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267295 different possible chords. Thats a lot.

music theory chords

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#1 lettuce

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Posted 29 July 2018 - 20:11

Check it out, this guy says that there are 267,295 possible different chords playable on piano.

He says he has created an algorithm to prove this and also created a beautiful and cool chord calculator.

He is counting the maximum number of simultaneous keypresses as 10...not sure about maximum range reachable with two hands fully stretched out though?

 

Do you agree with this?

Also, he did not include inversions in his chord count.

If inversions were included, what would be the total number of possible playable chords ( on keyboard )?

 

"What is the total number of chords playable on a piano keyboard?

 

It's difficult to say. A particular set of notes can conceivably be called by many different names. By your rules, and following the generally accepted conventions of chord symbol rules, what would we call D♯ and F played together? If we respelled F as E♯, it could be called D♯(sus2omit5) or D♯(add9omit3,5). Do those count separately?

 

Then, are we talking about the note D♯ or the piano key sometimes called D♯? If it's the latter and we kept F as F, we could also include E♭(sus2omit5), E♭(add9omit3,5), and F7(omit3,5). And how about G♭♭7(omit3,5)?

 

I could go on, but what I can't do is think of a properly named chord that has just D♯ and F in it. Yet, how can anyone say those two notes can't be sounded together? You see the problem?

 

So if a chord is defined as 2 to 10 unique pitch classes and inversions don't count, there would still be additional things to take into consideration, and counting the combinations is way more than simple math. You need to consider the compatibility of each interval. You can't, for example, have a diminished 5th and an augmented fourth in the same chord, can you? That's the same note. But let's say we define a chord as a root plus one or more of the following intervals:

 

  • A second, either minor or major.

  •  

  • A third, either minor or major.

  •  

  • A fourth, either perfect or augmented.

  •  

  • A fifth, either diminished, perfect, or augmented.

  •  

  • A sixth, either minor or major.

  •  

  • A seventh, either diminished, minor, or major.

  •  

  • A ninth, either minor, major, or augmented.

  •  

  • An eleventh, either perfect or augmented.

  •  

  • A thirteenth, either minor or major.

  •  

...you would come up with 46655 chords for each root note. But before you go multiplying that by every root, you'd have to eliminate chords which don't make sense. A minor third with an augmented fifth is really just a different major chord, so let's reject those. You wouldn't want something like a Csus2add9 chord, because that's duplicating a pitch class that's already in the chord. You wouldn't want something like Cadd♯9omit3 because that ♯9 is better identified as a minor third. So, if you take away everything that doesn't make sense, you're down to 7637 possibilities, by my count. Many of these are enharmonic, but should still count separately. For example, C+7add♯4 and C7♭5add♭6 are different by interval, but the same by piano keys depressed.

Whatever the count, you'd have to multiply that by each possible root, of which there are 12. If you count typical enharmonics, there are 17. If you count B♯, C♭, E♯, and F♭, then there are 21. If you count double sharps and flats, that's 35 different root notes. 35 times 7637 (if you trust me on that) is 267,295 different chords. Again, you'd have tons of enharmonic chords.

This is an interesting theoretical question. I wrote an algorithm to explore the possibilities and I asked a few questions here to help me do it. (See this, this, and this if you're interested.) You can check out the fruits of my labor here:"

 

http://tomweissmusic.com/chords/


Edited by lettuce, 29 July 2018 - 20:15.


#2 Raul (ulneiz)

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Posted 29 July 2018 - 23:24

About this I observe 4 characteristics to be treated:

 

1.- The purely mathematical. This means that it does not have to be limited to 10 notes, because it has 2 hands. For example, with Renoise you can play more than 10 notes at a time, and that would still be considered a chord (more than one different note that sounds at the same time). Even defending the human character, it would be possible to play the piano between 2 people. This would be 10 +10 notes, strictly speaking.

 

2.- Limited by the capacity of the human body. Here the 5 + 5 fingers would enter.

 

3.- Limited by the piano itself, by the separation between semitones. Between a semitone and another could be another note, they are not represented on the keys. It is clear that the theme is based on a traditional piano (octaves of 12 notes), but why limit yourself to that?

 

4.- The search for the useful (or adequate) chord. This does not mean that the chord sounds fine, beautiful or soft, but that the chord should be suitable for different cases. An exaggerated and strident chord may be appropriate for specific cases. It does not have to sound good. Then this would reduce the amount of valid chords, from a point of view of a adequate chord.

 

In any case, what is the use of setting a limit or looking for a number of combinations? In reality there would be no limits, beyond finding the right chords (that you hear in the ear), and here many combinations of a large number of notes are lost, because they do not sound adequate.

 

This reminds me when I built my VPDpro tool, with a module called ChordPad, that allowed to mix up to 7 notes. The tool had 59 chord names defined. It could travel up to 9 octaves changing the root note (and therefore moving all the other notes a semitone), because there were chords that occupied 2 consecutive octaves. Then they left 59 x 9 x 12 = 6372 combinations, which already seemed to me a very high number.

 

In the end all this of the chords is reduced to learning those that are suitable for each case, beyond what is technically possible. Not all the music composed should be designed to touch for a human being. It is possible to overcome that barrier. It is still a curious topic. When I started to know the most common chord names, I thought we (those interested in music) were a little crazy :smashed:.


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#3 4Tey

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Posted 30 July 2018 - 07:01

Download/listen to say the 'little' fugue in G-Minor by Bach (for example -> http://forum.renoise...-minor-bwv-578/ )  Do you hear just chords or do you hear notes that (when they are played together) happen to form chords or do you just hear notes in 4 separate tracks?



#4 gentleclockdivider

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Posted 30 July 2018 - 10:08

Download/listen to say the 'little' fugue in G-Minor by Bach (for example -> http://forum.renoise...-minor-bwv-578/ )  Do you hear just chords or do you hear notes that (when they are played together) happen to form chords or do you just hear notes in 4 separate tracks?

J.S. BAch was the master of counterpoint , two (monophonic) interwoven  melodies .

You can't really call these chords , a chord needs to consists of at least 2 intervals .( 3 tones ) .


Edited by gentleclockdivider, 30 July 2018 - 10:09.

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#5 4Tey

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Posted 30 July 2018 - 11:36

I find it an interesting question, and one that I'm unsure about (I must admit I've not really spent a lot of time thinking about.)  I assume then that you GCD are of the opinion that in the context of my example through Bach there are no chords, just notes.  I think that it is both personally.  Notes can form chords (naturally.)  If you take the beginning of pattern 7 of that fugue:
chrds.png
 
At line 0 we have A# D and G struck at the same time.  At that moment in time we have the chord say Gm?  At line 8 we have A C and F#, so maybe say D-7th (without the D) roughly would harmonize?  But in the case of this piece and style we don't analyse it to that level.  We don't put names to the chords formed, because the piece is written more as 4 separate parts/melodies that just happen to be forming chords every so often in time.
In pop music there is more of a shift to play say a C major chord in bar 1, then play A minor in bar 2, then play F major in bar 3 and ride (hopefully) a catchy melody over the top of those chords.
 
Another example given this simple note line:
Image2.png
Silly me(?) (after about a minute or two thought) would roughly write:
Image3.png
Doesn't sound that good, but hey.
 
Bach wrote:
Image4.png

 

[Addendum:]  Say there are 267,000+ chords, the challenge is to select some musical ones and put them into a good order/time :)


Edited by 4Tey, 30 July 2018 - 18:50.


#6 lettuce

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Posted 30 July 2018 - 21:37

I'm not 100% convinced by the exact number that this guy came up with but I think he considered most of the factors well and gave it a serious try and came close to the correct answer.

 

I would say, most of the time, it is not actually possible to press 10 keys with 10 fingers simultaneously. There would be too much stretching involved.

So maybe the maximum number of simultaneously pressed keys would be more like 8?

I have seen people press two adjacent keys with just the thumb from time to time, maybe that technique sould be taken into consideration.

 

There are some statements I think I disagree with such as :

 

"A minor third with an augmented fifth is really just a different major chord, so let's reject those."

 

Seems to me that this chord structure would be '0 3 8', not like another major chord. Maybe I am missing something.

 

You wouldn't want something like Cadd♯9omit3 because that ♯9 is better identified as a minor third.

 

Personally, I think it would be better identified as a minor 10th.

 

Also I would add the rule that if the chord has a gap of one octave or more in between each hands key presses it should not be considered a chord.

What I'm thinking is that It should only be considered  a chord if the two hands play adjacent octaves ( Im sure some people would disagree ).

 

In addition to these points I think inversions should be counted as separate chords, so the total number of playable chords on a piano or keyboard may end up much higher than the figure stated as the final result above.

 

I have to say I totally agree with Raul in that, when it comes to computer music the chord count is not limited by number of total fingers of the individual ( or group ) and microtonal stuff would make the number of chords almost infinite depending on how many divisions are made in the complete range ( semitones, quartertones, eighthtones...128thtones...2048thtones? ).

 

If it could be all figured out properly and accurately each instrument could have 'specs' just like when you read computer reviews ( ie, maximum range, total number of playable chords, total number of playable harmonics etc ). Like when you are shopping for a ukelele or slide guitar, maybe even double chamber ocarina ( the label would have the 'specs' ).

 

Each chord could be further categorized taking into account which scales contain all the notes that make up the chord ( harmonic fields ). For example, you would have all the answers to questions like "which scales could I use to solo over a Cm7b5 chord?", "Which chords could I play over B hungarian gypsy minor?"...

 

It is such a difficult question. So many factors to consider ( double flats, double sharps, enharmonic equivalents, usefulness, playability, naming conventions etc )...If someone could get the algorithm completely correct, which seems near impossible, it would be the basis for the best chords and scales dictionary the world has ever seen. I would also include correct ( perhaps meaning most efficient ) fingering for each chord.

 

'Size of hands' and 'size of keys' may be important factors to consider as well.

 

Thankyou for your time.


Edited by lettuce, 30 July 2018 - 22:15.






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