How Many Root Notes Are There?

[23skidoo]

.... but what was the question?

[czardas]

That's easy: what is the meaning of life! (according to Douglas Adams)

I always get that one mixed up with the question to the answer to the ultimate question : what do you get if you multiply six by nine?

.... but what was the question?

_ _ _ / _ _ _ _ / _ _ _ _ / exist?

[czardas]

To make it a bit easier, here's another clue.

_ O _ / _ _ N _ / _ _ _ _ / EXIST?

Answer : 42!

[hed_b94]

It's not just me feeling like this about czardas, right?

[Jazzaluk]

Nope... this thread is out to lunch.

[mr. beaumont]

It's not just me feeling like this about czardas, right?

I think you're taking it too seriously...I don't czardas is taking it too seriously.

I think.

The answer's 1 though. As soon as you call something a chord, it can have one root.

A better way to phrase the question would have been "how many possible roots can a given collection of pitches have?

If one wanted a serious discussion

[ptrallan01]

So Long, and Thanks for all the fish!

Oh the answer to the original questions is it doesn't matter unless you know theory

[czardas]

F# Harmonic Minor
F#G#ABC#DE#F#
The secondary dominant II would be D#7 (D#FxA#C#)
The diminished chord leading to II would be Fxdim (FxA#C#E)
Using the logic that each of the 14 notes (7 flats and 7 sharps) has a double equivalent would yield 35.
Given the distaste and avoidance of double flats and sharps with people often choosing the easier enharmonic spellings, 35 may be the technical answer and 21 the pragmatic one.

I tested the notation program Encore and it chose G in my example above as the default spelling in the key of F# minor.

Hey bako, I was just wondering if there was an option (in the notation program Encore) to turn off autocorrection and write the double flat (if you choose to do so) for the above example.

A better way to phrase the question would have been "how many possible roots can a given collection of pitches have?

I'm often not the most eloquent person, and sometimes wording things can be a tricky business. There's a high probability that someone would have objected had I worded the question that way, on the grounds that a collection of pitches would be meaningless outside some kind of harmonic context. For example: if the collection of pitches were interpreted as a scale, I would not consider double sharps or double flats as potential root notes.

[bako]

In Encore I can go back and correct any individual note to double flats and sharps.
I am not sure if I can overide the defaults systematically for an individual file.

[czardas]

Okay thanks for the info bako. I imagine nearly all decent notation programs will have such an option. I have never tried using Encore.

[monk]

In order to find the answer....

[Patriots2006]

I can't believe I read this entire thread. It's like watching a really bad movie. It's so bad you have to watch the entire movie and see how it ends!

[czardas]

Well here's my take on it.

There are:

12 notes
35 note names
31 chord roots
18 key tonics (Ammended => See next post)
30 keys
48 Preludes and Fugues by JSB

11 people voted
0 People said the thread was useful
3 people expressed objection to the thread

The last three stats are of no particular significance, unless you're writing a psychological thesis.

[JonR]

Well here's my take on it.

There are:

12 notes

Should really be 7 notes, if you're counting the 35 names as 5 possible names for each one (natural, flat, sharp, double flat and double sharp).

35 note names
31 chord roots
21 key roots

I haven't absorbed the whole thread, so i don't know how you arrive at the last two.
The figure of 21 is what I associate with the chromatic scale (3 possible names for each of 7 notes, not including double sharps and flats), for the purpose of spelling the 15 major key scales (which again require no double sharps or flats). Add the 15 relative minors, and we get your figure of 30. (BTW, if there are 30 keys, I don't see why there should be only 21 key "roots"; and the correct term is "tonic" anyway.)
Of course double sharps occur as accidentals in three minor keys (G#m, D#m, A#m); and double flats may sometimes be necessary in spelling certain dim7 chords (out of key context), or maybe for certain alterations in some flat keys. I wouldn't care to quantify them (no, not even for fun ).

11 people voted
0 People said the thread was useful
3 people expressed objection to the thread

The last three stats are of no particular significance, unless you're writing a psychological thesis.

Or unless you are interested in what jazz musicians (specifically jazz guitarists) find interesting on forums like this - and therefore what kind of topics may be worth starting...

[Vasco]

I think each chord has one root note. if I'm not mistaken, It depends how you look at it-from which angle.

[czardas]

Should really be 7 notes, if you're counting the 35 names as 5 possible names for each one (natural, flat, sharp, double flat and double sharp)..

Yes, I am counting them all.

With chords, it seems inappropriate to use the note names 'Cbb', 'Fbb', 'Bx' and 'Ex' as root notes, as these notes already correspond to a different degree of the scale, regardless of key: ie a scale note that already exists, with a less confusing name. Has anybody ever seen the chord Fbb7, in any piece of music (in any style of music) anywhere?

BTW, if there are 30 keys, I don't see why there should be only 21 key "roots"; and the correct term is "tonic" anyway.

Because several major and minor keys share the same tonic. Although I was incorrect in saying that there are 21 key tonics. The number should be 18. I made the mistake of assuming that any note name (excluding double sharps and double flats) could be a key tonic. My previous post has now been ammended. Thanks for bringing this to my attention.

Of course double sharps occur as accidentals in three minor keys (G#m, D#m, A#m); and double flats may sometimes be necessary in spelling certain dim7 chords (out of key context), or maybe for certain alterations in some flat keys. I wouldn't care to quantify them (no, not even for fun ).

Some of us have a different concept of what is fun.

Or unless you are interested in what jazz musicians (specifically jazz guitarists) find interesting on forums like this - and therefore what kind of topics may be worth starting...

I never thought of that. ???

[JonR]

I think each chord has one root note. if I'm not mistaken, It depends how you look at it-from which angle.

Well, there's two responses to that:
1. Any group of notes might have more than one potential root. Can any of the given notes be a legitimate root? Or does the idea of a root note presuppose an acoustic governing role, ie does it have to sound like a root, like the gravitational centre or origin of the other notes? And can a root be some other note not present in the given group (as in rootless voicings)?
2. How many angles can you look at it from?

[JonR]

Because several major and minor keys share the same tonic.

They do? Could you explain?
I get 12 tonic notes (as sounds).
Each of those can have a major or minor key built on it, making 24 keys.
6 of those keys (3 majors and their relative minors) can have two possible enharmonic names - making 30 theoretical (named) keys in all.

(Of course, we're not considering modes and modalities... That would bump up the count considerably, but - again - in a highly debatable way.)

Some of us have a different concept of what is fun.

Clearly...

[czardas]

These are the 30 keys:

No sharps or flats
C major and A minor

Keys Containing Sharps
G major and E minor (1#)
D major and B minor (2#'s)
A major and F# minor (3#'s)
E major and C# minor (4#'s)
B major and G# minor (5#'s)
F# major and D# minor (6#'s)
C# major and A# minor (7#'s)

Keys Containing Flats
F major and D minor (1b)
Bb major and G minor (2b's)
Eb major and C minor (3b's)
Ab major and F minor (4b's)
Db major and Bb minor (5b's)
Gb major and Eb minor (6b's)
Cb major and Ab minor (7b's)

Counting the note names gives 18 different tonics.

C D E F G A B
F# C# G# D# A#
Bb Eb Ab Db Gb Cb

While I can appreciate that it's not necessarily of interest to everyone on this forum, it has some significance to me. In some ways it's confusing and surprising, and in other ways it's not surprising: due to the nature of the system. Although the maths relates to music theory, perhaps it has less practical value to a performer.

[Dad3353]

Without wishing to spoil the thread, this...

Gödel's Theorem

...may broaden the debate..?

Hope this helps...

[czardas]

Although I did enjoy reading some of Hofstadter's GEB, I find it hard to see how Gödel's Theorum helps me to decide which notes can be used, and which notes cannot be used, for specific purposes. One of the problems I find is that there are many rules stating what can be done, and almost nothing about the boundaries imposed by the system itself. Such considerations seem to have either been ignored or overlooked by authors of theory books. It seems a surprise to me, as the music notation system appears to be very simple compaired to many other systems.

Having said this, there still appear to be a few problems that I need to solve before I can achieve my goals, or before my project drives me completely round the bend. The problem I now am trying to solve is this: given any group of notes, how do I decide the correct spelling for the tonic when the notes are interpreted as a scale. Perhaps there is a simple solution that I've overlooked. I have a feeling it won't be long before I have tamed this beast.

Thanks for the input, some of which was useful.

[JonR]

These are the 30 keys:

No sharps or flats
C major and A minor

Keys Containing Sharps
G major and E minor (1#)
D major and B minor (2#'s)
A major and F# minor (3#'s)
E major and C# minor (4#'s)
B major and G# minor (5#'s)
F# major and D# minor (6#'s)
C# major and A# minor (7#'s)

Keys Containing Flats
F major and D minor (1b)
Bb major and G minor (2b's)
Eb major and C minor (3b's)
Ab major and F minor (4b's)
Db major and Bb minor (5b's)
Gb major and Eb minor (6b's)
Cb major and Ab minor (7b's)

Counting the note names gives 18 different tonics.

C D E F G A B
F# C# G# D# A#
Bb Eb Ab Db Gb Cb

Right - I see what you mean. Interesting that some notes can act as either a major or minor tonic, others only as one (because of whatever enharmonic spelling of the scale is practical, avoiding double sharps or flats).
So - eg - we have a G# minor key, but not a G# major key. But we have (say) both C# major and C# minor.

While I can appreciate that it's not necessarily of interest to everyone on this forum, it has some significance to me. In some ways it's confusing and surprising, and in other ways it's not surprising: due to the nature of the system. Although the maths relates to music theory, perhaps it has less practical value to a performer.

Well, the above is certainly of essential value to any musician.
It's the extension of the question into all those other areas that starts to get unnecessary (for most musicians).

I understand the curiosity, and I've always approached theory from the angle of curiosity myself, rather than from any desire to improve my playing. But for me there comes a point where the information loses any meaningful connection with the sounds - and the sounds are what matter, after all.

[czardas]

Thanks for this response JonR. Of course I appreciate that there will be less practical value to these musings from the perspective of some players. From my own perspective these questions have as much to do with creating an option to autodetect a scale tonic (or the root of a chord) using the computer program I am attempting to write. Some surprises have appeared along the way: things which I would never have considered in any other circumstance. I figured it would be of interest to some people to discuss such things (on reflection, perhaps that was a mistake), and perhaps even helpful to those who are interested in music theory. Such discussion can sometimes be revealing and may also help point me in the right direction.

It's the extension of the question into all those other areas that starts to get unnecessary (for most musicians).

At the end of the day, there will just be an autodetect tick box option in the program. Either you click on it or you ignore it. However the program performs it's magic internally is generally considered to be of little interest. You don't even have to understand what ticking the box does.

[tele jazz]

I'll give the iq test answer.

Any given chord can only have one root. If we change the root, it's a different chord.

Now, any given collection of pitches...well, I'll let y'all duke that one out...

+1

[czardas]

For a short while there I was beginning to doubt my own conclusions, but I'm now convinced that there can only be (at most) 31 note names used for chord roots. I also suspect that this may come as a surprise to many of you.

Where is ksjazzguitar when you need him?

Judging by people's reactions to my questions here, it is apparent that it sure is going to be one hell of a nightmare writing the help file. Possibly even as difficult as the code itself.