From: Hatunen on
On Fri, 11 Aug 2006 08:34:32 -0500, barney2(a)cix.compulink.co.uk
wrote:

>In article <v8mod29jovghn6ns4jerg1n4g48funs1nb(a)4ax.com>,
>mxsmanic(a)gmail.com (Mxsmanic) wrote:
>
>> *From:* Mxsmanic <mxsmanic(a)gmail.com>
>> *Date:* Fri, 11 Aug 2006 12:17:30 +0200
>>
>> Martin writes:
>>
>> > The pink oboe?
>>
>> I simply wanted to know if it was equal temperament (such as a piano)
>> or not (such as a violin).
>
>Now that you know, are you going to answer my enquiry as to why a major
>triad with far-from-integer ratios among the frequencies is nevertheless,
>in the West, broadly considered a 'pleasing' sound?

The ratio of 1.259921 in the even-tempered scale is the best
approximation to a ratio of 5:4 of the diatonic scale; the ideal
5:4 ratio would be the ideal harmonic. The well-tempered scale is
simply a good approximation the well-tempered scale having a
number of practical advantages over the diatonic scale.

************* DAVE HATUNEN (hatunen(a)cox.net) *************
* Tucson Arizona, out where the cacti grow *
* My typos & mispellings are intentional copyright traps *
From: Hatunen on
On Fri, 11 Aug 2006 09:24:36 -0500, barney2(a)cix.compulink.co.uk
wrote:

>In article <9t2pd218v75s89pn4vequsson0313ptjf7(a)4ax.com>,
>mxsmanic(a)gmail.com (Mxsmanic) wrote:
>
>> *From:* Mxsmanic <mxsmanic(a)gmail.com>
>> *Date:* Fri, 11 Aug 2006 15:54:01 +0200
>>
>> barney2(a)cix.compulink.co.uk writes:
>>
>> > Now that you know, are you going to answer my enquiry as to why a
>> > major triad with far-from-integer ratios among the frequencies is
>> > nevertheless, in the West, broadly considered a 'pleasing' sound?
>>
>> Because it approaches integer ratios.
>
>Why, then, was an augmented fourth e.g. C4-F#4 long considered among the
>worst of dissonances, despite being closer to an integer ratio than the
>frequently-used and entirely-acceptable perfect fifth e.g. C4:G4?
>
>> At one time, many pianos were tuned to make the more popular ratios
>> exact, and the less popular ones relatively inaccurate. This was
>> abandoned as popular piano playing broadened to include all sorts of
>> music, and not just a few popular hits.
>
>What are the differences in the piano repertoire before and after equal
>temperament?

The problem with a diatonic tuned piano is taht the diatonic
scale is base one note, perhpas C; that piano can't be used to
play in another key.

************* DAVE HATUNEN (hatunen(a)cox.net) *************
* Tucson Arizona, out where the cacti grow *
* My typos & mispellings are intentional copyright traps *
From: dgs on
Dave Frightens Me wrote:

> On Fri, 11 Aug 2006 12:18:51 +0200, Mxsmanic <mxsmanic(a)gmail.com>
> wrote:
>
>
>>Dave Frightens Me writes:
>
>
>>>Intelligent people live in the same world as anyone else.
>>
>>But they are smarter than other people are.
>
>
> Not necessarily. You can be intelligent, but not very smart.

Like, for instance, those with Asperger's syndrome, perhaps?
--
dgs
From: Mxsmanic on
Hatunen writes:

> The ancient Greeks demonstrated the rleationship between harmony
> and integer ratios, although, of course, they knew nothing of
> frequency and did it by the measurementof instrumental string
> lengths.

It's lucky for them that they didn't post their findings on this
newsgroup.

--
Transpose mxsmanic and gmail to reach me by e-mail.
From: barney2 on
In article <pfdpd2d9uvs94du0bnlb352a7p91kkeb9d(a)4ax.com>, hatunen(a)cox.net
(Hatunen) wrote:

> *From:* Hatunen <hatunen(a)cox.net>
> *Date:* Fri, 11 Aug 2006 09:57:44 -0700
>
> On Fri, 11 Aug 2006 08:34:32 -0500, barney2(a)cix.compulink.co.uk
> wrote:
>
> >In article <v8mod29jovghn6ns4jerg1n4g48funs1nb(a)4ax.com>,
> >mxsmanic(a)gmail.com (Mxsmanic) wrote:
> >
> >> *From:* Mxsmanic <mxsmanic(a)gmail.com>
> >> *Date:* Fri, 11 Aug 2006 12:17:30 +0200
> >>
> >> Martin writes:
> >>
> >> > The pink oboe?
> >>
> >> I simply wanted to know if it was equal temperament (such as a piano)
> >> or not (such as a violin).
> >
> >Now that you know, are you going to answer my enquiry as to why a
> major >triad with far-from-integer ratios among the frequencies is
> nevertheless, >in the West, broadly considered a 'pleasing' sound?
>
> The ratio of 1.259921 in the even-tempered scale is the best
> approximation to a ratio of 5:4 of the diatonic scale; the ideal
> 5:4 ratio would be the ideal harmonic.

So the reason that C4-G4 sounds 'better' than C4-F#4 is that the ratio of
the former, 1:1.498303, is closer to 10:15 than the latter, 1:1.41421, is
to 10:14?

(This is a genuine question.)