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 Some of these systems are in current use, and some appear in the historical references cited on Flutopedia.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
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
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 range of Helmholtz Pitch notations 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 C_ii.

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