overlaps in the voicing or if on piano – the finger config. In other words – I am asking you to help me understand it or to teach me.
If you do not want to do that, well why asked me in a first place to transcribe it.
I am mostly sure this piece is intended for piano but it also could be purposed for a quartet. I can only guess.

To answer to your questions:
I have studied Spanish and English years before I moved and lived in such speaking countries to the point where I see the problems in those languages.
But here is something even more outrageous – I have written a whole treatise on the quite frankly plainly visible mistakes inherited in my own native language and its alphabet (how it was misunderstood by the "reforms" in the last 200 years) as it uses the Cyrillic alphabet created yet again by my own people 1200+ years ago where they used old runics combined with the Coptic (north Egypt, egyptian christians) alphabet.

So, I hope you now understand where I am coming from (not the country, it is an figure of speech).

MRC

PASHKULI I am mostly sure this piece is intended for piano but it also could be purposed for a quartet. I can only guess.

It is indeed a piano piece, but the notation here shows more than just what notes to play when: it shows the underlying voice writing. It just happens that two voices converge on the same note. There is no special technique for playing this note, it's just important to know that it belongs to both voices.

This sort of voice writing is common in keyboard music, specially in pieces such as fugues where several voices may converge and cross. We pianists use the information this communicates in deciding how to interpret the music. Often it will help to imagine an orchestra or a choir.

Here are a few bars from the 24th fugue in the first book of Bach's Well-Tempered Clavier:

In bar 12, voices 2, 3 and 4 are playing. The first voice enters in bar 13, and at the end of this bar the second voice coincides with the first. At the beginning of bar 14 the two voices cross over. You can see which notes belong to which voice in these two bars by looking at the tails: the tails of the first voice go upwards and the tails of the second voice go downwards.

A notation system needs to reflect faithfully the wishes of the composer, so there needs to be a way of showing voices that may converge on one note, or cross over.

PASHKULI I have studied Spanish and English years before I moved and lived in such speaking countries to the point where I see the problems in those languages

Maybe you concentrate too much on what you consider to be problems? I know English, French and German intimately and take great delight in the subtleties of each language. Since most of my work has been in opera theatres, I have had the pleasure of working with wonderful language coaches who all adore their respective languages and have helped singers of various nationalities sing in Italian, Russian, Czech and Hungarian.

All these languages have their quirks, but I don't see them as problems. I relish them: they add spice. Sometimes a word or a phrase intrigues me and I will research its origins, maybe finding out that it comes from a misunderstanding or mispronunciation of a foreign word. Sometimes something strikes me as particularly illogical, and I will try to find out if there was as some point a logic to it that has been lost.

The idiosyncrasies are bound up with the history of each language. This history may have dark sides, there may be racism and oppression involved, and there are certainly cases where it is good to think of using different words or phrases, but most of the time this isn't necessary. Languages are rich, multi-faceted, fascinating things that have been shaped over centuries, and for me a constant source of wonder.

PASHKULI

MRC In bar 12, voices 2, 3 and 4 are playing. The first voice enters in bar 13, and at the end of this bar the second voice coincides with the first.

This is very well known as the stems sort of separate the voices – usually up to 4 – two for each stave.
I have an example of that in PMN. It was just confusing with so many symbols to keep track. If they are intended for different imstruments they shal be kept separate. My PMN notation allows for that. The standart notation would take up too much staves if voices have to be separated in such cases – overlaps of notes. It can also be seen in bar 14 and you have to admit (I know you won't) quite frankly that it looks… cumbersome especially with all those "accidental" symbols next to each other. But again those overlaps are exeptions (or maybe not). But the higher notes could have gone on v1 (top voice). A bit redundent on Bach's behalf to intertwine them as such, more over they share same duration (¹/₈).

Which reminds me that… because in my PMN the ¹/₈ notes do not have tails\stems, it will be intersting to see how the voices will come out and get separated. I will try this as well. Ravel's example is not that interesting anymore.

Thank you for the clarifications indeed.
My background is not bound (in Music as well) to the Church though. Quite the opposite. I prefer the millenia old tradition of folklore (you may call it 'common folk' or ethnic music).
With the PMN when you write on a row you immediatelly have two more renovas ("octaves") belonging to the row above and row below to the row you write in. You can choose any clef (they also serve as 'renova separators') to represent tonality\modal change… even for every bar if it is significant.

On the standard notation a change in the clef changes all the notes and they now have to be accounted for a change.
Anyway, it has been here for more than 600 years now. People can not even think that there might be (a better) alternative. The 'geocentric' system is has too much and very deep roots.

PASHKULI

MRC
Brother, found other examples whilst searcihng for sources on the same bars and lo and behold:

So, there is… actually I could not find the original manuscript from Bach but regardless…
It is a mess. Hearing the piece… really nothing but it is more of an exercise than having any musical value.

PASHKULI

MRC
I was refering to the piano (fingers) to play different voices, so if two voices share the same note on the grand staff, logically that would imply presssing the same key on a piano with two different fingers – which would be redundant on a piano – as piano has one key per note, contrary to let's say a guitar, where a technique called 'tapping' can be used to tap the same note but on a adjacent string.
Nevermind. The piece (by Ravel) was supposedly written for the piano. That is why I asked.

MRC

PASHKULI I was refering to the piano (fingers) to play different voices, so if two voices share the same note on the grand staff, logically that would imply presssing the same key on a piano with two different fingers

No, the logical implication is not that the same key should be played with two different fingers. All this notation says is that the two voices converge on the same note, it says nothing about which fingers should play which note.

This notation of two voices converging on the same note is standard in piano music, nothing unusual. It's extremely common In the works of the most played romantic composers: you don't have to look far to find a host of examples in pieces by Schumann, Chopin, Liszt or Brahms.

I've already said this, but I'll stress it again:

If you want to create a better notation system, first you need to fully understand the existing one.

You need to understand what the notation is conveying. It's conveying meaning, not just which note to play when.

PASHKULI

MRC I've already said this, but I'll stress it again:

If you want to create a better notation system, first you need to fully understand the existing one.

You need to understand what the notation is conveying. It's conveying meaning, not just which note to play when.

Trust me, I understand it very, very well because I know how it came to be. Such overlaps are typical redundency… at least for the piano.
Because my next question is: what happens if such overlap happens on a note where both voices share it but with different duration? Can we see examples of that? It should again be reflectid on the stems' direction and flags\beams.
But that "same note" overlap can happen in such way (the so called 'middle C' for example and the surrounding notes) where it can be written on both staves (for voices 2 and 3).

P.S. At the moment I am writting articles for 'Piano Journal' (UK, part of EPTA Europe) but will get back to the translations soon, I hope.

MRC

PASHKULI Trust me, I understand it very, very well because I know how it came to be. Such overlaps are typical redundency… at least for the piano.

You may think you understand, but you don't. There is no redundancy.

PASHKULI Because my next question is: what happens if such overlap happens on a note where both voices share it but with different duration? Can we see examples of that?

You can easily find examples of that if you care to look.

PASHKULI

MRC
It is too ambiguous as the whole Music notation system, because it came from a 'special case' and chain of predelecitons.
I dare to say it was also due to trivial ignorance or inability to understand.

MRC

PASHKULI I dare to say it was also due to trivial ignorance or inability to understand.

You are referring to yourself there?

Tantacrul, in the video I posted earlier in this thread, divides the critics of the current notation system into three groups:

the 'Reformers', a small group of highly informed and imaginative people who have proposed alternative notation systems of their own, some which challenge Western notation in really compelling ways, the 'C-Reformers', a much larger group of reasonably informed musicians who exhibit a deep knowledge in one area, but who are blind to many others, and the 'Disruptors', a group of highly uninformed people, often with expertise in a different field (usually technology), who mistake their ignorance for a kind of fresh-eyed clarity, misrecognising the gaps in their understanding as actual gaps in notation itself.

Your remarks in this thread show clearly that you belong to that last group.

PASHKULI

MRC
If you say so, and if Tantaricul says those are (his personal) categorisations, so be it.

Here are mine:

• to understand what been told to learn an intelligent person should ask questions first! Not blindly to accept what has been told to do. As Steve Jobs said "Everything around you has been made by people who were not any smarter than you." (and I do not even like him, but he is right in this)

• the more intelligent a person is the less likely they could get manipulated by others

• if you know (at least interested in) the origin of things (this is more typical to people who are technical in mind) the better the chance to come up with new ideas, even completely new ones (plenty of examples in History of Science, Art, Crafts); a change does not necessarily mean better – but that is how current Music notation came to be – it changed a very old one by introducing 'special cases' and that is all there is to say about it really!

• to learn something does not equate to have been able to understand it! (in this group fall all "educated" and "highly versed\deeply invested" individuals, in any field of human interaction and creativity) – the best way to describe it would be by using the word 'indoctrination' (those people in modern times are known as 'followers' or 'apologetics' or even 'simps')
examples:
· being a good car driver does not also mean you understand how cars are made or how to rapair them
· just because you read much books does not also mean you understand what the written words convey, reveal

• when confronted by highly logical and systematic explanation the above people usually start usuing derogatory language and disparaging attitude towards the opponent in the discussion – thus turning the discussion into passive aggressive exchange of words completely irrelevant to the subject of discussion

Just because something has been around for hundreds of years does not make it the only one there is.

MRC

PASHKULI just because you read much books does not also mean you understand what the written words convey, reveal

Precisely. The same thing applies to reading music: musical notation is not just an indication of what to play, it conveys meaning. G and A double flat point to the same note on a piano, but they do not have the same meaning: there is no redundancy here.

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