Yahoo Tuning Groups Ultimate Backup tuning What is the Most "out- of- tune sounding" Microtonal Number of EDO??

Hi Frank,

you surely know that the matter has been fully investigated in two recent
books:
- in full detail, in a few chapters of Patrizio Barbieri, Enharmonic
Temperaments, Rome 2008.
- in my Unequal Temperaments book, section 19.9 SYSTEMATIC EXPLORATION OF
ETS.

The worst offenders are possibly 13EDO (all the fifths sharp by 36.5 Cents)
and 14EDO (all the major thirds sharp by 42.3 Cents).

For an improvement of BOTH fifths and major thirds over 12EDO, the next best
one is 31EDO.
(yes: any lower EDO has EITHER fifths worse than 12EDO, OR major thirds
worse, OR BOTH).

The next one is 53EDO, but it sports an inconsistency: 4 fifths do NOT add
up to a pure major third!

For consistency and an even slightly improvement, the next step is 74EDO.

Now you understand why humanity has kept to 12EDO, Equally Tempered or
otherwise: it is by far the most practical solution.
If you are really into microtones, then 31EDO is the thing, which is why it
was so much in fashion in Italy c.1550-1650.
By the way, all the above was found in Europe in the Centuries 16 to 18th,
but the Chinese knew it all 2,000 years ago.

Kind regards

Claudio
http://temper.braybaroque.ie/

_____

From: tuning@yahoogroups.com [mailto:tuning@yahoogroups.com] On Behalf Of
micro_piano
Sent: 22 January 2009 12:01
To: tuning@yahoogroups.com
Subject: [tuning] What is the Most "out- of- tune sounding" Microtonal
Number of EDO??

Okay Guys,

Here's a bit of a different question.

To the average "man on the street", what is the MOST out-of-
tune "sounding" Number of Microtonal EDO between a quarter-tone and a
semi-tone??

Is it 24EDO (quarter-tones)??
23EDO?
22EDO?
21EDO?
20EDO?
19EDO?
18EDO (third-tones)??
17EDO?
16EDO?
15EDO?
14EDO?
or 13EDO?

Thanks for all your answers in advance,

Frank Wilson, Ph.D (Musicology)

🔗Andreas Sparschuh <a_sparschuh@...>

🔗Daniel Forró <dan.for@...>

Average man of the street is used to 12EDO pop and has problem to distinguish second from fifth, so for such person any other tuning will be out of tune. Nothing to say about the microtonal music work itself which will be probably aesthetically also from the other world...

Daniel Forro

On 22 Jan 2009, at 9:01 PM, micro_piano wrote:

> Okay Guys,
>
> Here's a bit of a different question.
>
> To the average "man on the street", what is the MOST out-of-
> tune "sounding" Number of Microtonal EDO between a quarter-tone and a
> semi-tone??
>
> Is it 24EDO (quarter-tones)??
> 23EDO?
> 22EDO?
> 21EDO?
> 20EDO?
> 19EDO?
> 18EDO (third-tones)??
> 17EDO?
> 16EDO?
> 15EDO?
> 14EDO?
> or 13EDO?
>
> Thanks for all your answers in advance,
>
> Frank Wilson, Ph.D (Musicology)
>

🔗djtrancendance@...

Hmm...
Well I know in advance 5EDO, 12EDO, 19EDO, 24EDO...sound relatively consonant. So my guess is the EDO's between them IE 8 and 9EDO, 15 and 16EDO, 21 and 22EDO would be the "sour areas".
But, come the think of it, 24EDO, 19EDO, 12EDO and 5EDO come close to intersecting with 12EDO...and I think that explains a lot.

I tend not to like EDO-type scales so much in general, though, as the ones which can be used to make chords which sound good to most tend to also sound too much like 12TET. The more interestingly mood ones include tunings like 10TET which sound terribly dissonant...and, even with pure sine waves, still sound a good deal more sour than
12TET.
*****************************************************************************************************
I seriously wonder why the harmonic series has not been used...or split up and reformed into new scales very much (my own experimentation seems to say rearranging the harmonic series fractions 16/15, 15/14...and under absolutely beautiful scales to virtually any ear).

I also wonder why people don't use Sethares' method of "making an instrument's timbre match a scale harmonically" to make things like 10TET sound decent, if not good, to the "average" listener's ear.

But, to note: I am a huge fan of MOS-type scales (such as those featured in the "horagram scales" article which Wilson wrote). Still I would hesitate to compare an MOS scale with any more than 6 tones to the consonance of a 7-tone scale in 12TET favorably...hence I think a better method of forming scales under tunings would be
needed for 7+ note scales that can compete with 12TET in modern music (including the usual dreaded "pop" music).

-Michael

--- On Thu, 1/22/09, Daniel Forró <dan.for@...> wrote:

From: Daniel Forró <dan.for@...>
Subject: Re: [tuning] What is the Most "out- of- tune sounding" Microtonal Number of EDO??
To: tuning@yahoogroups.com
Date: Thursday, January 22, 2009, 4:46 PM

Average man of the street is used to 12EDO pop and has problem to

distinguish second from fifth, so for such person any other tuning

will be out of tune. Nothing to say about the microtonal music work

itself which will be probably aesthetically also from the other world...

Daniel Forro

On 22 Jan 2009, at 9:01 PM, micro_piano wrote:

> Okay Guys,

> Here's a bit of a different question.

> To the average "man on the street", what is the MOST out-of-

> tune "sounding" Number of Microtonal EDO between a quarter-tone and a

> semi-tone??

> Is it 24EDO (quarter-tones) ??

> 23EDO?

> 22EDO?

> 21EDO?

> 20EDO?

> 19EDO?

> 18EDO (third-tones) ??

> 17EDO?

> 16EDO?

> 15EDO?

> 14EDO?

> or 13EDO?

> Thanks for all your answers in advance,

> Frank Wilson, Ph.D (Musicology)

What is the Most "out- of- tune sounding" Microtonal Number of EDO??

🔗micro_piano <frankw802@...>

🔗Claudio Di Veroli <dvc@...>

🔗Andreas Sparschuh <a_sparschuh@...>

🔗Daniel Forró <dan.for@...>

🔗djtrancendance@...

🔗Herman Miller <hmiller@...>