h2g2 The Hitchhiker's Guide to the Galaxy: Earth Edition

Hmmmmm Rameau's a bit old hat now isn't he? I thought the search for perfect consonance in music went out with 'music of the spheres' about 250 years ago!

Post-Classical theory has the major mode defined by the tonic triad (C-E-G straight of the natural harmonic series of C), supported on one side by the (equal) dominant triad (G-B-D not only the nhs of G but also a subset of the nhs of C) and on the other by the (also equal) sub-dominant triad (F-A-C).

Rameau's 'problem' of not been able to find F in the nhs of C sort of misses the point - C is the strongest (non-F) consonsonance in the nhs of F, and it's this that defines the role of the F-A-C triad in the major mode. Sub-dominant is to tonic as tonic is to dominant.


Good description along with minor mode derivation and some nice dissonance curve applets can be found at:
http://home.austin.rr.com/jmjensen/musicTheory.html

That's a teriffic link! With links galore attached.

I wouldn't diss Rameau; he's still regarded as the most important figure in mathematical musical theory since Pythagoras, and his theory of the fundamental bass is the foundation of all modern tonal music including jazz; for instance the diminished seventh is best understood as a dominant minor ninth with the root omitted.

You say his 'problem' of not been able to find F in the harmonic series of C "sort of misses the point" -- not so. It was a slight embarrassment, perhaps, but he certainly knew all about the relation "sub-dominant is to tonic as tonic is to dominant" and he gave this, along with many other derivations.

There is no shortage of ways to explain the phenomenon of the subdominant. One could say that: as we stand to creation (tonic-dominant) God stands to us (subdominant-tonic). So just as the subdominant is not found in the natural harmonics, God is not found in nature; but both are easily inferred.

The trouble with that is, that one can infer a whole hierarchy of gods above the first. That's why that theory was shelved perhaps.

Only one God ?
God not found in nature

Drop me a line on my homepage, we have much to discuss (and this thread needs a breather)

hehe, i, for one, am lost... but i'm sorting it out.

ok, i'm going to try and finish editing this wish me luck

Hello again vanamonde.

I've been quiet about this entry for some while now, because it baffles me. I have a very limited understanding of music, but what I know about sound does not accord with the entry. In particular, the paragraph:-

'Notes are specified pitches on a scale. Pitch is determined by the frequency of the sound wave. Frequency is the measure of the number of times a single wave passes a given point. Therefore, a note is determined by the length of the wave produced. For instance, Middle C has a frequency of 262 Hz. Anything that can produce a sound wave with this frequency can produce a C.'

... is almost entirely wrong.

Here is how I think of it (which may be far too technical for the entry), if it helps.

Sound is minute, rapid variation of air pressure, giving peaks and troughs of pressure. These move through the atmosphere at a constant rate (the speed of sound). At this speed, the distance between one peak of pressure and the next is the acoustic wavelength, and is the same as the distance between troughs. Barring complications such as reflection, the wave motion is unidirectional. A single wave therefore passes a point only once.

It is a trick of perception that the fundamental note is heard, regardless of the timbre, which in technical terms means the harmonic content. Taking 'A' at 400Hz to keep the numbers simple, the fundamental is 400Hz, the harmonics (overtones) are at 800Hz, 1200Hz, 1600Hz, etc. A note comprising 800Hz, 1200Hz and !600Hz etc, with no 400Hz component, is heard as 400Hz. Such a sound does not occur naturally, but can be made electronically. (By the way, I used to be an electronics engineer, if that helps to explain my perspective.). Thus, referring to a 'C' at 262Hz, 'Anything that can produce a sound wave with this frequency can produce a C.' is not the whole story, as things which cannot produce a sound wave with this frequency can produce the sound of a C.

I do not have an ear for music, but do know that an 'A' at 400Hz sounds ghastly when sounded which another slightly off-tune note at say 404Hz. Knowing that this 1% frequency error sounds awful, I cannot then understand why your less accurate numerical ratios should sound pleasant.

Add to that your free interchange of synonyms/antonyms such as consonance/assonance/dissonance, and my bafflement is complete. Sorry.

However, as no-one else in this thread has raised these matters, I will not be overly distressed if this posting is disregarded (although I am keen to understand music in a technical way).

Old Hairy - for moral support I should add you are not alone. I gave up trying to understand the ratios and frequencies descriptions about post 37.

However I put my confusion down to my detailed ignorance of music and physics, with a vague memory of Hz and sine waves on oscilloscopes.

Pimms

It's a while since I looked at this. You're right, Old Hairy, that the physical description of pitch in the entry is wrong.

I think, on the other hand, that your fabricated sound with 800, 1200, 1600 etc and no fundamental is a very contrived example and should not form part of this entry at all. To all intents and purposes in music, the pitch of the note is the lowest frequency present in the note, and some or all of the harmonics may be present. (Bells are an exception).

The mathematics behind musical intervals has already been covered in Recumbentmans' Edited Entries on scales, so I don't see any reason to go through all that again!

Thanks for the mention, Gnomon. Refs: A1339337: "Sol-Fa - The Key to the Riddle of Staff Notation" and A1339076: "Sol-Fa - The Key to Temperament"

Is this still being worked on? I want to see it in the guide!

i think that i have worked on it as much as i can... i would love to see it in the guide as well... if anyone can help me polish it off i would love to add your name as a researcher

I'll look into the layout of the table of pitches; momentarily forgotten how to stuff out the cells to line them up well.

There are still some things I couldn't sign my name to, but they may be repairable . . .

Hi there!
Just came across your great entry, and it immediately reminded me of a guest lecture I attended in November last year by Dr Guerino Mazzola from MultiMediaLab, university of Zurich. He has been researching the connection between mathematics and music for quite some time, and he also wrote a book on that topic, "The Topos of Music".
Frankly, the theories he presented were far beyond my mathematical understanding, me then being only a first term student of computer sciences, but it was absolutely interesting, nonetheless.
For example, he offered a new mathematical approach to the whole consonance/dissonance problem.
I just wanted to mention his work to you, you might find it interesting.

If you want any help with tables, I can make them do most of what is possible, and get around some of the problems (for example, captions do not work in Brunel skin). Just ask, and I'll do the GuideML.

Thank you OH, I will mess about a bit and see how I do.

Well my first bit of messing about was to go the "Help" route via "GuideML Clinic" and after several shrewd moves I came upon a couple of conversations you and I had in October last, leading to the mention of CELLPADDING and CELLSPACING as posted by Ottox in F113568?thread=320593 on the 23rd of September, which was what I needed both then and now.

I feel very superior to my then self; this time I got there in a few minutes, last time it was a few hours if not days sprinkled with tears of rage and frustration.

Don't you think these indispensable tags should be posted a little nearer to the GuideML Clinic help page, such as for instance in the Tables paragraph? I'll go off and ask the Towers (again).

Thank you again, both for your help then and now.

Vanamonde~

This is how I think the table, and the line after it, should go, as I understand it:

(start of GuideML sample)


NoteFrequencyRatio to C

C261.6 1:1

D293.79:8

E329.65:4

F349.24:3

G392.03:2

A440.05:3

B493.915:8

It will be appreciated that these ratios are approximate!

(end of GuideML sample)

I have "corrected" the ratio of B to C to a more harmonic figure than 17:9. It is still approximately true!
~Recumbentman

If there are any tables with captions, then you may find A2496062 helpful (or just flagrantly self-publicising).

Ah. Interesting. I viewed it in Brunel, and the caption that should have been invisible wasn't. (I checked that you had done it using and you had).

Have they repaired Brunel? Must have.

If they have, it would have been jolly nice if they had told me. I have given this advice so many times recently that I decided to make an entry of it. Ah well ...

Oops no I'm wrong. It is invisible.

It was so invisible I didn't see it was missing.

The author seems to have left the building - flea market time?