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Re: CHAT: conlang and alternate tuning WAS: from the ashes...

From:Tony Hogard <james.hogard@...>
Date:Wednesday, January 9, 2002, 20:58
Christophe Grandsire:

> Well, I read the page, and though I understand the principle, I > still don't > understand the implications (the intervals must be expressed as > ratios of whole > numbers, but compared to what? And what is really a temperament?). > Maybe an > example would be welcome. Since the last conlang I created is > accompanied with > a conculture which has absolutely nothing to do with European > culture, I'd like > to come up with a musical scale which is original for them :)) .
If one applies the whole-number ratios to frequency values, one can derive a justly tuned scale. For example, taking the tone A = 440 Hz and a series of intervals for a major scale: 1/1, 9/8, 5/4, 4/3, 3/2, 5/3, 15/8, 2/1 gives us Note Ratio Freq (Hz) A 1/1 440.000 B 9/8 495.000 C# 5/4 550.000 D 4/3 586.667 E 3/2 660.000 F# 5/3 733.333 G# 15/8 825.000 A 2/1 880.000 The equal temperament systen divides the frequency range into (logarithmically) equal intervals, so the same scale notes would be somewhere like: A 440.000 B 493.333 C# 554.365 D 587.330 E 659.255 F# 739.989 G# 830.609 A 880.000 Of course, finer interval divisions result in more tones per "octave" (a poorly-named concept, as it turns out) than the 12 usual in Western music. The previously-cited Just Intonation Network http://www.dnai.com/~jinetwk has a good number of links to articles (from one of which I lifted the above example). -Tone generator

Replies

Christophe Grandsire <christophe.grandsire@...>
Danny Wier <dawier@...>