Received: by alpheratz.cpm.aca.mmu.ac.uk id TAA24016 (8.6.9/5.3[ref pg@gmsl.co.uk] for cpm.aca.mmu.ac.uk from fmb-majordomo@mmu.ac.uk); Thu, 18 Apr 2002 19:11:37 +0100 Date: Thu, 18 Apr 2002 11:06:16 -0700 From: Bill Spight <bspight@pacbell.net> Subject: Re: musical grammar To: memetics@mmu.ac.uk Message-id: <3CBF0B18.92307AE0@pacbell.net> Organization: Saybrook Graduate School X-Mailer: Mozilla 4.72 [en]C-CCK-MCD {Yahoo;YIP052400} (Win95; U) Content-type: text/plain; charset=us-ascii Content-transfer-encoding: 7BIT X-Accept-Language: en,ja References: <33BBDDC8-4DAA-11D6-B1DE-003065B9A95A@harvard.edu> Sender: fmb-majordomo@mmu.ac.uk Precedence: bulk Reply-To: memetics@mmu.ac.uk
Dear Wade,
> > why do we have a 12 tone scale.?
>
> Well, we do, most definitively after Schoenberg, but I don't think
> twelve-tones are quite as universal as all that. Tonics and harmonics
> are more important, with five and seven tone systems.
In the West, the well tempered 12 tone scale dates to classical times. I
believe that the Chinese had discovered it several centuries before. :-)
Why 12 tones? Because the log(1.5) base 2 = 0.585, which is close to
7/12 = 0.583. 1.5 is the ratio of the fifth to the dominant. A cycle of
12 5ths will take you back to back to the dominant (about 2% sharp). If
you flatten the 5th slightly, it takes you back exactly. That enables
you to have a piano-forte with 88 keys covering a bit over 7 octaves,
and play in any key. To get closer you need a 41 note well-tempered
scale. A cycle of 41 5ths takes you back to the dominant (about 2%
flat). But that would give you a piano range of a little more than 2
octaves.
Does tempering make a musical difference? Yes, as Wade indicates. I once
met a music professor who would not let his singing students practice to
piano accompaniment for that reason. ;-)
Best,
Bill
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