Music Theory Challenge

[Nightscape]

Here is a series of music theory-related questions.  More like mental excercises though.  A prize to whoever can answer them!

(They are listed from easiest to hardest.  You don't have to answer all of them, just whatever you can.)

1.  What is the key signature for Cb major (just list the notes flatted)?

2.  Write out the Lydian scale starting on C.

3.  Write out the sharp 4, flat 7 scale starting on G# (also known as Lydian-Myxolydian scale.)

4.  Write out the 2nd inversion dominant seventh chord of D# major.

5.  What is the key signature of Abb (A double flat) major?

6.  Write out the scale of Ex (E double sharp) major.

7.  Write out the Locrian scale starting on Bbb (B double flat).

8.  Write out the melodic minor scale (ascending and descending) of d triple sharp minor.

9.  How many sharps are in the key signature of G quadruple sharp major (count a double sharp as 2, triple as 3, etc)?

10.  What key signature contains the number of flats that is equal to the 18th number of the Fibonacci sequence?

[m1469]

Well that's it, I am taking up this challenge !  Primarily because I would like the prize (is it chocolate ?  I really need a BIG chunk of chocolate to give to xvimbi, don't ask why... shhhh it's a secret  ).


Now, actually my theory in general is maybe not so sharp, so I am going to do this and will report back to you promptly (no, but really, pssst... is it chocolate 'cause I really need a big chunk, okay?... help me out here )


m1469

[cadenz]

1.  What is the key signature for Cb major (just list the notes flatted)?

Bb Eb Ab Db Gb Cb Fb

2.  Write out the Lydian scale starting on C.

CDEF#GABC

3.  Write out the sharp 4, flat 7 scale starting on G# (also known as Lydian-Myxolydian scale.)

G# A# B# Cx D# E# F# G#

4.  Write out the 2nd inversion dominant seventh chord of D# major.

A# C# D# Fx

5.  What is the key signature of Abb (A double flat) major?

Bbb Ebb Abb Dbb Gb Cb Fb

6.  Write out the scale of Ex (E double sharp) major.

Ex F### G### Ax Bx C### D### Ex

7.  Write out the Locrian scale starting on Bbb (B double flat).

Bbb Cbb Dbb Ebb Fbb Gbb Abb Bbb

8.  Write out the melodic minor scale (ascending and descending) of d triple sharp minor.

D### E### F### G### A### B### Cxx D### C### Bx A### G### F### E### D###

9.  How many sharps are in the key signature of G quadruple sharp major (count a double sharp as 2, triple as 3, etc)?

29

10.  What key signature contains the number of flats that is equal to the 18th number of the Fibonacci sequence?

1,1,2,3,5,8,13,21,34,55,89,144,233,377,610,987,1597,2584,4181

2584?

F with 369 flats

zzzzz

please mark my answers

@ if they're all wrong

[Nightscape]

Cadenz, that is amazing!  And under two hours after posting it, too!

You are right on every one except on #4, I wanted the chord in the key of D# major, instead of spelled on D# major.  But I didn't make that too clear and you obviously know what you are doing, so I'll give it to you! 

Wow, I haven't had time to come up with a prize yet.  But in the meantime....

[m1469]

1. What is the key signature for Cb major (just list the notes flatted)?
flats: B-E-A-D-G-C-F

2. Write out the Lydian scale starting on C.
  C, D, E, F#, G, A, B, C

3. Write out the sharp 4, flat 7 scale starting on G# (also known as Lydian-Myxolydian scale.)
G#, A#, B#, C#, D#, E#, F#, G#

4. Write out the 2nd inversion dominant seventh chord of D# major.
E#, G, A#, Cx

5. What is the key signature of Abb (A double flat) major?
 Bbb, Ebb, Abb, Dbb, Gb, Cb, Fb

6. Write out the scale of Ex (E double sharp) major.
 Ex, Fx#, Gx#, Ax, Bx, Cx#, Dx#, Ex (How do you write triple sharps?)

7. Write out the Locrian scale starting on Bbb (B double flat).
Bbb, Cbb, Dbb, Ebb, Fbb, Gbb, Abb, Bbb

8. Write out the melodic minor scale (ascending and descending) of d triple sharp minor.
dx#, ex#, fx#, gx#, ax#, bx#, cxx, dx#     --    dx#, cx#, bx, ax#, gx#, fxx, ex#, dx#

9. How many sharps are in the key signature of G quadruple sharp major (count a double sharp as 2, triple as 3, etc)?
29

10. What key signature contains the number of flats that is equal to the 18th number of the Fibonacci sequence?
if one is counting the number of flats that each unique note of the scale gets, then it can be the key of :  C (approx)369 flat  Major

approximately totalling 2584 flats

(I know Cadenz already posted (blast !!!), but I want to anyway  )

m1469

[m1469]

Besides, I would like to draw your attention to the fact that Cadenz has a Cx in his answer for number 3, when it should be only C# as it should only be a half step between the 3rd and 4th note of the mixolydian scale.. 


he he, I am mean maybe (all in good humor  ).

[Nightscape]

I think we're ready for something more difficult.  Up for the challenge, Cadenz and m1469?
Let's begin!

11. Name the the enharmonic key with the lowest number of sharps or flats of: C with 4111 flats.

12.  Write out the whole tone scale starting on the note that is the 390th sharp in the key that has a number of sharps equal to the square of the 12th number of the fibonacci sequence.

13.  In the matrix for the 12-tone row {Cx, Abb, Dbb, Gbb, A#, Eb, G#, Bx, F#, Cb, E, Bbb}, what note is located at 4,7? (Where 4,7 means the fourth number across, seventh number down.)

14.  If one were to add up all of the numbers of sharps used in the first 28 sharp key signatures, and subtract that amount from the sum of the numbers of flats in the first 52 flat key signatures, the remainder would be equivalent to the number of sharps of what key signature?

15.  Taking the square root of the number of double flats in the key signature of Abb major, then dividing that number by the number of triple sharps in the key signature of D### major, then multiplying that number by the number of quadruple flats in the key signature of Ebbbb minor, then finally taking that number and adding it to the number of quintuple sharps in the key signature of B##### minor, you would have a number that when rounded up to the nearest whole integer, is the number of flats in what minor key signature?

[Nightscape]

Besides, I would like to draw your attention to the fact that Cadenz has a Cx in his answer for number 3, when it should be only C# as it should only be a half step between the 3rd and 4th note of the mixolydian scale.. 


he he, I am mean maybe (all in good humor  ).

Actually, m1469, it is the Lydian-Mixolydian combo scale I asked you to spell.  In that case, the fourth is raised and would indeed be Cx.

[m1469]

Okay, okay my bad.  Sorry, but now I am going to be really rude  . 

Question: As for question # 10; wouldn't the key of F with 369 flats technically not work as F already has one flat (I know, I know, I am ridiculous) ?  Or does it not matter ?   I am confused.  Anyway, this next challenge is going to take me even longer (we'll see how much brain I have left).  But, I am up for it.

(I want to win  )

[Dazzer]

you guys are way too smart... - all these fly over my head -

[Nightscape]

Okay, okay my bad.  Sorry, but now I am going to be really rude  . 

Question: As for question # 10; wouldn't the key of F with 369 flats technically not work as F already has one flat (I know, I know, I am ridiculous) ?  Or does it not matter ?   I am confused.  Anyway, this next challenge is going to take me even longer (we'll see how much brain I have left).  But, I am up for it.

(I want to win  )

Actually, you'll find a pattern if you do the following.  F has one flat, Fb has 8 flats, Fbb has 15 flats, Fbbb has 22 flats, etc.  This pattern will eventually hit 2584.  To check his answer, simply multiply 369 by 7 and add one.  You'll find that he is indeed correct.  The answer you gave, has 2583 flats, one less than needed.  You would have to go up one more key in the circle of fourths to get the last flat, which is F with 369 flats.

[Derek]

yikes.    and I thought *my* interest in music theory exceeded that which was neccessary to be a creative musician.

[cadenz]

11. Name the the enharmonic key with the lowest number of sharps or flats of: C with 4111 flats.

F major

12.  Write out the whole tone scale starting on the note that is the 390th sharp in the key that has a number of sharps equal to the square of the 12th number of the fibonacci sequence.

12th fibonacci sequence number: 144
squaring this gives 20736
key with this many sharps: D with 2962 sharps
the 390th sharp?
well the notes get sharpened in this order:
fcgdaebfcg.. etc

so it should be A getting a 56th sharp?

this A in this key.... D with 2962 sharps has 2962 sharps

A2962# B2962# C2963# D2963# E2963# G2962# A2962#

 

or enharmonically
G A B C# D# F G

13.  In the matrix for the 12-tone row {Cx, Abb, Dbb, Gbb, A#, Eb, G#, Bx, F#, Cb, E, Bbb}, what note is located at 4,7? (Where 4,7 means the fourth number across, seventh number down.)

but its a 12x1 matrix? 

{Cx,  Abb, Dbb, Gbb, A#, Eb,  G#,  Bx,  F#,  Cb,  E,   Bbb}
{Abb, Dbb, Gbb, A#,  Eb, G#,  Bx,  F#,  Cb,  E,   Bbb, Cx}
{Dbb, Gbb, A#,  Eb,  G#, Bx,  F#,  Cb,  E,   Bbb, Cx,  Abb}
{Gbb, A#,  Eb,  G#,  Bx, F#,  Cb,  E,   Bbb, Cx,  Abb, Dbb}
{A#,  Eb,  G#,  Bx,  F#, Cb,  E,   Bbb, Cx,  Abb, Dbb, Gbb}
{Eb,  G#,  Bx,  F#,  Cb, E,   Bbb, Cx,  Abb, Dbb, Gbb, A#}
{G#,  Bx,  F#,  Cb,  E,  Bbb, Cx,  Abb, Dbb, Gbb, A#,  Eb}

  if this is how its meant to continue perhaps then it'd be Cb

14.  If one were to add up all of the numbers of sharps used in the first 28 sharp key signatures, and subtract that amount from the sum of the numbers of flats in the first 52 flat key signatures, the remainder would be equivalent to the number of sharps of what key signature?

number of sharps: 28*(1+28)/2 = 406
number of flats:  52*(1+52)/2 = 1378

1378 - 406 = 972

F with 139 sharps major

15.  Taking the square root of the number of double flats in the key signature of Abb major, then dividing that number by the number of triple sharps in the key signature of D### major, then multiplying that number by the number of quadruple flats in the key signature of Ebbbb minor, then finally taking that number and adding it to the number of quintuple sharps in the key signature of B##### minor, you would have a number that when rounded up to the nearest whole integer, is the number of flats in what minor key signature?

(2/5)*3 + 2 = 3.2 rounds to 3
C minor

this doesn't feel much like music anymore

[pianonut]

#1  Dbb

#2  C##  D## E# F## G## A## B#

#3  Eb

#4  ns(28)-nf(24)=x    key of E

#5  too much work

[m1469]

Okay, I know I am taking a lot longer than the others here, but I don't care I just want to understand.  So, if I may, I have a few questions before I can confidently get anywhere with this stuff.



1. Name the the enharmonic key with the lowest number of sharps or flats of: C with 4111 flats.

Q-  Well, here I am not even sure where to begin.  Is there any way to give a hint on how to do this without giving away the answer?  I don't understand the principle.


2. Write out the whole tone scale starting on the note that is the 390th sharp in the key that has a number of sharps equal to the square of the 12th number of the fibonacci sequence.

Q- Uh...


3. In the matrix for the 12-tone row {Cx, Abb, Dbb, Gbb, A#, Eb, G#, Bx, F#, Cb, E, Bbb}, what note is located at 4,7? (Where 4,7 means the fourth number across, seventh number down.)

oh, heh, forget my last question here, I think I will figure this one out.

4. If one were to add up all of the numbers of sharps used in the first 28 sharp key signatures, and subtract that amount from the sum of the numbers of flats in the first 52 flat key signatures, the remainder would be equivalent to the number of sharps of what key signature?

Q- not sure what to ask


5. Taking the square root of the number of double flats in the key signature of Abb major, then dividing that number by the number of triple sharps in the key signature of D### major, then multiplying that number by the number of quadruple flats in the key signature of Ebbbb minor, then finally taking that number and adding it to the number of quintuple sharps in the key signature of B##### minor, you would have a number that when rounded up to the nearest whole integer, is the number of flats in what minor key signature?

This one I will figure out, I think (he he).


Thanks,


m1469  *humbly goes back to indexing the forum*

[m1469]

I will  modify as I go along.   Maybe I will figure the others out  :-


3. In the matrix for the 12-tone row {Cx, Abb, Dbb, Gbb, A#, Eb, G#, Bx, F#, Cb, E, Bbb}, what note is located at 4,7? (Where 4,7 means the fourth number across, seventh number down.)

my answer is : Gxx


p0   Cx   Abb   Dbb   Gbb   A#   Eb   G#   Bx   F#   Cb   E   Bbb
p7   Bbb   
p2   E   A   D   G   Ax#   E#   Gx#   Bxx   Fx#   C#   Ex   B
p9   Cb
p4   F#   Ax   Dx   Gx   Axx#   Ex#   Gxx#   Bxxx   Fxx#   Cx#   Exx   Bx
p11   Bx
p6   G#   Axx   Dx#   Gxx
p1   Eb   Ab   Db   Gb   Ax   E   Gx   Bx#   Fx   C   E#   Bb
p8   A#
p3   Gbb   A#   D#   G#   Axx   Ex   Gxx   Bxx#   Fxx   Cx   Ex#   B#
p10   Dbb
p5   Abb   Ax#   Dx#   Gx#   Axxx   Exx   Gxxx   Bxxx#   Fxxx   Cxx   Exx#   Bx#


5.   Taking the square root of the number of double flats in the key signature of Abb major, then dividing that number by the number of triple sharps in the key signature of D### major, then multiplying that number by the number of quadruple flats in the key signature of Ebbbb minor, then finally taking that number and adding it to the number of quintuple sharps in the key signature of B##### minor, you would have a number that when rounded up to the nearest whole integer, is the number of flats in what minor key signature?


Here is the equation I got : ((2/5) * 6) + 5 = 7.4 rounded up to 11

answer : Fb minor


m1469

[pianonut]

i think we're getting into hypothetical since the very first question was the flats involved in Cb (which is actually the key of B).  switching this around, the enharmonic of C would be B# - which has many sharps, but no flats, therefore - i change my answer to be

the LEAST amount of flats would be the enharmonic key of B# - zero flats, in the key of C.  what does the 4111 mean?

[pianonut]

oh, i see, you want Fbbbbbbbbbbbbbbb?  lets see, that would be F=1 Fb=8  Fbb=15  Fbbb=22  Fbbbb=29  Fbbbbb=36  Fbbbbbb=43  Fbbbbbbb=50

F(7)/4000 = approx. 80 flats plus 16 more = about 96 or 97 flats.  is this the least amount?

[pianonut]

7/4111=587 sharps in the key of B# (when adding that many afterwards? B###############?)

[Daevren]

11. Name the the enharmonic key with the lowest number of sharps or flats of: C with 4111 flats.

4111 / 12 = 342,...

342  * 12 = 4104

4111 - 4104 = 7

C - 7 semitones = F

12.  Write out the whole tone scale starting on the note that is the 390th sharp in the key that has a number of sharps equal to the square of the 12th number of the fibonacci sequence.

Haha.

Assuming 0 doesn't count, like Cadenz did.

144^2 = 20736

20736 / 7 = 2962,...

2962 * 7 = 20734

20736 - 20734 = 2

390 / 7 = 55,..

55 * 7 = 385

390 - 385 = 5

Fifth sharp is the sharp on A to make it A#

So the 390th sharp makes A 56#

Whole tone scale on  A 56#:

A 56#  B 56#  C 57#  D 57#  E 57# G 56#

Which is enharmonic to F G A B C# Eb

Cadenz, why did you add the sharps of the original key? You should have started a whole tone scale on the note you found.

I am quitting now. Waste of time

[pianonut]

if Fbb = 15x88=1320 flats  but that is not the enharmonic of C

then possibly E would be quadrupled?  let's see Ebbbb = ?

how about Gbbbbbbb?  that would be the same as F in terms of sharps=flats right?

how many flats?  oh, i give up. I go back to Dbb.

lets see: Db = 5 flats
Dbb=12
12 flats x 7.5 octaves = @900 flats

how can this be?  this is an 88 key keyboard.  whew!  and we are looking for the least amount of flats?
 

[m1469]

Okay, I am stuck and I would also like some clarification.  It reads "the square of" which I understand to mean taking the square of 144 vs 144 squared.  Which do you desire?


12. Write out the whole tone scale starting on the note that is the 390th sharp in the key that has a number of sharps equal to the square of the 12th number of the fibonacci sequence.

square of 144 = 12 (sharps)

12 sharps = B# Major (or Gx minor)

... a little stuck

[pianonut]

mayla, we're almost ready to work for the fbi.  keep you eyes peeled for numbers.  they are all important.  license plates, ss#, telephone, etc.  if you can add them up backwards and forwards, speak a little russian, arabic, french...this could be an interesting life.  of course webern went a little off the edge from all this.  and who knows why he was shot.  simply went out to smoke a cigarette, and there he was - dead on the ground.  numbers did him in.

[Nightscape]

Alright..... wow a lot got posted last night.  Let me clear up some questions for m1469 first.

When I say square of 12th number, I mean the 12th number multiplied by itself.  What you have is the square root of the 12th number.

Your answer for number 13 (the matrix one) is correct!  That's a tough one.

For question 11, I want you to tell me the key that is enharmonically equivalent to     {C 4111b} (C with 4111 flats in the key signature.)

----
Cadenz, you're answers are all right except for numbers
12, 13 and 15. 
On 12,  The key that is used is really irrelevant.  Just extra info.  What you're looking for is the 390th sharp in the circle of fifths.  To get this do long division.  Divide 390 by 7, and you will have 55 with a 5 remainder.  Then take 7 and subtract it from the remainder.  This will get you 2.  The note then you are looking for is two perfect fifths above C 55#.  That would be D55#.  From there, construct your whole tone scale.


On 13, that is not how to construct a 12 tone matrix.  Let me explain.  You got the top row correct.  Now to get the second note of the leftmost column, find the interval between the first two notes of the top horizontal row and the note you are looking for is the note that is in the opposite direction from the first note of the leftmost column. For example:

A,B,C,D,E,F,G,
G,A,Bb,C
Ab,Bb,B   ...etc.

On 15, remember to round the number up, not to the closest integer.

pianonut, you might want to look at Cadenz's methods for getting the answers.  You are definately on the right track, just remember we are in fact talking about the hypothetical, the theoretical now.  So even if such a key or note doesn't exist in the real world, that's okay for our purposes.

[pianonut]

ok. i will review cadenz's formulas.  can't believe i am on the right track.  tend to find correct answers by free thinking - not using absolutes, but approximations.  for instance, i might be the one that finds the needle in the haystack by sitting on it.

[m1469]

15.   Taking the square root of the number of double flats in the key signature of Abb major, then dividing that number by the number of triple sharps in the key signature of D### major, then multiplying that number by the number of quadruple flats in the key signature of Ebbbb minor, then finally taking that number and adding it to the number of quintuple sharps in the key signature of B##### minor, you would have a number that when rounded up to the nearest whole integer, is the number of flats in what minor key signature?

Okay, I take it that I got number 15 wrong?  I am just curious what I am not doing correctly ?  Here is how I went about it : 

The key of Eb minor has 6 flats, BEADGC, so wouldn't the key of Ebbbb minor have the same number of quadruple flats (= 6) as the number of single flats in Eb minor ?  I used the same (perhaps insufficient) logic for the key of B##### minor. The key of B minor, which normally has only 2 sharps, F and C, leaves 5 unsharped.  If the B suddenly becomes quintuple sharped, it would mean F and C are now sextuple sharped leaving the same five notes as in B minor quintiuple sharped = 5.

(I can't stop this challenge, I'm not giving up )


m1469

[dave santino]

Just as a reference to an earlier post, the lydian-mixolydian scale is more commonly referred to as lydian dominant. My interest in theory is mostly harmony and jazz thoery, especially wacky altered chords. That's the guitarist showing through!!! 

[pianonut]

#11   Bbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbb (B with 70 flats)

B - 5 sharps
Bb = 2 flats
Bbb = 2+7=9 flats
Bbbb=9+7=16
Bbbbb=16+7=23 flats
Bbbbbb=23+7=30 flats
Bbbbbbb= 37
Bbbbbbbb=42
Bbbbbbbbb=49
Bbbbbbbbbb=56
Bbbbbbbbbbb=63
Bbbbbbbbbbbb=70 flats  this work is unfinished.  didn't really get the idea fully, yet.

[Nightscape]

Okay, I take it that I got number 15 wrong?  I am just curious what I am not doing correctly ?  Here is how I went about it : 

The key of Eb minor has 6 flats, BEADGC, so wouldn't the key of Ebbbb minor have the same number of quadruple flats (= 6) as the number of single flats in Eb minor ?  I used the same (perhaps insufficient) logic for the key of B##### minor. The key of B minor, which normally has only 2 sharps, F and C, leaves 5 unsharped.  If the B suddenly becomes quintuple sharped, it would mean F and C are now sextuple sharped leaving the same five notes as in B minor quintiuple sharped = 5.

(I can't stop this challenge, I'm not giving up )


m1469

No, no!  Your answer is right.  I'm sorry for being misleading.  Although I think I did say that Cadenz's answer was incorrect.

[asyncopated]

I need to learn some music theory, so this is as good a place to start as any.   So I’m going try to answer all your questions WITH WORKING!

Music theory for the mentally insane.

1.
What is the key signature for Cb major (just list the notes flatted)?

The major scale as the following structure
TTSTTTS

Therefore, Cb Major would have
Cb (T) Db (T) Eb (S) Fb (T) Gb (T) Ab (T) Bb (S) and back

Since Cb is and enharmonic of B and B has 5 Sharps, Cb must have 5-12=-7 sharps or 7 flats ie.e all of them. (Same as cadenzs' and mayla's!)


2.
Write out the Lydian scale starting on C.

Let us first generalize, and consider scales with exactly 8 notes or 7 intervals.  Also, we assume that 12 semitones get us back to the same tone (modulo 12 semitones).  We also deal with symmetric ascending and descending scales only.

Let us also define the following

S-Semitone
T-Tone
U-augmented tone (Don’t know the technical name for the rest – basically an interval with 3 semitones)
V-bitone (4 semitones)
W- augmented bitone (5 semitones)
X- Tritone (6 semitones)


Notice that TTSTTTS ~ 2+2+1+2+2+2+1=12

We would first like to determine the number of possible scales with this structure.  Since an interval of 0 is not allowed, and the minimum interval is a semitone, we can simplify the problem by assuming that each not consist of at least one semitone and subtract 7, through out one from interval

So a major scale TTSTTTS can be represented as such 1+1+0+1+1+1+0=5.  Note that, all non zero numbers are admissible.  And they must add up to 5.  To get the number of scales possible with this structure, imagine 5 objects (numbers) with 6 partitions (pluses).  The number of structures like this is 11 Choose 5 which is 11!/(6!5!)=462 different scales!

Here is a list of them
1X 6S ~ 5  –  7!/(6!1!)=7 ways (must sound awful!)
1W  1T 5S ~ 4+1 -   7!/(5!1!1!)=42 ways
1V  1U 5S ~ 3+2 -   7!/(5!1!1!)=42 ways
1V  2T 4S ~ 3+1+1 -   7!/(4!2!1!)=105 ways
2U  1T 4S ~ 2+2+1 -   7!/(4!2!1!)=105 ways
1U  3T 3S ~ 2+1+1+1 -   7!/(3!3!1!)=140 ways
5T 2S ~ 1+1+1+1+1 -   7!/(5!2!)=21 ways (the usual scales/modes)

 Just to check 7+42+42+105+105+140+21=462 ! (opps, that is an exclamation mark, not a factorial)  Which is correct. 

So there are a list of the 21 usual scales that we know and their names (if any)

TTSTTTS – Major (Ionian)
TSTTTST – Dorian
STTTSTT – Phrygian
TTTSTTS – Lydian
TTSTTST – Mixolydian
TSTTSTT – Aelorian
STTSTTT – Locrian

Note the cyclic symmetry.  Here the semitones are 2-3 apart.  The other combinations are 1-4 and 0-5 as follows

TSTTTTS  STTTTST TTTTSTS TTTSTST TTSTSTT TSTSTTT STSTTTT

SSTTTTT STTTTTS TTTTTSS TTTTSST TTTSSTT TTSSTTT TSSTTTT

At this point, we assume that scales with the same number of semitones, tones etc are degenerate.  e.g. TTSTTTS and TSTTTST are degenerate

The Lydian scale given by the structure TTTSTTS would be
C (T) D (T) E (T) F# (S) G (T) A  (T) B  (S) And back (Think this is correct as well)

3.
Write out the sharp 4, flat 7 scale starting on G# (also known as Lydian-Myxolydian scale.)

The mixolydian sharp 4 scale is defined by the structure TTTSTST.  Comparing this with the mixolydian scale TTSTTST, we see that the forth is sharpened.

So,
G# (T) A#  (T) B#  (T) Cx (S) D# (T) E# (S) F# (T) and back  (Not the same as both!)
 
4.
Write out the 2nd inversion dominant seventh chord of D# major.

Root triad chords are given by the degrees
1 3 5

Common variations are as follows, with the number of semitone interverals
1 3 5 (major)  4 3 
1 b3 5 (minor) 3 4
1 3 #5 (augmented) 4 4
1 b3 b5 (diminished) 3 3

We ca also have harmonic extensions to the root chord.

1 3 5 7 (major seventh) 4 3 4
1 3 5 b7 (dominant seventh) 4 3 3

1 3 5 b7 9 (ninth) 4 3 3 4
1 3 5 b7 9  11 (eleventh) 4 3 3 4 3

Looking at the dominant seventh chord,

The D# scale looks like this

D# (T) E# (T) Fx (S) G# (T) A# (T) B# (T) Cx (S) and back

1 3 5 b7  These notes correspond to D# Fx A# C#.  The first second and third inversions are as follows
Fx A# C# D#
A# C# D# Fx
C# D# Fx A# -- I’m not sure how to do figured bass on this and I am not about to try.

So the answer is A# C# D# Fx  (Same as Cadenzs' but not m1469's ?!)

5.  What is the key signature of Abb (A double flat) major?

Abb (T) Bbb (T) Cb (S) Dbb (T) Ebb (T) Fb (T) Gb (S)

Cool!

Wow, that was fun, I will reply to the next 5 in the next post.

al.

[abell88]

4.
Write out the 2nd inversion dominant seventh chord of D# major.

Asyncopated, I think you missed something here...the dominant 7th chord should start on the dominant (eg. the dominant 7th chord of C major is G B D F).  The dom. 7th of d major would be A C# E G; therefore the dom. 7 of D# is A# Cx E# G#; 2nd inversion is:
E# G# A# Cx.

[asyncopated]

I see! I must have miss read the website on chords.  Just wondering if you can also have something C major sub-median 7 which would be A C E G?  Does that make sense?  But yes you must be right.
 
Ok on to more questions.

6. 
Write out the scale of Ex (E double sharp) major.
Ok we will try this another way.  The enharmonic of Ex major is F# major, which goes (Chopin’s fravourite key?)

F# G# A# B C# D# E#

Representing it as Ex (subtract a letter), you add one sharp to what is originally C and F, the two notes after the tone and two sharps to all the rest.

Ex Fx# Gx# Ax Bx Cx# Dx# (same answers as both, baring a representation for triple sharps)

7. 
Write out the Locrian scale starting on Bbb (B double flat).

We use the same enharmonic trick.  Bbb is an enharmonic of A.  Following the pattern STTSTTT

A Bb C D Eb F G

This time we (add a letter) to represent it as Bbb.  So all letters gain 2 flats except for what is originally E and B.

Bbb Cbb Dbb Ebb Fbb Gbb Abb.

(Where do you get these questions?)


8. 
Write out the melodic minor scale (ascending and descending) of d triple sharp minor.

The ascending melodic minor scale has the following intervals TSTTTTS
The descending minor scale has the same interval as the ascending Aelorian scale or altertively the decending Mixolydian scale.


Dx# minor is an enharmonic of F minor and has the same accidentals as Ab Major (the minor key is a minor third below – 5 semitones) which has the structure

Ab Bb C Db Eb F G

For rearranging to the aelorian scale F G Ab Bb C Db Eb

The ascending minor can be obtained by sharpening the sixth and seventh intervals and keep the same structure for the descending.

F G Ab Bb C D E – Eb Db C Bb Ab G F


There is another way to do this.  We know that the ascending melodic minor scale differs from the major scale by flattening the third.  Since Dx# is an enharmonic of F minor, we consider first F major by 

F G A Bb C D E.

Flattening the third, we get the ascending and flatten also the sixth and seventh to get the decending.

F G Ab Bb C D E – Eb Db C Bb Ab G F

We use the rule for subtracting letters – i.e. add one sharp to what is originally C and F and two to the rest.

Applying it once
E# Fx G# A# B# Cx Dx – D# C# B# A# G# Fx E#

And one more time
Dx# Ex# Fx# Gx# Ax# Bx# Cxx Dx# – Dx# Cx# Bx Ax# Gx# Fx# Ex# Dx#

(Same answer as Cadanz!)


9. 
How many sharps are in the key signature of G quadruple sharp major (count a double sharp as 2, triple as 3, etc)?


This is an enharmonic of B major!
So B C# D# E F# G# A#.  That make 5 sharps.  Recall that that subtracting a letter we add 2 sharps to all letters by 2 ( originally C and F) which we add 1. So we add 5*2+2=12 shapes, (which course make sense).  Since we do this twice, we get 12*2+5 = 29.


10.  What key signature contains the number of flats that is equal to the 18th number of the Fibonacci sequence?

The Fibonacci is governed by the recursive relation F(n+2) = F(n+1) + F(n) can be solved in the following way.  Assume that the solution is given by F= C a^n .  (Here ^ means power).  Where C and a are constants to be determined.  Inserting this into the relation, we find that

C a^(n+2)=C a^(n+1) + Ca^n.

And can therefore be reduced to a quadratic equation
a^2 – a -1 =0, which has solutions

a1=1/2*(1+sqrt(5)) [golden mean] and a2=1/2*(1-sqrt(5)).  We see that any linear combination of the two answers is admissible.  As such, the Fibonacci numbers are given by

F(n)=c1 a1^n + c2 a2^n.   Two initial conditions are needed to fix that constants c1 and c2.  The norm is F(0)=1 and F(1)=1. 
Hence, c1+c2=1 and c1 a1 +c2 a2 =1,
with solution c1 =(1-a2)/(a1-a2)  and c2=(a1-1)/(a1-a2).

By 18th number is that F(17)=2584 or F(18)=4181?

For F(17), the sensible enharmonic has 2584 (mod 12) == 4 sharps i.e. E major. 

And the letter has been subtracted int(2584/12)=215 times, where int() is an integer or floor function.

Since 215 (mod 12) = 11,
So the enharmonic is F 215 sharp major. (this almost sounds vulgar).


How about F(18)=4181?  4181 (mod 12) = 5 sharps which is B major and the letter has been subtracted int(4181/12)=384 times.

Since 348 (mod 12) =0, this will bring us back to doe! No B major.  The answer here is

B 348 sharp major!

Who came up with this junk anyway! I need sleep...

Al.

[Fugue]

Here's an old one, "what's the best way to spell a tristan chord, in relation to the possible tonal outcomes of its resolvation and/or progression to another chord, i.e.- from f-b-d#-g# to e-g#-d-b?"

[Nightscape]

asyncopated, that is excellent work.  It turns out I had the wrong answer for #10.

You obviously know your stuff!  I think I'll come up with a special question for you then.  Let's see if you can tackle this!

This question takes place during the Romantic Era.

"It so happened, that one day a famous music teacher, Bob, was walking to the market.  He stopped in, and bought 11 chaldrons of apples.  He also picked up 12 puncheons of champagne, and a coom of tarragon.  He then walked home, which was 7 furlongs from the marketplace.  Upon arriving at his homestead, he suddenly had a devious thought.  He decided to devise a particularly difficult and complex music theory question.  His question was so complex, it was really more of a mathematical excercise, than anything.  His question read as follows: 'How many sharps are contained in the key that is enharmonic to the key that has a number of flats equal to the number of pints in two pottles?'  He chuckled lightly to himself, knowing that his students would have a particularly difficult time figuring it out.

If one takes the twice the number of pints of apples that Bob purchased, and multiplies it by the three times the number of gallons of champagne Bob purchased, then adds it to the number of bushels of tarragon Bob purchased, then multiplies it by half of the number of inches Bob walked from the marketplace to his house, then added that to the answer of Bob's devious question, the number calculated would equal one half the number of flats in what minor key signature?"

[asyncopated]

Hi Nightscape,

Although, I am quite found of romantic era music I am unfornately not accainted with marketing and cullinary terms of that period.  In short, what might a puncheon, coom and a pottle be? 

Some champagne would be nice though.  Verve Cliquot?  If I do get this question right I do at least deserve that? . 

al.

P.S.  I actually found that first 9 questions amaizingly fun.  No. 10 was a stretching it a tad.   I've always wondered about these things, and never really bothered to figure it out till now.

[Nightscape]

Alright, I guess I can explain then..... I find old measurement terms fun!

7.92 inches = 1 link
25 links = 1 pole
4 poles = 1 chain
10 chains = 1 furlong
8 furlongs = 1 mile

2 pints(liquid) = 1 quart
4 quarts = 1 gallon
8 gallons = 1 firkin
2 firkins = 1 kilderkin
2 kilderkens = 1 barrel
2 barrels = 1 puncheon

2 pints (dry) = 1 quart
2 quarts = 1 pottle
2 pottles = 1 gallon
2 gallons = 1 peck
4 pecks = 1 bushel
2 bushels = 1 strike
2 strikes = 1 coom
2 cooms = 1 quarter
4 quarters = 1 chaldron
5 quarters = 1 wey
2 weys = 1 last

[asyncopated]

Hmm,

Thanks.  Why did we ever switch to SI units?  This is much better.

First we need to do Bob’s question.

We need to find the number of pints in two pottles.

2 pottles = 2 x 2 quarts = 2 x 2 x 2 pints (dry) = 8 pints (dry)

The key with 8 flats is Fb major which is the enharmonic of E major with 4 sharps.  I take it bob want’s the sensible answer.

Now to the second part

Bob bought
11 chaldrons = 11 x 2^2 quarters = 11 x 2^3 cooms = 11 x 2^4 strikes =11 x 2^5 bushels = 11 x 2^7 pecks = 11 x 2^8 gallons = 11 x 2^9 pottles = 11 x 2^10 = quarts = 11 x 2^11 pints (dry) of apples

I know that 2^10 = 1024 (from computing) , so 2^11 is 2048.  To get the 11 times table, we add 20480+2048 = 22528.

Bob also bought
12 puncheons = 12 x 2 barrels = 12 x 2^2 kilderkens = 12 x 2^3 firkins = 12 x 2^6 gallons of champagne.

Wow, lots of champagne.

So 64 x 12 = 640 + 128 = 768 gallons of champagne

Now the tarragon.  I love tarragon, especially with chicken and lemon.
He bought
1 coom = 4 bushels  of tarragon.

Bob then walked 7 furlongs, that’s a long way to walk! Must have taken him quite a while.  Would love to go to the derby to watch a 7 furlong race some time though.

Anyway, 7 furlongs = 7 x 10 chains = 7 x 10 x 4 x 25 links = 7 x 1000 x 7.92 inches
 Or 7x7920 = 55540 inches

So

(2 x 22528 x 3 x 768 + 4) x 55540/2  + 4= (22528 x 3 x 768 + 2) x 55540 + 4(I’m cheating here by using a calculator) = 2882776707564

The minor key signature would have 2882776707564  x 2 = 5765553415128 flats.  Any a number that is exactly divisible by both 3 and 4 is divisible by 12.  A number is divisible by 4 if the last to digits is divisible by 4.  28 is.  A number is divisible by 3 if the sum of its digits is also divisible by 3.  5+7+6+5+5+5+3+4+1+5+1+2+8=57 and 5+7 =12 which is certainly divisible by 3.  So the number is divisible by 12 exactly.
I.e.
5765553415128 (mod 12)==0.  So the key is an enharmonic of A minor.  The key signature associated with it has in total 5765553415128/12=480462784594 flats.  This number is not divisible by 12 but 480462784584 is.  The first 10 digits sum to 48.  The numbers closest and below are 94 divisible by 4 are 80 (not necessary), 84, 88 and 92.  As such the we can see that 480462784584 is divisible.  So the remainder is 94-84=10.
i.e. 480462784594 (mod 12) = 10.  Hence, shifting another 10 flats, we get

b 480462784594 flat minor!

Voila!

Haha… ermm is the answer right?

al.

[m1469]

*m1469's pride seems to be experiencing a distinct burning and furious sensation...* 

*m1469 suddenly feels the uncontrollable urge to beat things up... karate chopping her lettuce... kicking the dirt... throwing a tantrum... *   







*while wearing a leather mini skirt*

[asyncopated]

Since this is turning out to be more than just a music challenge, I'll throw in a question of my own.  The nice thing about this is that hardly any music theory is needed.  You just need to know the layout of the keyboard.

It has to do with adventures of bob from the Romantic Era.

"Bob after a couple of days of travel, finally reached home with all his produce.  Being an aspiring pianist, he decides to rest his mind and sooth his sole by practicing at the piano.  He sits upright, poised, and goes about his usual routine, doing drills much like those written by Hannon and Czerny.  However, the drill that he plays are special drills, that he believes will help improve his technique dramatically.  And they go like this :-

He starts by playing the chromatic scale with the left hand from the lowest to the highest note on the piano.  Bob then goes on to play whole tones starting with the lowest A.  So he practices... A, B, C#, D# and so on.  He does the same with 3 semitone intervals, then 4, then 5, until he reaches the 87 semitone interval.  He has been practicing in this way since he was a wee lad on the same, old piano many many times, everyday.  He then does the same with his right.

The following day, he carries out his usually routine but noticed something odd with his piano. Each time he pressed a key, it would stick and if he pressed it again, it would pop back up.  He calls for his good friend, George who is an aspiring pianist and a fantastic piano technician.  She says that she will come by the following morn to see what can be done. 

Bob, despite the difficulties, decides to carry on with his practice and starts by making sure that all the keys are not stuck.  He than practices as usual, with his left hand.  When he finishes with this hand. He notices that all but a handful of keys are stuck. 

Which keys remain unstuck?"