Readme file for RMCALC.EXE
RMCALC.EXE (c)2001 David R. Mooney
dmooney@city-net.com
The program may be freely used and distributed if accompanied by this
readme file.
I am not a programmer so the program is an inefficient brute force effort,
but it works.
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THE RHYTHMICON: BACKGROUND, DESCRIPTION, AND REFERENCES
Leon Theremin built the rhythmicon for Henry Cowell in 1931 so that Cowell
would have a device to test his theories linking the harmonic (overtone)
series with rhythm. The device had a keyboard for each harmonic H01 (the
fundamental) through H16. For each beat of H01, H02 beat twice, H03 three
times etc. The harmonic beat as long as the key was depressed. Thus,
a rhythmicon "measure" is the time it takes for the fundamental to beat
once and for all of the other harmonics to beat their respective number of
times.
I have used the principle of this device in a number of computer music
pieces via a "virtual rhythmicon environment" created with the Kyma system.
This environment extends the concept through the 24th harmonic. While much
of the math involved in getting the harmonics to beat at the appropriate
pitch and times can be scripted into Kyma sounds I have frequently found it
necessary to calculate beat lengths and specific beat times for a measure
of given length when timing events that occur outside of the rhythmicon
sounds controlled by Kyma. Since I have all of my music software set to
display time in SMPTE time (30 frame non-drop) I've also found it most
convenient to convert the beat times to SMPTE relative to the start time
of the piece. This involves tedious repetition of the same set of simple
calculations. Thus this program.
NOTE: rmcalc.exe deals only with the "rhythm" part of the rhythmicon,
not the pitch of the harmonics.
To learn more about the rhythmicon and hear sound samples, visit my web site
at . To learn more about Kyma, visit the
Symbolic Sound web site at .
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RUNNING THE PROGRAM
This program was written in C++ using using Borland's Turbo C++ ver 3.0. It
must be run from a DOS prompt. The program name is rmcalc.exe.
For you old folks out there who teethed on DOS, skip this part and go to
OUTPUT. For you young whipper-snappers raised on GUI, here's how to run the
program from windows. If you're using a MAC you're on your own:
In the Start menu under Programs, select "MS-DOS Prompt."
The DOS prompt will probably look like this:
C:\WINDOWS
Change the directory to the folder where you put rmcalc.exe:
Type: cd\
Press ENTER
Now the prompt looks like this:
C:\
Type: cd
Press ENTER
For example, if you created a new folder in C: called "progs", the
command would look like this:
cd progs
And the DOS prompt looks like this:
C:\PROGS
Once you're in the proper directory:
Type: rmcalc
Press ENTER
This will run the program. See OUTPUT, below. To get out of DOS hell:
Type: cd\
Press ENTER
Type: cd WINDOWS
Press ENTER
Type: exit
Press ENTER
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OUTPUT
The program prompts you for the start time, the measure length and asks
whether you want the output to go to the screen or to a text file.
Start Time:
Enter the start time in seconds. 0 and decimals are OK. This time will be
added to the SMPTE times for the beats. If your rhythmicon measure starts
at the beginiing of the piece, or you want to see absolute times for the
beats in SMPTE, enter 0. If your measure starts later, enter that time to
get beat times where they will be in the piece.
Measure Length:
Enter the measure length in seconds.
Output Selection:
You will then be prompted to enter "1" if ou want to see the output on
the screen (handy for a quick check) or "2" if you want to send it to a
text file (rmcalc.txt). The text file will be in the same directory as
the program. Open this in a text editor or word processor to view and
print. You may have to tweak it a bit for page breaks and alignment,
depending on your software and setup.
Sample Output:
The "BEAT LENGTHS IN SECONDS" are absolute. The start time has no effect
on this.
The "BEATS IN SMPTE TIME" are listed in reverse order, starting with H24.
This is an arbitrary convention that has arisen from my work habits.
Since in the rhythmicon the harmonics are associated with pitch with H24
being the highest I find it easier to conceptualize what's happening with
H24 on the top. Beats are designated by "(n)" with n = beat number. Note
that (1) is the same for all harmonics and is equal (in SMPTE) to the
start time. (1) is the downbeat of the measure, the only time when all
beats of all harmonics hit at the same time.
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BEAT LENGTHS IN SECONDS
Start time (secs): 30 Measure length: 54
HARMONIC LENGTH HARMONIC LENGTH HARMONIC LENGTH
H01 54.0000 H09 6.0000 H17 3.1765
H02 27.0000 H10 5.4000 H18 3.0000
H03 18.0000 H11 4.9091 H19 2.8421
H04 13.5000 H12 4.5000 H20 2.7000
H05 10.8000 H13 4.1538 H21 2.5714
H06 9.0000 H14 3.8571 H22 2.4545
H07 7.7143 H15 3.6000 H23 2.3478
H08 6.7500 H16 3.3750 H24 2.2500
BEATS IN SMPTE TIME
Start time (secs): 30.0000 Measure length: 54.0000
H24 (1)00:30:00 (2)00:32:08 (3)00:34:15 (4)00:36:23
(5)00:39:00 (6)00:41:08 (7)00:43:15 (8)00:45:23
(9)00:48:00 (10)00:50:08 (11)00:52:15 (12)00:54:23
(13)00:57:00 (14)00:59:08 (15)01:01:15 (16)01:03:23
(17)01:06:00 (18)01:08:08 (19)01:10:15 (20)01:12:23
(21)01:15:00 (22)01:17:08 (23)01:19:15 (24)01:21:23
H23 (1)00:30:00 (2)00:32:10 (3)00:34:21 (4)00:37:01
(5)00:39:12 (6)00:41:22 (7)00:44:03 (8)00:46:13
(9)00:48:23 (10)00:51:04 (11)00:53:14 (12)00:55:25
(13)00:58:05 (14)01:00:16 (15)01:02:26 (16)01:05:07
(17)01:07:17 (18)01:09:27 (19)01:12:08 (20)01:14:18
(21)01:16:29 (22)01:19:09 (23)01:21:20
H22 (1)00:30:00 (2)00:32:14 (3)00:34:27 (4)00:37:11
(5)00:39:25 (6)00:42:08 (7)00:44:22 (8)00:47:05
(9)00:49:19 (10)00:52:03 (11)00:54:16 (12)00:57:00
(13)00:59:14 (14)01:01:27 (15)01:04:11 (16)01:06:25
(17)01:09:08 (18)01:11:22 (19)01:14:05 (20)01:16:19
(21)01:19:03 (22)01:21:16
H21 (1)00:30:00 (2)00:32:17 (3)00:35:04 (4)00:37:21
(5)00:40:09 (6)00:42:26 (7)00:45:13 (8)00:48:00
(9)00:50:17 (10)00:53:04 (11)00:55:21 (12)00:58:09
(13)01:00:26 (14)01:03:13 (15)01:06:00 (16)01:08:17
(17)01:11:04 (18)01:13:21 (19)01:16:09 (20)01:18:26
(21)01:21:13
H20 (1)00:30:00 (2)00:32:21 (3)00:35:12 (4)00:38:03
(5)00:40:24 (6)00:43:15 (7)00:46:06 (8)00:48:27
(9)00:51:18 (10)00:54:09 (11)00:57:00 (12)00:59:21
(13)01:02:12 (14)01:05:03 (15)01:07:24 (16)01:10:15
(17)01:13:06 (18)01:15:27 (19)01:18:18 (20)01:21:09
H19 (1)00:30:00 (2)00:32:25 (3)00:35:21 (4)00:38:16
(5)00:41:11 (6)00:44:06 (7)00:47:02 (8)00:49:27
(9)00:52:22 (10)00:55:17 (11)00:58:13 (12)01:01:08
(13)01:04:03 (14)01:06:28 (15)01:09:24 (16)01:12:19
(17)01:15:14 (18)01:18:09 (19)01:21:05
H18 (1)00:30:00 (2)00:33:00 (3)00:36:00 (4)00:39:00
(5)00:42:00 (6)00:45:00 (7)00:48:00 (8)00:51:00
(9)00:54:00 (10)00:57:00 (11)01:00:00 (12)01:03:00
(13)01:06:00 (14)01:09:00 (15)01:12:00 (16)01:15:00
(17)01:18:00 (18)01:21:00
H17 (1)00:30:00 (2)00:33:05 (3)00:36:11 (4)00:39:16
(5)00:42:21 (6)00:45:26 (7)00:49:02 (8)00:52:07
(9)00:55:12 (10)00:58:18 (11)01:01:23 (12)01:04:28
(13)01:08:04 (14)01:11:09 (15)01:14:14 (16)01:17:19
(17)01:20:25
H16 (1)00:30:00 (2)00:33:11 (3)00:36:23 (4)00:40:04
(5)00:43:15 (6)00:46:26 (7)00:50:08 (8)00:53:19
(9)00:57:00 (10)01:00:11 (11)01:03:23 (12)01:07:04
(13)01:10:15 (14)01:13:26 (15)01:17:08 (16)01:20:19
H15 (1)00:30:00 (2)00:33:18 (3)00:37:06 (4)00:40:24
(5)00:44:12 (6)00:48:00 (7)00:51:18 (8)00:55:06
(9)00:58:24 (10)01:02:12 (11)01:06:00 (12)01:09:18
(13)01:13:06 (14)01:16:24 (15)01:20:12
H14 (1)00:30:00 (2)00:33:26 (3)00:37:21 (4)00:41:17
(5)00:45:13 (6)00:49:09 (7)00:53:04 (8)00:57:00
(9)01:00:26 (10)01:04:21 (11)01:08:17 (12)01:12:13
(13)01:16:09 (14)01:20:04
H13 (1)00:30:00 (2)00:34:05 (3)00:38:09 (4)00:42:14
(5)00:46:18 (6)00:50:23 (7)00:54:28 (8)00:59:02
(9)01:03:07 (10)01:07:12 (11)01:11:16 (12)01:15:21
(13)01:19:25
H12 (1)00:30:00 (2)00:34:15 (3)00:39:00 (4)00:43:15
(5)00:48:00 (6)00:52:15 (7)00:57:00 (8)01:01:15
(9)01:06:00 (10)01:10:15 (11)01:15:00 (12)01:19:15
H11 (1)00:30:00 (2)00:34:27 (3)00:39:25 (4)00:44:22
(5)00:49:19 (6)00:54:16 (7)00:59:14 (8)01:04:11
(9)01:09:08 (10)01:14:05 (11)01:19:03
H10 (1)00:30:00 (2)00:35:12 (3)00:40:24 (4)00:46:06
(5)00:51:18 (6)00:57:00 (7)01:02:12 (8)01:07:24
(9)01:13:06 (10)01:18:18
H09 (1)00:30:00 (2)00:36:00 (3)00:42:00 (4)00:48:00
(5)00:54:00 (6)01:00:00 (7)01:06:00 (8)01:12:00
(9)01:18:00
H08 (1)00:30:00 (2)00:36:23 (3)00:43:15 (4)00:50:08
(5)00:57:00 (6)01:03:23 (7)01:10:15 (8)01:17:08
H07 (1)00:30:00 (2)00:37:21 (3)00:45:13 (4)00:53:04
(5)01:00:26 (6)01:08:17 (7)01:16:09
H06 (1)00:30:00 (2)00:39:00 (3)00:48:00 (4)00:57:00
(5)01:06:00 (6)01:15:00
H05 (1)00:30:00 (2)00:40:24 (3)00:51:18 (4)01:02:12
(5)01:13:06
H04 (1)00:30:00 (2)00:43:15 (3)00:57:00 (4)01:10:15
H03 (1)00:30:00 (2)00:48:00 (3)01:06:00
H02 (1)00:30:00 (2)00:57:00
H01 (1)00:30:00