Yahoo Tuning Groups Ultimate Backup tuning High Third Sound Files (*.wav) available now

Jerry, Paul, et al,

I have made six audio files for your listening pleasure.

The files with a "1p" in the name are pure sine waves for each tone. The
files with a "32p" in the name have 32 integer partials (harmonics) per
tone, with a decay of 0.64 times the amplitude of the previous partial.
This still sounds pretty bright to me, but since we started with my
suggestion of 0.88 (which was way too bright, even if I wasn't), I
didn't want to lower it too much more. I can use a different decay at
your request, and even a different "formula" for decay if you folks can
suggest a better one.

If you have trouble playing these, let me know and also let me know
if there's some file format you know your browser/player likes. :-)

Note: These files are about 430k each, so if you have a slow modem,
you have been warned...

For comparison I made two files of the "normal third",
using the ratio 4:5:6 with "4" = middle C:
http://cjchapm.home.mindspring.com/N3_1p_4_5_6.wav
http://cjchapm.home.mindspring.com/N3_32p_4_5_6.wav

Then two files of the "high third" candidate with the ratio 14:18:21
with "14" = middle C:
http://cjchapm.home.mindspring.com/H3_1p_14_18_21.wav
http://cjchapm.home.mindspring.com/H3_32p_14_18_21.wav

Finally I made two files with the ratio 12:14:18:21
with "14" = middle C:
http://cjchapm.home.mindspring.com/H3_1p_12_14_18_21.wav
http://cjchapm.home.mindspring.com/H3_32p_12_14_18_21.wav

In case anyone cares, here's the technical info.:
* Windows PCM format (*.wav)
* the data is *not* compressed
* 44.1 kHz sample rate (CD quality)
* 16 bits per sample (for amplitude)
* mono (not stereo)
* about 5 seconds long
* reference tone is middle C (roughly 261.6 Hz)

Let me know if you have other parameters you'd like me to try.

Cheers,
Christopher

p.s. Sorry about the "[This message contained attachments]" stuff --
it's MS Outlook (my mail program) attaching something, not me. I'll try
to turn it off, but no guarantees. :-)

🔗Paul H. Erlich <PErlich@Acadian-Asset.com>

🔗Daniel Wolf <djwolf@snafu.de>

It sounds even better transposed up one or two octaves. (Coincidentally,
open 9:7 thirds above the treble staff are central -- and beautiful -- in La
Monte Young's String Quartet "Kronos Christalla", played in natural
harmonics. the same intervals, two octaves lower, have a much different
effect in _The Well Tuned Piano_).

Daniel Wolf
Frankfurt am Main

----- Original Message -----
From: Paul H. Erlich <PErlich@Acadian-Asset.com>
To: <tuning@onelist.com>
Sent: Friday, February 04, 2000 12:23 AM
Subject: RE: [tuning] High Third Sound Files (*.wav) available now

> From: "Paul H. Erlich" <PErlich@Acadian-Asset.com>
>
> > http://cjchapm.home.mindspring.com/H3_32p_14_18_21.wav
>
> To all: note how much better this one sounds when played quietly than when
> played loudly. The utonal representation 1/9:1/7:1/6 helps explain this. A
> full 1/9:1/7:1/6:1/5:1/4 (Partchian complete 9-limit utonality) would
> demonstrate this effect even better.
>
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🔗Christopher J. Chapman <christopher.chapman@conexant.com>

[Paul H. Erlich, TD 515.18 + 19]:
>> http://cjchapm.home.mindspring.com/H3_32p_14_18_21.wav
>To all: note how much better this one sounds when played quietly than when
>played loudly. The utonal representation 1/9:1/7:1/6 helps explain this. A
>full 1/9:1/7:1/6:1/5:1/4 (Partchian complete 9-limit utonality) would
>demonstrate this effect even better.
...
>This one made me think, "Who fell asleep on their car horn???!!!"

:-)

That reminds me...

I forgot to mention in my technical info. and warnings that I generated
the files with a signal amplitude of -1 dB (i.e. they are just 1 dB
below the loudest a .WAV file can be) in order to ensure that the signal
to noise ratio was good (granted, this was probably over-engineering a
non-existant problem, but since you guys had already had problems with
general MIDI vibrato, etc. I thought I should be err on the side of
over-zealousness). I'm sorry if anyone's ears got a shock as a
consequence.

[Paul H. Erlich, TD 515.19]:
>Thanks a bunch, Christopher!!!

You are certainly welcome. Would you like me to generate a file with
the full 1/9:1/7:1/6:1/5:1/4 (that's 140:180:210:252:315, right?)? If
so, with what parameters?

[Daniel Wolf, TD 515.22]:
>It [14:18:21 -- CJC] sounds even better transposed up one or two
>octaves.

Interesting... does a transposition of two octaves up sound better than
one octave? Would you guys like me to generate files starting from a
higher (or lower) reference pitch?

Jerry? Were you able to play the sound files?

Cheers,
Christopher

p.s. I really like the "[FirstName I. LastName, TD ###.##]:" citation
notation. My thanks to whoever introduced it and to all who use it. :-)

🔗David C Keenan <d.keenan@uq.net.au>

>Finally I made two files with the ratio 12:14:18:21

This can be called a "subminor seventh" chord since it has, from the root each time, a subminor third 6:7, a perfect fifth 2:3, and a subminor seventh 4:7. It could also be called a "subminor augmented 6th".

If we instead take the 14 to be the root, i.e. 14:18:21:24, it's a "supermajor sixth" (or "supermajor diminished seventh"), in the same way that a change of root makes a minor seventh chord into a sixth chord.

But without any context to the contrary, "subminor seventh" seems simplest, particularly with its similarity to the 10:12:15:18 minor seventh chord (another of the "chords Partch forgot").

My apologies to those who are still coming to grips with the 1/6:1/5:1/4 notation for a minor triad, or 1/(6:5:4) for short, but here's another notation I find useful, particularly when the chords are "necessarily tempered" (which the above are not). It's the use of a vertical bar | to stack intervals or chords. e.g. the above subminor seventh chord could be written 6:7:9|6:7 which means a 6:7:9 subminor triad with a 6:7 subminor third stacked on top. i.e. despite the fact that there are five numbers there are only four notes since the 9 of the triad is the same as the 6 of the upper sm3. So "|" has lower operator precedence than ":" which is lower than "/".

The sm7 chord can also be written utonally as 1/(7:6|9:7:6). Also 6:7|7:9|6:7 and 1/(7:6|9:7|7:6). It's annoying though that none of these transformations show the existence of the 4:7 at a glance (or the 2:3's). It's all because we're trying to write something that's better represented as a 3 dimensional graph (a tetrahedron), as a one-dimensional string of text.

Here's another addition to the notation. Square-brackets used to nest one interval or chord inside another. Consider a major triad 4:5:6. We could write it as 2[4:5]:3. This says that the 2 of the outer 2:3 is the same note as the 4 of the inner 4:5. We could also write it as 2:[5:6]3 or maybe even 2[4:5:6]3 although the latter has problems. There is an implied rule that for a chord of N notes there must always be exactly N-1 colons in the expression, no matter how it is "factored". And any two numbers separated only by | or [ or ], but not :[ or ]:, represent the same note.

For example, to show all the intervals from the root, in the subminor seventh chord, we can write it as 4[2[6:7]:3]:7. This makes more sense when you see it as
4 :7
2 :3
6:7

i.e. "[" means drop down a line (and backspace) and "]" means pop up (and backspace).

Notice also that 6:7|7:9|6:7 can just be considered shorthand for [6:7][7:9][6:7], which is equivalent to 6:7[7:9][6:7] and [6:7][7:9]6:7 and [6:7]7:9[6:7], but not 6:7[7:9]6:7. The latter would be nonsense if we allow notation like 2[4:5:6]3 for a major triad. It would imply a 6:7:6:7 chord where the 7:6 agrees with a 7:9. Not possible.

So we've got to where we can show all but one of the six relations in this tetrad, in lowest terms, in linear text.

4[2[6:7:9]3|6:7]7 or 1/(7[7:6|3[9:7:6]2]4

What we can't do with this notation is to simultaneously show two intervals that overlap without one being wholly inside the other, such as the two 2:3's in this chord.

Pretty obscure huh? Sorry, I got carried away there, somewhat off-thread.

Oh by the way, the other 11-limit chord that Partch forgot (from Graham Breed's web site) looks like

12:18:22:33
= 2:3|9:11|2:3
= 6:9:11|2:3
= 1/(3:2|11:9:6)
= 4[2:3|9:11|2:3]11
= 4[6[2:3]:11]:11
= 4[6[2:3|9:11]11|2:3]11

Are there any of these things with more than 4 notes?

-- Dave Keenan
http://dkeenan.com

🔗D.Stearns <stearns@capecod.net>

[David C Keenan:]
> the 1/6:1/5:1/4 notation for a minor triad, or 1/(6:5:4) for short,

FWIW, I like this abbreviated 1/(...) notation much better. It's not
so cumbersome looking and (in the straightforward cases) it's clear at
glance.

Dan

but here's another notation I find useful, particularly when the
chords are "necessarily tempered" (which the above are not). It's the
use of a vertical bar | to stack intervals or chords. e.g. the above
subminor seventh chord could be written 6:7:9|6:7 which means a 6:7:9
subminor triad with a 6:7 subminor third stacked on top. i.e. despite
the fact that there are five numbers there are only four notes since
the 9 of the triad is the same as the 6 of the upper sm3. So "|" has
lower operator precedence than ":" which is lower than "/".
>
> The sm7 chord can also be written utonally as 1/(7:6|9:7:6). Also
6:7|7:9|6:7 and 1/(7:6|9:7|7:6). It's annoying though that none of
these transformations show the existence of the 4:7 at a glance (or
the 2:3's). It's all because we're trying to write something that's
better represented as a 3 dimensional graph (a tetrahedron), as a
one-dimensional string of text.
>
> Here's another addition to the notation. Square-brackets used to
nest one interval or chord inside another. Consider a major triad
4:5:6. We could write it as 2[4:5]:3. This says that the 2 of the
outer 2:3 is the same note as the 4 of the inner 4:5. We could also
write it as 2:[5:6]3 or maybe even 2[4:5:6]3 although the latter has
problems. There is an implied rule that for a chord of N notes there
must always be exactly N-1 colons in the expression, no matter how it
is "factored". And any two numbers separated only by | or [ or ], but
not :[ or ]:, represent the same note.
>
> For example, to show all the intervals from the root, in the
subminor seventh chord, we can write it as 4[2[6:7]:3]:7. This makes
more sense when you see it as
> 4 :7
> 2 :3
> 6:7
>
> i.e. "[" means drop down a line (and backspace) and "]" means pop up
(and backspace).
>
> Notice also that 6:7|7:9|6:7 can just be considered shorthand for
[6:7][7:9][6:7], which is equivalent to 6:7[7:9][6:7] and
[6:7][7:9]6:7 and [6:7]7:9[6:7], but not 6:7[7:9]6:7. The latter would
be nonsense if we allow notation like 2[4:5:6]3 for a major triad. It
would imply a 6:7:6:7 chord where the 7:6 agrees with a 7:9. Not
possible.
>
> So we've got to where we can show all but one of the six relations
in this tetrad, in lowest terms, in linear text.
>
> 4[2[6:7:9]3|6:7]7 or 1/(7[7:6|3[9:7:6]2]4
>
> What we can't do with this notation is to simultaneously show two
intervals that overlap without one being wholly inside the other, such
as the two 2:3's in this chord.
>
> Pretty obscure huh? Sorry, I got carried away there, somewhat
off-thread.
>
> Oh by the way, the other 11-limit chord that Partch forgot (from
Graham Breed's web site) looks like
>
> 12:18:22:33
> = 2:3|9:11|2:3
> = 6:9:11|2:3
> = 1/(3:2|11:9:6)
> = 4[2:3|9:11|2:3]11
> = 4[6[2:3]:11]:11
> = 4[6[2:3|9:11]11|2:3]11
>
> Are there any of these things with more than 4 notes?
>
> -- Dave Keenan
> http://dkeenan.com
>
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through
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🔗D.Stearns <stearns@capecod.net>

🔗Paul H. Erlich <PErlich@Acadian-Asset.com>

🔗David C Keenan <d.keenan@uq.net.au>

[Paul Erlich, TD 517.17]
>Dave Keenan wrote,
>
>>It's all because we're trying to write something that's better represented
>as a 3 >dimensional graph (a tetrahedron), as a one-dimensional string of
>text.
>
>These chords (14:18:21:24 and 10:12:15:18) are actually only 2 dimensional:
>
>14------21
> `. ,' `.
> 24------18
>
>
>10-------15
> \ /\
> \ / \
> \ / \
> \/ \
> 12------18

But these graphs omit one consonance each (the 14:18 = 7:9 and the 10:18 = 5:9 respectively). But of course you're right that any tetrahedral graph can be drawn in two dimensions without crossing (a triangle with the fourth node inside it). And that on our usual prime-axis lattices these chords _are_ planar _with_ crossings. Thanks Paul.

Of course, my point still stands if one replaces "3 dimensional" with "2 dimensional".

-- Dave Keenan
http://dkeenan.com