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G8MNY  > TECH     14.11.23 07:56z 79 Lines 2953 Bytes #6 (0) @ WW
BID : 60300_GB7CIP
Read: GUEST
Subj: Musical Scales
Path: SP7YDD<SR1BSZ<IW0QNL<IZ3LSV<I0OJJ<GB7CIP
Sent: 231114/0754Z @:GB7CIP.#32.GBR.EURO #:60300 [Caterham Surrey GBR]
From: G8MNY@GB7CIP.#32.GBR.EURO
To  : TECH@WW

By G8MNY                               (Correction Apr 10)
(8 Bit ASCII graphics use code page 437 or 850, Terminal Font)

Not at all musical myself, but if your working on musical instruments this may
help.

Scales are not all the same, initially 7 notes ABCDEFG (white keyboard notes)
per octave (doubling in frequency) were used & later gaps were filled in (black
sharp & flat notes) to give 12. In the east, 20 notes are used, making the
music sound strange to the western ear.

DIATONIC SCALE
This is a mathematically true scale & sounds perfect, it is used for solo
string & wind instruments.

C Ref  1    9/8   5/4   4/3   3/2   5/3  15/8    2
Note   C'    D     E     F     G     A     B     C
Ratio  9/810/916/159/810/99/816/15

9/8 & 9/10 are whole tones, 16/15 are semitone.

Other intervals & Ratios
2/1 e.g. from C' to C is an octave,
3/2 e.g. from G to C is a 5th
4/3 e.g. from C' to G is a 4th
5/4 e.g. from A to F is a 3rd.

Music can be played in different keys from which it was written, but it will
not work well with this scale. Also it is not possible to tune a multi-octave
keyboard instrument to this true scale & still do shifts in "the key", so...

EQUAL TEMPERED SCALE
The tuning problem was initially solved a long time ago by Pythagoras(?). It
uses 122 (1.05956) intervals between all notes in the octave. So to go from
one note to the next just multiple or divide by 1.05956. Now musical can be
shifted up & down notes (KEYS) (to fit singer's range for example) & it still
works.

PITCH
Any instrument can be tuned to itself, but several are to play together they
will need to be up tuned together. This lead to a common standard of 256Hz for
middle C now called the "old physical pitch" and gave a Diatonic A of 426.67Hz.

INTERNATIONAL ORCHESTRAL PITCH
This has A' set at exactly 440Hz & used the Equal Tempered Scale..

ABCDEFGABCDEFGABCDEFGABCDE---Note
------------------------11111111111222222233---
22333334444555666778899011233456789023467912---\
79024681369158159374728306208654456703617319--- Hz
............................................---/
51977792730903743484350806586968600701962727---

 
FGABCDEFGABCDEFGABCDEFGABC---Note
-------------------1111111111112222222333334--
33344445556667788990112334567890234679135791-- \
47914692582594838364074198666679158796322358-- Hz
90250633572980400277955970810563809340630016-- /
...................---------------------------/
2004029344334007048---------------------------

All electronic keyboard instruments should have the above scale built in & any
pitch tuning will fine tune the whole set.


Comment from Kevin VK2YPZ... 
"While Bach is not accredited as creator of the Equal Tempered Scale, he was
the first to publish a work that used it. This is certainly much later than
Pythagoras' time."


Why don't U send an interesting bul?

73 De John, G8MNY @ GB7CIP


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