New to the list, and "tuning" higher tertian chords?

Greetings all,

I just subscribed to this list, as tuning and the harmonic series have long been addictions of mine. I'm still a relative novice in this field, but I'm learning...

Anyways -- I did some experimenting with computer sine-wave generators as an undergrad, as a result of a fight I got into with a conductor about whether to tune a minor seventh flat or sharp from equal temperament. He insisted flat (7:4), I insisted sharp (9:5), so I empirically tested it and discovered we were both right, depending on the context (i.e., is it in a dominant seventh chord, or a minor seventh chord).

What I'm curious about -- are there "standard" ways to tune other tertian chords that aren't as apparent in the harmonic series, such as a fully-diminished seventh chord, or a dominant-ninth-sharp-eleven chord? I was just curious -- chords like the dominant ninth (4:5:6:7:9) and even the minor seventh (10:12:15:18) occur naturally within the first 20 partials of the series, but I don't see a convincing fully diminished seventh chord...

Maybe I'm missing the boat on all this -- if so, please go gentle with me, as I'm still fairly new to all of this. I mean, just this past week I finally discovered Bach's WTC has nothing to do with equal temperament...

Eric

>What I'm curious about -- are there "standard" ways to tune
>other tertian chords that aren't as apparent in the harmonic
>series,

What's a tertian chord?

>such as a fully-diminished seventh chord,

The classical way is 10:12:14:17. You might also have fun
with the likes of 11:13:15:17 or even 9:11:13:15.

>or a dominant-ninth-sharp-eleven chord?

4:5:6:7:9:11 is the simplest one.

-Carl

--- In tuning@yahoogroups.com, "Eric T Knechtges" <knechtge@m...>
wrote:
> Greetings all,
>
> I just subscribed to this list, as tuning and the harmonic
>series have long been addictions of mine. I'm still a relative
>novice in this field, but I'm learning...
>
> Anyways -- I did some experimenting with computer sine-wave
>generators as an undergrad, as a result of a fight I got into with a
>conductor about whether to tune a minor seventh flat or sharp from
>equal temperament. He insisted flat (7:4), I insisted sharp (9:5),
>so I empirically tested it and discovered we were both right,
>depending on the context (i.e., is it in a dominant seventh chord,
>or a minor seventh chord).
>
> What I'm curious about -- are there "standard" ways to tune
>other tertian chords that aren't as apparent in the harmonic series,
>such as a fully-diminished seventh chord, or a dominant-ninth-sharp-
>eleven chord? I was just curious -- chords like the dominant ninth >
(4:5:6:7:9) and even the minor seventh (10:12:15:18) occur naturally
>within the first 20 partials of the series, but I don't see a
>convincing fully diminished seventh chord...
>
> Maybe I'm missing the boat on all this -- if so, please go
>gentle with me, as I'm still fairly new to all of this. I mean,
>just this past week I finally discovered Bach's WTC has nothing to
>do with equal temperament...
>
> Eric

hi eric,

certain chords don't lend themselves to just intonation at all, for
example a C six-nine or C-E-G-A-D . . .

the diminished seventh chord, say in second inversion as C Eb F# A,
can be tuned with both the minor thirds near 5:6, the major sixth
near 3:5, and the augmented second near 6:7. this requires some
fudging (you may wish to put all the error in the 6:7), but you end
up with C:F# and Eb:A both near or at 5:7 and so all six intervals
are close to simple just ratios.

a more complex example like this is the G13#11 chord. monzo had a
wonderful, detailed web page with sound example on this chord, but i
can't find it for the life of me, and it's driving me nuts! monz?

anyway, once you get beyond a single chord, there are plenty of other
tuning issues that come into play, notably pitch drift and pitch
shifts. these will affect your choices for the *horizontal* intervals
by which the chords progress. it can even affect the tuning of
isolated chords. a G13#11 chord can be tuned with the #11 as 11/4
over the root and sound great in some contexts, while in others, the
voice-leading in and out of it would end up totally unworkable with
such a tuning of the chord.

so monz, where's that darn page? ;)

--- In tuning@yahoogroups.com, "Carl Lumma" <ekin@l...> wrote:

> >What I'm curious about -- are there "standard" ways to tune
> >other tertian chords that aren't as apparent in the harmonic
> >series,
>
> What's a tertian chord?

a chord spelled as a chain of thirds (possibly with some members
omitted)

> >such as a fully-diminished seventh chord,
>
> The classical way is 10:12:14:17.

"classical" may suggest a time period before helmholtz/ellis, which
wouldn't be appropriate. unless you can find an earlier
attribution . . .

>>>such as a fully-diminished seventh chord,
>>
>>The classical way is 10:12:14:17.
>
>"classical" may suggest a time period before helmholtz/ellis,
>which wouldn't be appropriate. unless you can find an earlier
>attribution . . .

I meant this in a very general way. It is sometimes taught as
the 'derivation' of the chord in undergrad theory courses, for
example.

-Carl

Another idea to keep in mind is that you might want to tune these 'jazzier' chords to
non-'purely harmonic' just intervals. Although following the harmonic series up
through the chord results in the most 'at-rest' sounds, many altered chords do not
have at-rest *functions*-- using Euler's tritone instead of the undecimal tritone for
the #11, for example, could add a surprising 'pinch' to the harmony when sounding
against the other tertian intervals. Of course, this would be harder to tune by ear... -
Justin

--- In tuning@yahoogroups.com, "Paul Erlich" <perlich@a...> wrote:
> --- In tuning@yahoogroups.com, "Eric T Knechtges" <knechtge@m...>
> wrote:
> > Greetings all,
> >
> > I just subscribed to this list, as tuning and the harmonic
> >series have long been addictions of mine. I'm still a relative
> >novice in this field, but I'm learning...
> >
> > Anyways -- I did some experimenting with computer sine-wave
> >generators as an undergrad, as a result of a fight I got into with a
> >conductor about whether to tune a minor seventh flat or sharp from
> >equal temperament. He insisted flat (7:4), I insisted sharp (9:5),
> >so I empirically tested it and discovered we were both right,
> >depending on the context (i.e., is it in a dominant seventh chord,
> >or a minor seventh chord).
> >
> > What I'm curious about -- are there "standard" ways to tune
> >other tertian chords that aren't as apparent in the harmonic series,
> >such as a fully-diminished seventh chord, or a dominant-ninth-sharp-
> >eleven chord? I was just curious -- chords like the dominant ninth >
> (4:5:6:7:9) and even the minor seventh (10:12:15:18) occur naturally
> >within the first 20 partials of the series, but I don't see a
> >convincing fully diminished seventh chord...
> >
> > Maybe I'm missing the boat on all this -- if so, please go
> >gentle with me, as I'm still fairly new to all of this. I mean,
> >just this past week I finally discovered Bach's WTC has nothing to
> >do with equal temperament...
> >
> > Eric
>
> hi eric,
>
> certain chords don't lend themselves to just intonation at all, for
> example a C six-nine or C-E-G-A-D . . .
>
> the diminished seventh chord, say in second inversion as C Eb F# A,
> can be tuned with both the minor thirds near 5:6, the major sixth
> near 3:5, and the augmented second near 6:7. this requires some
> fudging (you may wish to put all the error in the 6:7), but you end
> up with C:F# and Eb:A both near or at 5:7 and so all six intervals
> are close to simple just ratios.
>
> a more complex example like this is the G13#11 chord. monzo had a
> wonderful, detailed web page with sound example on this chord, but i
> can't find it for the life of me, and it's driving me nuts! monz?
>
> anyway, once you get beyond a single chord, there are plenty of other
> tuning issues that come into play, notably pitch drift and pitch
> shifts. these will affect your choices for the *horizontal* intervals
> by which the chords progress. it can even affect the tuning of
> isolated chords. a G13#11 chord can be tuned with the #11 as 11/4
> over the root and sound great in some contexts, while in others, the
> voice-leading in and out of it would end up totally unworkable with
> such a tuning of the chord.
>
> so monz, where's that darn page? ;)

>using Euler's tritone instead of the undecimal tritone for the
>#11, for example, could add a surprising 'pinch' to the harmony
>when sounding against the other tertian intervals.

I assume this is 45/32, which is a 5:4 above the 9. This works
nicely in some voicings.

>Another idea to keep in mind is that you might want to tune
>these 'jazzier' chords to non-'purely harmonic' just intervals.

Any other examples?

[Paul E.]
>> certain chords don't lend themselves to just intonation at all,
>> for example a C six-nine or C-E-G-A-D . . .

Depending on how this is voiced, it can be tuned quite nicely (to
my ear) with pure fifths and octaves.

>> the diminished seventh chord, say in second inversion as C Eb F# A,
>> can be tuned with both the minor thirds near 5:6, the major sixth
>> near 3:5, and the augmented second near 6:7. this requires some
>> fudging (you may wish to put all the error in the 6:7), but you end
>> up with C:F# and Eb:A both near or at 5:7 and so all six intervals
>> are close to simple just ratios.

Cool.

>> a more complex example like this is the G13#11 chord.

G13! (Ever see _Outside Out_?)

I think at this point, the voicing, and the musical context become
overridingly important.

-Carl

--- In tuning@yahoogroups.com, "Carl Lumma" <ekin@l...> wrote:

/tuning/topicId_45559.html#45567

> >>>such as a fully-diminished seventh chord,
> >>
> >>The classical way is 10:12:14:17.
> >
> >"classical" may suggest a time period before helmholtz/ellis,
> >which wouldn't be appropriate. unless you can find an earlier
> >attribution . . .
>
> I meant this in a very general way. It is sometimes taught as
> the 'derivation' of the chord in undergrad theory courses, for
> example.
>
> -Carl

***Wow, that impresses me. When *I* went to school, nobody in theory
classes *ever* related chords, even simple ones, to the harmonic
series...

J. Pehrson

>***Wow, that impresses me. When *I* went to school, nobody in theory
>classes *ever* related chords, even simple ones, to the harmonic
>series...

I haven't read Ellis, but we might infer from Paul's post that
Ellis suggested this. If so, that could explain how it got into
the 100-level theory at the University of Oregon, and elsewhere.

-Carl

Actually, Euler's Tritone is 10/7 (about 618 cents). It's a simpler ratio than the
undecimal 11th but it seems less intuitive to tune in practice, especially since it
clashes with scale deg. 2 (creating a 414 cent third!). I like to use it as the tritone in
music that approximates Eastern Orthodox canting in contrast with a 'tense' Lydian
#4 at 16:11 (649 cents). -Justin

--- In tuning@yahoogroups.com, Carl Lumma <ekin@l...> wrote:
> >using Euler's tritone instead of the undecimal tritone for the
> >#11, for example, could add a surprising 'pinch' to the harmony
> >when sounding against the other tertian intervals.
>
> I assume this is 45/32, which is a 5:4 above the 9. This works
> nicely in some voicings.
>
> >Another idea to keep in mind is that you might want to tune
> >these 'jazzier' chords to non-'purely harmonic' just intervals.
>
> Any other examples?
>
> [Paul E.]
> >> certain chords don't lend themselves to just intonation at all,
> >> for example a C six-nine or C-E-G-A-D . . .
>
> Depending on how this is voiced, it can be tuned quite nicely (to
> my ear) with pure fifths and octaves.
>
> >> the diminished seventh chord, say in second inversion as C Eb F# A,
> >> can be tuned with both the minor thirds near 5:6, the major sixth
> >> near 3:5, and the augmented second near 6:7. this requires some
> >> fudging (you may wish to put all the error in the 6:7), but you end
> >> up with C:F# and Eb:A both near or at 5:7 and so all six intervals
> >> are close to simple just ratios.
>
> Cool.
>
> >> a more complex example like this is the G13#11 chord.
>
> G13! (Ever see _Outside Out_?)
>
> I think at this point, the voicing, and the musical context become
> overridingly important.
>
> -Carl

>Actually, Euler's Tritone is 10/7

Ah.

>I like to use it as the tritone in music that approximates
>Eastern Orthodox canting in contrast with a 'tense' Lydian
>#4 at 16:11 (649 cents).

Nice.

-Carl

--- In tuning@yahoogroups.com, "Paul Erlich" <perlich@a...> wrote:

> the diminished seventh chord, say in second inversion as C Eb F# A,
> can be tuned with both the minor thirds near 5:6, the major sixth
> near 3:5, and the augmented second near 6:7. this requires some
> fudging (you may wish to put all the error in the 6:7), but you end
> up with C:F# and Eb:A both near or at 5:7 and so all six intervals
> are close to simple just ratios.

Translating this into language I find easier to understand (YMMV), if
you start out with a 1--6/5--7/5--5/3 chord, you might notice that
the 25/21 ratio between 7/5 and 5/3 is close to a 6/5; in fact,
(6/5)/(25/21) = 126/125. Hence if we fudge so as to equalize the
error, we should fudge so as to make 126/125 go away (or become a
unison.)

--- In tuning@yahoogroups.com, "Carl Lumma" <ekin@l...> wrote:

> I meant this in a very general way. It is sometimes taught as
> the 'derivation' of the chord in undergrad theory courses, for
> example.

Be that as it may, I've had fun with this chord. If you use this
chord together with its utonal version, and insist all harmony
changes must have a shared interval, you can still ooze very nicely.
People who like mictrotonal oozing might try it.

--- In tuning@yahoogroups.com, "Justin Weaver" <improvist@u...> wrote:

> Another idea to keep in mind is that you might want to tune
>these 'jazzier' chords to
> non-'purely harmonic' just intervals. Although following the
>harmonic series up
> through the chord results in the most 'at-rest' sounds,

sometimes . . .

> many altered chords do not
> have at-rest *functions*-- using Euler's tritone instead of the
>undecimal tritone for
> the #11, for example, could add a surprising 'pinch' to the harmony
>when sounding
> against the other tertian intervals. Of course, this would be
>harder to tune by ear... -
> Justin

well, this is kind of the idea i was talking about below. the G13#11
chord i was referring to seems to be best tuned with the #11 about
7/5 above the root . . . if only we could find that darn webpage!
it's not necessarily a question of sounding "against" anything -- all
these intervals can fit together quite nicely with only very slight
fudging!

>
> --- In tuning@yahoogroups.com, "Paul Erlich" <perlich@a...> wrote:
> > --- In tuning@yahoogroups.com, "Eric T Knechtges" <knechtge@m...>
> > wrote:
> > > Greetings all,
> > >
> > > I just subscribed to this list, as tuning and the harmonic
> > >series have long been addictions of mine. I'm still a relative
> > >novice in this field, but I'm learning...
> > >
> > > Anyways -- I did some experimenting with computer sine-wave
> > >generators as an undergrad, as a result of a fight I got into
with a
> > >conductor about whether to tune a minor seventh flat or sharp
from
> > >equal temperament. He insisted flat (7:4), I insisted sharp
(9:5),
> > >so I empirically tested it and discovered we were both right,
> > >depending on the context (i.e., is it in a dominant seventh
chord,
> > >or a minor seventh chord).
> > >
> > > What I'm curious about -- are there "standard" ways to tune
> > >other tertian chords that aren't as apparent in the harmonic
series,
> > >such as a fully-diminished seventh chord, or a dominant-ninth-
sharp-
> > >eleven chord? I was just curious -- chords like the dominant
ninth >
> > (4:5:6:7:9) and even the minor seventh (10:12:15:18) occur
naturally
> > >within the first 20 partials of the series, but I don't see a
> > >convincing fully diminished seventh chord...
> > >
> > > Maybe I'm missing the boat on all this -- if so, please go
> > >gentle with me, as I'm still fairly new to all of this. I mean,
> > >just this past week I finally discovered Bach's WTC has nothing
to
> > >do with equal temperament...
> > >
> > > Eric
> >
> > hi eric,
> >
> > certain chords don't lend themselves to just intonation at all,
for
> > example a C six-nine or C-E-G-A-D . . .
> >
> > the diminished seventh chord, say in second inversion as C Eb F#
A,
> > can be tuned with both the minor thirds near 5:6, the major sixth
> > near 3:5, and the augmented second near 6:7. this requires some
> > fudging (you may wish to put all the error in the 6:7), but you
end
> > up with C:F# and Eb:A both near or at 5:7 and so all six
intervals
> > are close to simple just ratios.
> >
> > a more complex example like this is the G13#11 chord. monzo had a
> > wonderful, detailed web page with sound example on this chord,
but i
> > can't find it for the life of me, and it's driving me nuts! monz?
> >
> > anyway, once you get beyond a single chord, there are plenty of
other
> > tuning issues that come into play, notably pitch drift and pitch
> > shifts. these will affect your choices for the *horizontal*
intervals
> > by which the chords progress. it can even affect the tuning of
> > isolated chords. a G13#11 chord can be tuned with the #11 as 11/4
> > over the root and sound great in some contexts, while in others,
the
> > voice-leading in and out of it would end up totally unworkable
with
> > such a tuning of the chord.
> >
> > so monz, where's that darn page? ;)

--- In tuning@yahoogroups.com, Carl Lumma <ekin@l...> wrote:
> >***Wow, that impresses me. When *I* went to school, nobody in
theory
> >classes *ever* related chords, even simple ones, to the harmonic
> >series...
>
> I haven't read Ellis, but we might infer from Paul's post that
> Ellis suggested this.

you haven't purchased or borrowed a copy of _on the sensations of
tone_ ????!!!

> If so, that could explain how it got into
> the 100-level theory at the University of Oregon, and elsewhere.
>
> -Carl

elsewhere? where else? i certainly was never taught any such thing in
my 200- and 300- level theory classes, and none of the educated
musicians i play with (berklee, new england conservatory, boston
conservatory, etc.) have any clue about such things (but they usually
love to listen to me talk about them). it sure seems to me like the
vast majority of music educators treat the 12 tones and the diatonic
scale as "givens" and explain the derivation of harmonies purely from
that foundation, never going any deeper into the nature of hearing or
sound and never going broader into alternative tuning systems.
occasionally, a passing reference to the first few harmonics (not 17
of them!) of the harmonic series is made, but that's if you're lucky.

a truly sad state of affairs. you've been extremely fortunate, carl.

Right... I meant "sound against" = "sound at the same time as"

--- In tuning@yahoogroups.com, "Paul Erlich" <perlich@a...> wrote:
> --- In tuning@yahoogroups.com, "Justin Weaver" <improvist@u...> wrote:
>
> > Another idea to keep in mind is that you might want to tune
> >these 'jazzier' chords to
> > non-'purely harmonic' just intervals. Although following the
> >harmonic series up
> > through the chord results in the most 'at-rest' sounds,
>
> sometimes . . .
>
> > many altered chords do not
> > have at-rest *functions*-- using Euler's tritone instead of the
> >undecimal tritone for
> > the #11, for example, could add a surprising 'pinch' to the harmony
> >when sounding
> > against the other tertian intervals. Of course, this would be
> >harder to tune by ear... -
> > Justin
>
> well, this is kind of the idea i was talking about below. the G13#11
> chord i was referring to seems to be best tuned with the #11 about
> 7/5 above the root . . . if only we could find that darn webpage!
> it's not necessarily a question of sounding "against" anything -- all
> these intervals can fit together quite nicely with only very slight
> fudging!
>
> >
> > --- In tuning@yahoogroups.com, "Paul Erlich" <perlich@a...> wrote:
> > > --- In tuning@yahoogroups.com, "Eric T Knechtges" <knechtge@m...>
> > > wrote:
> > > > Greetings all,
> > > >
> > > > I just subscribed to this list, as tuning and the harmonic
> > > >series have long been addictions of mine. I'm still a relative
> > > >novice in this field, but I'm learning...
> > > >
> > > > Anyways -- I did some experimenting with computer sine-wave
> > > >generators as an undergrad, as a result of a fight I got into
> with a
> > > >conductor about whether to tune a minor seventh flat or sharp
> from
> > > >equal temperament. He insisted flat (7:4), I insisted sharp
> (9:5),
> > > >so I empirically tested it and discovered we were both right,
> > > >depending on the context (i.e., is it in a dominant seventh
> chord,
> > > >or a minor seventh chord).
> > > >
> > > > What I'm curious about -- are there "standard" ways to tune
> > > >other tertian chords that aren't as apparent in the harmonic
> series,
> > > >such as a fully-diminished seventh chord, or a dominant-ninth-
> sharp-
> > > >eleven chord? I was just curious -- chords like the dominant
> ninth >
> > > (4:5:6:7:9) and even the minor seventh (10:12:15:18) occur
> naturally
> > > >within the first 20 partials of the series, but I don't see a
> > > >convincing fully diminished seventh chord...
> > > >
> > > > Maybe I'm missing the boat on all this -- if so, please go
> > > >gentle with me, as I'm still fairly new to all of this. I mean,
> > > >just this past week I finally discovered Bach's WTC has nothing
> to
> > > >do with equal temperament...
> > > >
> > > > Eric
> > >
> > > hi eric,
> > >
> > > certain chords don't lend themselves to just intonation at all,
> for
> > > example a C six-nine or C-E-G-A-D . . .
> > >
> > > the diminished seventh chord, say in second inversion as C Eb F#
> A,
> > > can be tuned with both the minor thirds near 5:6, the major sixth
> > > near 3:5, and the augmented second near 6:7. this requires some
> > > fudging (you may wish to put all the error in the 6:7), but you
> end
> > > up with C:F# and Eb:A both near or at 5:7 and so all six
> intervals
> > > are close to simple just ratios.
> > >
> > > a more complex example like this is the G13#11 chord. monzo had a
> > > wonderful, detailed web page with sound example on this chord,
> but i
> > > can't find it for the life of me, and it's driving me nuts! monz?
> > >
> > > anyway, once you get beyond a single chord, there are plenty of
> other
> > > tuning issues that come into play, notably pitch drift and pitch
> > > shifts. these will affect your choices for the *horizontal*
> intervals
> > > by which the chords progress. it can even affect the tuning of
> > > isolated chords. a G13#11 chord can be tuned with the #11 as 11/4
> > > over the root and sound great in some contexts, while in others,
> the
> > > voice-leading in and out of it would end up totally unworkable
> with
> > > such a tuning of the chord.
> > >
> > > so monz, where's that darn page? ;)

>> I haven't read Ellis, but we might infer from Paul's post that
>> Ellis suggested this.
>
>you haven't purchased or borrowed a copy of _on the sensations of
>tone_ ????!!!

I got a nice 50's-looking copy in good condition for a song at
Moe's in '98, but I haven't read it, and it's in Montana at the
moment.

>elsewhere? where else?

I'll try and remember.

>i certainly was never taught any such thing in my 200- and 300-
>level theory classes,

I went through 200-level theory at IU, and I don't remember it
being in that.

>a truly sad state of affairs. you've been extremely fortunate, carl.

I wasn't me at Oregon!

-Carl

--- In tuning@yahoogroups.com, Carl Lumma <ekin@l...> wrote:
>
> I wasn't me at Oregon!

who were you?

seriously, you think it's the 100-level classes that tend to cover
ratios and the harmonic series and such? i placed out of mine, so i
wouldn't know, and in high school orchestration and composition, they
were covered only because i was sent to the blackboard to explain
them to the class for three days!

>> I wasn't me at Oregon!
>
>who were you?

Marduk, slayer of Tiamat!

>seriously, you think it's the 100-level classes that tend to cover
>ratios and the harmonic series and such? i placed out of mine, so
>i wouldn't know, and in high school orchestration and composition,
>they were covered only because i was sent to the blackboard to
>explain them to the class for three days!

I placed out of 100-level theory too.

-Carl

What high school was this? There isn't supposed to be education like that in the US!

--- In tuning@yahoogroups.com, "Paul Erlich" <perlich@a...> wrote:
> --- In tuning@yahoogroups.com, Carl Lumma <ekin@l...> wrote:
> >
> > I wasn't me at Oregon!
>
> who were you?
>
> seriously, you think it's the 100-level classes that tend to cover
> ratios and the harmonic series and such? i placed out of mine, so i
> wouldn't know, and in high school orchestration and composition, they
> were covered only because i was sent to the blackboard to explain
> them to the class for three days!

well there wouldn't have been had i not been in the class! the
teacher (actually a former student of mario davidovsky's) and i
reversed roles for these three days.

http://www.hchs.hunter.cuny.edu/

this is a public (free) high school.

if you or someone you know are in the sixth grade or below, and live
in new york city, you might want to take the entrance exam.
apparently people are now in the business of helping you with these
things:

http://www.nytutoring.com/testprep/gifted/hunterhs.html

then again, you might prefer to stay away from the "brick prison"!

sorry for the off-topic material . . . i'll try to keep those to
private e-mails in the future.

--- In tuning@yahoogroups.com, "Justin Weaver" <improvist@u...> wrote:
> What high school was this? There isn't supposed to be education
like that in the US!
>
> --- In tuning@yahoogroups.com, "Paul Erlich" <perlich@a...> wrote:
> > --- In tuning@yahoogroups.com, Carl Lumma <ekin@l...> wrote:
> > >
> > > I wasn't me at Oregon!
> >
> > who were you?
> >
> > seriously, you think it's the 100-level classes that tend to
cover
> > ratios and the harmonic series and such? i placed out of mine, so
i
> > wouldn't know, and in high school orchestration and composition,
they
> > were covered only because i was sent to the blackboard to explain
> > them to the class for three days!

--- In tuning@yahoogroups.com, "Paul Erlich" <perlich@a...> wrote:

/tuning/topicId_45559.html#45595

>
> elsewhere? where else? i certainly was never taught any such thing
in
> my 200- and 300- level theory classes, and none of the educated
> musicians i play with (berklee, new england conservatory, boston
> conservatory, etc.) have any clue about such things (but they
usually
> love to listen to me talk about them). it sure seems to me like the
> vast majority of music educators treat the 12 tones and the
diatonic
> scale as "givens" and explain the derivation of harmonies purely
from
> that foundation, never going any deeper into the nature of hearing
or
> sound and never going broader into alternative tuning systems.
> occasionally, a passing reference to the first few harmonics (not
17
> of them!) of the harmonic series is made, but that's if you're
lucky.
>
> a truly sad state of affairs. you've been extremely fortunate, carl.

***Well, I went to school a little time ago now... but the only two
instances where tuning and harmonics were brought up at all were in
an *acoustics* class (yes, even with some *math*, Paul! :) taught by
John Clough and a course in "piano technology" which is what piano
tuning was called at that time... Oh... and I guess the electronic
composers were also talking about it, but with regard to their
*compositions*... not in a classroom setting.

J. Pehrson

--- In tuning@yahoogroups.com, "Paul Erlich" <perlich@a...> wrote:

/tuning/topicId_45559.html#45611

> well there wouldn't have been had i not been in the class! the
> teacher (actually a former student of mario davidovsky's) and i
> reversed roles for these three days.
>
> http://www.hchs.hunter.cuny.edu/
>
> this is a public (free) high school.
>

***Somehow, Paul, I keep forgetting that New York is really
your "hometown" through and through (more than myself...) Sounds
like you got off to a really good start!

Joseph