why does the most natural scale start on 'C', instead of 'A'?

[keiths]

I asked this same question of my Piano teacher some 55 years ago when I was in my first year of lessons.  The answer that I got was essentially this: The letters of the notes were assigned before there were keyboard instruments.  If you stop and think about it, they could have chosen to have all the keys be white. The reason that the keyboard is arranged with the white and black keys is because the instrument was designed to be played so that the musician can look at the music and be able to know exactly what notes his fingers are on by feeling the keys.  C is the note with a white key directly next to it to the left and a group of two black keys to the right.  I won't go through all 12 notes but the arrangement of the two black keys above the C and the 3 black keys below the B gives each note a unique position that you can feel and identify without looking.  Assigning any key other than C to be the major key with all white keys yields a pattern where the key groupings are not unique....meaning you would not know by feel what notes your fingers were on.  The fact that you can identify the piano notes by feel is why you have so many blind piano tuners and blind pianists. 

[cactusinalaska]

I wondered this same question when i was new. To add to the above post, my music theory teacher told me once that "Middle C is the pitch that most men cannot sing above, and women below". Maybe that's a lie to avoid a nuisance question...however the fact that C4 sits directly between the Bass and Treble clefs suggests some importance to pitch. With C4 as a solid reference point to both clefs and supposedly women and men alike, this seems like a note worth building new theory around. With the logical explanation that notes were named before the western 12 tone conversion, this should hopefully answer your question. Maybe an E# just didn't fit the ear of the converter...

[yessir]

To build a piano, first a pitch has to be assigned to one of the keys. That's agreed upon as A440. The first pitch chosen is logically called A. 440Hz is chosen for the pitch because it's easy to work with; i.e., easily divisible by, or multiplied by 2 (to get the octaves). It's also somewhat near the middle range of human hearing and singing.
But A is not chosen to be the lucky key of no sharps or flats. Instead we go down 6 notes to middle C, which is closest to the middle of human hearing, singing, and the middle of the piano keys. C will have a tempered pitch corresponding to A440.
To recap, the first pitch chosen is called A.

[Bob]

I don't think anyone's really answered this question for sure -- How did they determine which letter goes with each pitch, or at least each key on the keyboard?

[yessir]

For centuries it's known that the natural diatonic scale has 7 different pitches, which come from the 3 major triads of tonic, subdominant, and dominant.
The 7 pitches are logically name A thru G.
One pitch---the first pitch (called A of course) has to be assigned a frequency (440 is chosen for more than one reason), then all of the other (87) come from it.
After all of the 87 notes are tuned from A, it turns out that C4 falls in the middle of the 88, and is the winning key of having no sharps or flats (only 1 of the 7 keys can have no sharps or flats).

[Bob]

But why did they pick that spot on the keyboard?  Haha.

[yessir]

At the beginning (of the piano), a popular harpsichord had 5 octaves with 2 and 1/2 octaves on either side of a middle C.

[nyiregyhazi]

For centuries it's known that the natural diatonic scale has 7 different pitches, which come from the 3 major triads of tonic, subdominant, and dominant.
The 7 pitches are logically name A thru G.
One pitch---the first pitch (called A of course) has to be assigned a frequency (440 is chosen for more than one reason), then all of the other (87) come from it.
After all of the 87 notes are tuned from A, it turns out that C4 falls in the middle of the 88, and is the winning key of having no sharps or flats (only 1 of the 7 keys can have no sharps or flats).

You've stated well known facts but given no reasoning about the question. Also, the centre of the 88 is the crack between e and f. Oh and a used to be lower than 440 so the reasons you give are wrong, sorry.

[dima_76557]

why does the most natural scale start on 'C', instead of 'A'?

The question cannot really be answered conclusively because the musical universe is not centered around the Latin alphabet. Why "do" is "do" as a starting point is a more practical question that can at least be speculated about.

[j_menz]

Why "do" is "do" ... is a more practical question that can at least be speculated about.

And can also be answered.  Giovanni Battista Doni in the 17th century.  Before that it wasn't "do", it was "ut". He changed it because "do" is an open syllable, whereas "ut" is a closed one.

[dima_76557]

And can also be answered.  Giovanni Battista Doni in the 17th century.  Before that it wasn't "do", it was "ut". He changed it because "do" is an open syllable, whereas "ut" is a closed one.

That wasn't the underlying meaning of my remark. We all know where "ut re mi" comes from.

The OPs question seems to be: why is C (= Do, = Ut) the central tone of the system, and not A? In "fixed-do" solfege, for example, do (ut) is absolute; it's a fixed point and you cannot name the first tone of an A major scale "do". I think this has something to do with young children's voice range.

[j_menz]

That wasn't the underlying meaning of my remark. We all know where "ut re mi" comes from.

Well, latin or Arabic, depending on your school of thought.

The OPs question seems to be: why is C (= Do, = Ut) the central tone of the system, and not A? In "fixed-do" solfege, for example, do (ut) is absolute; it's a fixed point and you cannot name the first tone of an A major scale "do". I think this has something to do with young children's voice range.

Hmm... we use (to the extent "use" isn't an overstatement) moveable-do here, so do = A is eminently possible.

I suspect the historical primacy of fixed or moveable is contested territory, but in moveable it doesn't advance the OPs question.

[dima_76557]

@ j_menz

An attempt at an (un)educated guess.

I read somewhere that Boethius (?) was the first to make attempts at categorizing sounds with Latin letters. I don't know how he did that exactly, but the lowest tone he could imagine was "A" (of course). If we assume that he (as an adult) laid the foundation for "A-B-C", then his absolute/fixed "C" coincided with the absolute/fixed "ut"/"do" they established later as the tonal center, probably based on the average child's natural voice range, to be trained to sing in church. In order to avoid unnecessary complications, "Ut"/"Do" was kept "C" (in Boethius' system) to teach the simple crowd something about music. Does that make sense as a theory?

[j_menz]

@ j_menz

An attempt at an (un)educated guess.

I read somewhere that Boethius (?) was the first to make attempts at categorizing sounds with Latin letters. I don't know how he did that exactly, but the lowest tone he could imagine was "A" (of course). If we assume that he (as an adult) laid the foundation for "A-B-C", then his absolute/fixed "C" coincided with the absolute/fixed "ut"/"do" they established later as the tonal center, probably based on the average child's natural voice range, to be trained to sing in church. In order to avoid unnecessary complications, "Ut"/"Do" was kept "C" (in Boethius' system) to teach the simple crowd something about music. Does that make sense as a theory?

Haha, you might have read it here:

The first person to call notes by letter names was a monk and music theorist called Boethius. His musical discourse De Institutione Musica was written in the 6th century.

At that time, "A" was the lowest note used in music, or at least church music.  The whole of music was divided into various "modes", inherited from the Greeks, and the idea of the modern "scale" did not really exist (although the (present) Ionian mode corresponds to the major scale, modal theory also underwent some revison in the time since Boethius, and the correspondence with the modes described by him could be contested).

A parrallel line of development (as described by keypeg in an earlier post) gave us the sol-fa (do re mi fa sol la ti do) system, which corresponds to the modern scale.  The putting of these two lines of theoretical development together resulted in "C" being the bottom note of the all naturals major scale.

Interestingly, the modern standard piano still has "A" as it's lowest note.

You may well be right about how the two strands were interwoven, or at least that that was part of what went on. I suspect the move from fully modal systems to the major/minor duopoly likely had something to do with it as well.

[dima_76557]

Haha, you might have read it here:

I was already expecting the question: "Do you have a source?", but it turns out you are my source.

P.S.: Actually, I read it (+ overviews of his work) in Russian, that's why I put a question mark after his name since Russian naming often does not coincide with English naming.

[j_menz]

Russian naming often does not coincide with English naming.

Haha, many hours spent deciphering miscellaneous Russian edition collections have convinced me of the truth of this!

[jomki]

I was thinking about this the other day and found this forum so I signed up to answer. Hopefully the OP is still around. I skimmed through the answers and have formed my own opinion/theory which may not be exactly correct, but I believe it is a little closer.

The short answer is that the letter names were assigned to the notes first, based on the lowest note that they used, and eventually the scale which is now "natural" to us, C major, actually just became the most popular or pleasing to us.

This article (https://www.ars-nova.com/Theory%20Q&A/Q65.html) is a little bit of a different question but I think it provides insight into this answer also. Basically what the article states is that Boethius, as other posters have mentioned, started the convention of naming the notes of the scale with Latin letters, starting with the lowest note that they thought of back then being called A.

I don't think we know exactly what kind of scale Boethius was thinking of when he started on A, but if you think that this is in the context of sacred music you can sort of see that he may have used a more minor like scale, maybe Dorian or something similar. When I think of sacred chant music a lot of it uses those natural minor type scales. Cudo's explanation above, of the Hypo-Dorian scale, would seem to make sense, although Guido of Arezzo did not introduce the letter names. What Guido did was to develop the solfege system of learning to sing and read and be musical. What the article above states is that he developed the solfege letter names (Ut (later changed to Do), Re, Mi, etc.) from a well known Latin Hymn called Ut Queant Laxis. Each new line of the Hymn starts on the next note of the scale and the Hymn starts on note C so C became Ut (Do). This is much like the Sound of Music song "Do a deer, a female deer, Re a drop of golden sun..." etc. (I wonder if Sondheim knew all this history? Probably)

Anyway, what I believe is that church music used many minor type scales in their hymns and that minor type scales were probably thought to be lower or first and so when they named the first note of their scale with a letter they started with A. It is all a little arbitrary, really, but it does make sense to start with A, rather than start A on the third note and have the two lower notes below that be F and G. Which wouldn't make sense for Boethius because he didn't actually repeat A to G but kept just going on up the alphabet from the lowest note A up to the highest note which was O or H.

Eventually, the scale which started on C became more popular and memorable for people, to the point where Guido used it for his system which probably solidified the idea that in a key with no sharps or flats the scale starting on the third note is C and it also probably solidified the C scale as the more popular scale.

This was all way before the modern keyboard configuration, I believe, and so it was already established that C major had no sharps or flats, so it wouldn't make sense to have all the white keys represent A major, since, for example, C natural and F natural would then be black keys!

Hopefully this helps!

[superstition2]

C = Christós

 

[falala]

It's because musical notation was invented before there was any idea of C as the most "natural" scale. It wasn't invented around the idea of the modern seven-note scale at all; it was invented around a system of three interlocking hexachords, based on G, C and F with the interval structure tone-tone-semitone-tone-tone. Each note of the hexachord had a name - ut, re, mi, fa, sol, la - the precursor to the modern sol-fa system of koday etc, but with "ut" instead of "do".

The entire system of these devised by Guido d'Arezzo covered 11 lines - what we now call the "great stave". The bottom line was called "Gamma Ut", from which we get the word "gamut", meaning the complete span or scale of something. The other spaces and lines were then named alphabetically from A through G, returning to A again because of octave equivalency. "Gamma Ut" corresponds to the bottom line of our bass stave, and the following A to the first space.

There was no accidentals as such within this system, but two different forms of "B" were required: a "hard B" (later becoming B natural) in the G hexachord, and a "soft B" (later becoming B flat) in the F hexachord. These were shown by different shaped noteheads.

There was no particular reason to create the names around C being A instead, because the C hexachord wasn't any more special than the others. Furthermore, the importance of MIDDLE C is just a diagrammatic accident that came later. When they split the great stave into the now familiar 5 + 1 + 5 stave of keyboard music, the note on the middle line just happened to be C.

More information here:

https://www.bbc.co.uk/dna/place-london/plain/A1339337

[yessir]

You've stated well known facts but given no reasoning about the question. Also, the centre of the 88 is the crack between e and f. Oh and a used to be lower than 440 so the reasons you give are wrong, sorry.

Oops, you're right. The reason for the 6th degree of the scale ("La") being named "A", instead of the 1st degree ("Do") has already been given above. The monks who invented the staff and the note names (Do-Re-Me) used mostly the Aeolian mode which is the minor scale, which starts on "A" (all white keys). So to them it was most logical to call "La", "A". It's all so simple that it goes right over our heads.

[andjrew]

Check out this video on the topic!
https://livingpianos.com/why-is-c-not-a-music-theory-questions/

[pashkuli]

my question: why are we using a naming system that names the most basic scale starting with the letter 'C'?! it seems arbitrary that the name of the first note of the most basic scale we use is /C/, instead of A. why C?

Hi, silph
I will answer your question because believe or not it caused me to realize and express certain criticism over the so called "standard" music notation which got me banned from many forums related to Piano and Music.

We have to go way back in time… in times when the Church dominated all aspects of human activity (at least in Europe… most of Europe and consequently in America after 1500s). Also, times when Latin language was the de facto international language as today is its (indirect) successor the English language (they share the same alphabet more than less).

Contrary to popular belief, many will say that it was Boethius (end of 5th and beginning of 6th century CE) who gave us the first letters of the notes as arranged by the Latin language alphabet (he was Italian so it makes sense). That is incorrect and incomplete because all he was marking with the first 14 letters were… intervals (in his time the letter J did not exist by the way).
Boethius did not name the notes. A common misconception apparently is that he did. He named the intervals using the Latin letters. All notes still had their own symbols (runic like, mirrored, rotated, etc., a long story) as derived from the cumulative work of Aristoxenes and then Ptolemy and Alypius (the latter in 3rd century CE, two centuries before Boethius). In his work "Fundamentals of Music" can be seen he used AB as a full tone interval, then AD as a semi-tone interval, and DB as another semi-tone. In another diagram he would use AB (full tone), BC (again a full tone!, not a semi-tone), CE (semi-tone). AB could be a semi-tone or a tone, as it is appointed as 'movable' interval (read his work!), not a specified pitch (or string). In his work "Fundamentals of Music" we can read the following:

"Take four middle notes:
A, B, C, and D.
A should hold the sesquitertian ratio-the diatessaron in relation to D; likewise A should stand a tone away from B, and B a tone away from C. The remainder, C to D, should maintain the interval of a semitone [Fig. D.22] → A I B I C I D"

— Boethius

Note: The letters only designated intervals! Above, Boethius clearly says C to D to represent a semi-tone! He used the letters as we today use them for geometry problems (or alike). No indication of pitch is given in conjunction with this alphabetical series Boethius used. The enumeration of species here may be seen as an abstract demonstration that, given a two "octave" system, one octave segment remains after the seven species have been computed, and that this segment may become the basis of an eighth mode. If this series is taken concretely, on the other hand, letter A must represent the highest pitch (the nete hyperboleon). In Boethius's numbering of species and derivation of the modes, the first species of diapason, that between the nete hyperboleon and the mese, becomes the basis for the first mode.

Only occasionally in his work certain tetrachords A, B, C, D will match the intervals "tone, semi-tone, tone". But mostly, any two of those they make other intervals.
He is credited for constructing the modes from lower strings to higher as today we would call and present the scales in Music (in his time the typical representation would be downwards, where 'cadence' comes from as it was very popular modal move).
Anyway, using an alphabetic letter sequence (of a language) as a Music alphabet is a predilection and should be avoided as otherwise it dismisses other writing systems. Music must have its own alphabet and I created it long time ago. Certainly, Latin was the sort of the international (at least in Europe, so hardly ever international!) language at that time and English today as its successor but that should not be "the norm".

Keep in mind that in that time up until the late 14th century there were no 'piano keyboards' with all the 'black' notes we know today. The black keys were slowly introduced by the century on portative organs with the complete set of 7 big and 5 small keys described by Henri Zwolle in 1430 for a portable clavichembalo instrument he designed.
(can't add attachment image)

Before him similar thing did Nicholas Faber in Halberstadt, Germany in 1361 for a organ but there were no keys, rather levers pushed with a whole hand\grip or fist.
(can't add attachment image)

You can see that in those illustrations A and C are placed on the keys as they are today. So, we should go back in time when there were no black keys. The times of Boethius (6th century CE) and Guide d'Arezzo and Odo\pseudo-Odo (in 10th and 11 century CE). As you can see, back then the portative and positive organs did not have any black keys. Encyclopedia Britannica also mentions that the key for Bb were also a big "white" key and Sebastian Virdung and Hans Beham (early and mid 16th century CE) have illustrated positive organs having a couple of black keys (B♭) and they referred to historical development of its keys as in their time all 12 keys were present.

So, we go back where the keys were just big key levers with no "accidentals" (black keys). I am talking about the time of the ignorant church monks Odo, Petri, and finally that same Guido d'Arezzo. They were totally clueless and applied the ratio 9:8 (Pythagorean\Aristoxenian "major second = whole-tone") to the string of the monochord they called Г… and I quote

"Because Г is a little known Greek letter here and many do not use it."

…and it looked like the hook or pin they attached the string of the used monochord. Oddly enough, phonetically Г corresponds to G (but Г is the third letter in the Greek alphabet, not the seventh in Latin). So, as one of the correspondents there says…

"Divide it in 9 and take 8

Note: Means, next tone is the length 8 of those 9 divisions

and call it A

As our Latin alphabet's first letter.

then from that A divide again with 9:8 and write B. But then go back to Г (open string) and divide its length of string into 4

means take 3/4ths of it

and write C. Then repeat from C."

As you can see here we clearly have Г (open string), A, B, C following tone, tone, semi-tone strict interval rule by construction (Г_A_B-C).

Imagine if they had called the whole string A as a main note from the get go (no use of a Greek letter) and started from there. We would have had A being where G is today but let's see why… because there were no 'black' keys in that time, remember?

It is ridiculous how they destroyed the works of Alypius and Boethius who lived centuries before those ignorant church monks who only took the Pythagorean ratios of 3/2 (9/8 if you power by 2 and divide in 2 to lower the note one diapason\octave\renova) and 3/4. They constructed "the G Myxolidian mode" in today terms, which should be the real natural major mode also for the reasons of 'overtone series' but that is another topic and criticism I hold against modern "standard" Music notation!!!

The actual naming of notes started by an ignorant application of both Boethius interval naming and Aristoxenus' 'division of genera' by the church monks\clerks Odo ("Musicae artis disciplina"), then Guido and Theodaldus around year 1017 (500 years after Boethius).

They started with a string (not keyboard + pipes) only "god" knows at what pitch and started dividing it in order of bigger to smaller (contrary to how Pythagoras started) because they used the divisions already documented by Aristoxenus (no written work\evidence we have from Pythagoras anyway). Oddly enough (as ironic fate can be!) they named the string with the greek letter Г (it is the third letter in Greek alphabet, which phonetically in Latin is G – the seventh letter) because, I kid you not, this is what they say to each other:
"On the monochord string, at the attachment pin, make it as the letter Г (gamma), that is – the Greek G, which, because no one knows it here.". Then they proceed without any understanding and explanation how to match the diatonic genera starting with what Aristoxenus called 'a tone' and call it A (in their Latin alphabet but also it is in Greek an Cyrillic). The ignorant thing is that in the first half they do not encounter what is known as B♭, but in the next renova ("octave") they see it in the ratios (they get smaller → better "resollution") and have no idea how to call it. So they write it as a 'square' shaped b (or b quadratus if you combine b and q and write it in a sqare-like script you'll get the symbol for ♮, if you take a and d, d is for diesis, and write in a similar combination, you'll get what today is the symbol for sharp ♯):

"Et dum voces per medium diviseris,
dissimiles easdem litteras facere debes.
Verbi gratia, dum a Г per medium dividis,
et pro Г scribe G, et pro A mediata pone
similiter a, similiter quoque et pro B aliam ♮.
Praeterea et a voce sexta F per IIII divide,
et retro B aliam ♮ ivenies b quam dicimus rotundam."

(the round b is actually known to you as 'B flat')

"Alius vero dividendi modus sequitur, qui etsi memoriae minus adiungitur, eo tamen monochordum velociori celeritate componitur, hoc modo:
Cum primum a Г ad finem novem passus id est particulas facis,
primus passus terminabit in A, secundus vacat, tertius in D,
quartus vacat, quintus in a, sextus in d, septimus in aa, reliqui vacant.
Item cum ab A ad finem novenis partiris, primus passus terminabit
in B, secundus vacat, tertius in E, quartus vacat, quintus in ♮, sextus in e, septimus in a', reliqui vacant."

So, that structure got with the tuning of the then developing portative organs for the Church and now they had assigned the letters to specific notes by matching the sounds with those on the monochord. There were mostly two possible matches → either today's G or C, maybe F if you push it, because the organs already had a tonal structure and did not care about how the string of their monochord was tuned! Rather they tuned the monochord to a note on the organ till their "invented" A, B, C structure matched as much as possible. It was that ignorant on their behalf, if you ask me!
Later when the key for what they called B♭ (B flat, as on an organ you had to flatten the nozzle of the pipe to lower the pitch and literally sharpen it to raise it).

There you have the answer. It was due to pure ignorant application of a Pythagorean ratios and even more ignorant assignment of letters to shortened string lengths following Latin alphabet sequence.

[pashkuli]

Related question:  Why do Germans call "H" what English-speakers call "B"?

It is due to misunderstanding of the b-square (known as B natural) in the manuscripts. This b in the typical gothic script looked to the Germans as a small letter h. You can still see it here:


Keep in mind that we are dealing with very ignorant people who wrote that system. See my previous post above.

[pashkuli]

Later, in the middle ages, Dorian mode was designated "mode no.1", not for its aural qualities, but for its mathematical symmetry.
Take any note, and calculate perfect 5ths above and below it, until you have a 7-note scale. This gives you Dorian mode:

Going upward in fifth:
D x 3/2 = A; A x 3/2 = E; E x 3/2 = G
Going downward in fifth:
D x 2/3 = G; G x 2/3 = C; C x 2/3 = F.

Bingo - that's where we get our note names from.

Cool story and mathematical "symmetry" but it is not even remotely close to the truth. There are other modes with symmetric interval structure not related to the Church modes though.

[kosulin]

I must dissapoint you. It can't be right what your are telling us.
When the names A B C D E F G where introduced by Guido of Arezzo in 1025 there were no Ionian and no Aeolian scale at all!

'do-re-mi-fa-sol-la-si' syllables were introduced by Guido d'Arezzo, who took the first syllable from each line of the hymn "Ut queant laxis" to help in memorization:
    Ut: queant laxis
    Re: sonare fibris
    Mi: ra gestorum
    Fa: muli tuorum
    Sol: ve polluti
    La: biis reatum
    (S): ancte **(I)**ohannes

From google search: Around the year 500 AD, the Roman philosopher Boethius is widely credited with assigning the first 14 letters of the Latin alphabet to the notes of the two-octave range used during his era. The simple, systematic nature of the alphabet provided a convenient way to label notes in ascending order. The system was later condensed to letters A through G.

And here is my though: while C scale is considered base in modern times, the Am chord was quite possibly the most popular in ancient times. Many guitar teachers use the Am as the first chord they teach - easy and musical.

[kosulin]

duplicate, sorry

[kosulin]

duplicate, sorry

[pashkuli]

'do-re-mi-fa-sol-la-si' syllables were introduced by Guido d'Arezzo, who took the first syllable from each line of the hymn "Ut queant laxis" to help in memorization:
    Ut: queant laxis
    Re: sonare fibris
    Mi: ra gestorum
    Fa: muli tuorum
    Sol: ve polluti
    La: biis reatum
    (S): ancte **(I)**ohannes

This is correct. I should add the fact that he used his favorite chant and took the syllables of the first six notes which matched the diatonic structure of the first different notes. At Guido's time the seventh note was not used (at least not in church chants). It was added later when it was used and quite possibly when the organs extended to positive organs (around 12 and 13 century CE). Only 7, because at those times organs did not have 'black keys'!
Both such naming of notes and A, B, C… are predilections as inherited by their Latin speaking creators. Music must and should have its own Musical alphabet, the 12 notes named (not just 6 or 7). The system is incomplete, and leads to inconveniences later in time. I have dedicated articles (books) and now making videos about it with lots and lots of criticism.

From google search: Around the year 500 AD, the Roman philosopher Boethius is widely credited with assigning the first 14 letters of the Latin alphabet to the notes of the two-octave range used during his era. The simple, systematic nature of the alphabet provided a convenient way to label notes in ascending order. The system was later condensed to letters A through G.

To answer to this I must quote myself and I urge anyone to really read Boethius' work on "The Fundamentals of Music":

Contrary to popular belief, many will say that it was Boethius (end of 5th and beginning of 6th century CE) who gave us the first letters of the notes as arranged by the Latin language alphabet (he was Italian so it makes sense). That is incorrect and incomplete because all he was marking with the first 14 letters were… intervals (in his time the letter J did not exist by the way).
Boethius did not name the notes. A common misconception apparently is that he did. He named the intervals using the Latin letters. All notes still had their own symbols (runic like, mirrored, rotated, etc., a long story) as derived from the cumulative work of Aristoxenes and then Ptolemy and Alypius (the latter in 3rd century CE, two centuries before Boethius). In his work "Fundamentals of Music" can be seen he used AB as a full tone interval, then AD as a semi-tone interval, and DB as another semi-tone. In another diagram he would use AB (full tone), BC (again a full tone!, not a semi-tone), CE (semi-tone). AB could be a semi-tone or a tone, as it is appointed as 'movable' interval (read his work!), not a specified pitch (or string).

And here is my though: while C scale is considered base in modern times, the Am chord was quite possibly the most popular in ancient times. Many guitar teachers use the Am as the first chord they teach - easy and musical.

Not true at all.

[pashkuli]

I asked this same question of my Piano teacher some 55 years ago when I was in my first year of lessons.  The answer that I got was essentially this: The letters of the notes were assigned before there were keyboard instruments.  If you stop and think about it, they could have chosen to have all the keys be white. The reason that the keyboard is arranged with the white and black keys is because the instrument was designed to be played so that the musician…

Total misunderstanding on behalf of your piano teacher and false info. He did not know. Keyboard instruments existed just about when the Roman empire was at its peak or maybe towards declining\splitting. At the time of Boethius there were portative organ instruments (the ancestors of accordions) and they had only big "white" keys. Rather taking the colour of the wood they were made from and possibly tinted for protection.

[pashkuli]

And can also be answered.  Giovanni Battista Doni in the 17th century.  Before that it wasn't "do", it was "ut". He changed it because "do" is an open syllable, whereas "ut" is a closed one.

Correct!

[pashkuli]

In Boethius' "The Fundamentals of Music" there is the 3rd chapter in the 'Book 4'. The text gives the names of the notes, first using the Greek terms found in 'Book 1', then the later Latin names for the first time:

3. The naming of musical notes in Greek and Latin scholarship
Since we are left with the task of dividing a string by means of a rule (according to the consonances just discussed), and since this same partition will display the requisite sounds through three genera of melody, at this point we must set out musical notes; in this way, when we inscribe the divided line 18 with these same written symbols, 19 the name of each individual note will be recognized very easily.
For the present, let us take just one of the modes, the Lydian, and arrange its written symbols through the three genera; we defer doing the same with the other modes until another time. Surely if I sketch the disposition of notes using the names of Greek letters, the reader should not be put off by anything unusual.

Then Boethius uses the actual note symbols for all notes as they were created in earlier times (Aristoxenes to Alypius) including chromatic changes and each had its own symbol (actually two for each, as they differentiated the note symbols between hardware instruments and vocal singing but that is not important)! (see attached image)

If you claim that Boethius used notation for notes that is not really how he proceeded. We can see that in his work the notes B and C were "movable" or as we could say today they could have "accidental" counterparts. Same with E and F. Completely different from what the monks did in the 10th and 11th century CE. They ruined it all!