updated definition: "tritone"

I've updated the Dictionary entry for "tritone" to include
all possible rational approximations of the tritone from
580 to 620 cents, which are elements of the set of pitch-classes
3^(-10...10) * 5^(-2...2) 7^(-1...1) * 11^(-1.0..1) *13^(-1...1)

http://www.ixpres.com/interval/dict/tritone.htm

-monz

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For reasons of historical completeness and even more for the
simple reason that newbies quite likely have heard these
terms, I'd welcome a mention of the terms "augmented fourth"
for the succession of three whole tones and "diminished
fifth" for its complement.

klaus

monz schrieb:
>
> I've updated the Dictionary entry for "tritone" to include
> all possible rational approximations of the tritone from
> 580 to 620 cents, which are elements of the set of pitch-classes
> 3^(-10...10) * 5^(-2...2) 7^(-1...1) * 11^(-1.0..1) *13^(-1...1)
>
> http://www.ixpres.com/interval/dict/tritone.htm
>
> -monz
>
>
>
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> From: klaus schmirler <KSchmir@z.zgs.de>
> To: <tuning@yahoogroups.com>
> Sent: Tuesday, January 15, 2002 2:36 AM
> Subject: Re: [tuning] updated definition: "tritone"
>
>
> For reasons of historical completeness and even more for the
> simple reason that newbies quite likely have heard these
> terms, I'd welcome a mention of the terms "augmented fourth"
> for the succession of three whole tones and "diminished
> fifth" for its complement.
>
> klaus

Good show, Klaus! You were right to ask me to include
those terms. I've made two brief new entries for both
of them (simply linking to the "tritone" definition),
as well as a detailed explanation of both intervals
within the "tritone" definition itself:

http://www.ixpres.com/interval/dict/tritone.htm

-monz

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--- In tuning@y..., "monz" <joemonz@y...> wrote:

> http://www.ixpres.com/interval/dict/tritone.htm

Monz, besides equal temperaments, there are quite a few _linear
temperaments_ which contain an exact 600-cent tritone as
the "period". A 5-limit example is the linear temperament you get if
you temper out the diaschisma (2048:2025), as some theories of Indian
music seem to imply.