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.

[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!

[keypeg]

This thread has been revived in 2026, an altered version of the question being put into a new thread and I prefer to answer the original question here.   I answered in 2011 and 15 years later see different things.

The essence of the question, and source of perplexity would be this:

* The idea that "the most natural" scale (the default scale) if you will is the major scale.
* Note names for much of the world are designated by letters of the alphabet.  We always learn the alphabet letters in a specific order, A being the first letter.
* If so, why wouldn't the first note of "the most natural scale" be designated by the first letter of the alphabet?

That is the actual source of perplexity.  It would be the same if we designated numbers and said that the notes of the major scale are 3, 4, 5, 6, 7, 1, 2

If you remove the idea of the major scale being the default or "most natural scale" - If you imagine that at the time that this evolved some minor scale was the default, so A, B, C, D, E, F...  then it all adds up.

* Some minor scale, starting with A
* Alphabet starts with A
* First note of the default scale designated by first letter of the alphabet

That's what I thing might be at the bottom of this.

[balabolka]

If you imagine that at the time that this evolved some minor scale was the default, so A, B, C, D, E, F...  then it all adds up.

* Some minor scale, starting with A
* Alphabet starts with A
* First note of the default scale designated by first letter of the alphabet

That's what I thing might be at the bottom of this.

Ok, but who and when said that the minor scale is the default? And actually there were no scales, rather tetrachords → four of them, each with the semitone interval moving around as Boethius wrote.
s t t (phrygian upwards)
t t s (ionian upwards)
t t t (lydian)
t s t (dorian)

Combining those (in groups of two) give us the scales.
All of them were, well, natural. And they are.
The problem comes when someone says one is "more natural" than the other.

We can also include hiatus intervals. Those are natural for some folk music too (including in ancient Greece, the Balkans and Middle east).

[keypeg]

Ok, but who and when said that the minor scale is the default? And actually there were no scales, rather tetrachords .....

Sure, but if a student learning theory is confused about something, then the aim would be to help them out of the confusion and its source.  None of the info you gave (which I also studied) would help with that.

[balabolka]

then the aim would be to help them out of the confusion and its source.

But the confusion is in the source if you read how it came to be from the source. Those monks were confused. They made it fit to what they had at hand.
It is obvious they did not understand Pythagoras, even Boethius. They simply took the ratio 8:9 as the wholetone procedure and applied it untill they had to fit 3:4.
Imagine if they indeed started by naming the whole open string A. We would have had A today where G is. It is this simple. So the whole system is rather personal choice out of well, half ignorance, I guess.
And we followed and no one knows why, apparently.

[newbie2]

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.

But Pythagoras was “ignorant”.  He incorrectly believed that all numbers were a ratio of 2 integers.  I think I read where he drowned someone for believing otherwise.  I’m not saying that Pythagoras was not a genius.  But the Pythagoras ratios were built on Pythagoras' ignorance of the completeness property of the real numbers and his ignorance of the existence of irrational numbers. 

His musical ratios 1:1 and 2:1 are correct.  However, his musical ratios, 3:2, 4:3, etc. are ALL faulty and resulted in music that avoided the "ugly 3rd" for maybe 2000 years.

Perfect 5th
3/2 = 1.5 is WRONG
Correct is 2^(7/12) = 1.498307

Perfect 4th:
4/3 = 1.33333 is WRONG
Correct is 2^(5/12) =1.334840

Etc, Etc.

So, a couple monks were not properly informed about an ignorant tuning system developed by Pythagoras?  And this resulted in "A" being where it is on the piano?   

How many centuries did the "ignorant" tuning system of Pythagoras delay the development of western music?

BTW - I think Pythagoras was a super genius.  I just think you might be coming down a little hard on a couple of well intentioned monks.   

EDIT:   I asked AI how long the Pythagorean tuning delayed the development of western music.  I think it said maybe 300 years.  My personal thought: It Delayed its development by maybe 2000 years.  The triad is the fundamental building block of western music written 1600-1900 and beyond.  Had the correct equal temperament tuning system been developed on day 1 in year 500 BC, it seems obvious that music would have developed quite differently.

[balabolka]

But Pythagoras was “ignorant”.  He incorrectly believed… and his ignorance of the existence of irrational numbers. 

So, a couple monks were not properly informed about an ignorant tuning system developed by Pythagoras?

I will try to be short. Maybe you really are a newbie after all.
Pythagoras was far, far from ignorant. He did not believe, he new very well about the irrational numbers. One look at his triangle theorem is enough. And most likely he would use the Babylonian (sumerian) method of finding square roots.
Nothing written as proof has left from him rather his students of later generations. That story about the drowning is a legend. The guy killed himself for revealing geometric structures related to irrational numbers. They simply did not have a method of writing irrational numbers as we do today ⁷√5 or here is the best part → that they are actually numbers raised to a rational power. This is the power (pun intended!) they kept secret. For example 7¹/² is √7 and so on. Let's leave that because nothing written has left from Pythagoras himself.

Pythagoras ratios were correct, all of them. But he was not a musician. Even today his tuning is most closest to ET than all later tunings including Meantone which involved irrational numbers (as ET does). Imagine that!
It was correct because it referred to a base note → a monochord's open string. This is what those monks did not get. As they started A from the much later division of 8:9, which was also from Pythagoras (well Aristoxenes who in many ways criticized Pythagoras). Simple tetrachordal moves to that open string note (root, modal) is fine. Chants in similar move – also. But when Music became more complex with inclusion of folk songs from many peoples around, expanding the range to include many more instruments, that is where all tunings fall behind compared to ET.
Math will say it is imprecise, but Music and instruments are physical entities, wood, metal so ET is perfect in an Imperfect ever evolving Nature. For our human hearing today we have found 7 × 12 = 84 musical notes (chromatonic) which are suitable for tonal music as sound range.
And to be honest you need only the middle 60 (5 × 12) tuned according to ET. The rest (lowest and almost percussive highest) ca be tuned "rationally". But let's not get that deep.

The monks had no idea. They wanted to divide the string faster which is ironic because dividing into 9 (for 8/9) is not a simple task compared to dividing by 3 (for 2/3). More on that in the other more comprehensive thread.

Also, silph's title is bound to indoctrinated word phrasing, namely "the most natural scale". That is also why many participants could not understand his question.

[newbie2]

I will try to be short. Maybe you really are a newbie after all.
Pythagoras was far, far from ignorant. He did not believe, he new very well about the irrational numbers. One look at his triangle theorem is enough. And most likely he would use the Babylonian (sumerian) method of finding square roots.
Nothing written as proof has left from him rather his students of later generations. That story about the drowning is a legend. The guy killed himself for revealing geometric structures related to irrational numbers. They simply did not have a method of writing irrational numbers as we do today ⁷√5 or here is the best part → that they are actually numbers raised to a rational power. This is the power (pun intended!) they kept secret. For example 7¹/² is √7 and so on. Let's leave that because nothing written has left from Pythagoras himself.

Pythagoras ratios were correct, all of them. But he was not a musician. Even today his tuning is most closest to ET than all later tunings including Meantone which involved irrational numbers (as ET does). Imagine that!
It was correct because it referred to a base note → a monochord's open string. This is what those monks did not get. As they started A from the much later division of 8:9, which was also from Pythagoras (well Aristoxenes who in many ways criticized Pythagoras). Simple tetrachordal moves to that open string note (root, modal) is fine. Chants in similar move – also. But when Music became more complex with inclusion of folk songs from many peoples around, expanding the range to include many more instruments, that is where all tunings fall behind compared to ET.
Math will say it is imprecise, but Music and instruments are physical entities, wood, metal so ET is perfect in an Imperfect ever evolving Nature. For our human hearing today we have found 7 × 12 = 84 musical notes (chromatonic) which are suitable for tonal music as sound range.
And to be honest you need only the middle 60 (5 × 12) tuned according to ET. The rest (lowest and almost percussive highest) ca be tuned "rationally". But let's not get that deep.

The monks had no idea. They wanted to divide the sting faster which is ironic because dividing into 9 (for 8/9) is not a simple task compared to dividing by 3 (for 2/3). More on that in the other more comprehensive thread.

Also, silph's title is bound to indoctrinated wording, namely "the most natural scale". that is also why many participants could not understand his question.

YOU: I will try to be short. Maybe you really are a newbie after all.

ME: I will also try to be short.  And no maybe about it.  I am a newbie. I see that you are now a junior member.  Congrats!

YOU: Pythagoras was far, far from ignorant. He did not believe, he new very well about the irrational numbers.

ME: This is likely false by historical accounts, yet you state it like a fact. Pythagoras and his early followers originally believed that "all is number," meaning every phenomenon in the universe could be expressed as a ratio of whole numbers (rational numbers). The existence of irrational numbers directly contradicted their core religious and philosophical worldview.

YOU: Pythagoras ratios were correct, all of them. But he was not a musician. Even today his tuning is most closest to ET than all later tunings including Meantone which involved irrational numbers (as ET does). Imagine that!

ME: Great, except it’s not true. Musicologists generally consider Pythagorean tuning to be further from standard 12-tone equal temperament (12-TET) than meantone systems for most harmonic contexts. Pythagorean tuning is significantly further from equal temperament when considering the major third, a staple of Western harmony. 

And so Pythagoras tuning has that UGLY THIRD.

You still need to answer my question.

How many centuries did the "ignorant" tuning system of Pythagoras delay the development of western music?


YOU: The monks had no idea

ME:  Again with the monks.

BTW - I think Pythagoras was a super genius.  I just think you might be coming down a little hard on a couple of well intentioned monks.   

[balabolka]

You still need to answer my question.

How many centuries did the "ignorant" tuning system of Pythagoras delay the development of western music?

Well, one of the legends surrounding this myth says that student of Pythagoras, allegedly murdered for this, revealed the proof "irrational" numbers are… real. But that was a sequence of finding sides of any right triangle, so they already knew it (how would they get sides and lengths).
It was obvious from the Sumerian method of finding square roots. You can get as accurate as you need, provided you can divide with larger and larger ratios.
Today we simply say that the number is multiplied a rational number times (not with, but by) and we write it x^¹/₂. For music is more like x^¹/₁₂ namely to find the step tone (real tone interval) all 12 notes in ET. So, in essence it is all rational. The 'irrational' name is a bit misleading just because you have to divide at nauseam in a physical setup to get accuracy in music instrument proportions (string lengths, pipe, fret distance, etc.).

Let's be clear. Pythagoras found proportions from a base note, length of string, mass. And do not worry about the fourth (you call it "major third"). Musicians tuned it as adjusted by ear for the specific tetrachord or two they used. That is for the enharmonic type of arguments. Just to make it clear: there are many Meantone variants for they sacrifice mostly sevenths (what you call "perfect fifths") , which are no longer perfect, hence the rule to not use "parallel fifths" in compositions → because they sounded horrible. For contrast, Pythagorean fourths ("major thirds") sounded ok, although no one used them in parallel (what you call "augmented chord"). 2:3, 3:4 and 4:5 = 0.8 compared to 64:81=0.790 were well known even in that time. Yes, on a string with length suitable for humans 0.79 makes a shift but I prefer that over someone telling me not to use parallel seventh ("fifths"). Damn, those are one of the most gorgeous sounding chords.

I do not know what makes you think that the fourth (your "major third") is the "staple of Western (rather European) harmony"? Do you mean singing harmonies in "diatonic thirds" one step before stacking maj with min chords to form what you call "7th" chords? Maybe they were some counterpoints "happy accidents" back in those times and I do not mean church chants or Greek tetrachords. Rather Baroque and in common folk music. Certainly, a single interval can not be a hallmark.
Ok, maybe the hiatus is… for it sounds "exotic" to the westerners (europeans, but not all). Again, we are talking about style and folk music, although it is perfectly fine in harmonic minor.

I still do not understand your assumption that the tuning of Pythagoras allegedly "delayed the development" of western music. I think that by the time of Aristoxenes (3rd century BCE) no one used the whole Pythagorean tuning besides probably 2:3 and 3:4. Pythagorean tuning gets cumbersome pretty fast. For every day tuning of lyres having not more than 9, 10 strings the diatonic frames of 1:2, 2:3, 3:4 with 4:5 were rather the norm. I doubt there were instruments with more than 2 renova ("octave") ranges or extended one capable of transposing. Rather, they had lyres and woods (pipes?) tuned to tetrachords for each area (that is how the name of the tetrachords came down the History of European music).

[keypeg]

Given that the other thread has been locked, I will put my response to the Dominant thread here.  As a general point, threads are for everyone, not just the person who started it, and if some people are not interested in a conversation they can skip the thread.  I don't like being in mid-convo, forming my response and ideas, and when there is time to post the response, the door has been locked.  I don't like wasting my time like that.

keypeg,
despite the fact I know what you mean by saying my answer is "by the book" I can assure you, you won't find it in any book (besides mine).

When you wrote that I saw we were talking about different things, and that is important.  You are talking about your system.  I was talking about the underlying premises that you are trying solve, and those premises come from the books.

So, are going to share your view or not? 

I had shared it in general, and I gave specific examples.  You did not respond to the general broad ideas.  For the examples, you dismissed them, by citing book definitions.  That meant both that the alternate definitions were not understood or entertained, and also suggested that the book definitions were still the underlying premises, since you cited them.

I do agree that the entire "dominant" thread was a misstep.  Even my alternate goes beyond  what the word too often implies.

And with that I'm done.

[essence]

As a general point, threads are for everyone, not just the person who started it, and if some people are not interested in a conversation they can skip the thread.

No. If the forum gets filled with stupid threads, it puts people off from participating, and it fills the 'recent threads' list.

These kinds of discussions are best put  in the same place as 'next post' discussions, not because of the topic, but because of the way the discussion has proceeded.

I don;t go into a bar where some idiots are having a shouting match, I take my custom elsewhere.

The most natural scale for the hand starts on a B, and this was taught by Chopin.
The most natural scale for beginners starts on a C, because it is all white notes.

Simples, end of story.

[keypeg]

No. If the forum gets filled with stupid threads, it puts people off from participating, and it fills the 'recent threads' list.

True.  Let's say it bugged me that I had a response that I had already written, and wanted at least to be able to post it. Which I now have.

[balabolka]

The most natural scale for the hand starts on a B, and this was taught by Chopin.
The most natural scale for beginners starts on a C, because it is all white notes.

This is a total misunderstanding on the OP's question, but I appreciate your twist of interpretation for the word "natural".
Yes, on a typical Halberstadt piano keyboard layout it starts on either what is B (Ionian) or what is E (Lidian) → the long fingers play the raised black keys.
This is what Chopin advised for beginners.

The most "natural" (easy) to read on the abstraction method called score is that of C (Ionian), F (Lydian) because it does not have 'key signatures' and\or 'accidentals' such as ♮, ♭, ♯. It is not so "natural" for the fingers though, especially young people with small hands (beginners).
Please, read Chopin's advises with attentiveness.

[Bob]

What was the question and the answer?  Why is C on the staff the pitch of C?  Or why is A 440, similar idea?  I remember I looked for an answer but didn't quite find 'the' answer.  I've still thought about it.

[potato12]

What was the question and the answer?  Why is C on the staff the pitch of C?  Or why is A 440, similar idea?  I remember I looked for an answer but didn't quite find 'the' answer.  I've still thought about it.

I think the question is why is A the first letter of the alphabet.

[potato12]

So why nost ask?  'A' is the first letter because it comes from the Phoenician word "aleph," meaning "ox," which was represented by a symbol looking like an ox head.

Still confused.

[balabolka]

So why nost ask?  'A' is the first letter because it comes from the Phoenician word "aleph," meaning "ox," which was represented by a symbol looking like an ox head.

Still confused.

That is an offtopic but you are correct… mostly. A was inverted → representing the head of an ox. Egyptian or phoenician, who knows. The word aleph is in hebrew too, but has nothing to do with A as a letter.
More precisely, for the Latin it came from the etruscans → their alphabet was mirrored Latin or Latin is mirrored theirs (simply explained).
The word alphabet comes from the first two hebrew letters → which have nothing in common to A, B respectively (as symbols).
The next common is the Greek α, β but the β is pronounced vita, not beta. So, β is v phonetically.

The order of letters in an "alphabet" is useless.
You do not need to know it. You need to associate those symbols to phonetic sounds. And with many exceptions:
for example L in 'Love' is different than L in 'Let' → first is hard, second is soft.

But…

In many countries they use one or the other. For example "indian L" is always soft. American (USA) L is always hard (or mostly, just look at some usaian says 'liberty').

Serbo‑Croatian L is always hard. In Polish it is close to u (as in 'put').
We can say those are accents and can accept it but sometimes either use changes the meaning of a word.

Some sounds lost their original letters → 'th' in English or 'ch'

One of the youngest alphabets is Hangul (Korean). Completely made up alphabet as ordered by a Korean king who got fed up with Chinese characters and struggle for power over Korean peninsula. Of course it has nothing in common to A, B, C.

I am sure even by this off‑topic you have learned a lot new stuff.

[balabolka]

We are really going strongly off‑topic here but since the OP's question has been answered by me, lets dive into the question why the letters of the alphabet have been ordered as they are now (mostly Latin based because the Church used Latin so that order is superior and demanded by God… obviously).
Sarcastic jokes aside, now the order is hard to trace back and fully justified or explained.

A good approach would be to have such order:
• vowels at the start or at the back, where first are the open vowels O (pot), A (pat), E (pet), then closed I (pit), U (put), Ə (girl) and Y maybe here is W as well (for English not for German).

• pair the consonants by voiced to voiceless counterparts
B→P
V→F
Z→S
D→T
G→K, C (well G and C are an odd ball in English, consider 'pacific ocean' and you'll understand or 'celtic cross' then for 'ginger' → ['jin jer] vs 'gurgle' you get it or in Spanish 'guerra' vs 'gerundio' → 'herundio' G is pronounced as H or rather as J due to H being silent in Spanish which as a direct Latin derivative)
Q, J, L, R, M, N, X

Here is a modern approach at the sequence of the English alphabet:
A, O, E, U, I, Y, B, P, D, T, V, F, Z, S, H, C, W, G, K, Q, J, L, R, M, N, X

Or similar. Any person with a bit of ability of sound awareness can guess what happened.

Ages ago I proposed similar names (letters) for the 12 tone 'Music alphabet'.
You can guess what I did:
• white piano keys → voiceless consonants (P, T, F, S, K)
• black piano keys → voiced counterpart (B, D, V + R, L, M, N or maybe Z)

I abandoned the idea as it was too bound to the special case of a Halberstadt piano keyboard layout. No need for that if we want to be completely neutral as we should.
So, I proposed the current which is still not set in stone.
A world wide agreement and summit should be placed to set the 12 tone Musical alphabet (although none of its letter can be really a "starting" one). With proper vowels to form syllables suitable for singing (similarly to Do, Re, Mi) but 12 and unique.

This is an intelligent and modern approach.