Friday, 23 February 2018

More mental multiplication

In my last post I described a way of multiplying any two two-digit numbers using the difference of two squares method. I find it useful, but it has the drawback that you have to memorize the first 25 perfect squares, not all of which are easy for everyone to remember.  It also isn't very useful when you're multiplying an odd number by an even one.

I've been thinking about an alternative method that avoids both of these drawbacks.  It can be thought of as a generalization of the difference of two squares method.  I don't think I've seen it described in detail anywhere, although it may have similarities with some of the techniques used in so-called Vedic Maths, which I've only recently become familiar with.  It works best when the two numbers are reasonably close together.

It's best illustrated with an example, say 17 x 28.

Imagine the two numbers at the ends of a regular linear scale, as on a ruler, and imagine a movable marker at each end.  Push the two markers simultaneously towards each other at the same rate until one of them is on a round number.  So the left-hand marker moves three units right to 20, and the right-hand marker moves three units left to 25.

Now multiply these two numbers together: 20 x 25 = 500 (double 25 and add a zero).

Now look at the position of either of the markers relative to the end of the scale.  It doesn't matter which marker you use, although the one on the round number will probably be easier to calculate with.  20 - 17 = 3, and 28 - 20 = 8, so the marker is 3 units from one end and 8 units from the other.

Now multiply these two numbers together: 3 x 8 = 24.

Finally subtract from the earlier total: 500 - 24 = 476.  And that's the answer.

But what if there's no conveniently situated round number between the two original numbers?  Then you can pull the markers outwards, away from each other.  In this case you need to imagine the number line extending beyond the ends of the original scale, and the final step requires addition rather than subtraction.

Example: 22 x 29.  Pull the left-hand marker two units left to 20, and the right-hand marker two units right to 31.

20 x 31 = 620 (by doubling 31 and adding a zero).

The left-hand marker is 2 units from one end (22-20 = 2) and 9 units from the other (29-20 = 9).

2 x 9 = 18.

Add because you pulled outwards: 620 + 18 = 638.

Of course, these examples hinge on the fact that 20 is a reasonably easy number to multiply by mentally, but it works with other multipliers.  Try it with 26 x 33:

Push the markers three units inwards, to 29 and 30.
29 x 30 = (30 x 30) - 30 = 900 - 30 = 870
3 x 4 = 12 (33 - 30 = 3, 30 - 26 = 4)
870 - 12 = 858

Or 32 x 39:  push outwards to 31 and 40.
31 x 40 = 1240 (double 31 to 62, double again to 124, add a zero)
1 x 8 = 8 (40 - 39 = 1, 40 - 32 = 8)
1240 + 8 = 1248

As with the other technique, there will eventually come a point where it's more trouble than it's worth, but I think it's useful for relatively small numbers.

Saturday, 17 February 2018

Mental multiplication


Here's a technique that I sometimes use for multiplying two-digit numbers in my head.  It has the advantage that you don't have to use most of the multiplication table at all - just addition and subtraction, and division by 2.  It's based on the well-known difference of two squares formula from algebra, but you don't need to know any algebra to apply the technique.  It has similarities with the old quarter squares method but is explicitly designed for mental calculation.  I'm not aware of anyone else who uses this exact method.

You will need to know the perfect squares up to 25 x 25.   This isn't as daunting as it may sound, as the traditional multiplication table takes you up to 12 x 12, and there are a number of mnemonics that can help you remember most of the rest.

The "pivot" rule

As a simple example, suppose you want to multiply 7 by 13.  (For the moment, we'll stick to examples where both numbers are odd, or both are even.)

Imagine a seesaw.  At the two ends of the seesaw are the two numbers you want to multiply.  In between the two numbers there's a regular scale, as on a ruler.  The "pivot" number is the halfway point between the ends of the seesaw.   So if you have 7 at one end and 13 at the other, the pivot will be 10.  You might be able to spot this straight off, but if not you can calculate it by adding the end numbers together and dividing by 2; 7 + 13 = 20, and 20/2 = 10.

Now calculate the distance from the pivot to either end of the seesaw: 10 - 7 = 3, or 13 - 10 = 3.  It doesn't matter which end you choose.

Now calculate the square of the pivot: 10 x 10 = 100
and the square of the distance from the pivot: 3 x 3 = 9 
Finally subtract the second from the first: 100 - 9 = 91.

And that's your answer!

In this case it was relatively easy because the squares of 10 and 3 are well known.  The key to this technique is knowing how to compute the square of any two-digit number.  Fortunately, you only need to know the squares of the first 25. 


Memorizing the first 25 perfect squares

The first twelve perfect squares are 1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121 and 144.

13 x 13 = 169 - anagram of the next one
14 x 14 = 196 - anagram of the previous one
15 x 15 = 225 - all squares of numbers ending in 5 end in "25" (cf. 25 squared)
16 x 16 = 256 - 2 to the power of 8 (crops up a lot in computing)
17 x 17 = 289
18 x 18 = 324 - "graph" of digits dips down 1 and up 2 (cf. 24 squared)
19 x 19 = 361
20 x 20 = 400 - easily derived from 2 x 2 = 4 and 10 x 10 = 100
21 x 21 = 441 - 12 squared backwards (21 is 12 backwards)
22 x 22 = 484 - think 11 squared = 121, times 4 (also note 22 and 484 are both palindromic)
23 x 23 = 529
24 x 24 = 576 - "graph" of digits dips up 2 and down 1 (cf. 18 squared)
25 x 25 = 625 - all squares of numbers ending in 5 end in "25" (or think of old 625-line TV)

I don't know any easy way of memorizing 289, 361 and 529.  My old school was near a road called the A361 but that's unlikely to be much help to anyone else!   Hopefully you can find your own personal connections for the numbers.

When you've mastered these you should be able to multiply any two odd or two even numbers whose sum is 50 or less.

Multiplying two odd or two even numbers whose sum is 50 or less

As an example, try 14 x 22.

The pivot is 18.  (14 + 22 = 36; 36/2 = 18.)
The distance to the pivot is 4 (18-14 or 22-18).
18 squared is 324, and 4 squared is 16.
So the answer is 324 - 16 = 308.

Another example: 17 x 27.

The pivot is 22.  (17 + 27 = 44; 44/2 = 22.)
The distance to the pivot is 5 (22-17 or 27-22).
22 squared is 484, and 5 squared is 25.
So the answer is 484 - 25 = 459.

Try these for yourself (solutions in white, with method):

13 x 27     Pivot = 20; distance = 7; answer = 400 - 49 = 351
14 x 34     Pivot = 24; distance = 10; answer = 576 - 100 = 476
17 x 21    Pivot = 19; distance = 2; answer = 361 - 4 = 357
18 x 28   Pivot = 23; distance = 5; answer = 529 - 25 = 504


Deriving the next 25 perfect squares

Once you feel comfortable with the first 25 perfect squares, there's a simple rule that allows you to derive the next 25, from 26 to 50.  To explain it we can use the seesaw analogy again.  Call the number you want to square the "base" number.

Imagine a seesaw with the pivot at 25 and the base number at one end.  The number at the other end will be 50 minus the base number.  For instance, if you want to square 33, then 17 will be at the other end.

Now square this number: 17 x 17 = 289 (from the list above)
Now take the distance from the pivot to one end of the seesaw and multiply by 100: 8 x 100 = 800
Add these two together: 289 + 100 = 1089

Another example: find 42 x 42.
Pivot is 25, 8 is at opposite end.  Distance is 17.
So 42 squared is 8^2 + (17 x 100) = 64 + 1700 = 1764

A few for practice:

49 x 49    1 at opposite end.  Distance is 24.  1^2 + (24 x 100) = 1 + 2400 = 2401  
29 x 29    21 at opposite end.  Distance is 4.  21^2 + (4 x 100) = 441 + 400 = 841 
39 x 39    11 at opposite end.  Distance is 14.  11^2 + (14 x 100) = 121 + 1400 = 1521  
36 x 36     14 at opposite end.  Distance is 11.  14^2 + (11 x 100) = 196 + 1100 = 1296  

If you practise using the squares from 26 to 50 often enough you'll find that the values start to come automatically after a while.  Here's the full list for reference:

26 x 26 = 676  ( = 576 + 100)                  38 x 38 = 1444 ( = 144 + 1300)
27 x 27 = 729  ( = 529 + 200)                  39 x 39 = 1521 ( = 121 + 1400)
28 x 28 = 784  ( = 484 + 300)                  40 x 40 = 1600 ( = 100 + 1500)
29 x 29 = 841  ( = 441 + 400)                  41 x 41 = 1681 ( = 81 + 1600)
30 x 30 = 900  ( = 400 + 500)                  42 x 42 = 1764 ( = 64 + 1700)
31 x 31 = 961  ( = 361 + 600)                  43 x 43 = 1849 ( = 49 + 1800)
32 x 32 = 1024 ( = 324 + 700)                 44 x 44 = 1936 ( = 36 + 1900)
33 x 33 = 1089 ( = 289 + 800)                 45 x 45 = 2025 ( = 25 + 2000)
34 x 34 = 1156 ( = 256 + 900)                 46 x 46 = 2116 ( = 16 + 2100)
35 x 35 = 1225 ( = 225 + 1000)               47 x 47 = 2209 ( = 9 + 2200)
36 x 36 = 1296 ( = 196 + 1100)               48 x 48 = 2304 ( = 4 + 2300)
37 x 37 = 1369 ( = 169 + 1200)               49 x 49 = 2401 ( = 1 + 2400)
                                                                 50 x 50 = 2500            Distance is 11.  14^2 + (11 x 100) = 196 + 1100 = 1296

Multiplying two odd or two even numbers whose sum is 100 or less

So now you have enough knowledge to multiply any two odd or even numbers whose sum is 100 or less!  Here's an example: 44 x 24.  You might find it difficult to hold all the necessary information in your head at first, so write down the pivot if necessary.

The pivot is 34, and the distance is 10.
34 squared is 1156 (either from the list above or by doing 16^2 + 900).
10 squared is 100, so the answer is 1156 - 100 = 1056.

Another example: 47 x 29.

Pivot = 38, distance = 9.
38 squared is 1444 ( = 12^2 + 1300), 9 squared is 81.
Answer is 1444 - 81 = 1363.

Practice examples:

38 x 22    Pivot = 30, distance = 8.  30^2 = 900, 8^2 = 64, answer = 836
37 x 27    Pivot = 32, distance = 5.  32^2 = 1024, 5^2 = 25, answer = 999
46 x 32    Pivot = 39, distance = 7.  39^2 = 1521, 7^2 = 49, answer = 1472
63 x 31    Pivot = 47, distance = 16.  47^2 = 2209, 16^2 = 256, answer = 1953

You probably found with the last example that the numbers were quite a long way from the pivot and it was difficult to do the final subtraction in your head, which is a limitation to this as a purely mental technique.  Nevertheless you can always write the final step down - the number of operations you need to do is still fewer than in conventional long multiplication.


Multiplying an odd number by an even number

If you've got this far you're almost certainly shouting "Well that's all very well if they're both odd or even, but what if there's one of each?"

There are various ways of dealing with this, but the simplest is to subtract 1 from the higher number, perform the calculation as normal, and then add the lower number.  So for 26 x 37 you'd do 26 x 36, which is 31^2 - 5^2 = 961 - 25 = 936, and finally add 26 to give 962.

Another example: for 33 x 42, calculate 33 x 41 = 37^2 - 4^2 = 1369 - 16 = 1353, and add 33 to give 1386.

Try the following:

13 x 18    13 x 17 = 15^2 - 2^2 = 225 - 4 = 221 and 221 + 13 = 234
16 x 29    16 x 28 = 22^2 - 6^2 = 484 - 36 = 448 and 448 + 16 = 464
23 x 32    23 x 31 = 27^2 - 4^2 = 729 - 16 = 713 and 713 + 23 = 736
17 x 44    17 x 43 = 30^2 - 13^2 = 900 - 169 = 731 and 731 + 17 = 748


Multiplying any two two-digit numbers

All that remains now is to learn the technique for squaring two-digit numbers between 50 and 100, and in theory you should be able to multiply any two two-digit numbers. The sum of any two two-digit numbers is always less than 200, so the pivot will always be less than 100.  You might find that the final subtraction becomes rather unwieldy with the higher numbers and the method is no longer useful.  Nevertheless I'll include this section for completeness.  There are different methods for numbers above and below 75.

Squaring a number from 51 to 75: subtract 50 from the number, take the square and then add on the original number less 25, multiplied by 100.  Note that the number of hundreds you add on is the "pivot" between the number and the number less 50.

E.g. for 63 squared: 63 -50 = 13, 13 squared = 169 and add (63 - 25) x 100 = 3800 to give 3969.
You might find it useful to imagine a seesaw with 63 at one end and 13 at the other; the pivot will be at 38, so you add on 38 x 100 to 13 squared.

Another example: for 72 squared, 72 - 50 = 22, 22 squared = 484 and add (72 - 25) x 100 = 4700 to give 5184.  (47 is the "pivot" between 22 and 72.)

Squaring a number from 76 to 100: subtract the number from 100, take the square and add on 100 less twice the original number, multiplied by 100.  In this case you might imagine a seesaw with the pivot at 50, and the number of hundreds you add on is the entire length of the seesaw.

E.g. for 93 squared, think 100 - 93 = 7.  The length of the seesaw is 93 - 7 = 86.  So the answer is 7^2 + (86 x 100) = 49 + 8600 = 8649.
Another example: for 78 squared, 100 - 78 = 22, length = 78 - 22 = 56, answer is 22^2 + 5600 = 484 + 5600 = 6084.

Here's a sample multiplication sum using these squares: 57 x 79.
The pivot is 68.  68 squared is 18^2 + 4300 = 4624.
The distance is 11, and 11^2 = 121.  So the answer is 4624 - 121 = 4503.

Another example: 62 x 92.
The pivot is 77.  77 squared = 23^2 + 5400 = 5929.
The distance is 15, and 15^2 = 225.  So the answer is 5929 - 225 = 5704.

If you dare, here are some examples to try:

56 x 74   Pivot = 65, distance = 9.  65^2 = 15^2 + 4000 = 4225, 9^2 = 81, answer 4144
67 x 81   Pivot = 74, distance = 7.  74^2 = 24^2 + 4900 = 5476, 7^2 = 49, answer 5427
81 x 97   Pivot = 89, distance = 8.  89^2 = 11^2 + 7800 = 7921, 8^2 = 64, answer 7857
66 x 86   Pivot = 76, distance = 10.  76^2 = 24^2 + 5200 = 5776, 10^2 = 100, answer 5676

Don't worry if you've given up by this point!   I don't find numbers of this size easy by this method either.  In practice I might use a variety of different techniques.  E.g. for 56 x 74 I might think

56 = 7 x 8
8 x 75 = 600 (6 is three-quarters of 8), so 56 x 75 = 7 x 600 = 4200
So 56 x 74 = 4200 - 56 = 4144

I hope some of this has been useful (or at least interesting) anyway!

Saturday, 21 January 2017

The importance of key in understanding and creating music

I was at a jam session the other night.  A couple of other musicians started playing an unfamiliar song.  I listened to it for a little while and then started joining in with the chords at the keyboard.

How did I do that, since I don't have perfect pitch?  Well, first of all I had to work out what key they were in, so I tried a few notes on the piano until I found the one that matched the keynote.  Then I just listened to the chords.  Irrespective of what key I'm in, I can recognize the tonic chord, dominant chord, subdominant chord, chord of the relative minor and all the other common ones.  I then used my theoretical knowledge to translate those chords into the relevant key.  So if we'd been in D major and I heard tonic-dominant-subdominant-dominant, I'd have played D major-A major-G major-A major.  I wouldn't normally have to think about that sort of thing consciously, unless we were in a remote key with lots of sharps or flats, or unless the piece used lots of chords remote from the actual key.

It's the same when I'm composing music.  In my head I imagine a tonic chord, or a dominant seventh, or whatever.  When I come to actually play the piece on the keyboard, or write it down, I'll choose an appropriate key and use the appropriate chord sequence.  Ditto the melody - it doesn't really matter what key I imagine the melody in, as long as I sing it in the same key as I'm playing in.

So you can see that, for me at least, the key is literally the "key" to understanding the whole song.  If I had no concept of key, I'd be completely lost.  I don't really think of chords as C major or G major when I'm composing.  The C major chord has no special significance of its own, except relative to a given key.  If I'm in C major, it's the tonic chord - the "home" chord that the song finishes on.  But if I'm in F major, it's the dominant chord - the one that naturally leads towards the tonic chord and requires resolution.  It has a very different character.

Let's use Ralph McTell's "Streets of London" as an example.  I won't write out all the chords - just the first and last ones of each pair of lines.  It's in C major.

C [Have you seen the old man, in the closed-down market/Picking up the papers in his worn-out shoes] G7
C [In his eyes you see no pride, hand held loosely by his side/Yesterday's papers, telling yesterday's news] C
F [So how can you tell me, you're lo - ne - ly/And say for you that the sun don't shine?] G7
C [Let me take you by the hand, and lead you through the streets of London/I'll show you something, to make you change your mind] C

The first pair of lines starts with C major, the tonic or "home" chord, as is common in many songs.  It ends with G major (ignore the seventh for now), the dominant chord, creating an "unresolved" feeling.  You couldn't finish the song there.

Then we go back to the tonic chord for the start of the next pair of lines, and we finish on the tonic chord at the end of the verse.  The song could, in theory, end there, although it'd be pretty short!  There's a feeling that we've arrived back home again.

The chorus starts on F major, the subdominant chord, which is quite common, creating a change of key-colour.  We go through a brief key-change in the middle of the line before arriving at the dominant chord again, G major.  We feel as though we're heading towards a conclusion.  The final section begins and ends on the tonic chord, and there's a resolution to the song.

Now let's transpose the song into F major.
F ------------------------- C7
F ------------------------- F
Bb ----------------------- C7
F ------------------------- F

The chord of C major (ignore the seventh again) is now playing the role that G major did in the earlier key - the dominant chord.  It's the one that requires resolution.  We don't feel we've completed the song until we've got back onto F major.

So my point is that it's not the actual letter-names of the chords that are important.  It's their roles relative to the key you're playing in.

When you're singing, unless you've got perfect pitch, you've got no absolute concept of pitch - it's all relative.  In any given key, you've hopefully got a feel for which note is the keynote, which is the fifth, which is the third and so on, but not for the actual letter-names of the notes.  That's why it's so easy to sing a song in several different keys (if your range allows it).  You don't have to think about transposing as you do with an instrument - it happens automatically.  That's why some people recommend tonic sol-fa as a way of teaching singing (doh-ray-me).  "Doh" is always the keynote of the scale, regardless of what key you're in.  "Soh" is always the fifth, "me" is always the third, and so on.

That's not true with most instruments, of course.  Nevertheless it's the way I think when I'm playing by ear, or when I'm composing in my head.  The realization of "doh-ray-me" at the keyboard might be "C-D-E" or "F-G-A" but really that's irrelevant.  It's the relative pitches of the notes that are important, not the absolute ones.

There is simply no way that I could interpret a chord sequence as just a sequence of letter names.  Let's look at "Streets of London" again.  It starts with the sequence C-G-Am-Em.  In my mind I imagine that as "tonic-dominant-submediant-mediant".  I don't think in words, of course - I think in sounds.  But I'm not trying to imagine what G major sounds like in isolation.  I'm imagining what it sounds like relative to C major.  If it were written in F major, as F-C-Dm-Am, I'd imagine the same thing.  I might not imagine it at the right pitch but I'd get all the intervals right.

It's interesting to note in passing that the chord symbols used in the Baroque era were relative to the key rather than absolute - they'd use "I" for the tonic, "V" for the dominant, "IV" for the subdominant and so on.  I think that's a much more intuitive way of notating chords, to be honest, although if you're playing an instrument you have to learn which symbol corresponds to which chord in each key.  But it comes with practice.

So that's the way that I interpret and create music, at any rate. It works for me and I couldn't do it any other way.

Wednesday, 11 May 2016

How I write a song lyric

This post is to do with recent discussions on the Songwriter Forum about the construction of song lyrics.  I'm going to give an indication of the type of thought-processes that I typically go through when I'm writing a song.  As an illustration, I'm going to use this couplet from "Don't Mix Your Drinks" - a comedy song about the difference between two types of alcoholic drink.

Yes, perry comes from pears now, and cider comes from apples,
An obvious distinction with which every brewer grapples.

The "hook" line at the end of each chorus is "cider comes from apples, and perry comes from pears", but (employing a fairly common comedy technique) the wording is changed at the beginning of each chorus so that a different rhyming word comes last.  I'd already had "perry" and "cider" at the end, so now it was the turn of "apples".  Getting "apples" to the end was no problem, apart from a minor problem with the scansion - "pears" is only one syllable, so I added in the "now" as a filler.  Not ideal but good enough.  The second line was a lot harder though. 

The first problem was finding a rhyme for "apples", which has far fewer rhymes than the other words.  Off the top of my head I could only think of "dapples", which didn't really fit the context, and "grapples".  Something like "a problem with which [someone-or-other] grapples"?  That seemed promising - in conversation you'd be more likely to say "a problem which [someone-or-other] grapples with", but the other version is perfectly grammatical and the slightly pedantic tone may even enhance the humour.  So that was a start.

So who's this person grappling with the problem?  No idea.  It's really a problem with which lots of people grapple, but then you need the plural version of the verb "grapple", which doesn't rhyme.  What about "everybody", though?  That refers to lots of people, but takes a singular verb.  Now I've got "a problem with which everybody grapples".  Scans OK but is two beats short.  Stick in an adverb and adjective, then, and here's the first draft: 

A really tricky problem with which everybody grapples.

It's not really a problem, though - it's a difference that people don't observe.  I'd already used "difference" in a previous chorus so I needed a synonym.  "Distinction" fitted, but then the adjective needed to be shorter:

A really clear distinction with which everybody grapples.

OK but I thought I could do better - "really" is a bit of an over-used filler word and I'd rather do without it.  Is there a synonym for "clear" with three syllables that fits?  Indeed there is - "obvious":

An obvious distinction with which everybody grapples.

Nearly there now, but does everybody grapple with it?  It's only really the people in the brewing industry who name the product - that's who the song is trying to make fun of.  So the line now becomes:

An obvious distinction with which every brewer grapples.

And I went with that, but actually it's still not right.  You don't brew cider, you ferment it.  But "fermenter" doesn't scan, and anyway I don't think people who make cider are called "fermenters" - just "cider-makers".  But then I'd have had to repeat "cider" in the line, and rewrite the whole thing again because the scansion would be different.  I just had to hope that no one would notice.

In performance it's just a little throwaway gag that hopefully gets a titter from one or two people in the audience.  But it represents something like an hour's work, I'd guess.  I'm not saying that every line in the song was as hard to write as that one, but it gives an indication of the type of work that goes into writing what to most people would sound like a light, frothy lyric. 

You don't want it to sound like hard work - you want it to sound like the sort of thing that anyone might naturally say, which just happens to be set to music.  And that's the challenge of writing lyrics as far as I'm concerned.

Sunday, 27 March 2016

Counties of England*

*For the Purposes of Lieutenancy


Oh there's Cornwall, Devon, Dorset, Wiltshire, Hampshire, Isle of Wight,
West Sussex and East Sussex, Surrey, Berkshire if I'm right,
Greater London, City of London, Essex, Hertfordshire and Kent,
There used to be a Middlesex - I don't know where it went.
And Oxfordshire and Buckinghamshire and Bedfordshire and all,
Northamptonshire and Cambridgeshire, and Rutland's rather small,
And there's Suffolk, Norfolk, Lincolnshire and Leicestershire and Notts,
These are the counties of England - there are lots and lots and lots.

[SPOKEN:] Well, only forty-eight actually.  And "Nottinghamshire" was too long to fit into the line.

[Pause]

These are in fact the ceremonial counties of England, defined under the Lieutenancies Act 1997 as the areas to which a Lord Lieutenant is appointed.  They are not be confused with the 83 metropolitan and non-metropolitan counties defined for the purposes of local government.

[Pause]

Nor are they to be confused with the 39 historic counties of England established by the Normans and promoted by the Association of British Counties, whose continued existence was acknowledged by the Government in 2013.

[Pause]

Actually I do know where Middlesex went.  It was abolished in 1965 when the Greater London Council was established, and was mostly absorbed into Greater London with the exception of two small areas now in Hertfordshire and Surrey.

[Pause]

And to clarify the next bit: there are only three historic Ridings of Yorkshire, but there are four current subdivisions for the purposes of lieutenancy, only one of which - the East - is referred to as a Riding, and whose boundaries do not correspond exactly to those of the historic East Riding.

[Pause]

But hey, it's only a bloody song.

[SUNG:]
Now Yorkshire is a county that's so big it needs dividing
Into South and West and North and East - that's what they call a Riding,
Northumberland and Cumbria, County Durham, Tyne and Wear,
Greater Manchester and Merseyside and proper Lancashire.
And Cheshire, Shropshire, Staffordshire and Derbyshire, I claim,
And Worcestershire and Warwickshire, West Midlands (dreadful name!),
And Herefordshire and Gloucestershire and Bristol in the West,
Which leaves us only with Somerset - the one we love the best!



Don't Mix Your Drinks


In every supermarket there's a most delicious drink,
In every corner shop and any pub of which you think.
It's cheap and it's refreshing, so it's such a dreadful shame
That they sell it as pear cider, which is not its proper name.

For cider comes from apples and perry comes from pears.
I don't know when they changed it, but it caught me unawares.
I want to start a protest, but it seems nobody cares
That cider comes from apples and perry comes from pears.
Yes apples give you cider, and pears will give you perry.
You can look the meanings up in any dictionary.
Just Google it, you'll find that Wikipedia declares
That cider comes from apples and perry comes from pears.

When I went just along the road I found to my delight
That one brave manufacturer had named the product right,
In big three-litre pouches, it was really quite a shock.
I went and got one every day, and drank them out of stock.

Oh, pears will give you perry, and apples give you cider.
The diff-er-ence between the two could not be any wider.
I asked some local farmers and I sent them questionnaires,
They said "Cider comes from apples and perry comes from pears".
Yes perry comes from pears now, and cider comes from apples,
An obvious distinction with which every brewer grapples.
The people who rebranded it may all be millionaires,
But cider comes from apples and perry comes from pears.

So if you're feeling angry you should write to your MP,
He'll think that you're a fruitcake, but he won't dare disagree.
Remember as you sip your pint of perry at the bar,
It wasn't Cider Como singing "Catch a Falling Star".

Oh, perry isn't cider, and cider isn't perry,
Bitter isn't lager, and brandy isn't sherry,
Whisky isn't vodka, and my own dear mother swears
That cider comes from apples and perry comes from pears.
Cider comes from apples and perry comes from pears,
Cider comes from apples and perry comes from pears.
Go and change the label if anybody dares,
For cider comes from apples...
...and perry comes from pears!