Nov 122011
 
This short article about pitch notation standards is primarily targeted at computer musicians who are interested in making microtonal and xenharmonic music with software plug-in instruments, and since I’ve not seen this information compiled in a concise form before on the web, I thought publishing this on Xen-Arts would be a good first step in a series of future microtuning tutorials. Very special thanks goes out to X.J. Scott for his deep insight into matters related to musical instrument intonation, and for helping to compile the lists of musical hardware and software developers detailed here.
MIDI Notes, Pitches and Notation Standards
An important foundation for making music with alternative intonation systems is having an understanding of how the pitches of 12 Tone Equal Temperament are mapped to MIDI Notes, because this is the default tuning of most software plug-in instruments and the starting point from which we will re-tune, or microtune, to other intonations.
Another dimension of the way specific pitches are mapped to MIDI Notes is considering the various Pitch Notation Standards, of which there are three in current popular usage:
1. For purposes of discussion, we’ll call the first one the MIDI Standard, which is probably the most widely used in software virtual instruments.
MIDI Standard, Middle C: C3
Range: C -2 to G 8
Middle C (MIDI Note 60) = C3 @ 261.626 Hz
Middle A (MIDI Note 69) = A3 @ 440.000 Hz
Musical hardware manufacturers, software developers and applications known to be using this standard by default:
Ableton Live
Apple GarageBand
Apple Logic
Camel Audio
Dave Smith Instruments
Linplug
Modart Pianoteq
Novation
Propellerhead Reason
Sequential Circuits
Steinberg Cubase
Yamaha
2. Sometimes (perhaps erroneously) referred to as Scientific Pitch, we’ll call the second standard ISO 16:1975, which was first proposed by the Acoustical Society of America back in the 1930s.
ISO 16:1975, Middle C: C4
Range: C -1 to G 9
Middle C (MIDI Note 60) = C4 @ 261.626 Hz
Middle A (MIDI Note 69) = A4 @ 440.000 Hz
Musical hardware manufacturers, software developers and applications known to be using this standard by default:
Casio
Cockos Reaper
Korg
Kurzweil
Roland
3. The third popular pitch notation standard we’ll refer to as the Cakewalk Standard, as it appears that this one originated with this developer.
Cakewalk Standard, Middle C: C5
Middle C (MIDI Note 60) = C5 @ 261.626 Hz
Middle A (MIDI Note 69) = A5 @ 440.000 Hz
Musical hardware manufacturers, software developers and applications known to be using this
standard by default:
Cakewalk Sonar
FL Studio
Additional comments:
1. It’s worth noting that some developers do give users the option to change to any desired pitch notation standard, a detailed explanation about which is outside of the scope of this brief article.
2. While there are three different pitch notation standards to deal with in computer music, it’s crucial to realize that the MIDI Specification of the MIDI Manufacturers Association always maps MIDI Note 60.C (Middle C) to a frequency of 261.626 Hz and 69.A (Middle A) to 440.000 Hz. Point being, no matter what note-naming convention is being used, MIDI Note Numbers always have the specific pitches of 12 tone equal temperament mapped to them by default. And understanding what this default is will prepare us for freely microtuning our instruments to other intonation systems using software musical instruments that features arbitrary MIDI-pitch microtuning (aka full-keyboard microtuning).
Below is a convenient reference table detailing the MIDI Note Numbers and their associated specific pitches from 12 tone equal temperament in Hz, the cents values, and the three above discussed pitch notation standards.
MIDI Note Number Hz Cents MIDI Standard
Middle C: C3
ISO 16:1975
Middle C: C4
Cakewalk Middle
C: C5
0 8.176 0.000 C -2 C -1 C 0
1 8.662 100.000 C#, Db -2 C#, Db -1 C#, Db 0
2 9.177 200.000 D -2 D -1 D 0
3 9.723 300.000 D#, Eb -2 D#, Eb -1 D#, Eb 0
4 10.301 400.000 E -2 E -1 E 0
5 10.913 500.000 F -2 F -1 F 0
6 11.562 600.000 F#, Gb -2 F#, Gb -1 F#, Gb 0
7 12.250 700.000 G -2 G -1 G 0
8 12.978 800.000 G#, Ab -2 G#, Ab -1 G#, Ab 0
9 13.750 900.000 A -2 A -1 A 0
10 14.568 1000.000 A#, Bb -2 A#, Bb -1 A#, Bb 0
11 15.434 1100.000 B -2 B -1 B 0
12 16.352 1200.000 C -1 C 0 C 1
13 17.324 1300.000 C#, Db -1 C#, Db 0 C#, Db 1
14 18.354 1400.000 D -1 D 0 D 1
15 19.445 1500.000 D#, Eb -1 D#, Eb 0 D#, Eb 1
16 20.602 1600.000 E -1 E 0 E 1
17 21.827 1700.000 F -1 F 0 F 1
18 23.125 1800.000 F#, Gb -1 F#, Gb 0 F#, Gb 1
19 24.500 1900.000 G -1 G 0 G 1
20 25.957 2000.000 G#, Ab -1 G#, Ab 0 G#, Ab 1
21 27.500 2100.000 A -1 A 0 A 1
22 29.135 2200.000 A#, Bb -1 A#, Bb 0 A#, Bb 1
23 30.868 2300.000 B -1 B 0 B 1
24 32.703 2400.000 C 0 C 1 C 2
25 34.648 2500.000 C#, Db 0 C#, Db 1 C#, Db 2
26 36.708 2600.000 D 0 D 1 D 2
27 38.891 2700.000 D#, Eb 0 D#, Eb 1 D#, Eb 2
28 41.203 2800.000 E 0 E 1 E 2
29 43.654 2900.000 F 0 F 1 F 2
30 46.249 3000.000 F#, Gb 0 F#, Gb 1 F#, Gb 2
31 48.999 3100.000 G 0 G 1 G 2
32 51.913 3200.000 G#, Ab 0 G#, Ab 1 G#, Ab 2
33 55.000 3300.000 A 0 A 1 A 2
34 58.270 3400.000 A#, Bb 0 A#, Bb 1 A#, Bb 2
35 61.735 3500.000 B 0 B 1 B 2
36 65.406 3600.000 C 1 C 2 C 3
37 69.296 3700.000 C#, Db 1 C#, Db 2 C#, Db 3
38 73.416 3800.000 D 1 D 2 D 3
39 77.782 3900.000 D#, Eb 1 D#, Eb 2 D#, Eb 3
40 82.407 4000.000 E 1 E 2 E 3
41 87.307 4100.000 F 1 F 2 F 3
42 92.499 4200.000 F#, Gb 1 F#, Gb 2 F#, Gb 3
43 97.999 4300.000 G 1 G 2 G 3
44 103.826 4400.000 G#, Ab 1 G#, Ab 2 G#, Ab 3
45 110.000 4500.000 A 1 A 2 A 3
46 116.541 4600.000 A#, Bb 1 A#, Bb 2 A#, Bb 3
47 123.471 4700.000 B 1 B 2 B 3
48 130.813 4800.000 C 2 C 3 C 4
49 138.591 4900.000 C#, Db 2 C#, Db 3 C#, Db 4
50 146.832 5000.000 D 2 D 3 D 4
51 155.563 5100.000 D#, Eb 2 D#, Eb 3 D#, Eb 4
52 164.814 5200.000 E 2 E 3 E 4
53 174.614 5300.000 F 2 F 3 F 4
54 184.997 5400.000 F#, Gb 2 F#, Gb 3 F#, Gb 4
55 195.998 5500.000 G 2 G 3 G 4
56 207.652 5600.000 G#, Ab 2 G#, Ab 3 G#, Ab 4
57 220.000 5700.000 A 2 A 3 A 4
58 233.082 5800.000 A#, Bb 2 A#, Bb 3 A#, Bb 4
59 246.942 5900.000 B 2 B 3 B 4
60 261.626 6000.000 C 3 C 4 C 5
61 277.183 6100.000 C#, Db 3 C#, Db 4 C#, Db 5
62 293.665 6200.000 D 3 D 4 D 5
63 311.127 6300.000 D#, Eb 3 D#, Eb 4 D#, Eb 5
64 329.628 6400.000 E 3 E 4 E 5
65 349.228 6500.000 F 3 F 4 F 5
66 369.994 6600.000 F#, Gb 3 F#, Gb 4 F#, Gb 5
67 391.995 6700.000 G 3 G 4 G 5
68 415.305 6800.000 G#, Ab 3 G#, Ab 4 G#, Ab 5
69 440.000 6900.000 A 3 A 4 A 5
70 466.164 7000.000 A#, Bb 3 A#, Bb 4 A#, Bb 5
71 493.883 7100.000 B 3 B 4 B 5
72 523.251 7200.000 C 4 C 5 C 6
73 554.365 7300.000 C#, Db 4 C#, Db 5 C#, Db 6
74 587.330 7400.000 D 4 D 5 D 6
75 622.254 7500.000 D#, Eb 4 D#, Eb 5 D#, Eb 6
76 659.255 7600.000 E 4 E 5 E 6
77 698.456 7700.000 F 4 F 5 F 6
78 739.989 7800.000 F#, Gb 4 F#, Gb 5 F#, Gb 6
79 783.991 7900.000 G 4 G 5 G 6
80 830.609 8000.000 G#, Ab 4 G#, Ab 5 G#, Ab 6
81 880.000 8100.000 A 4 A 5 A 6
82 932.328 8200.000 A#, Bb 4 A#, Bb 5 A#, Bb 6
83 987.767 8300.000 B 4 B 5 B 6
84 1046.502 8400.000 C 5 C 6 C 7
85 1108.731 8500.000 C#, Db 5 C#, Db 6 C#, Db 7
86 1174.659 8600.000 D 5 D 6 D 7
87 1244.508 8700.000 D#, Eb 5 D#, Eb 6 D#, Eb 7
88 1318.510 8800.000 E 5 E 6 E 7
89 1396.913 8900.000 F 5 F 6 F 7
90 1479.978 9000.000 F#, Gb 5 F#, Gb 6 F#, Gb 7
91 1567.982 9100.000 G 5 G 6 G 7
92 1661.219 9200.000 G#, Ab 5 G#, Ab 6 G#, Ab 7
93 1760.000 9300.000 A 5 A 6 A 7
94 1864.655 9400.000 A#, Bb 5 A#, Bb 6 A#, Bb 7
95 1975.533 9500.000 B 5 B 6 B 7
96 2093.005 9600.000 C 6 C 7 C 8
97 2217.461 9700.000 C#, Db 6 C#, Db 7 C#, Db 8
98 2349.318 9800.000 D 6 D 7 D 8
99 2489.016 9900.000 D#, Eb 6 D#, Eb 7 D#, Eb 8
100 2637.020 10000.000 E 6 E 7 E 8
101 2793.826 10100.000 F 6 F 7 F 8
102 2959.955 10200.000 F#, Gb 6 F#, Gb 7 F#, Gb 8
103 3135.963 10300.000 G 6 G 7 G 8
104 3322.438 10400.000 G#, Ab 6 G#, Ab 7 G#, Ab 8
105 3520.000 10500.000 A 6 A 7 A 8
106 3729.310 10600.000 A#, Bb 6 A#, Bb 7 A#, Bb 8
107 3951.066 10700.000 B 6 B 7 B 8
108 4186.009 10800.000 C 7 C 8 C 9
109 4434.922 10900.000 C#, Db 7 C#, Db 8 C#, Db 9
110 4698.636 11000.000 D 7 D 8 D 9
111 4978.032 11100.000 D#, Eb 7 D#, Eb 8 D#, Eb 9
112 5274.041 11200.000 E 7 E 8 E 9
113 5587.652 11300.000 F 7 F 8 F 9
114 5919.911 11400.000 F#, Gb 7 F#, Gb 8 F#, Gb 9
115 6271.927 11500.000 G 7 G 8 G 9
116 6644.875 11600.000 G#, Ab 7 G#, Ab 8 G#, Ab 9
117 7040.000 11700.000 A 7 A 8 A 9
118 7458.620 11800.000 A#, Bb 7 A#, Bb 8 A#, Bb 9
119 7902.133 11900.000 B 7 B 8 B 9
120 8372.018 12000.000 C 8 C 9 C 10
121 8869.844 12100.000 C#, Db 8 C#, Db 9 C#, Db 10
122 9397.273 12200.000 D 8 D 9 D 10
123 9956.063 12300.000 D#, Eb 8 D#, Eb 9 D#, Eb 10
124 10548.082 12400.000 E 8 E 9 E 10
125 11175.303 12500.000 F 8 F 9 F 10
126 11839.822 12600.000 F#, Gb 8 F#, Gb 9 F#, Gb 10
127 12543.854 12700.000 G 8 G 9 G 10

 

Further Information:
MIDI Manufacturers Association
ISO 16:1975

j:l

 Posted by at 4:00 pm
Apr 162011
 

Today over on the Dubbhism blog, Tony Dubshot has published a great introduction to microtuning: Xenharmonic tutorial ~ harmonic exploration made easy.

Created for computer musicians who may be new to the topic, and are curious about how to get started exploring the vast expressive potential of making music with alternative intonation systems, the article discusses the use of software synthesizers and the implications of the interactions between musical instrument intonation and timbre.

This is a richly illustrated presentation including streaming audio and video. Check it out, and while there, also consider exploring these xenharmonic Tony Dubshot albums on the Dubbhism label, which have generously been made available for free download:

Tony Dubshot – Dub Experryments
Glamma Woods – Keepin it Steady
Scratchy Dubplate Crew – Scientific Dancehall

 Posted by at 6:32 pm