after a decent interval.

[Richard Moody]

You have to know which pentatonic scale he is referring to.
Otherwise you do a series of arithmetic exercises and come up with a
number that is given significance in reference to another arithmetic
consideration.   While obviously not numerology, it does conform to
number theory but the inferences are usually specious to say the
least.  The best way to make sense of it is to give it 30 seconds or
60 seconds or 90 seconds and if still perplexed, come back to it later
and don't worry about how much later.    ---ric

| >From the tuning list:
|       On a more serious note about Pythagoras. The 81/64 third

You know from tuning theory that a Pythagorean 3rd has the ratio 81/64
while the pure 3rd (5/4) in comparrison has the ratio 80/64.  By
arithmetic 80/64 reduces to 5/4
(40/32--20/16--10/8--5/4)   Now the "difference"  (you gotta remember
this is the "rational (as in rational numbers ie ratio) difference
which is found by multiplying and dividing, not by adding and
subtracting) between 81/64  and 80/64  is
81/80.   Here you don't subtract 80/64  from 81/64.  No, you divide
81/64  by 80/64  which equals  81/80.   Remember 5th grade rules for
dividing fractions by fractions?  You invert and multiply. If not
forget about understanding anything the microtonalists are saying
about math and musical intervals.  So don't worry about "how much
later".  ; )
    But if you have followed the derivation of 81/80 then this is the
value or amount of the comma called "syntonic" or the arithmetic
difference between a pure 3rd (5/4) and a pythagorean 3rd (81/64).
They Pythagorean 3rd is one that is gotten by a tuning a series of
pure 5ths and then tuning two octaves down.   If starting from C you
come to E.  The Pythagorean 3rd is sharp from the pure 5/4 3rd....
because -- the ratio of the 5th is 3/2.  When you raise a fifth by a
fifth you multiply 3/2 by 3/2   which looks like 3.2 * 3/2  which
comes out to 9/4.   Now raise this by another 5th which is
computed...9/4 * 3/2 = 27/8.  OK you need to go up another 5th so 27/8
* 3/2 = 81/16.    So 81/64  is two octaves above the starting note.
Reducing by an octave looks like in arithmetic,
81/64 *1/2  =  81/32 .   You need to go down another octave so 81/32 *
1/2 = 81/64.
Again if you don't understand the arithmetic you don't need to unless
you want to know the difference between a Pythagorean 3rd and a pure
3rd.

    So lets check the arithmetic you posted from another post..
            6/5 * 80/81 = 2/1 * 16/27 = 32/27 (ol 294cents).

Here we see 6/5  multiplied by 80/81 .  We know 6/5  is the ratio of a
minor 3rd and since this is mutiplied by 80/81  it is being reduced
rather than being increased.  So you are looking af a "flat" minor
3rd.   It does indeed reduce to 32/27  and that ratio is also equal to
294 cents.  The "ol" is probably a typoo for "or".   As to the
significance of 294 cents I dunno.   A pure 6/5 minor 3rd is equal to
315.6 cents.   So the question is so what?

 |   This sounds quite|
| interesting in a pentatonic. (Try the classic oscillating minor
third, like|
| a child's 'see saw dickory daw', 'I'm the king of the castle', or
many|
| other playground chants. (The minor third is the first interval a
child can
| recognise and sing). The 294cent third is quite tense. See Bartok
articles
| on folk music for discussion of this property.

Ok we come again to what is meant by the "pentatonic".
Regarding "a child's 'see saw dickory daw'..."    That should read
  "see saw majory daw"   by my recolection and confirmed by wife's
also.  Well that is interesting we both knew the same nursery rhymes
and tunes, she comming from a Czech/American background (im 1880) and
me from  Anglo/America (im 1750) There were other words.... what were
they....   Oh yes I recollect, "cross patch draw the latch"

That the minor 3rd is "first interval a child can
| recognise and sing"
    I dunno, and again what does it matter?  That the 294 3rd should
be "quite tense"  is his/her opinion but what does it matter that a
294 3rd is tense, (we assume compared to a 6/5 or 315.6 3rd)?





----- Original Message -----
From: <A440A@AOL.COM>
To: <pianotech@ptg.org>
Sent: Tuesday, March 19, 2002 4:17 PM
Subject: after a decent interval.


| Greetings,
|     On occasion, while surfing, I find bits of academic algae stuck
to my
| board,and this has been hanging around long enough, food for
thought, or
| fishes..,
| Regards,
| Ed Foote
|
| >From the tuning list:
|       On a more serious note about Pythagoras. The 81/64 third is
obviously
|
| further 'up the series' than 5/4 but in some ways it's closer than
at first
|
| thought possible, via the pentatonic scale:
|
|
| The corresponding minor third: small by one comma:
|
|
| 6/5 * 80/81 = 2/1 * 16/27 = 32/27 (ol 294cents). This sounds quite
|
| interesting in a pentatonic. (Try the classic oscillating minor
third, like
|
| a child's 'see saw dickory daw', 'I'm the king of the castle', or
many
|
| other playground chants. (The minor third is the first interval a
child can
|
| recognise and sing). The 294cent third is quite tense. See Bartok
articles
|
| on folk music for discussion of this property. (Oh and Lendvai -
whose
|
| theories I am sure are not a function of the twelve-tone scale, but
rather
|
| the mean-tone one).