The Significance of The Number 8.

The Significance of The Number 8.

I’ve always thought it was interesting that while we musicians traditionally count in 4’s, dancers count in 8’s. But it wasn’t until just now that I made a connection that I’ve never made before…

…As a community integrationist, my job is to help special needs people integrate into the general population in inclusive spaces. So right now I’m at a line dance with one of my participants because he loves to dance. Two young couples walk in, and the dance caller asks if they’re familiar with line dancing. One of the gentleman comments, “I can’t dance, I have two left feet…”. The caller responds, “Well, can you count to eight? If you can count to eight, you’ll be fine!”.

For a moment, a spark of light flashed… …Now, I’ve known for a long time now that dancers count in 8’s but I never considered that 8 is also a very significant number in it’s own right for us musicians. 8 is the number of the diatonic scale, the most common scale in western theory. But this also means that counting the notes of the scale equals 8 counts in 4/4 time. In other words, the diatonic scale is perfectly suited to count for dancing.

This may not be the most exciting or insightful revelation, but things like this fascinate me. Maybe it’s because I’m a keys players and the diatonic scale is so foundational to our study. But how did we end up with eight distinct pitches, instead of seven or nine? Aren’t there other scale systems that include notes outside of traditional western theory?(I’m not talking about scales that utilize accidentals, or modes of course. Rather, I mean pitches you wouldn’t find in any scale system @A440; Or even scales that aren’t modal but use a more custom pitch system). I feel like in the past I heard rumors that there was a pitch missing from the piano, but I never followed up on it. Whatever the case, it’s like every time I feel like I understand the dynamics between music and dance, there’s always something left to surprise me.

Re: The Significance of The Number 12.

I would vote for the number 12, as in 12 notes of the chromatic scale, 12/8 time signature (as would Bach).
Lots of interesting googleable material for “tonality and meter” or “pitch and time” out there.
My own particular interest is in it’s divisibility, of most note by both 3 and 4.

Re: The Significance of The Number 8.

It’s nothing to do with scales, pitches, etc, but all to do with dance figures, e.g. Dashing White Sergeant starts with 8 steps to the left followed by 8 to the right. All the ensuing figures are based on 8 bars of music or multiples of. Many, though not all, dances are based on 32 bars of music, during which there will be figures based on 8 bars or multiples of: one run of 32 bars will be one round of the dance, then you repeat the pattern again: in a set dance with, say, 4 couples, there will then be a new “top couple” to take up the next round of the dance.

Re: The Significance of The Number 8.

There are 7 pitches in a scale, not 8. Then you move to the octave.

In Bulgarian dance the meters are compound combinations of 2s and 3s. The 2s are one step on each foot, the 3s have an extra step with one of the feet, a kind of pause in the rhythm.

In a waltz, we count to 3 or 3x2, in a jig 2x3 or 3x3 for a slip jig.

So no we don’t just count in 4s or 2s.

Re: The Significance of The Number 8.

As noted by @sally, there are 7 tones in a major scale. If you play them as you suggest you land on the octave on eighth beat, which is irritating because really you want to arrive here on the ninth beat (the first beat of bar 3, in other words).

The bebop major scale includes the passing note Ab (in C major) which helps to solve this problem. Try it, it lines up with your count much more conveniently than the diatonic major because you land on the octave at the start of bar 3.

You can of course add in all sorts of passing notes into your runs to make you land on the right note at the right time.

You could also try out the diminished scale. As a true 8 note scale it falls into your counting nicely. (It is also interesting because where the major is ‘symmetrical’ every 7 notes, the diminished, as a repeating half-step whole-step pattern, is symmetrical every 2 notes. Which means phrases can be moved around it by a minor third while remaining ‘in-scale’.)

The real significance of the notes in the major scale comes from the harmonics of the overtone series.

Re: The Significance of The Number 8.

I know that there are 7 tones in a major scale, but I would argue that a diatonic major scale is *incomplete* without it’s octave note. Which is where I get the number 8. Is my theory faulty with this logic? If so, that’s embarrassing because it’s the entire premise of the discussion ’:D

Re: The Significance of The Number 8.

I’ll never hear the song Do-re-me in the same way, again.

Posted by .

Re: The Significance of The Number 8.

In a diatonic scale there are 7 intervals and that takes eight notes.

Posted by .

Re: The Significance of The Number 8.

I wonder if that’s why they call it an octave.

Posted by .

Re: The Significance of The Number 8.

Jerone, your diatonic scale over one octave has eight notes but over two octaves has fifteen notes, so it doesn’t count in eights - more like 7n+1, where n is the number of octaves.

Re: The Significance of The Number 8.

We have two feet for dancing, you can rock left and right with a rhythm, up and down to beat with a hand, powers of two, two, four, eight, sixteen, thirty two. Makes sense! (Which is not to say that there aren’t other options.)

My understanding is that if you go far enough up the harmonic series you get to something very like a diatonic scale - as played by natural horns.

Re: The Significance of The Number 8.

That got me thinking…I wonder how many distinct microtones the ear can hear, in an octave?

Re: The Significance of The Number 8.

“My understanding is that if you go far enough up the harmonic series you get to something very like a diatonic scale” For a (very) comprehensive account see https://archive.org/details/onsensationsofto00helmrich (published 1895 and still in print).

The gist of it is that as you build up a scale starting with the most consonant intervals with the tonic (octave, fifth, fourth etc) by the time you get to seven notes all the big gaps and have been filled and the ones you have are musically useful (for western music) and of roughly two sizes ( one or two semitones). Adding any more in means using less consonant notes and consecutive intervals smaller than all the others.

I guess that’s why to ‘western ears’ accidentals sound, well, accidental. Do blue notes still sound blue to those immersed in such music?

Re: The Significance of The Number 8.

“My understanding is that if you go far enough up the harmonic series you get to something very like a diatonic scale - as played by natural horns.”

Except that the eighth and sixteenth notes of the harmonic series will be the same (as in name) as the first note (root), leaving another seven in between which means that there will be nine notes making up that octave. The eleventh and thirteenth notes of the series are particularly “out”.
See here: https://www.audiolabs-erlangen.de/resources/MIR/FMP/C1/C1S3_HarmonicSeries.html

Re: The Significance of The Number 8.

“That got me thinking…I wonder how many distinct microtones the ear can hear, in an octave?”

I read recently that a musically well-trained ear can differentiate consecutive tones 5 cents apart; for the average human ear, it is around 10 cents. There’s not much point having notes that are only detectable by a trained musician can hear, so we’ll stick with 10 cents… There are 1200 cents in an octave, so that’s 120 microtones.

I think there is a little more to it, however, that simply how narrow an interval one can hear. We conceptualise a scale as sort of a framework with x-number of ‘points’ on it. With just 7 points, it is easy to perceive the relationships between the different points; with 12, the relationships can be a little more abstruse; with 25 (as in Arabic, Persian and Indian classical music), it takes a higher level of attunement, yet not insurmountable – but it is probably no accident that it stopped there. Whilst it may be possible to hear much smaller intervals between consecutive tones, it would be much more difficult to identify each tone relative to a ‘tonic’ – which is what we need to be able to do to understand them as part of a musical framework.

Re: The Significance of The Number 8.

If we’re talking musical numbers, my vote goes for five - the pentatonic. It preceded the diatonic way before the Greeks started analysing and theorising about the subject. It seems to be a natural scale.
In a TED Talk Bobby McFerrin give a marvellous demonstration of just how instinctive the major pentatonic is.
https://youtu.be/ne6tB2KiZuk

Re: The Significance of The Number 8.

I don’t think it’s *directly* to do with the harmonic series, as in taking notes from them. The more consonant notes are small number frequency ratios with the tonic. (2:1 octave, 3:2 perfect fifth, 4:3 perfect fourth, 5:4 major third etc). The reason that they are consonant is that the small-number ratio means that there are fewer ‘clashes’ amongst the notes of the two harmonic series. Beats resulting what IIRC Helmholz’s translator calls ‘roughness’.

Even those first ratios are enough point to a something of about the sizes of semitones and tones being useful. If you want to make up a musical scale with no intervals smaller than a semitone or larger than twice that, and to get fairly consonant intervals *between* some other pairs of notes in the scale, you end up with the diatonic scale. But you could stop at a pentatonic scale and have a higher proportion of the note pairs that don’t clash. Brilliant clip that.

Or, of course, you could use different musical system and maybe not have the number 8 so prominent.

Q: Are there cultures with predominantly 12 bar dances. Divisible by 3 as well as 2 and 4. Might give more options for figures,

Re: The Significance of The Number 8.

@DonaldK - The eleventh and thirteenth notes of the series are particularly “out”.
Although note here that it is our equally tempered scale - or as I like to call it, equally out of tune in all keys - that is “out”, and not the harmonic series (compare the superposition of each at the end of the article).

Re: The Significance of The Number 8.

“…it is our equally tempered scale…that is “out”…”

True, Rick, but not all the common ratios occur in the harmonic series so, for example, there is no 4:3 for a perfect fourth (or 6:5 for a minor third). There is a fourth (ratio 11:8), but it’s by no means perfect.
And, whether or not they are “out”, that fourth octave still has nine notes rather than eight.

Re: The Significance of The Number 8.

A lot of interesting comments made, for sure. That’s all i’m allowing myself to say, as I am admittedly the least informed/educated person in the room on this topic. Now, I have a Tedtalk to watch and some reading material to get into, so thanks everyone!

Re: The Significance of The Number 12.

@DonaldK
The interval between the 1st and 2nd harmonics (C2-C3) is an octave (ratio 2:1)
The interval between the 2nd and 3rd harmonics (C3-G3) is a perfect fifth (ratio 3:2)
The interval between the 3rd and 4th harmonics (G3-C4) is a perfect fourth (ratio 4:3)
The interval between the 4th and 5th harmonics (C4-E4) is a major third (ratio 5:4)
The interval between the 5th and 6th harmonics (E4-G4) is a minor third (ratio 6:5)
I’ve personally made no argument for the number 8 - I support the number 12.

Re: The Significance of The Number 8.

Rick, I meant that there is no perfect fourth of the scale. Obviously all possible ratios can be found within the infinite harmonic series but your never going to find a note that is a perfect fourth in relation to the first harmonic.

But all this is beside the point. I was trying to argue that the diatonic scale does not appear in the harmonic series.

Re: The Significance of The Number 8.

“I was trying to argue that the diatonic scale does not appear in the harmonic series.” My post refering to Helmholtz was agreeing that the scale doesn’t ‘come from’ the harmonic series.

If you pick two notes that have a small-number frequency ratio they will be consonant because they share some frequencies in their harmonics. Not because you can find them both in a harmonic series.

Re: The Significance of The Number 8.

First of all, I would have thought we’d known Jerome for long enough to trust that he knows his way round the major scale.

To go back onto the topic of rhythm and structure, I think there’s a simple symmetry that goes a long way to explaining what’s going on in dance music: step forward, step back. Every action can be paired with it’s reverse, and that leads naturally to powers of two: two steps forward, two steps back, around for four, back for four, and so on. Each power of two gives you a number of beats into which certain dance steps fit.

Posted by .

Re: The Significance of The Number 8.

Thank you Calum.

In my defense, since no one else has mentioned it yet: To make 8 dance counts work consistently in the scheme of my 8 note scale, all you have to do is simply start over from the tonic, or repeat the tonic. Since pitch is circular(or rather, helical) I don’t believe it’s unnatural to assume that a new phrase could start on a repeated note.

However, I say all of that with the understanding that my original questions have been answered thoroughly and that I no longer believe that the “8-count” in dance has anything to do with the diatonic scale and it’s octave. Though, it is clear that the number 8 is still very significant in it’s own right, as a multiple of 2, and 4, and a quotient of 32.

Re: The Significance of The Number 8.

My wife and I used go to sequence dancing where all couples did the same steps
We had a number of keyboard players but one kept adding an extra bar (measure) to the tune.
It caused confusion, but we would listen to the tune and start the sequence at the right time.
Not everyone did.