# A number sequence of a different kind

My brother and I spent some time hanging out this weekend and he taught me a specific sequence of numbers during a particular activity.

58, 567, 57, 578, 58, 58

What does it represent and what were we doing?

Some more sequences:

357, 356, 357, 45, 346, 357
135, 245, 235, 24, 235, 135
357, 467, 457, 46, 457, 357
81012, 81011, 81012, 910, 8911, 81012
6810, 7910, 7810, 79, 7810, 6810
81012, 91112, 91012, 911, 91012, 81012
91012, 91113, 91112, 911, 91112, 91012


Hints:

- Our activity didn't require electricity
- Taught is a key word. These sequences are memorised for a specific purpose.
- The sequence lengths are important. To elaborate upon this, the fact that there are the same number of groups per sequence is very useful information.
- My brother knows these sequences very well because he uses them for a living.

• You were doing a puzzle, and this is a number sequence. Am i right ? :D More seriously I'll work on this one. Aug 11 '15 at 9:09
• haha :D Not as meta as that, lol.
– user2674
Aug 11 '15 at 9:31
• 4 very good and 2 very very BAD rounds of golf? Aug 11 '15 at 14:42
• If you press these number on a Nokia phone you havea really nice song!
– Alex
Aug 11 '15 at 16:25
• You were watching TV and channel-hopping between a very large number of channels. You must be paying a fortune. And you must have a very short attention span. The last four lines are the religion and craft channels. Aug 12 '15 at 0:51

It looks like fingering instructions for some strange scales on a guitar. That would explain why

1. there's always six of the numbers,
2. they can always be split into concatenated strictly rising finite sequences of small integers with small differences (like 91112 -> 9 11 12),
3. the individual entries do not exceed 12 by much,
4. the fourth sequence is one element shorter.

It's also compatible with the provided hints. The only problem is that I tried playing them and they don't sound like anything usual. But that could simply be a nonconventional style or not the default tuning, perhaps even a different but related instrument.

Update: You were playing guitar and practising the following scales (only first octave listed, then it repeats as high as fingers reach without leaving position):

• 5 8 5 6 7 5 7: A C D E♭ E G A: hexatonic blues scale from A [1]
• Lines 1 and 4 in "Some more sequences" (differing only by a constant shift of 5 positions, i.e., G->C): G A B C D E♭ F G: "major minor" scale as described in [2]
• Lines 2, 3, 5, and 6 (ditto, from F, G, B♭, C, respectively): F G A B C♯ D E F: "Lydian raised 5th" [2]
• Last line: C♯ D E F♯ G♯ A♯ B C♯: "Phrygian raised 6th" [2]

Alternatively, all the heptatonic scales could just be of one type (e.g., all major minor), just not starting from the base tone. The most likely explanation, subjectively speaking, is that they are "melodic ascending minor" scales [2] from C, D, E, F, G, A, B, C (this would be the full C-major scale in order). But the above is a more precise formulation for as a matter or principle you wouldn't start a scale on something that is not its first tone.

• This is mostly right. If you can specify what the scales are, I'll give you a checkmark.
– user2674
Aug 20 '15 at 14:26
• After a bit of research and guesswork I identified the first in the topmost of these: jayskyler.com/images/Guitar-Fingering-Chord-Scale-Chart-Diagram/… The other ones are probably also used in blues. I can't know them all. Aug 20 '15 at 15:33
• Or it could be some n-tonic (mixed hexa and hepta) variants. Aug 20 '15 at 15:43
• OK, I have them all, I'll put them into my answer. Aug 20 '15 at 15:53
• what does your brother do for a living? @Stacey
– JMP
Aug 21 '15 at 5:57

Is this some kind of dance with six steps which can be performed doing serveral of those 6 step sequences? I noticed that the last number is the same as the first number in each sequence.

The numbers might indicate positions on a floor which you have to touch with your arms and legs.

• You're closer than the other guesses, but each number represents a more specific purpose that is not arbitrary (like a body position).
– user2674
Aug 17 '15 at 21:59