tetrachords (Digest 1417 Topic 4)

Hey hey, Haverstick!

At 04:49 PM 5/16/98 -0400, you wrote (Digest 1417 Topic 4):
>From: Aline Surman
>Subject: tetrachords
>
>Here's a question which I was originally going to post privately to
>Chalmers, but thought I'd air it out here for maximum response; why are
>scales formed by tetrachords in the first place? I've read about them for
>many years, and all of a sudden I realized that I don't know the
>fundamental reason behind their origin. Any thoughts are surely
>appreciated....thanks...Hstick

I've tripped on tetrachord explanations myself. The explanation usually
goes "a little something like this":

A tetrachord is four notes; e.g., "C D E F".
Now, repeat that sequence starting at "G",
put 'em together and you get a major scale.
"C D E F, G A B C".

Now to what always bugged me. In "justly intoned" scales, along with
"semitones", 16/15 interval, there's that distinction between "major tones",
9/8 interval, and "minor tones", 10/9 interval. C major is USUALLY:

C 9/8 D 10/9 E 16/15 F 9/8 G 10/9 A 9/8 B 16/15 C

The two "tetrachords" are not the same! For example, there's a major tone
between C and D, but a minor tone between G and A.

Apparently this issue bugged Helmholtz and/or Ellis too, 'cuz there's a
footnote about it in "On the Sensations of Tone" (English translation of 4th
German edition, p. 255 bottom, for those of you reading along).

--Mark
+------------------------------------------------------+
| Mark Nowitzky |
| email: nowitzky@alum.mit.edu AIM: Nowitzky |
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Hello Everyone,

I've been racking my brains and searching the net for a solution to my
quest for an accurate real-time microtuning synth.I use software
synthesis to finally realise a composition,but for the initial process
of composing,I need a real-time system.

I considered using samples indivually tuned,but it's too tedious & not
flexible.

One possibility I thought of follows.I don't know if it will work as I
have never used a Yamaha FM synth,so I'm hoping someone can shed some
light.

-Since the carrier frequency can be specified in hertz (I hope it can,
along with floating point no.s,anyone here know ?)
, it should be possible to tune one accurate note per MIDI
channel,thereby giving 16 notes on a 16-part synth like the SY/TG-77 &
SY-99.then depending on how fast these synths respond to program change
messages ( anyone here know how fast in ms ?) ,it could be possible to
obtain all neccessary pitches/notes.

It would require real-time MIDI proccessing using something like MAX to
build an application that
had the neccessary user-specified intelligence to know when to send pgm
changes,and on what channels depending on which are occupied and what
tuning you are using.It would also possible to assign notes from your
controller to do specific things.

I would appreciate any advise and insights,perhaps from anyone who has
tried this.

On a related note,I think it's a shame that there are barely any current
synths that are actual synths and not actually glorified sample-playback
devices.


Cheers,
Drew

> From: Drew Skyfyre
> I've been racking my brains and searching the net for a solution to my
> quest for an accurate real-time microtuning synth.I use software
> synthesis to finally realise a composition,but for the initial process
> of composing,I need a real-time system.
>
> One possibility I thought of follows.I don't know if it will work as I
> have never used a Yamaha FM synth,so I'm hoping someone can shed some
> light.
>
> -Since the carrier frequency can be specified in hertz (I hope it can,
> along with floating point no.s,anyone here know ?)
> , it should be possible to tune one accurate note per MIDI
> channel,thereby giving 16 notes on a 16-part synth like the SY/TG-77 &
> SY-99.then depending on how fast these synths respond to program change
> messages ( anyone here know how fast in ms ?) ,it could be possible to
> obtain all neccessary pitches/notes.
>

Carriers on Yamaha FM synths are specified in decimal ratios relative to
the tonic, 0.50 to 61.69 on a Yamaha DX7IIFD, for instance. Since the
ratios only have 2 decimal points of resolution and the resolution worsens
as you go higher, you'll actually get worse frequency resolution using this
method instead of the built-in tuning tables (1024 steps per octave).

If you need better than 0.2 cent resolution your only current option is a
Kyma system or CSOUND.

John Loffink
jloffink@pdq.net

Hello,

>>I've been racking my brains and searching the net for a solution to my
>>quest for an accurate real-time microtuning synth.
>
> Couldja clarify what you specifically you mean by "accurate"?
>
Shoulda been a little more specific.I meant being able to actually tune a
synth for real-time use using Hertz.Each MIDI ch. would have one precise
note.I'd like to be able to hear ,in real-time,the result of generating
random/specific frequencies using computer programs.etc.

> As for real-time, I'm inclined to think that any of the (few) machines
>that support the MIDI tuning standard, like Ensoniq's ASR-X or MR series,
>would be a good possibility.
I have considered them.They allow increments of @0.1 Hz (by my calc.)
,so most notes would be a little off.

It was David First's contributions,starting in TD-1391,that seriously
started me thinking about this.

While actual human ability to recognise differences in pitch may be
limited ,I think it is more extended when dealing with psychoacoustic
efx.Such as if one were using individually tuned multi-tap delays mixed
at a low level with reverb.

Besides the fact that I find MIDI annoying in general, I specifically do
not think in terms of ,and do not work with Cents.MIDI is like thinking
in English,but having to translate to and from Latin before actually
speaking.Leaving something to be desired in the end result.

Also,if the approach actually works,used Yamaha FM synths are a bargain.


Later,
Drew

>I have considered them.They allow increments of @0.1 Hz (by my calc.)
>,so most notes would be a little off.

I suppose it's worth pointing out that that's not very far off. A 1/5Hz
beat is pretty darned slow. You'd have to have some very high harmonics on
some very long, sustained tones to be able to hear that.