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In 12 tone equal temperament, why are the notes named:

C, C#, D, D#, E, F, F#, G, G#, A, A#, B

instead of, for example,

A, A#, B, B#, C, C#, D, D#, E, E#, F, F#

or any other thing?

junil
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  • Just to clarify, you mean to ask why there're no unified descriptors for enharmonic equivalents like D#/Eb? –  Sep 17 '14 at 14:05
  • Nope, but why we specifically selected those notes symbols at this specific order for 12 tone equal temperament (7 letter symbols with extra 5 symbols, one after c, another after d, another after f, other after g and another after a). It would be possible to include thing where all symbols are letters or that the extra 5 notes without letters are after B. – junil Sep 17 '14 at 14:19
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    @junil, could you please clarify your question? Otherwise it's in danger of being closed. – empty Sep 17 '14 at 15:51
  • @junil I attempted to make your question a bit easier to read. If you feel I changed the meaning of something, feel free to revert it. – Caleb Hines Sep 17 '14 at 16:59
  • Aren't you aware of the "do re mi fa sol la si" system? It's used in most countries I know. That'll make things a lot clearer – phuclv Sep 18 '14 at 08:06
  • See here: http://music.stackexchange.com/a/317/16938 – commonhare Dec 24 '14 at 12:38
  • It looks like the question is: Why does a scale starts from C rather than from A? Similar to Why is C the base note of standard notation and keys? – mins Jul 30 '22 at 15:11

4 Answers4

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I feel like I've already at least partly answered this question here. But I'll endeavor to add more here.

First of all, you aren't quite right in your description of the note-naming system. There are seven letters, and every one of these can be sharped or flatted:

  • A♭, A, A♯
  • B♭, B, B♯
  • C♭, C, C♯
  • D♭, D, D♯
  • E♭, E, E♯
  • F♭, F, F♯
  • G♭, G, G♯

It's just that many of these end up being multiple names for the same pitch (at least in 12TET), thus they are called 'enharmonic'. There are also double sharps and double flats, but let's not go there...

The key point is that Western music, both classical and pop styles, is almost entirely tonal (or modal), and these systems are actually based on a 7-note (diatonic) scale, not a 12-note scale. The system of using letters to identify pitches dates at least to the 6th century (Boethius). Repeating the same 7 letters each octave came a few centuries later (by the 11th c., and Guido of Arezzo). Sharps and flats were added latter to introduce alterations to these notes, but these shouldn't be seen as new notes, so much as replacements for existing notes, still leaving you with a 7-note scale. All of this long predates 12TET, which, initially, was developed as a system of tuning keyboard instruments. (One alternative possibility that never caught on: a keyboard with 36 notes per octave).

The first note that people tried adjusting was B, which formed a dissonant interval of a 'tritone' with F. There came to be two forms of the letter b, written in different styles -- a rounded, or 'soft' b that meant to use the lower form of the note, and a square-ish, or 'hard' b that meant to use the higher form of the note. As these symbols became more widely used, the rounded b eventually evolved into a flat symbol, and the square b eventually evolved into both the natural symbol and the sharp symbol.

Because of the shape of the diatonic scale (consisting of whole steps and half steps: WWHWWWH), many of these altered notes ended up being the same as (or close enough to) other notes, so that you got multiple names referring to the same pitches, in different contexts.

BTW, with the advent of atonal music, some music theorists decided they didn't like this naming system based on the 7-note diatonic scale, and decided to invent a new system, called Pitch Class, in which each pitch in an octave, starting from C, is given a unique number, from 0 to 11.

Community
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Caleb Hines
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    I wish more music books/classes would explain this – Mark G. Sep 17 '14 at 19:37
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    Interesting answer, but any idea why the first note of the "all-ivory scale" is named 'C' and not 'A'? (I've always suspected that (s)he-who-made-up-the-names liked minors.) – Dale Wilson Sep 17 '14 at 21:57
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    When the notes were named, majors, minors and keys had not been invented yet, 3rds were dissonant, and everything was in modes. A was named 'A' because it was the lowest note expected to be sung. Later, the G below it was added, but was called Γ (gamma), since G already referred to an octave higher. The most common modes during this time were actually those ending on D, E, F, and G (not A or C). See also: http://music.stackexchange.com/questions/893/why-is-c-the-base-note-of-standard-notation-and-keys – Caleb Hines Sep 17 '14 at 22:11
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    To elaborate, Guido's note-naming system covered three octaves plus a note: The G on the bottom of the bass staff was Γ, the first full octave was A-G, the second octave (spanning middle c) was a-g, and the third octave was aa-gg. (gg being the top of the treble staff). This was the entire 'gammut' of singable notes ('gammut' = 'gamma' + 'ut'; 'ut' was a solfege syllable similar to 'do'). – Caleb Hines Sep 17 '14 at 22:23
  • This is incredibly interesting. German note naming has B for Bb, and H for natural B, I suppose it has to do with "The first note that people tried adjusting was B, which formed a dissonant interval of a 'tritone' with F. " I would love a source for this! – Gauthier Sep 18 '14 at 08:36
  • @Gauthier http://music.stackexchange.com/questions/10195/why-note-b-is-marked-with-h-in-scandinavia-and-germany?rq=1 – Caleb Hines Sep 18 '14 at 17:56
  • @Caleb Hines, my understanding is that Guido set up 3 hexachords in his solmisation system running from ut to la on C (the natural hexachord), on G (the hard hexachord) and on F (the soft hexachord), transposed by octaves to fill the available vocal range (as you say, about 3 octaves at the time). When practising in a given mode, the singers would pivot their solfège syllables on a note common to two of the hexachords to arrange that the sensitive mi-fa interval fell in the right place for the mode. This might explain C's subsequent privileged position even before the Ionian mode took off. –  Dec 26 '14 at 08:31
  • @user16935 well maybe, but while the hexachords started on F, C, and G in that they were the lowest note of each hexachord, the tonic note is typically the second -- re -- with the lowest note most frequently playing the role of the lower neighbor to the tonic (because most music was "minor" to modern ears, or actually Dorian). This of course puts A back into the running for the "default home" pitch, though even by Guido's day it had begun to be eclipsed by D. That explains why, as the preference for major tonality grew, C became the default home pitch. – phoog Nov 10 '23 at 22:31
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The "base names", i.e. the letters, are much older than 12-edo. Music used to be played in just one diatonic scale (derived e.g. from Pythagorean/Ptolemaean tuning), and only when switching to another key you'd adjust some of the scale steps by way of an accidental. The order of accidentals you need to introduce is dictated by the circle of fifths.

This by itself does in no way imply there should be 12 steps – it just so happens that the third of the ♭-tones (a♭) comes out with almost the same frequency as the third of the ♯-tones (g♯); if you pretend they are the same and extend the system accordingly this gives you the number 12.

leftaroundabout
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Why are the notes named what they are "instead of something else?"

All note-naming schemes are ultimately arbitrary. There are, in fact, many other systems for naming notes. For example, a good portion of Europeans use H for B and B for B♭ whereas, in other parts of Europe, the notes are named Do Re Me Fa Sol La and Ti (or Si). Sa Re Ga Ma Pa Dha and Ni are the note names in Indian music. All these systems evolved over centuries.

Any new and potentially more logical system of notation would be equally arbitrary. For example, MIDI, which was developed in the early 1980s, uses 128 different note "names", which are really bit strings and can be represented by numbers. Middle C, for example, equates to binary 111100 or decimal 60.

You asserted, "it would be possible to include [systems] where all symbols are letters or that the extra 5 notes without letters are after B." That's true. You could devise a system where the notes would be:

  • A (same as C)
  • B (same as C♯ / D♭)
  • C (same as D)
  • D (same as D♯ / E♭)
  • E (same as E)
  • F (same as F)
  • G (same as F♯ / G♭)
  • H (same as G)
  • I (same as G♯ / A♭)
  • J (same as A)
  • K (same as A♯ / B♭)
  • L (same as B)

This may have some advantages (and a new set of disadvantages), but you can't expect it to replace the existing systems any time soon.

trw
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    In Vietnam it's called Do Re Mi Fa Sol La Si too, in Korean: to, re, mi, pa, so, ra, shi, and in Japan it's called i, ro, ha, ni, ho, he, to http://music.stackexchange.com/questions/4957/what-is-the-relationship-between-do-re-mi-and-note-letter-names http://en.wikipedia.org/wiki/Iroha#Usage – phuclv Sep 18 '14 at 08:04
  • These syllables (originally Ut, Re, Mi, Fa, Sol, La) are ultimately derived from the initial syllables of successive phrases in a Gregorian chant, "Ut Queant Laxis". Since each phrase of this chant started one pitch higher than the previous, Guido (whom I mentioned in my answer) used them as a mnemonic device for memorizing the scale. Si/Ti was a later addition. http://en.wikipedia.org/wiki/Ut_queant_laxis – Caleb Hines Sep 18 '14 at 20:25
  • @CalebHines it seems that Guido's treatise must be the oldest source for that hymn, or at least I assume so because I've seen in more than one place the suggestion that he may have composed it for the purpose of demonstrating his system. – phoog Nov 10 '23 at 22:35
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The simple answer is that the notes were named using a minor, not major, tonality. The relative minor of C Major is A minor, ABCDEFG.

David
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    I would upvote this if there were a reference to any source. It would also be better if this answer were not included in Caleb's answer. As it is, this answer adds no new information. – Todd Wilcox Sep 23 '15 at 17:54
  • There is no relative scale involved when defining note A. Boethius invented a scale with pitches A to O (2 octaves) c. 500, based on Greeks work who had a letter scale too, with alpha assigned to the highest pitch. Later an octave was added, notes were grouped by octave and renamed giving A..G, a..g, aa..gg. Later when a note below the first A was necessary (a lower G), it was named Γ (gamma) for the similarity with G. Major and minor modes appeared much later than note names. More. – mins Jul 30 '22 at 15:00
  • @mins but interestingly gamma is the third, not the seventh, letter of the Greek alphabet. I wonder whether anyone ever called the low F below gamma "beta" and the low E "alpha" -- now that would be confusing. – phoog Nov 10 '23 at 22:38
  • @phoog, actually 3 Latin letters, C, G and Ɣ, were derived from Greek gamma (Γ) (more), it was used here in replacement of G. Later the playable range Γ-ut, was named gamut, which now means a colorimetric scale in English, but derivatives still mean a musical scale in Latin languages, e.g. in French gamme. – mins Nov 11 '23 at 10:42