12 ET and the Major Third

From my own point of view,

1: you have to get retrained to hearing 5/4 as a major third. The conflict
lies perhaps between 5/4 and 81/64, but perhaps only through fifths. None
yet could say they've heard the 81st harmonic, it's just too weak. You can
sound the tone where it would be, brought down several octaves. For example
C at 128Hz approx. makes the pythagorean E at a whopping 10368Hz, whereas
the 5/4 occurs at 640. Makes 12ET a kind of pythagorean meantone, like
everyone knows and hates.

2. The ear likes to make the major third brighter. Same goes for minor
third: some trans-Danubian minor thirds get really close to major ones, or a
re best seen as neutral thirds. Russian/Czech/Hungarian/Romanian folk music
uses this kind of third very often.

3. Piano inharmonicity causes all sorts of effects, but the ear likes things
sharp. Classic acoustic test: two lines *exactly* a 4/1 or 5/1 apart sounds
wrong, the upper line sounds flat. Stretch the octave a bit, and hey presto,
things are in tume again. The difference is very small, of the order of a
schizma or less, at four octaves or five. At six or seven 2/1s, the ear can
get confused very easily, and even sevenths or 9ths can sound in tune. This
of course is due to partials occuring in the same area. are you plaing in
2/1s or are you playing in 9/8 or 15/16 or closer ratios. By definition, a
just 'otonal' ratio will, if played with its fundamental will sound
consonant. Lowering it into closer position will result in dissonance
through clashing overtones. Then comes that question: if 2/1s are stretched,
won't the others be also?

The answer is yes. So where precisely and at what actual ratio of
frequencies is the harmonic series? Physics and physiology are at odds. You
can do sums forever, but will it sound like you worked it out to be?

But hey, teach your grandmother to suck eggs as they say; I suspect you knew
all this anyway.

Mark

--- In tuning@y..., Mark Gould <mark.gould@a...> wrote:

> 2. The ear likes to make the major third brighter. Same goes for minor
> third: some trans-Danubian minor thirds get really close to major ones, or a
> re best seen as neutral thirds. Russian/Czech/Hungarian/Romanian folk music
> uses this kind of third very often.

My ear likes the major third just, and is quite fond of 7/6 in place of 6/5.

--- In tuning@y..., Mark Gould <mark.gould@a...> wrote:
>
> 2. The ear likes to make the major third brighter.

this is totally subjective. in india pure 5/4 major thirds are the
norm. in classical byzantine scales one finds ~367 cents over
the tonic.

> Same goes for minor
> third:
> some trans-Danubian minor thirds get really close to major
>ones, or a
> re best seen as neutral thirds.
Russian/Czech/Hungarian/Romanian folk music
> uses this kind of third very often.

neutral thirds are very common in arabic, thai, and african
scales. how do you know they're sharp minor thirds and not flat
major thirds?

> 3. Piano inharmonicity causes all sorts of effects, but the ear
likes things
> sharp. Classic acoustic test: two lines *exactly* a 4/1 or 5/1
apart sounds
> wrong, the upper line sounds flat. Stretch the octave a bit, and
hey presto,
> things are in tume again.

the octave stretching effect is true in some cases, especially
melodic sine waves, but to any significant extent for
simultaneous vocal harmonies (or any periodic synthesizer
waveform you should care to try it for). i don't feel that ratios more
complex than 4:3 have any relevance for unaccompanied
melody. cultural factors are overwhelmingly more important in
determining melodic correctness.

> The difference is very small, of the order of a
> schizma or less, at four octaves or five.

can you clarify what you mean by this please, and cite your
research (a schisma is only 2 cents, you know).

> At six or seven 2/1s, the ear can
> get confused very easily, and even sevenths or 9ths can sound
in tune. This
> of course is due to partials occuring in the same area.

can you clarify this statement as well?

> are you plaing in
> 2/1s or are you playing in 9/8 or 15/16 or closer ratios. By
definition, a
> just 'otonal' ratio will,

all ratios are equally otonal or utonal. you need a chord of three
or more notes to possibly qualify as 'otonal' or 'utonal'.

> if played with its fundamental will sound
> consonant. Lowering it into closer position will result in
dissonance
> through clashing overtones.

possibly, though several other effects are at play as well. if it
were simply about clashing overtones, how would you explain
octave stretching? i refer you to ernst terhardt's website for
discussion of many of these issues.

> Then comes that question: if 2/1s are stretched,
> won't the others be also?
>
> The answer is yes.

if you stretch the octaves by a schisma every four or five octaves,
the major third will be stretched by a fraction of a cent. this is a
far cry from the fourteen cent difference between the 5/4 and an
et major third.

> Physics and physiology are at odds.

physics should never be never be the end of the story, or even
more than a preface. there is a human nervous system and
mind at work. psychoacoustics is progressing at an
unprecedented rate and one needs to have some sense of what
has been discovered. we are not living in helmholtz's world
anymore.

--- In tuning@y..., "genewardsmith" <genewardsmith@j...> wrote:
> --- In tuning@y..., Mark Gould <mark.gould@a...> wrote:
>
> > 2. The ear likes to make the major third brighter. Same goes
for minor
> > third: some trans-Danubian minor thirds get really close to
major ones, or a
> > re best seen as neutral thirds.
Russian/Czech/Hungarian/Romanian folk music
> > uses this kind of third very often.
>
> My ear likes the major third just, and is quite fond of 7/6 in
>place of 6/5.

this same aesthetic is associated with much of the american
minimalist movement including lamonte young and micheal
harrison. definitely a style of music that calls for something
different than outgoing "brightness".

I tend to agree with Gene on the 5/4 and 7/6. It is true than under certain circumstances on like
thirds bright but not for everything. It is probably the reason in India you find both -being
dependent on what one wants to say

genewardsmith wrote:

> --- In tuning@y..., Mark Gould <mark.gould@a...> wrote:
>
> > 2. The ear likes to make the major third brighter. Same goes for minor
> > third: some trans-Danubian minor thirds get really close to major ones, or a
> > re best seen as neutral thirds. Russian/Czech/Hungarian/Romanian folk music
> > uses this kind of third very often.
>
> My ear likes the major third just, and is quite fond of 7/6 in place of 6/5.
>
>

-- Kraig Grady
North American Embassy of Anaphoria island
http://www.anaphoria.com

The Wandering Medicine Show
Wed. 8-9 KXLU 88.9 fm

Paul!
I believe La Monte avoids all intervals of 5

paulerlich wrote:

>
>
> this same aesthetic is associated with much of the american
> minimalist movement including lamonte young and micheal
> harrison. definitely a style of music that calls for something
> different than outgoing "brightness".
>
>

-- Kraig Grady
North American Embassy of Anaphoria island
http://www.anaphoria.com

The Wandering Medicine Show
Wed. 8-9 KXLU 88.9 fm