Harmonic Series and Midi

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Hi John,

--- In tuning@yahoogroups.com, "Redeemed By Him"
<preciousatonement@...> wrote:
>
> Dear Tuning,
>
> Greetings. I would like to gain some knowledge on how
> you can tune to the exact pitches of the harmonic series
> using MIDI, perhaps by pitch bend assignments although I
> am only a newbie to a lot of high MIDI concepts. If
> anyone has some knowledge about how to go about tuning
> to the proper and exact (hopefully so) pitches of the
> harmonic series for any given fundamental using MIDI,
> please write about it here or email me personally.
> I like you guys and girls (any girls?)
>
> PEACE
> JOHN

"Exact" is really a loaded word when talking about
producing microtones electronically. With digital instruments,
there is always some amount of error, because of the
limits on quantization. The limits of *perception* of
these errors are extremely debatable, but there is no
denying that the errors are there mathematically.

So with that out of the way ... let's assume a "standard"
pitch-bend resolution of 4096 steps per 12-edo semitone
(49,152 per octave), a unit which some of us call a
"dodekamu", which i like to abbreviate "12mu" ... because
it uses 12 bits to convey the MIDI tuning data. So this
will be your margin of error.

I don't know how far up the harmonic series you want to go
... here i've provided a table which goes up to the 72nd,
which is 6 octaves above the fundamental.

* The "cents" column is provided only as a reference.

* The "semitones" column indicates how many 12-edo
semitones above the fundamental, for your starting point.

* the "12mus" column show the pitch-bend to be applied
to the note in the "semitones" column.

(To view this properly on the Yahoo web interface, you
have to click the "Option" link at the top right of this
message, then click on the "Use Fixed Width Font" link
in the menu which appears.)

harmonic . cents .. semitones . 12mus

.. 1 ... 0000.0 ......... 0 .... 0
.. 2 ... 1200.0 ........ 12 .... 0
.. 3 ... 1901.955001 ... 19 ... +80
.. 4 ... 2400.0 .... ... 24 .... 0
.. 5 ... 2786.313714 ... 28 ... -561
.. 6 ... 3101.955001 ... 31 ... +80
.. 7 ... 3368.825906 ... 34 ... -1277
.. 8 ... 3600.0 .... ... 36 .... 0
.. 9 ... 3803.910002 ... 38 ... +160
. 10 ... 3986.313714 ... 40 ... -561
. 11 ... 4151.317942 ... 42 ... -1994
. 12 ... 4301.955001 ... 43 ... +80
. 13 ... 4440.527662 ... 44 ... +1660
. 14 ... 4568.825906 ... 46 ... -1277
. 15 ... 4688.268715 ... 47 ... -481
. 16 ... 4800.0 ........ 48 .... 0
. 17 ... 4904.95541 .... 49 ... +203
. 18 ... 5003.910002 ... 50 ... +160
. 19 ... 5097.513016 ... 51 ... -102
. 20 ... 5186.313714 ... 52 ... -561
. 21 ... 5270.780907 ... 53 ... -1197
. 22 ... 5351.317942 ... 54 ... -1994
. 23 ... 5428.274347 ... 54 ... +1158
. 24 ... 5501.955001 ... 55 ... +80
. 25 ... 5572.627428 ... 56 ... -1121
. 26 ... 5640.527662 ... 56 ... +1660
. 27 ... 5705.865003 ... 57 ... +240
. 28 ... 5768.825906 ... 58 ... -1277
. 29 ... 5829.577194 ... 58 ... +1211
. 30 ... 5888.268715 ... 59 ... -481
. 31 ... 5945.035572 ... 59 ... +1845
. 32 ... 6000.0 ........ 60 .... 0
. 33 ... 6053.272943 ... 61 ... -1914
. 34 ... 6104.95541 .... 61 ... +203
. 35 ... 6155.13962 .... 62 ... -1837
. 36 ... 6203.910002 ... 62 ... +160
. 37 ... 6251.344039 ... 63 ... -1993
. 38 ... 6297.513016 ... 63 ... -102
. 39 ... 6342.482663 ... 63 ... +1740
. 40 ... 6386.313714 ... 64 ... -561
. 41 ... 6429.062406 ... 64 ... +1190
. 42 ... 6470.780907 ... 65 ... -1197
. 43 ... 6511.517706 ... 65 ... +472
. 44 ... 6551.317942 ... 66 ... -1994
. 45 ... 6590.223716 ... 66 ... -400
. 46 ... 6628.274347 ... 66 ... +1158
. 47 ... 6665.506622 ... 67 ... -1413
. 48 ... 6701.955001 ... 67 ... +80
. 49 ... 6737.651813 ... 67 ... +1542
. 50 ... 6772.627428 ... 68 ... -1121
. 51 ... 6806.91041 .... 68 ... +283
. 52 ... 6840.527662 ... 68 ... +1660
. 53 ... 6873.504545 ... 69 ... -1085
. 54 ... 6905.865003 ... 69 ... +240
. 55 ... 6937.631656 ... 69 ... +1541
. 56 ... 6968.825906 ... 70 ... -1277
. 57 ... 6999.468017 ... 70 ... -22
. 58 ... 7029.577194 ... 70 ... +1211
. 59 ... 7059.171659 ... 71 ... -1672
. 60 ... 7088.268715 ... 71 ... -481
. 61 ... 7116.884805 ... 71 ... +692
. 62 ... 7145.035572 ... 71 ... +1845
. 63 ... 7172.735908 ... 72 ... -1117
. 64 ... 7200.0 ........ 72 .... 0

-monz
http://tonalsoft.com
Tonescape microtonal music software

Hello John.

You wrote:

> Greetings. I would like to gain some knowledge on how you can tune to the
> exact pitches of the harmonic series using MIDI, perhaps by pitch bend
> assignments although I am only a newbie to a lot of high MIDI concepts.
If
> anyone has some knowledge about how to go about tuning to the proper and
> exact (hopefully so) pitches of the harmonic series for any given
> fundamental using MIDI, please write about it here or email me personally.

I'll speak for myself. First of all, it's important how much you wish to be
compatible with other instruments than yours. If you want to hear harmonic
scales on an "GM-only" synth which is not designed for alternate tunings in
the first place, the only way is to use pitch-bend messages. One of the ways
to do this, for example, is to write a scale of your choice and then retune
your MIDI files with Scala (for more details see
www.xs4all.nl/~huygensf/scala). FIY: If you have trouble playing the
resulting MIDI file (this is a special kind of SMF1), you can convert it to
SMF0 using some other software. - Another way of using pitch-bends is to use
Graham Breed's MIDI Relay (sorry, what was the URL, Graham?) which can do
this in real time so that you can actually play in the scale you write.

Petr

--- In tuning@yahoogroups.com, "Redeemed By Him"
<preciousatonement@...> wrote:
>
> Dear Tuning,
>
> Greetings. I would like to gain some knowledge on how you can tune
to the
> exact pitches of the harmonic series using MIDI, perhaps by pitch bend
> assignments although I am only a newbie to a lot of high MIDI concepts.

This is awfully vague. You can tune a voice in a midi file on a
note-by-note basis by sticking in pitch bends, and you can stick in
pitch bends for just intonation using Scala if you put in the tuning
information in just intonation format, as parenthesis surrounding a
rational number, in a Scala seq file; which is a kind of score file.

An error correction and a clarification ...

--- In tuning@yahoogroups.com, "monz" <monz@...> wrote:
>
> <snip>
>
> I don't know how far up the harmonic series you want to go
> ... here i've provided a table which goes up to the 72nd,
> which is 6 octaves above the fundamental.

Oops, my bad ... it actually goes up to the 64th harmonic,
which is 6 octaves above the fundamental ... which is
72 semitones.

> * The "cents" column is provided only as a reference.
>
> * The "semitones" column indicates how many 12-edo
> semitones above the fundamental, for your starting point.

In other words, this is how you determine your MIDI-note
(which is 12-edo).

-monz
http://tonalsoft.com
Tonescape microtonal music software

Petr Par�zek wrote:

> I'll speak for myself. First of all, it's important how much you wish to be
> compatible with other instruments than yours. If you want to hear harmonic
> scales on an "GM-only" synth which is not designed for alternate tunings in
> the first place, the only way is to use pitch-bend messages. One of the ways
> to do this, for example, is to write a scale of your choice and then retune
> your MIDI files with Scala (for more details see
> www.xs4all.nl/~huygensf/scala). FIY: If you have trouble playing the
> resulting MIDI file (this is a special kind of SMF1), you can convert it to
> SMF0 using some other software. - Another way of using pitch-bends is to use
> Graham Breed's MIDI Relay (sorry, what was the URL, Graham?) which can do
> this in real time so that you can actually play in the scale you write.

http://x31eq.com/software.htm

Don't have high hopes. I wrote it for Windows 3.1 and converted it to Windows 95, but I heard it crashes on NT. As all current versions of Windows descend from NT that probably means it won't work. Scala does do real time tuning so there's no reason for me to keep up to date.

Graham

--- In tuning@yahoogroups.com, Graham Breed <gbreed@...> wrote:

> > Graham Breed's MIDI Relay (sorry, what was the URL, Graham?) which
can do
> > this in real time so that you can actually play in the scale you
write.
>
> http://x31eq.com/software.htm
>
> Don't have high hopes. I wrote it for Windows 3.1 and converted it to
> Windows 95, but I heard it crashes on NT. As all current versions of
> Windows descend from NT that probably means it won't work. Scala does
> do real time tuning so there's no reason for me to keep up to date.
>
>
> Graham
>

I use a freeware midi relay program called InTun that is quite stable
in WinXP, the author says that it's based on Graham's MidiRelay.
http://rainwarrior.thenoos.net/intun/index.html

DJW