Meaning of EDO for some musicians (was Re: How do microtonal people hear?)

Hi all.

I think one of the problems of presenting microtonal music to some people,
including some unexperienced or conservative musicians, is the fact that the
basic scale used to play most of the "famous pieces" both in classical and
in popular music is an equal division of the octave. Many people find the
evenness of 12-EDO as the main reason for their preference to use it. They
have some sort of sonic image in their mind of what a 100 cent interval more
or less sounds like. Then, when they hear a microtonal piece, they in some
way try to find a way how they could get some of the heard harmonic or
melodic intervals by layering multiples of the steps that they believe to be
those of 100 cents. If they find an interval, either in a melody or in a
chord, that they can't imagine as a multiple of these 100-cent distances,
they say the music is out of tune. I think these false assumptions about
what's "in tune" and what isn't would be much less frequent if the basic
scale for most of the commonly played/heard music was a different kind of
tuning than an EDO. This is not my invention, I've met many musicians who
think about music and intonation just this way indeed.

Petr

On 2/4/06, Petr Parízek <p.parizek@chello.cz> wrote:
> Hi all.
>
> I think one of the problems of presenting microtonal music to some people,
> including some unexperienced or conservative musicians, is the fact that the
> basic scale used to play most of the "famous pieces" both in classical and
> in popular music is an equal division of the octave. Many people find the
> evenness of 12-EDO as the main reason for their preference to use it. They
> have some sort of sonic image in their mind of what a 100 cent interval more
> or less sounds like. Then, when they hear a microtonal piece, they in some
> way try to find a way how they could get some of the heard harmonic or
> melodic intervals by layering multiples of the steps that they believe to be
> those of 100 cents. If they find an interval, either in a melody or in a
> chord, that they can't imagine as a multiple of these 100-cent distances,
> they say the music is out of tune. I think these false assumptions about
> what's "in tune" and what isn't would be much less frequent if the basic
> scale for most of the commonly played/heard music was a different kind of
> tuning than an EDO. This is not my invention, I've met many musicians who
> think about music and intonation just this way indeed.
>
> Petr

In my experience most classical and popular music does not use
enharmonic equivalence (C# = Db) at all, so it would make sense in any
meantone temperament. I would say extended meantone temperament (i.e.
using more than 12 successive pitches of meantone) is the most
mainstream direction to explore alternate tuning, and a very promising
one at that. After all, meantone is arguably the best possible linear
temperament in both the 5 limit and the 7 limit.

I think this would also be the best direction to "market" alternate
tuning, so to speak, to kids in music theory classes. Just mention
that C# and Db aren't necessarily the same pitch and that should get
the ball rolling. It would also help a lot if keyboards with split
black keys were more popular.

Keenan

--- In tuning@yahoogroups.com, Keenan Pepper <keenanpepper@...> wrote:

> In my experience most classical and popular music does not use
> enharmonic equivalence (C# = Db) at all, so it would make sense in any
> meantone temperament. I would say extended meantone temperament (i.e.
> using more than 12 successive pitches of meantone) is the most
> mainstream direction to explore alternate tuning, and a very promising
> one at that. After all, meantone is arguably the best possible linear
> temperament in both the 5 limit and the 7 limit.

Moreover, if you stick to mostly triadic harmony, you don't get
complaints about out of tuneness. If septimal sounds come into it, it
will seem a bit exotic to many people unless you stick to a relatively
tame meantone like 55-et.

> I think this would also be the best direction to "market" alternate
> tuning, so to speak, to kids in music theory classes. Just mention
> that C# and Db aren't necessarily the same pitch and that should get
> the ball rolling.

If kids in theory classes are not being taught that C# and Db are not
necessarily the same in a meantone context the curriculum needs to be
changed.

It would also help a lot if keyboards with split
> black keys were more popular.

Better yet, two ranks of white keys, suitable for either extended
meantone or 19-edo.

On 2/4/06, Gene Ward Smith <genewardsmith@coolgoose.com> wrote:
[snip]
> If kids in theory classes are not being taught that C# and Db are not
> necessarily the same in a meantone context the curriculum needs to be
> changed.

I remember being taught that they were just different names for the
same note, and the enharmonic spelling wasn't important. I even
remember this rule always to use sharps when ascending and flats when
descending...

> It would also help a lot if keyboards with split
> > black keys were more popular.
>
> Better yet, two ranks of white keys, suitable for either extended
> meantone or 19-edo.

Hmm, interesting. When I think of a 19-edo keyboard I picture either 7
white keys, with single black keys between E&F and B&C and double
black keys for the rest, or 12 white keys with 7 black keys suitably
arranged. 14 white keys would confuse me.

Keenan

Hi Keenan.

You wrote:

> I remember being taught that they were just different names for the
> same note, and the enharmonic spelling wasn't important.

Yes, this was another thing I had in mind when I was saying that. It reminds
me of an event that happened when I was in the last year of my conservatory
studies. One day, I met a student who was in the first year at that time.
And I clearly remember him having said that the C minor chord was the one
made of the tones "C-D#-G". When he said this, I imagined a chord similar to
6:7:9 or something like that and I thought: "I'd wish him to hear how this
sounds."

> I even remember this rule always to use sharps when ascending and flats
when
> descending...

As late as after doing a few experiments with this in 5-limit JI and later
in meantone, I finally understood this was partly a result of an idea of a
possible melodic or harmonic phrase where the tones with accidentals are the
ones to be resolved (i.e. the leading tones) and the naturals are the ones
to which the resolution leads (i.e. the results of common melodic or
harmonic cadences). If it was the opposite, then surely you'd have to use
sharps when descending and flats when ascending.

Petr

--- In tuning@yahoogroups.com, Keenan Pepper <keenanpepper@...> wrote:
>If kids in theory classes are not being taught that C# and Db arenot
>necessarily the same in a meantone context the curriculum needs to be
>changed.
Correct, because in 19tone keyboard-instruments, like on:
http://www.denzilwraight.com/roman.htm
are B#=Cb and E#=Fb equal same instead C#=Db, as in 12et.

Here are my frequencies absolute in Hertzians for that harpsichord
as tuning instruction in the circle of 19 times 5ths like i did in:
http://www.strukturbildung.de/Andreas.Sparschuh/
(sorry! available only in german at the moment)

A 55,110,220,440 Hz <=start with tuning-fork A4 pitch
E 165:=55*3 begin with an just pure 5th: A>E
B 247,494(495:=165*3) flatten 5th E4>B4 down one single Hz flat
F# 185,370,740(741:=247*3) flatten 5th B4>F#5 also down 1 Hz flat
C# 69,138,276,553(555=185*3)F#4>C#5 too, 3rd A>C# 275:=55*5 1Hz sharp
G# 103,206(207) &ct.
D# 77,154,308(309) attend the septimal-tritonus A>D# ratio: 7/5
A# 321:=77*3=33*7 pure,in order to yield an harmonic 7th to F1:=33 Hz
E#=Fb 43,86,172,344,688(693) meantonic 19-tone enharmonics E#=Fb
B#=Cb 64,128(129:=43*3)located on the keyboard inbetween keys B and C
Gb (95,190)191(192:=64*3) now b-flats accidentials instead #-sharps
Db 71,142,284(285:=95*3) 4th Db4>Gb4 beats 1 Hz sharp
Ab 53,106,212(213:=71*3)
Eb 79,158(159:=53*3)
Bb 59,118,236(237:=79*3)
F 11,22,44,88,176(177) wanting F:C:A:D#:G == 1:3:5:7:9 partial series
C 33 also C:E:G:A# septimal C major 4-chord C:E:G:A#==1:3:5:7
G 99 do you really like an pure 11:33:55:77:99 sounding just 5-chord?
D 37,74,148,296(297) SC=81/80=(297/296)*(111/110) two subdivions
A 55,110(111) cycle of 19 tones complete ready closed on A1=55Hz

> I remember being taught that they were just different names for the
> same note, and the enharmonic spelling wasn't important.
here an other enharmonic identity than Db=C# is valid:

B#1=Cb2:=64Hz & E#1=Fb1:=43 Hz

have equally the same pitch-frequencies by defintion.
Attend:
~41 Hz is about the lowest E1 string on a electric or double-bass.
http://www.41hz.com/
but E1 becomes here in above tuning concrete an quarter Hertzian
sharper that that:
E1=41.25Hz ,82.5Hz ,165Hz:=E3

> I even
> remember this rule always to use sharps when ascending and flats
> when
> descending...
You can forget that here, because:
C#2=69 Hz and Db2=71 Hz are appearently different,
even well audiable distinguishing.
>
> > It would also help a lot if keyboards with split
> > > black keys were more popular.
Even the 19 tone Denzils W. harpsichords too?
> >
> > Better yet, two ranks of white keys, suitable for either extended
> > meantone or 19-edo.
logarithmic 19et has only good minor 3rds, because
(6 / 5)^19 = ~ 31.948...=~ 32=2^5 , 5 times an 8th=octave.
but has only an bad approximation for the harmonic 7th with ratio 7/4,
barely 19 minor 3rds sound simply to much sad for my ears.
>
> Hmm, interesting. When I think of a 19-edo keyboard I picture either 7
> white keys, with single black keys between E&F and B&C and double
> black keys for the rest, or 12 white keys with 7 black keys suitably
> arranged. 14 white keys would confuse me.
Do
"^"=E#=Fb & "^" =B#=Cb disturb really, if they
are located on that way as further accidentials
above the classical white and black in the 3rd
column on the top of the board?:

beyboard-layout:

|+-+-+-+-+-+-+-++
||b|#|^|b|b|#|^||
|+-+-+|+-+-+-+|||
||#|b|||#|#|b||||
|+-+-+|-+-+-+-|-+
|C|D|E|F|G|A|B|C|
+-+-+-+-+-+-+-+-+

>
> Keenan
>
anyhow, most of my sudents, that had
played with their fingers and listened by own ears,
above just pure resonant 5-chord:

F:C:A:D#:G == 11:33:55:77:99

liked the amazing sound in resonance.
and considered afterwards 12et-instruments as
inacceptable out of tune.

kind regards
A.S.

--- In tuning@yahoogroups.com, "a_sparschuh" <a_sparschuh@...> wrote:

> anyhow, most of my sudents, that had
> played with their fingers and listened by own ears,
> above just pure resonant 5-chord:
>
> F:C:A:D#:G == 11:33:55:77:99

Normally we'd express this as 1:3:5:7:9 -- "lowest terms".

> liked the amazing sound in resonance.
> and considered afterwards 12et-instruments as
> inacceptable out of tune.
>
> kind regards
> A.S.

--- In tuning@yahoogroups.com, "wallyesterpaulrus"
<wallyesterpaulrus@...> wrote:
>
> --- In tuning@yahoogroups.com, "a_sparschuh" <a_sparschuh@> wrote:

> > above just pure resonant 5-chord:
> >
> > F:C:A:D#:G == 11:33:55:77:99
Take concrete to 2^6Hz=64 Hz or middle c=256Hz=2^8Hz
as absoulte reference, then
>
> Normally we'd express this as 1:3:5:7:9 -- "lowest terms".

but you divided out the 11th partial the Alphorn FA 11/8
11 the (Oberton) Overtone f2xx = 551 (Alphorn-Fa)

http://delphi.zsg-rottenburg.de/ttmusik.html

neglecting the Swiss (11/8)/(4/3)=33/32 Alphorn comma of:
1 200 * (ln(33 / 32) / ln(2)) = ~53.2729432....Cents
above an ordinary usual FA 4th 4/3 of:

1 200 * (ln(4 / 3) / ln(2)) = ~498.044....Cents

called
"Natur-tone 11 (Alphornfa)"
http://www.margotmargot.ch/mmnaturt.html
Confrim about
use and meaning of the 11. parttial in Switzerland (in german)
www.alphornmusik.ch/aufsatz/acrodateien/melodik.pdf

Here 2 english sources too about the usage of 11th partial as Alphorn FA:
http://www.music.princeton.edu/~ted/alphorn.html
(#10)
Also, the Alphorn FA, the 11th partial, written F#, top line treble
clef, is a raised 4th leading to the G [written]: in the key of F# it
sounds in-between B natural and C natural; it is a very distinct sound

or
http://www.findarticles.com/p/articles/mi_m2822/is_2001_Spring-Summer/ai_100808915/pg_5
Although Alphorns vary in length and therefore the number of pitches
available, most horns produce pitches through the twelfth overtone.
Certain pitches in the harmonic series sound "out of tune" to western
ears (see Ex. 1). In particular, the 11th partial or overtone, often
used in Swiss music and famously known as the "Alphorn-fa" ("fa" being
the fourth pitch of a scale), contributes to the uniqueness and exotic
appeal of mountain music;

therefore
44:55:66:77:99
sounds in my ears completely different as
32:40:48:56:72
which can be reduced in deed to simply
4:5:6:7:8:9
by the inherent common factor 8,
if you relate both 5-chords to the
common reference C4=256 Hz=2^8 Hz

Attend:
compared to 256Hz contains our actual normal pitch

440Hz := 256Hz * (5/4) * (11/8) or = 55Hz*8

an pure 3rd 5/4 times an pure 11/8 Alphorn yodel FA 4th,
as used since many centuries.

Remark:
~53 Cents leads to funny quartertones.
You can't temper them out by "Stopfen", plugging with the hand.
(a grip into the mouth of your horn)
because your arms will be to short
in order to reach to the sounding opening end.

kind regards
A.S.

I'm afraid I can't follow the logic of your response at all. I am *not* neglecting 33:32 or any other comma in expressing 11:33:55:77:99 as 1:3:5:7:9. The two chords contain exactly the same arrangement of intervals.

--- In tuning@yahoogroups.com, "a_sparschuh" <a_sparschuh@...> wrote:
>
> --- In tuning@yahoogroups.com, "wallyesterpaulrus"
> <wallyesterpaulrus@> wrote:
> >
> > --- In tuning@yahoogroups.com, "a_sparschuh" <a_sparschuh@> wrote:
>
> > > above just pure resonant 5-chord:
> > >
> > > F:C:A:D#:G == 11:33:55:77:99
> Take concrete to 2^6Hz=64 Hz or middle c=256Hz=2^8Hz
> as absoulte reference, then
> >
> > Normally we'd express this as 1:3:5:7:9 -- "lowest terms".
>
> but you divided out the 11th partial the Alphorn FA 11/8
> 11 the (Oberton) Overtone f2xx = 551 (Alphorn-Fa)
>
> http://delphi.zsg-rottenburg.de/ttmusik.html
>
> neglecting the Swiss (11/8)/(4/3)=33/32 Alphorn comma of:
> 1 200 * (ln(33 / 32) / ln(2)) = ~53.2729432....Cents
> above an ordinary usual FA 4th 4/3 of:
>
> 1 200 * (ln(4 / 3) / ln(2)) = ~498.044....Cents
>
> called
> "Natur-tone 11 (Alphornfa)"
> http://www.margotmargot.ch/mmnaturt.html
> Confrim about
> use and meaning of the 11. parttial in Switzerland (in german)
> www.alphornmusik.ch/aufsatz/acrodateien/melodik.pdf
>
>
> Here 2 english sources too about the usage of 11th partial as Alphorn FA:
> http://www.music.princeton.edu/~ted/alphorn.html
> (#10)
> Also, the Alphorn FA, the 11th partial, written F#, top line treble
> clef, is a raised 4th leading to the G [written]: in the key of F# it
> sounds in-between B natural and C natural; it is a very distinct sound
>
> or
> http://www.findarticles.com/p/articles/mi_m2822/is_2001_Spring-Summer/ai_100808915/pg_5
> Although Alphorns vary in length and therefore the number of pitches
> available, most horns produce pitches through the twelfth overtone.
> Certain pitches in the harmonic series sound "out of tune" to western
> ears (see Ex. 1). In particular, the 11th partial or overtone, often
> used in Swiss music and famously known as the "Alphorn-fa" ("fa" being
> the fourth pitch of a scale), contributes to the uniqueness and exotic
> appeal of mountain music;
>
>
> therefore
> 44:55:66:77:99
> sounds in my ears completely different as
> 32:40:48:56:72
> which can be reduced in deed to simply
> 4:5:6:7:8:9
> by the inherent common factor 8,
> if you relate both 5-chords to the
> common reference C4=256 Hz=2^8 Hz
>
> Attend:
> compared to 256Hz contains our actual normal pitch
>
> 440Hz := 256Hz * (5/4) * (11/8) or = 55Hz*8
>
> an pure 3rd 5/4 times an pure 11/8 Alphorn yodel FA 4th,
> as used since many centuries.
>
> Remark:
> ~53 Cents leads to funny quartertones.
> You can't temper them out by "Stopfen", plugging with the hand.
> (a grip into the mouth of your horn)
> because your arms will be to short
> in order to reach to the sounding opening end.
>
> kind regards
> A.S.
>