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Flutopedia Symposium

Octave Notation

There are many systems in use to indicate the octave for a particular note. Some of these systems are in current use, and some appear in the historical references cited on Flutopedia. Some of these systems use the format of note name (such as “C” or “F#” or “Bb”) followed by an octave indication, and are generally called note-octave systems.

This page gives the correspondence between these various systems of notating the octave for a particular note.

International Pitch Notation

Flutopedia uses International Pitch Notation (IPN) when talking about musical notes. IPN is a note-octave notation termed “Scientific Pitch Notation” in the original proposal by the Acoustical Society of America ([Young-RW 1939]) and now commonly called “International Pitch Notation”. IPN set the standard of using 440 Hertz as the reference frequency for the note A4.

The notes (C, C# or Db, D, D# or Eb, D, F, F# or Gb, G, G# or Ab, A# or Bb, B) are followed by an octave number. For example: C2, F#3, and Bb4.

These may also be written in various publications as: C(2), F#(3), Bb(4), C[2], F#[3], Bb[4], or C2, F#3, and Bb4.

The note an octave below C1 is C0. The note an octave below C0 is written C-1, and the next lower octave is written C-2, etcetera.

C4 in IPN corresponds to middle C on a piano.

Correspondence

These tables show how IPN lines up with various other systems for naming the notes. For description of the rows in these tables, scroll down below the tables.

Octave Correspondence below Middle C
International Pitch Notation C0 to B0 C1 to B1 C2 to B2 C3 to B3
Modern Music Notation   Classical Staff Notation for C1-B1 Classical Staff Notation for C2-B2 Classical Staff Notation for C3-B3
Helmholtz Pitch Notation C‚‚ - B‚‚ C‚ - B‚ C - B c - b
English Notation CCC - BBB CC - BB C - B c - b
Approximate Sound Chamber Length 16′ to 8′ 4″
(488-254 cm)
8′ to 4′ 2″
(244-127 cm)
4′ - 2′ 1″
(122-63 cm)
24″ - 12½″
(61-32 cm)
Typical NAF Descriptions Sub-Bass Ultra-Low
Contrabass
Very Low
Bass
Low
Baritone
Octave Name sub-contra octave contra octave great octave Small Octave
German: Subkontra-Oktave Kontra-Oktave Große-Oktave Kleine Oktave
French: double contre-octave contre-octave grande octave petite octave
Organ Naming for
the note C
  Double Pedal C Pedal C Bass C
IPN Frequency Range
(A4=440 Hertz)
16.352 to
30.868
32.703 to
61.735
65.404 to
124.47
130.81 to
246.94
Scientific Pitch Frequency Range
(C4=256 Hertz)
16.00 to
30.204
32.00 to
60.408
64.00 to
120.816
128.00 to
241.632
Piano Key Numbers - 3** 4 - 15 16 - 27 28 - 39
MIDI Note Numbers 12 - 23 24 - 35 36 - 47 48 - 59

**A0 is the lowest note on a standard 88-key piano keyboard and is Piano Key #1.

 

Octave Correspondence - Middle C and Above
International Pitch Notation C4 to B4 C5 to B5 C6 to B6 C7 to B7
Modern Music Notation Classical Staff Notation for C4-B4 Classical Staff Notation for C5-B5 Classical Staff Notation for C6-B6  
Helmholtz Pitch Notation c’ - b’ c’’ - b’’ c’’’ - b’’’ c’’’’ - b’’’’
English Notation cc - bb ccc - bbb cccc - bbbb ccccc - bbbbb
Approximate Sound Chamber Length 12″ - 6¼″
(30.5-15.9 cm)
6″ - 3.13″
(15.2-7.9 cm)
3″ - 1.56″
(7.6-3.96 cm)
 
Typical NAF Descriptions Mid-Range
Medium
Tenor
High
Alto
Very High
Soprano
Ultra-High
Sopranino
Octave Name one-line octave
once-accented octave
two-line octave
twice-accented octave
three-line octave
once-accented octave
four-line octave
once-accented octave
German: Eingestrichene Oktave Zweigestrichene Oktave Dreigestrichene Oktave Viergestrichene Oktave
French: 2me petite octave 3me petite octave 4me petite octave 5me petite octave
Organ Naming for
the note C
Middle C Treble C Top C Double Top C
IPN Frequency Range
(A4=440 Hertz)
261.63 to
493.88
523.25 to
987.77
1,046.5 to
1,975.5
2,093.0 to
3,951.1
Scientific Pitch Frequency Range
(C4=256 Hertz)
256.00 to
483.265
512.00 to
966.530
1,024.00 to
1,933.059
2,048.00 to
3,866.118
Piano Key Numbers 40 - 51 52 - 63 64 - 75 76 - 87
MIDI Note Numbers 60 - 71 72 - 83 84 - 95 96 - 107

 

Modern Music Notation

This row in the tables above shows the range of notes in modern music notation. This style of musical notation originated from the European classical music tradition and now commonly in use to represent a wide variety of music. It uses a five-line staff and the placement of notes that indicate pitch and duration.

Helmholtz Pitch Notation

A note-octave notation system that uses upper-case and lower-case letters to indicate octaves. The Helmholtz Pitch notation C-B corresponds to the IPN range C3-B3 and Helmholtz c-b corresponds to IPN C4-B4 ([Helmholtz 1912]).

To indicate octaves below C-B, Helmholtz Pitch Notation calls for the use of small “hash marks” below the line, such as C‚ and C‚‚. However, those hash marks are usually typeset using commas or the letter "i" as small subscripts, and may appear as C, or C,, or Cii.

To indicate octaves above c-b, Helmholtz Pitch Notation add hash marks above and following the lower-case note letter, such as c’ and c’’. Those hash marks may be typeset using a variety of characters, including "i" as small superscipts. Some examples: c′′ c'', c", c”, c′, c″ and cii.

The sequence of octaves for C is: …  C‚‚‚  C‚‚  C‚  C  c  c’  c’’  c’’’  …

c’ in Helmholtz Pitch Notation corresponds to C4 in IPN and to middle C on a piano.

The English Octave Naming Convention

This system is really just another way of writing notes in the Helmholtz Pitch Notation system. For example, C‚‚‚ is replaced by CCCC and c’ is replaced by cc.

Sound Chamber Lengths

This row in the tables above lists very approximate length of a sound chamber that generates the notes within the octave. The very approximate length for the lowest and highest notes within the octave are shown. This follows from the old nomenclature that the IPN note C1 was called the “eight foot note” on pipe organs because the length of the pipe to produce that note was about 8′ (see the Dolmetsch Online Music Theory page).

Looking at the sound chamber lengths in the tables above can help identify the octave of the fundamental note for a given flute. However, make sure that:

  • You are using a measurement for just the sound chamber of the instrument. If the flute has direction holes, take their location to be the end of the sound chamber.
  • You are considering the note when all holes are closed (the fundamental note), and
  • The instrument is resonating in its first register, and not a higher register or octave.

So, for example, I roughly measure the sound chamber of the mid-range F# minor Native American flute I happen to have sitting next to me, from the sound hole to the direction holes at the bottom: 15″. From the tables above, that would place it in the IPN Octave of C4-B4 … so its fundamental note is an F#4.

Typical Native American flute Descriptions

This row in the tables above lists some typical terminology for Native American flutes that have a fundamental note in that octave. Some of these names are from the Table of Native American flute Keys on this web site, and some are from general usage.

Note also that makers do not always group the descriptions of their keys into nice one-octave ranges, so you sometimes have to read between the lines when figuring out which octave a maker means.

The Octave Name

A name given to the octave in English, German, and French, as described on the Dolmetsch Online Music Theory page. See the tables above for the names used.

Organ Naming

A name given to the note C at the lower end of each octave, as described on the Dolmetsch Online Music Theory page. See the tables above for the names used.

Frequency Range

This row in the tables above shows the frequency of the lowest and highest notes in the range, based on A4 being calibrated to 440 Hertz.

Scientific Pitch

This is a completely different system of notating pitch, sometimes used in scientific references. In scientific pitch, the absolute pitch of C4 (middle C) is 256 Hertz rather than the IPN standard of 261.63 Hertz. This has the advantage for scientific work that any C above or below C4 has a whole number of vibrations per second (Hertz), and also that the Hertz value is a power of two ([Allen-SA 1916], page 202).

Some examples in scientific pitch:

  • C-4 = 1 Hertz - 1 cycle per second
  • C0 = 16 Hertz - just below the lower limit of human hearing (as typically cited)
  • C4 = 256 Hertz
  • C45 = 562,949,953,421,312 Hertz = about 563 terra-Hertz (THz). In the electromagnetic spectrum, this frequency is a green color in the spectrum of visible light.

The note A4 has a frequency of 430.54 Hertz in the scientific pitch system rather than the IPN standard of 440 Hertz.

Scientific pitch is not used on Flutopedia, but may appear in some of the cited references.

Piano Key Numbers

The keys on a full 88-key keyboard (piano, organ, synthesizer, etc) are numbered from left to right, beginning from piano key #1, including the white and black keys.

Piano Key #40 is middle C (Italian: do centrale, German: eingestrichenes c, French: do central, Spanish: do central) and corresponds to C4 in IPN.

MIDI Note Numbers

MIDI [mi-dee] (“Musical Instrument Digital Interface”) is a electronic standard for conveying music. Each event of musical score or performance is assigned a specific standardised binary code or “instruction”.

The MIDI standard specifies numbers for the notes, beginning with MIDI note #0 an octave below IPN C0. Middle C, IPN C4, corresponds to MIDI note #60 in the MIDI standard ([Heckroth 1996]).

However, there is considerable ambiguity in the implementation of MIDI note numbers. Some manufacturers deviated from the standard and mapped middle C to MIDI note #72. Others map middle C to MIDI note #48.

Here is a table that provides the mapping between IPN notation and MIDI note numbers:

Mapping: MIDI Note Numbers <=> IPN Notes
Octave Note Numbers
C C#
Db
D D#
Eb
E F F#
Gb
G G#
Ab
A A#
Bb
B
-1 0 1 2 3 4 5 6 7 8 9 10 11
0 12 13 14 15 16 17 18 19 20 21 22 23
1 24 25 26 27 28 29 30 31 32 33 34 35
2 36 37 38 39 40 41 42 43 44 45 46 47
3 48 49 50 51 52 53 54 55 56 57 58 59
4 60 61 62 63 64 65 66 67 68 69 70 71
5 72 73 74 75 76 77 78 79 80 81 82 83
6 84 85 86 87 88 89 90 91 92 93 94 95
7 96 97 98 99 100 101 102 103 104 105 106 107
8 108 109 110 111 112 113 114 115 116 117 118 119
9 120 121 122 123 124 125 126 127  

 

 
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