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This is first time I've stumbled onto the diatonic table in my life. I Googled a lot, but I couldn't find answer for following:

the table mentioned in the book I am reading, I don't understand where this A# G# F# D# C# come from in this diatonic table (below)?

This is the text written in the book for the table:

First, the octave consists of seven different tones (i.e. gaps between notes), but only five semi-tones. Hence, two semi-tones are missing – namely, those between E and F and between B and CHI (see Table 7-1). In the terminology of the tonic sol-fa, progress upwards through the octave is retarded between Me and Fa, and between Ti and DoHI.

Second, and in another way of making the same point, there are seven points of potential change in vibration between the eight notes in the octave – namely C-D, D-E, E-F, F-G, G-A, A-B, and B-CHI. In Table 7-1, the vibrations are given in column 6 as ratios, with the rate of vibration of the note C as the numeraire. The difference between ratios, upwards through the octave, is retarded at E-F and at B-CHI.

Table 7-1

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  • Please give the title and author of the book in case someone else has the same question.
    – Aaron
    Commented Feb 1, 2023 at 4:07
  • 1
    Welcome to Music.SE, and great question! That's as confusing an explanation of the diatonic scale as I've ever read, so no wonder you're asking.
    – Richard
    Commented Feb 1, 2023 at 12:13

2 Answers 2

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Disclaimer: This post is intended only to offer as clear and simple an explanation of the table as I can manage. It should not be read as historically accurate. Things such as the structure of the octave, the naming of pitches, and so forth, are broad over-generalizations and simplifications.


Early on in the development of Western music, the octave comprised 8 pitches:

C D E F G A B C-Hi

The perceived difference in sound between pitches was considered in terms of "tones" and "semitones". C-D, for example, differed by a "tone" (T), for example; whereas, E-F differed by a "semitone" (S).

C   D   E   F   G   A   B   C-Hi
  T   T   S   T   T   T   S

Over time, new pitches were introduced that fit "in between" the existing pitches. That is, the tones were divided into semitones (the existing semitones were left alone). The new pitches were indicated with a "#" symbol.

C   C#    D   D#   E   F   F#   G   G#   A   A#   B   C-Hi
  S    S    S    S   S   S    S   S    S   S    S   S

The sequence of tones and semitones (T T S T T T S) is known as the diatonic scale, and the sequence entirely of semitones is known as the chromatic scale.


If you search this site, you will find much more, and more detailed, information about the origins of the diatonic scale, its uses, and the meaning of the various ratios given in the table.

Two relevant posts:

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  • 1 . Why did they name semi tone and tone between pitches, why not just kept the name "tones" 2. Why did they add '#' in C D F G, why not add in between all tones? Commented Feb 1, 2023 at 4:45
  • @administr4tor Other posts on this site will answer those questions. But in short, the musical distance between "tones" is greater than the distance between "semitones". So each "tone" was divided into two "semitones"; the semitones were left as they were.
    – Aaron
    Commented Feb 1, 2023 at 5:21
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First note that the author of this books uses "tone" and "semitone" in a slightly non standard way. The author is using "tone" for intervals between neighboring scale notes (such as C→D) and "semitone" for a scale tone to its higher alterations such as C→C#.

The standard use of the term "tone" goes back to the tónos of Aristoxenos of Tarantinos. This denotes a specific interval which he divides in half tones, third tones, &c. and uses these to form other intervals, such as a fifths being 3 tones and 1 half tone.

And this is exactly the usual meaning of tone and semitone. A tone is a big step such as in C→D and a semitone is a small step such as E→F.

Now, in modern music (modern in the sense of non ancient) we have no use for third tones and lower, we just use intervals explainable by whole tones and half tones (as long as we ignore tuning systems and such, which immediately makes things more complicated).

But not all notes reachable from the root by tones and semitones where actually used (which would form our modern "chromatic scale"). To understand this we need again consider ancient greek music theory. Here scales are built by using so called "Tetrachords". These are stringed instruments with four chords, which where tuned in different systems or genera. A diatonic tetrachord would have most classically been one made up from two whole tones and one semitone.

Scales built using two diatonic tetrachords would then be diatonic scales. So a diatonic scale is a scale made of of whole tones except of two semitones (usually also demanding that there are either two or three whole tones between the semitones).

And this system forms the basis of medieval music theory, just instead of tetrachords one would extend to hexachords (i.e. six strings). Medieval music theory then used three different hexachords, the hexachordum naturale which would be the first six notes of a major scale, the hexachordum molle, which is the same but a fifth higher and the hexachordum durum which is a fifth higher.

So in note names we’d have

  • C D E F G A
  • F G A Bb C D
  • G A B C D E

So if you pay attention in total you get the whole major scale plus a minor 7th:

  • C D E F G A Bb B

This system is the basis for both note names and solfeggio. Guido of Arezzo assigned to each step of the hexachord a syllable (ut, re, mi, fa, so, la, from the hymn:

Ut queant laxis
resonare fibris
mira gestorum
famuli tuorum
solve polluti
labii reatum
Sancte Iohannes. 

with each verse starting one step higher). This is the origin of solfeggio. And he assigned a letter to every note used in this medieval system, which where Gamma, A, B, C, D, E, F, G, a, b, b*, c, d, e, f, g, aa, bb, bb*, cc, dd, ee.

Here we have two different (small) bs, one of the mollum hexachord and one of the durum one, so a lower one and a higher one. This was represented by using a round b for mollum and a rectangular b for durum.

Later people started to fill up the gaps with semi tones. These letters then developed into our common note names (C D E F G A B) and the syllables to solfeggio. The two different bs turned into ♭ and ♮ as well as ♯ (these have quite a lot of history until they arrived at what we have today though). They were then applied to signify that a note should be played a semitone lower or higher, giving next to [C D E F G A B] also the alterations [C♯ D♯ (E♯) F♯ G♯ A♯ (B♯)] and [(C♭) D♭ E♭ (F♭) G♭ A♭ B♭]. And from there these got adopted to English note naming.

But in fact there are different note naming systems. In northern europe it is quite common to refer to notes by names, but add "is" or "es" for "#" and "b". In the Romanic languages it is quite common to use solfeggio instead with using a variant of diesis and b mollum for "#" and "b". The latter comes directly from the hexachordum mollum, the first one is a bit different (it comes from a thing called diesis, which is the distance between an Octave and either three big thirds or four small thirds. I suppose since B# and C are a diesis this names got adopted).

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