Major/Minor ratios

[VitaminD]

I am reading Music Theory for Computer Musicians and it gets to a point where it begins discussing chords (still mentioning intervals). In such it has a chart of ratios for Major and Minor thirds and sixths.

For instance

Major third 5:4
Minor sixth 8:5

but it doesn't appear to explain HOW it came about these values nor what they really mean.



Would someone please share what these mean and in simple, non-music degree seeking terms.

[tapper mike]

Demand a refund it's claptrap filler.

[geroyannis]

Google "just intonation".

[DocAtlas]

I am reading Music Theory for Computer Musicians and it gets to a point where it begins discussing chords (still mentioning intervals). In such it has a chart of ratios for Major and Minor thirds and sixths.

For instance

Major third 5:4
Minor sixth 8:5

but it doesn't appear to explain HOW it came about these values nor what they really mean.



Would someone please share what these mean and in simple, non-music degree seeking terms.

The numbers represent the ratio between two harmonics; in the examples above, between the 5th and 4th harmonics, and between the 8th and 5th. A perfect fifth would be the ratio between the 3rd and 2nd harmonics; you'll often see it written as 3:2. If you see the harmonic series written out on a musical staff, you'll see where the intervals occur; this is where the ratios for Just Intonation, among others, is gotten.

[tapper mike]

And it falls to what purpose unless you are learning to pull off harmonics on a stringed instrument like guitar harmonics.

Yes it's lovely scientific data but it's not something that one references in songwriting which is the ultimate goal of music theory. Although the information might be useful for synth dev's

[Gamma-UT]

Would someone please share what these mean and in simple, non-music degree seeking terms.

Given the context, it's hard to disagree with tapper mike. Normally music theory books don't fall apart until you get to the chapter on modes. This one got off to a good start. I haven't read the book but it sounds as though it's a mostly irrelevant detail.

The ratios just represent the relationships of the frequencies of notes in a scale. A major third is 1.25x higher in frequency than the root note of a scale, so if we take 440Hz concert-pitch A4 as our starting point, C#5 will be 550Hz. Except, er um, it isn't. C#5 in equal temperament is 554.37 - it's a bit sharper than you expect.

The ratios in the book apply to 'pure' methods of tuning, such as just intonation. The reason people use those ratios is because of the way that the scale is constructed: by successively taking pure fifths (a ratio of 3:2) on a monochord - basically a resonator box with a couple of strings on it. You use a moveable bridge to divide the string into sections so you can construct frequency ratios easily. If you find one fifth and then the fifth of that then divide by two to bring the note into the same octave, you get 9:8 - the major second (and the next fifth along in the circle of fifths). Keep on doing it and you get all the notes of the 12-tone scale and, in theory, get back to the beginning.

Except you don't. Because, after all those divisions, the A you derive from those 12 steps comes out slightly too low. This needs to be fixed up in some way and each of the intonation or tuning systems has a way round it. Just intonation keeps the purity of the key ratios such as fifths and thirds but other, more dissonant intervals come out really dissonant. Equal temperament, which almost all western music uses today, evens up the difference between each of the notes so that the ratios are not pure - but most people don't tend to mind.

[JumpingJackFlash]

but it doesn't appear to explain HOW it came about these values nor what they really mean.
Would someone please share what these mean and in simple, non-music degree seeking terms.

This goes back to the discoveries of Pythagoras; a very clever chap.

To put it ridiculously simply, imagine you have one string that is 5 inches long, and another string of the same thickness which is 4 inches long. If you twang them, the difference between the resultant sounds will be approximately a major third. (It works with metal bars and glasses full of water too).

There's a lot more too it that that, but that's enough for now. Although this is interesting from a historical perspective, like the others said, it's more important that you get on with the actual music and worry about the mathematics later (if at all).

[jancivil]

And it falls to what purpose unless you are learning to pull off harmonics on a stringed instrument like guitar harmonics.

Yes it's lovely scientific data but it's not something that one references in songwriting which is the ultimate goal of music theory.

who knew

this is one of the actual FACTS of 'music theory', ratios as the origin of intervals. Don't let it upset you, you know. Jesus.

[jancivil]

The ratios in the book apply to 'pure' methods of tuning, such as just intonation. The reason people use those ratios is because of the way that the scale is constructed: by successively taking pure fifths (a ratio of 3:2) on a monochord - basically a resonator box with a couple of strings on it. You use a moveable bridge to divide the string into sections so you can construct frequency ratios easily. If you find one fifth and then the fifth of that then divide by two to bring the note into the same octave, you get 9:8 - the major second (and the next fifth along in the circle of fifths). Keep on doing it and you get all the notes of the 12-tone scale and, in theory, get back to the beginning.

Except you don't. Because, after all those divisions, the A you derive from those 12 steps comes out slightly too low. This needs to be fixed up in some way and each of the intonation or tuning systems has a way round it. Just intonation keeps the purity of the key ratios such as fifths and thirds but other, more dissonant intervals come out really dissonant. Equal temperament, which almost all western music uses today, evens up the difference between each of the notes so that the ratios are not pure - but most people don't tend to mind.

Most people don't mind? what people? a lot of musicians notice it and ARE INTERESTED IN IT. it's available in virtual instrument design, the ability to have non-ET intonations, as there is a demand for it. eg., VI Pro lets you set an intonation for every matrix so you can eat your cake and have it too, eg., just intonation at every new key level. and the turkish musicians et al frequently made the feature requests and got a number of their maqams included in the design. but 'most people'... sure, you know, so let's just act like this is 'irrelevant information'. christ.

also 'more dissonant intervals come out really dissonant' [in just intonations] is nonsense, and it's strange nonsense. do you mean eg., 15/8 vs 1100¢? to whose ears? 16/15 vs 100¢? how? the thing is, the concordances are natural and not compromised. this is a physical matter which can be demonstrated! Do you believe that the difference of a whopping 13.69¢ [just M3rd vs ET's, sharper to that degree] is negligible? Me, I'm glad to have the understanding which I use all the time. YMMV.

[jancivil]

Although this is interesting from a historical perspective, like the others said, it's more important that you get on with the actual music and worry about the mathematics later (if at all).

well, it's interesting as a practical matter. I'm not sure why it's in that text, made as though for the apparently very special subgroup 'computer' musicians, but it is a matter of the reality of intervals and since melody and harmony are comprised of intervals I would say it's interesting qua music knowledge interest.

I'm not sure how 'music theory', ie., some information in such a text gets to be central to 'getting on with the actual music' really. these opinions kind of amount to an anti-knowledge thrust for this thread, which is just daft.

[jancivil]

Just intonation keeps the purity of the key ratios such as fifths and thirds but other, more dissonant intervals come out really dissonant. Equal temperament, which almost all western music uses today, evens up the difference between each of the notes so that the ratios are not pure - but most people don't tend to mind.

NO. Just intonations reflects the more simpler bases of intervals. if you have just intonation based on eg., tonic = C and you find yourself in a key distant to C, the more complex interval you have the more out-of-intonation it will be according to how distant (and to what interval). asserting the intervals themselves are 'more dissonant' is not a true statement.

if you want that 'most people' ignoring the sharper by ~14¢ major 3rd (for me a real problem in virtual orchestration), I'm sure their missing just intonation's 12¢ flatter Major seventh (or 12¢ sharper minor second) in a harmony is equally viable an idea.

[JumpingJackFlash]

I'm not sure how 'music theory', ie., some information in such a text gets to be central to 'getting on with the actual music' really. these opinions kind of amount to an anti-knowledge thrust for this thread, which is just daft.

The point is, in my opinion, a newbie should not be concerning himself with this kind of thing. In musical terms, it is important that someone knows the difference between a major third and a minor third, but the actual physics behind it doesn't really matter at that stage.

Most people drive cars perfectly well without understanding how they are manufactured.

It's a question of priorities. All knowledge is good, but one should not run before they can walk.

Unless of course the OP has a particular interest in this sort of thing, or desires a career where such knowledge would be useful, then by all means it should be pursued.

[jancivil]

Yeah, I get that that's your opinion. I don't find it a very compelling one.

[jancivil]

Most people drive cars perfectly well without understanding how they are manufactured.

It's a question of priorities. All knowledge is good, but one should not run before they can walk.

So. you think following your articles of information - with no particular context - as far as roman numbers and scale degrees etc is more valuable for a noob than other information. As though it will get one on one's feet in some way through itself. I guess because it's more along your frame of reference? You know, Paul McCartney drove his music perfectly well without it.

your car analogy is weak btw. if you drove a straight shift, knowing the mechanism of a clutch could be useful.
And knowing what an interval IS is not analogous to understanding manufacturing in Detroit.

[JumpingJackFlash]

You know, Paul McCartney drove his music perfectly well without it.

I wonder if Paul McCartney understood just intonation?

That's the problem with forums like this. If I was newbie just taking my first steps in music, statements like the following would make give up and run a mile:

do you mean eg., 15/8 vs 1100¢? to whose ears? 16/15 vs 100¢? how? the thing is, the concordances are natural and not compromised. this is a physical matter which can be demonstrated! Do you believe that the difference of a whopping 13.69¢ [just M3rd vs ET's, sharper to that degree] is negligible?

I suppose you'll be lecturing them on the Chromatic Mediants and the Lydian Augmented mode next