I have a question regarding commas...

I know the diesis is the difference between 3 major thirds and an octave, and that the Pythagorean comma the difference between 7 octaves and 12 fifths..

But how do you conclude from the diesis that a chromatic semitone has 4 commas and diatonic semitone has 5 commas? I think pythagorean ones, since a tone is equal to 200 cents and the Pythagorean comma is equal to 23, so you divide the tone in 9 Pytha commas, 4 being chromatic and 5 diatonic...

And I have been wondering how this diesis affects the chromatic scale, as in why shouldn't the fifth of the chromatic scale be altered etc?
That's funny, I was wondering the exact same thing.
Guitars:
1968 Telecaster (MIA)
1979 Strat (MIA)
1983 Fender Bullet S3 (MIA)
2007 Gibson VM LP (MIA)
2007 Fender Telecaster Highway I (MIA)
1978 Fender Acoustic (MIT)
No one?

I will try to take a guess...

4/5 is the frecuency of major thirds...
1/2 is the frecuency of octave...
(4/5)³=/=1/2
64/125=/=1/2
128/250=/=125/250
So the difference is 3/250....

Pythagorean comma--
2/3 frecuency operfect 5ths
1/2 frecuency of octave
(2/3)^12=/=(1/2)^7

4096/531441=/=1/128
524288/68024448=/=531441/68024448
Difference=7153/6802448

Where do I go from here?
Last edited by gonzaw at Aug 7, 2008,
*luaghs at every dip**** that thought they understood theory because they know "modes"*

spell check: "frequency"

your problem is you dont understand math. if you were to take a fraction and raise both numerator and denominator to the same power, the result will no longer be in the same ratio as it was. I still do not understand what your question is but i understand what your talking about.

that's a whole lot of numbers. what are you, a guitar / guitar parts manufacturer?
if not, how does it matter? (being serious here, not flaming or insulting)

PS:
Quote by LawnDwarf
*luaghs at every dip**** that thought they understood theory because they know "modes"*

massive nerd fail.
Last edited by RCalisto at Aug 6, 2008,
Quote by LawnDwarf
*luaghs at every dip**** that thought they understood theory because they know "modes"*

spell check: "frequency"

your problem is you dont understand math. if you were to take a fraction and raise both numerator and denominator to the same power, the result will no longer be in the same ratio as it was. I still do not understand what your question is but i understand what your talking about.

I know, if you halve a string, the ratio is 1/2, if you half it again, the ratio is not 1/2, but 1/4 (1/2^2), and that is what I am saying, because everytime you half the string you are going up an octave. So if you half a string 7 times, it should be the same as going up 12 fifths, aka 2/3 ratio (dividing the string in 2/3), but in reality it isn't...

Now, it is the same with the diesis, only it uses 1 octave (1/2) and 3 major thirds (4/5 ratio I think, can't remember that well), so if you half the string to 4/5 three times, it should be the same as halving it in half, like this...

---------------------------/-|-------|--------|----------|

The | represent major thirds and the / an octave...

I want to know how that "-" difference matters when saying that a diatonic semitone has 5 commas and a chromatic semitone has 4.

Quote by RCalisto

that's a whole lot of numbers. what are you, a guitar / guitar parts manufacturer?
if not, how does it matter? (being serious here, not flaming or insulting)

Lol no, I am just interested in music theory, specially how it started....
(Although I would like to be a luthier or some in the future, but first I have to understand this stuff )
Last edited by gonzaw at Aug 7, 2008,
this is something i never studied because it has very little importance to me. might i suggest you take college music classes (or any other classes) where you will be guided rather then guided by amateurs in this sub forum. sorry i cannot help
I go to a school of sorts, but they teach basic stuff (basicly what every other teacher teaches, only more in depth with the basic stuff), so they don't teach this complicated tuning issue...
I don't even know if they learnt this stuff...

But I thought the all-mighty theory nerds of UG could answer
Last edited by gonzaw at Aug 7, 2008,
Quote by gonzaw
I go to a school of sorts, but they teach basic stuff (basicly what every other teacher teaches, only more in depth with the basic stuff), so they don't teach this complicated tuning issue...
I don't even know if they learnt this stuff...

But I thought the all-mighty theory nerds of UG could answer

You'll need to study physics and, more specifically, acoustic physics, in order to get a straight answer.

I'll attempt and answer when I have time.
Quote by gonzaw

And I have been wondering how this diesis affects the chromatic scale, as in why shouldn't the fifth of the chromatic scale be altered etc?

The thing is that the fifth is altered in tempered tuning; so you are on the right track. If you flatten the fifth by something like a tenth of a Pythagorean comma, you correct the discrepency of the 12 fifths, 7 octaves contradiction.

I was sort of confused as to your question. Are you inquiring about the mathematics involved, or the concept as a whole?
Quote by 5/4
You'll need to study physics and, more specifically, acoustic physics, in order to get a straight answer.

I'll attempt and answer when I have time.

Quote by 5/4

The thing is that the fifth is altered in tempered tuning; so you are on the right track. If you flatten the fifth by something like a tenth of a Pythagorean comma, you correct the discrepency of the 12 fifths, 7 octaves contradiction.

I was sort of confused as to your question. Are you inquiring about the mathematics involved, or the concept as a whole?

Makes sense, since it is a 3/250 difference (if the calculations I made before are correct)....

I think I inquire both, but mostly the concept as a whole, while in the semitone question I ask more about a mathematical point of view.

Supposedely the chromatic scale isn't written taking equal tempering tuning into mind, but I would think just tuning (if that is what it is called).
I want to know how the commas affect which tone you alter in a chromatic scale.
Sorry to bother you but I don't think a lot of people in this forum know about such things...
Last edited by gonzaw at Aug 7, 2008,
Okay, I will copy the things I found here

So 3 major thirds stacking would be C-E-G#-B# while an octave is just C-C right?

B# and C are supposedely enharmonic, yet the diesis shows they aren't, right?
So the diesis is 41 cents, the pythaorean comma is 23 cents, and a tone is 200 cents.

There is 41 cents in difference between C and B#, and there are 200 cents in a tone (I dunno really, I will have to check later), so the difference between B and C#/Db is 200 cents. There is a chromatic semitone between B and B#, and a diatonic one between B and C. Since the difference between B# and C is 41 cents, then that means a diatonic semitone is higher than a chromatic one (and well, in meantone tuning, and chromatic semitone is like 75 cents and a diatonic one is 115 cents, with a 40 cents difference, so I guess what I am doing now is correct).

Well, that is something, but I still don't know how to come up with the difference

But between B and C there is a diatonic semitone.
A diatonic semitone would be the cents between a major third and perfect fourth right?
So a perfect fourth's ratio is 3/4 and a major third's one is 4/5 (I am using it as if it were a string, like halfing the string, not as in pitch, in which it is 4/3 and 5/4 and 2, making the pitch double, etc)....

You divide them right? like 3/4 / 4/5=15/16 ratio...
So if you have B, its pitch multiplied by 16/15 is C, minus diesis is B#....
Diesis was (5/4)^3/2 (I think this is the right way to determine these commas or intervals, I dunno, just did a google search). This is 125/68*1/2 which is 125/128, or the other way round depending if the pitch rises or not...

So from B to C it is 16/15, and from B# to C is 128/125, so from B to B# it is 16/15*125/128=2000/1920=100/96=25/24

So a diatonic semitone is 16/15 and a chromatic semitone is 25/24?
16/15*25/24=400/360=10/9

So 10/9 is the interval of a tone?

Is this right?

Now how do I find them in cents?

EDIT:The only thing I know is that an octave is 1200 cents...
So 2/1=1200 then 10/9=x

x=1200/(2*10/9)=1200/(20/9)=540?

Can someone tell me what is wrong here? (I dunno if cents are proportional, maybe that was the mistake, but I don't know any other way of finding them)
Last edited by gonzaw at Aug 7, 2008,
Anyways, so 10/9 is a tone 25/24 is a chromatic semitone and 16/15 a diatonic semitone...
Pythagorean comma is 524288/531441 from what I got...
Diesis is 128/125

So I would have to find how many commas (and decide which one) there are in each semitone (at least when I know the cents of each comma, I can calculate the cents of each semitone better).

First I will make the denominator of each semitone the same-
25/24---16/15
375/350----384/350

Now I will try with the diesis-
128/125-----1792/1750
375/350=1875/1750
384/350=1920/1750

So in essence it would be (1792/1750)^n=1875/1750 Since I am trying to see how many times the diesis should be done so it becomes the chromatic semitone
Logarythms I suppose n=log 1792/1750 (1875/1750)
I can't find a calculator that allows rational numbers

Well, lets try for pythagorean comma
524288/531441= 183500800/186004350
375/350= 199290375/186004350
384/350= 204073344/186004350

So we do the same:
n=log 183500800 (199290375)
n²=log 193500800 (204073344)

anybody knows how to do these ones?

But lets assume a chromatic semitone has 4 commas (don't know which ones) and the diatonic semitone has 5...
Let's verify:
183500800/186004350^4=199290375/186004350
And
1792/1750^4=1875/1750

First one=11338401925370018158084096/11808840723598373339824128=0.96
And 199290375/186004350=1.07

Well, not really

Second one=10312216477696/9378906250000= 5156108238848/4689453125000=1.09951162
And 1875/1750=1.07.... it is not it, but it is more closer than the pythagorean one, by 0.02, so let's take it

But let's check with the other one
1792/1750^5=1920/1750
18479491928031232/16413085937500000=1.125
1920/1750=1.097
0.02 difference again....

So it means that roughly a chromatic semitone is equal to 4 diesis and a diatonic semitone is equal to 5 diesis right?

Now how do I figure them in cents?

Well, in reality the comma is 375/384, but is it a newly named comma or is it a preexistant one? (if the second, then I guess it is the diesis)

So 2/1=1200 cents, and I wanna know how much it is 10/9 right?
But I can't figure how to do the maths...
Last edited by gonzaw at Aug 8, 2008,
Anyways, I found out that to find cents I use this formula...

cent=(log2 a:b) x 1200

(got it from here http://www.medieval.org/emfaq/harmony/pyth4.html )

so to find how many cents is 10/9, and I get 182 cents?
Kay, so a tone has 182 cents
But it could be 9/8 instead of 10/9, since if you go up to fifths (3/2^2=9/4) you go up a 9th, and if you go down an octave (x1/2) you get a major second, which would be a tone I guess (I am not too sure) which would be 9/8, and it would be equal to 204 cents..

Anyways, so lets try with 16/15 and 25/24

16/15=111.7 cents
25/24=70,6 cents

Now the diesis:
128/125=41.05

So I have another question:
How many cents are there in a tone?
Are they 204, as there are in a major second?
Or are they 182, as it is the sum of a chromatic and a diatonic semitone? (111.7+70.6)

EDIT:That site I quoted said that chromatic semitones are higher than diatonic ones, it kind of confuses me (if you look at a chart below)
Also, that would be because one takes a tone (a diatonic one that is) being 204 cents, and that, along with how it shows you get the other intervals (by going up fifths, etc) kind of makes my 25/24 and 16/15 ratios obsolete...
Last edited by gonzaw at Aug 10, 2008,
I kinda stopped reading when it got so far over my head I couldn't even pretend to know what you're talking about. I just figured I'd say that you finding that B# and C are a little different sounds correct to me because I've heard people extremely skilled on fretless stringed instruments will play B# a minuscule amount flatter than C. not even enough difference for most people to detect.

all the numbers and crap... I got the basic idea of what you're talking about but the numbers made no sense to me whatsoever. I don't really think anyone in MT will know much
Last edited by The4thHorsemen at Aug 10, 2008,
we are all dumbies, not the right forum to ask that xD
try the geekynerd.com forum
Interesting....

I have no idea about the answer to your question, exactly, but I'll agree with the person above who said this is more of an acoustical physics question than a music question.

To put it in perspective, I have an honours degree in music, and never learned anything in that entire program about acoustical physics.

CT
Could I get some more talent in the monitors, please?

I know it sounds crazy, but try to learn to inhale your voice. www.thebelcantotechnique.com

Chris is the king of relating music things to other objects in real life.
I don't know if anyone here knows about psychoacoustics that much...

But it is interesting, since it actually tells you how the "notes" you know nowadays are found...

I would like to know how middle eastern musicians form their scales and how they deal with microtonal music...
In the same way that I mean the pythagorean one, like how do they know which note goes between E and F (microtonal music for instance) and how do they find it, etc...

IT also kind of helps you know more about natural harmonics and such, if you know the ratios and intervals, etc