[imcool]

hello,
This is first time I stumbled about diatonic table in my life. I googled a lot but I couldnt find answer for following,
the table mentioned in the book I am reading, I dont get it that Where did this A# G# F# D# C # come from in this diatnoic table ?
This is 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. ""
Please help me understanding that table.
Regards

 

[bagpipers]

Looks like an accending pentatonic scale Bf Af Gf Ef Df

Df-Ef-Gf-Af-Bf-Df(octave) whole step-whole step-minor third-whole step-minor third

 

[Nate Miller]

What that table is trying to show is the harmonic ratios of the intervals of a diatonic scale. "Diatonic" just means your normal "major" and "minor" scales that create all the common music we hear in life. So dont think "diatonic" means anything special. Its just a big word for a simple everyday thing.

Now, in any "diatonic" scale, there are 7 notes. There are 12 half steps between each octave. On a piano keyboard, from "C" to "C" there will be 12 keys, 7 white and 5 black.

In a diatonic scale, there are 7 out of the 12 notes included. So the answer to where are the notes "A# G# F# D# C # " is simple: they do not belong to this scale and so are left off the chart.

Now, the reason those two intervals are smaller than the others is because there is a smaller interval between the 3-4 and the 7-CHi than the rest of the scale. Why is that? The answer is simple: music is hard and tricky.

The scale is made of 7 out of the 12 notes. If you look at a piano keyboard, notice that the keys do not alternate black, white, black white....There are 2 places where there are white keys side by side. The notes E and F and B and C do not have a black key between them. That is because of what you see in your table....in a major scale there are half steps between 3 and 4 and 7 and 1. This bit of asymmetry is what gives life to our western style of music. Its just the way it is.

Alot of music theory book start off trying to derive the major scale from the overtone series. J.J. Rameaux wrote a famous treatise in 1722 that introduced the idea of chords using these harmonic ratios. It can make it seem like Magical Musical Mystery Tour because its new material and all that math, but its really just taking a very common idea like a C major scale and going into the nth detail, so dont get too caught up in it. It is just laying out a foundation, so the author is being very exact

 

[bagpipers]

I played the scale on the piano and it sounded very Oriental

 

[Nate Miller]

I played the scale on the piano and it sounded very Oriental

that's the pentatonic scale of the 5 notes in the 2nd column, right? that chart is hard to figure out just what they meant with the "semitone" column. I assumed that was the note they were skipping over.

but you're right, the pentatonic scale of the other 5 notes does have an Oriental sound to it

 

[SuperTonic]

The ratios in the table would be for the just intonation intervals. In actual practice almost everyone uses equal temperment these days, so the true ratios would be irrational numbers.

Also the frequencies look off, probably as a consequence of the above observation. They have A at 427 Hz, which looks very flat to me. Standard tuning is to set A at 440 Hz, though in practice it does vary, so maybe this is within an acceptable tolerance.

Based on these observations alone, I'm not sure how useful this table really is. Of course it depends on the context in which it is being presented.

 

[Georgieva]

(apologies)

 

[Enthalpy]

Why so much fuss?

Said diatonic scale is C major, the white keys of a piano. The second column are the sharp notes, the piano's black keys, which build a usual pentatonic scale.

The "ratio" column gives frequency ratios in the Zarlino scale. This scale isn't normally used to play music, because it's not equally-tempered, but it can serve to understand cross-fingerings on woodwinds or harmonics on string instruments.

The pitch isn't used in music. Some physicists who never meet musicians would like to take it as a standard.