The subject of this article is technical in nature and requires an understanding of organ terminology. This is in the process of being rectified. Many of the terms used here are defined in the pipe organ

Pipe organ

The pipe organ is a musical instrument that produces sound by driving pressurized air through pipes selected via a keyboard. Because each organ pipe produces a single pitch, the pipes are provided in sets called ranks, each of which has a common timbre and volume throughout the keyboard compass...

 article.

Scaling is the term used to describe the ratio

Ratio

In mathematics, a ratio is a relationship between two numbers of the same kind , usually expressed as "a to b" or a:b, sometimes expressed arithmetically as a dimensionless quotient of the two which explicitly indicates how many times the first number contains the second In mathematics, a ratio is...

 of an organ pipe

Organ pipe

An organ pipe is a sound-producing element of the pipe organ that resonates at a specific pitch when pressurized air is driven through it. Each pipe is tuned to a specific note of the musical scale...

's length to its diameter

Diameter

In geometry, a diameter of a circle is any straight line segment that passes through the center of the circle and whose endpoints are on the circle. The diameters are the longest chords of the circle...

. The scaling of a pipe is a major influence on its timbre

Timbre

In music, timbre is the quality of a musical note or sound or tone that distinguishes different types of sound production, such as voices and musical instruments, such as string instruments, wind instruments, and percussion instruments. The physical characteristics of sound that determine the...

. Reed pipe

Reed pipe

A reed pipe is an organ pipe that is sounded by a vibrating brass strip known as a reed. Air under pressure is directed towards the reed, which vibrates at a specific pitch. This is in contrast to flue pipes, which contain no moving parts and produce sound solely through the vibration of air...

s are scaled according to different formulas than are flue pipe

Flue pipe

A flue pipe is an organ pipe that produces sound through the vibration of air molecules, in the same manner as a recorder or a whistle. Air under pressure is driven down a flue and against a sharp lip called a Labium, causing the column of air in the pipe to resonate at a frequency determined by...

s. In general, the larger the diameter of a given pipe at a given pitch

Pitch (music)

Pitch is an auditory perceptual property that allows the ordering of sounds on a frequency-related scale.Pitches are compared as "higher" and "lower" in the sense associated with musical melodies,...

, the fuller and more fundamental

Harmonic series (music)

Pitched musical instruments are often based on an approximate harmonic oscillator such as a string or a column of air, which oscillates at numerous frequencies simultaneously. At these resonant frequencies, waves travel in both directions along the string or air column, reinforcing and canceling...

 the sound becomes.

The system most commonly used to fully document and describe scaling was devised by Töpfer

Töpfer

- PEOPLE :* Klaus Töpfer , German politician* Ernst Toepfer , German painter* Tomáš Töpfer, see Divadlo Na Fidlovačce* Alfred Toepfer , German entrepreneur, founder of Alfred Toepfer Stiftung F.V.S.* Reinhard Töpfer, author...

. In this system, the diameter of a given note is compared with a reference scale by means of half-tone deviations larger or smaller (indicated by the abbreviation ht). This reference scale is called Normalmensur. Normalmensur is a rank of pipes based on an internal diameter of 155.5mm at 8′ C (the lowest note of the modern organ compass) and a mouth width which is one-quarter of the circumference of such a pipe. The scale provides for a reduction in diameter of the pipes by half at every succeeding 17th pipe. This system can be used to produce Normalmensur variation tables or line graphs for the analysis of existing ranks or the design of new ranks.

The following is a list of representative 8′ stops in order of increasing diameter (and, therefore, increasing fundamental tone) at middle C

Middle C

C or Do is the first note of the fixed-Do solfège scale. Its enharmonic is B.-Middle C:Middle C is designated C4 in scientific pitch notation because of the note's position as the fourth C key on a standard 88-key piano keyboard...

with respect to Normalmensur, which is listed in the middle. Deviations from Normalmensur are provided after the pipe measurement in brackets.

• Viole d'orchestre (thin, mordant string stop): 35.6 mm [-10 ht]
• Salicional (broader-toned, non-imitative string stop): 40.6 mm [-7 ht]
• Violin diapason (thin-toned principal stop): 46.2 mm [-4 ht]
• Principal (typical mid-scale principal stop): 50.4 mm [-2 ht]
• Normalmensur: 54.9 mm [+/-0 ht]
• Open diapason (broader-toned principal stop): 57.4 mm [+1 ht]
• Gedeckt (thin-toned flute stop): 65.4 mm [+4 ht]
• Flûte à cheminée (typical mid-scale flute stop): 74.4 mm [+7 ht]
• Flûte ouverte (broader-toned flute stop): 81.1 mm [+9 ht]

Normalmensur scaling table, 16th halving ratio:

		32'		16'		8'		4'		2'		1'		1/2'		1/4'		1/8'		1/16'
	mm	scale	mm	scale	mm	scale	mm	scale	mm	scale	mm	scale	mm	scale	mm	scale	mm	scale	mm	scale
C 1	439.7	20	261.5	32	155.5	44	92.4	56	54.9	68	32.6	80	19.3	92	11.5	104	6.8	116	4.0	128
C# 2	421.2	21	250.4	33	148.9	45	88.5	57	52.6	69	31.3	81	18.6	93	11.0	105	6.5	117	3.9	129
D 3	403.2	22	239.8	34	142.6	46	84.7	58	50.4	70	29.9	82	17.8	94	10.5	106	6.3	118	3.7	130
D# 4	386.2	23	229.6	35	136.5	47	81.1	59	48.2	71	28.7	83	16.9	95	10.1	107	6.0	119	3.6	131
E 5	369.9	24	219.9	36	130.7	48	77.7	60	46.2	72	27.4	84	16.3	96	9.7	108	5.7	120	3.4	132
F 6	354.1	25	210.6	37	125.2	49	74.4	61	44.2	73	26.3	85	15.6	97	9.3	109	5.5	121	3.3	133
F# 7	339.1	26	201.6	38	119.9	50	71.3	62	42.3	74	25.2	86	14.9	98	8.8	110	5.2	122	3.1	134
G 8	324.7	27	193.1	39	114.8	51	68.2	63	40.5	75	24.1	87	14.3	99	8.5	111	5.0	123	3.0	135
G# 9	311.0	28	184.9	40	109.9	52	65.3	64	38.8	76	23.1	88	13.7	100	8.1	112	4.8	124	2.8	136
A 10	297.8	29	177.1	41	105.3	53	62.6	65	37.2	77	22.1	89	13.1	101	7.8	113	4.6	125	2.7	137
A# 11	285.2	30	169.5	42	100.8	54	59.9	66	35.6	78	21.1	90	12.6	102	7.4	114	4.4	126	2.6	138
B 12	273.1	31	162.3	43	96.5	55	57.4	67	34.1	79	20.2	91	12.0	103	7.1	115	4.2	127	2.5	139

From Organ Supply Industries catalog

External links

• Calculs de tailles de tuyaux d'orgues, 'L'Hydraule' (in French)