Alexander Ellis - 1885
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Of the ancient Persian scale we know nothing, but it was most probably the progenitor of the older Greek. At the earliest period of which we have precise knowledge, the writings of Al Farabi (who died A.D. 950), give an account of the Lute, Tambours (long-necked guitars) of Bagdad and of Khorassan, the Flute, and Rabab (a two-stringed viol). These have been published by Prof. J. P. N. Land, of Leyden, in Arabic, with a French translation under the care of M. Goeje, and a preliminary dissertation.a

The Arabs and Persians — for we must consider their systems identical in Al Farabi's time — had very various scales which not only could not be played together, just as our major and minor scales cannot be played together, but which were composed on such different principles for different instruments, that two instruments of different kinds could not be tuned to play the same scale together. They must, therefore, have been simple accompaniments for the voice, not in our modern sense of accompaniment (for there was and is no notion of harmony), but merely as steadiers of the voice, touching the notes that had to be sung, or else instruments for solo performance. We must, therefore, take them separately.

(1.) The Lute (al'ood, whence our word lute is derived). An instrument like the European lute, with four, and subsequently five, strings, nearly touching at the nut, and spreading out at moderate angles, so as to be well apart at the striking place. This was originally tuned in Fourths, each successive string being a Fourth higher than the next lower. A series of ligatures, answering to frets, were tied across the finger board. The places were at an early time, though perhaps not originally, determined so as to give on each string the Greek tetrachord of I 204 II 204 III 90 IV, where I, II, &c., represent the names of the notes. Of these I occupied the open string, II was stopped by the first, III by the fourth, and IV by the little finger, after which, and the string, they were named. Theoretically the note II used 89 of the string, the note III used 89 of this or 6481 of the whole length, and the note IVused 34 of the whole string. Practically, this would have made the notes too sharp, hence doubtless the position of the frets was accommodated as on the Japanese Biwa, which is an existing form of Al Farabi's lute. Calling the notes for the first or C string, C 204 D 204 E 90 F; those for the next, or F string, would be F 204 G 204 A 90 B fl ; for the third, or B fl string, Bfl 204 C 204 D 90 Efl ; and for the fourth, or Efl string, Efl 204 F 204 G 90 Afl. The first octave, then, was C 204 D 204 E 90 F 204 G 204 A 90 Bfl 204 C, the Greek G-mode (see Sect. V), with which Al Farabi was quite familiar, using the Greek names. Observe that the middle finger had nothing to do. The old plan was to introduce a fret for it between D and E, at E fl, a tone 204 cents flatter than F, so that the length of string for E fl was 98 the length for F (corrected of course). On the second string there was, therefore, a corresponding A fl. This gave as the scale —

But this old middle finger note did not please. First a Persian modification was tried, by tying a ligature halfway between those for 204 and 408 cents, which would (theoretically) give 303 cents on the first string, and 801 cents on the second. But these notes, which were as nearly as possible our own equally-tempered E fl 300, and A fl 800, also grew out of favour. Something sharper was required. Possibly they longed for the perfect minor Third E fl 316, and minor Sixth A fl 814. But they went much sharper. One Zalzal, a celebrated lutist, who died a century and a half before Al Farabi, tied a ligature halfway between the Persian 303 cents and the Greek 408 cents, and got a tone of 355 cents on the first and 853 cents on the second string. These notes became of great importance in Arabic music, and effectually distinguished this older Arabic form from the later Greek. The scale now practically became —

where E°, A° represent for the moment these new tones. To this important scale, quite different from anything we have yet met with, I shall have to devote considerable attention presently.

Designating the strings as simply FIRST (or lowest), SECOND, THIRD, FOURTH, and FIFTH, and the notes as Open, Index, Middle, Ring, Little — namely, played with those fingers — as more generally intelligible than the Arabic names used by Professor Land, I give all the notes that arose in different times in the two octaves, with the interval from the lowest note to the nearest cent. Professor Land, at my suggestion, gave them in equal Semitones to three places of decimals. On account of the notes in any string being a Fourth higher than those in the preceding, the two Octaves do not quite agree, and hence the cents are given for each, but are reduced by omitting the 1200 cents which would have to be added to each note in the second Octave. Of course is must be well understood that all these divisions were not in use at the same period, but some at one and some at another, and that at all times the scales were made by selections from them. Two near index notes and some exceptional middles are omitted by Professor Land, as presenting no difficulties to those who take an interest in them.

Notes.First Octave.Second Octave.Cents.
1st Oct.2nd Oct.
CFIRST : openTHIRD : index00
D flancient near indexancient middle9090
Persian middle99
Persian near index145
Zalzal's middle151
Zalzal's near index168
E flancient middlelittle=FOURTH : open294294
Persian middle303
Zalzal's middle355
F flFOURTH : ancient near index384
Persian near index439
Zalzal's near index462
Flittle = SECOND : openindex498498
G flSECOND : ancient near indexancient middle588588
Persian middle597
Persian near index643
Zalzal's middle649
Zalzal's near index666
A flancient middlelittle = FIFTH : open792792
Persian middle801
Zalzal's middle853
B fflFIFTH : ancient near index882
Persian near index937
Zalzal's near index960
B fllittle = THIRD : open996
C flTHIRD : ancient near indexFIFTH : ancient middle10861086
Persian middle1095
Persian near index1141
Zalzal's middle1147
Zalzal's near index1164

It will be seen that each string is divided exactly like the first; that the cents on SECOND are found by adding 498 to those on FIRST; those on THIRD 498 to those on SECOND (rejecting 1200 when we reach the second octave), those on FOURTH by adding 498 to those on THIRD, and those on FIFTH (which was Al Farabi's proposal) by adding 498 to those in FOURTH. There is one extra note not in the table, the little on FIFTH which is 90 (properly 2490) cents, but which was probably not used.

On observing the names of the notes in the above table they will be found to contain the following 14 forming Fourths up, as the Arabs considered them, or Fifths down, as we should say, E A D G C F Bfl Efl Afl Dfl Gfl Cfl Ffl B ffl. But that these did not comprehend the Persian or Zalzal's middle upon any string, which refused to fit into this series of Fourths. This offended the systematic spirit of subsequent theorists, and we find, four centuries later, in the writings of Mahmoud of Shiraz (died A.D. 1315) and Abdulqadir, that they succeeded in replacing these Zalzal notes by adding three more Fourths proceeding from B ffl 882, contained in the former series, to E ffl 180, A ffl 678, D ffl 1176. The name of Zalzal was retained, but used for F fl 384 and B ffl 882, which already existed in the second octave (see table). Persian was used for E fl 294, and Persian and Zalzal middle were banished. The term near was used for near the index and made 180 instead of 145 and 168. While the ancient near index became the remnant 90, or what was left after going back two whole tones from the Fourth (498-408=90). The scale then became simply the later 17 division of the Octave.

No.Notes.First Octave.Second Octave.Cents.
1st Oct.2nd Oct.
1CFIRST : openTHIRD : index00
2D flremnantPersian9090
3E fflnearZalzal180180
5E flPersianlittle294294
6F flZalzalFOURTH : remnant384384
near G ffl474
9G flSECOND : remnantPersian588588
10A fflnearZalzal678678
12A flPersianlittle792792
13B fflZalzalFIFTH : remnant882882
near C ffl972
15B fllittleindex996996
16C flTHIRD : remnantPersian10861086
17D fflnearZalzal11761176

This, in fact, gives 19 notes, but G ffl 474 and C ffl 972 only found in the second octave, although they occur in this table, seem not to have been reckoned in. They do not form part of the scales. Without them the octave would be divided into 17, and with them into 19 unequal parts. But Villoteau supposes that the Arabs proceeded by intervals of the Third of an equal tone, or 66 23 cents. It is not easy to see how he could have muddled himself to such an extent. That he was quite wrong appears from the above table arranged from Professor Land's. The interval between any two notes in the same octave is either 90 or 24 cents, that is, the Pythagorean limma or comma. But in going from E in the first to G ffl in the second octave, and also from A in the first to C ffl on the second, we do get intervals of 1266 cents, which is in fact an Octave and one-third of a Tone. This, however, is the only approach to division by thirds of a Tone, and even for this purpose two tones have to be used which the Arabs ignored in their scales. Hence Professor Land has quite disproved this erroneous conception of thirds of Tones.

Now this large collection of notes was of course not used as a single scale, but, like our own 12 semitones, as a fund out of which scales might be formed by selection. And the following are the 12 historical scales reported by the Arabian systematists as described by Prof. Land. But I have here given the letter names to the notes which are used in the above list (the Arabic names have no connection with them) and added the cents both between the notes, and from the lowest note. The orthography adopted by Professor Land for the names of the maqamat or scales is French.


  1. 'Ochaq
  2. Nawa
  3. Bousilik
  4. Rast
  5. 'Iraq
  6. (There are eight tones to this scale, because there are two forms of C, namely B ffl and C, differing from each other by a Pythagorean comma, but these two forms were probably not played in succession, but were alternated, just as the major or minor Seventh, and the major or minor Sixth in our own minor scale, which, if these were included, would be made to have 9 tones. The grave Second in our just major scale would have been a more apt illustration, had it not been lost in tempered music.)
  7. Içfahan
    (Another eight tone scale, see remarks on last.)
  8. Zirafkend
    (Eight notes, four intervals semitones.)
  9. Bouzourk
    (Eight tones.)
  10. Zenkouleh
  11. Rahawi
  12. Hhosaïni
  13. Hhidjazi

Suppose we begin this last scale on B fl, it would become Bfl 204 C 180 Effl 114 Efl 204 F 180 Affl 204 Bffl 114 Bfl, where the intervals 180, 114 cents differ only by 2 cents each from 182, 112, which would occur in our just scale of B fl, which is Bfl 204 C 182 D 112Efl 204 F 182 G 204 A 112 Bfl. Now this difference is imperceptible even in chords, and this 12th scale could therefore be used for harmony even better than our usual equally tempered scale. Yet the Arabs never used harmony at all, and were probably quite unaware of this property of their scale, which was pointed out by Professor Helmholtz.

Zalzal's intervals of 355 and 853 cents, although effectually banished from classical music during our middle ages by this new scale of 17 (or 19) unequal divisions, was evidently too deeply rooted in popular feeling to be really lost. Eli Smith, an American missionary at Damascus, having been forced to study the Arabic musical system in order to make the children sing in his mission schools, as they could not be taught the European intervals, fortunately became acquainted with Michael Meshaqah, a very intelligent man, a mathematician and a musician, who had written a treatise on Arabic music. This treatise Eli Smith translated in an abridged form and published at Boston, U.S. America, in 1849, in the Journal of the American Oriental Society (vol. 1, pp. 171-217, with a plate). It shows that Meshaqah adopted an equal temperament of 24 Quartertones, or 24 equal divisions of the octave, each containing 50 cents, and that in this he considered the following as the normal scale, which might begin upon any one of the Quartertones —


Comparing Zalzal's

we find a practical identity, showing that Meshaqah's scale is a pure survival of Zalzal's. It appears, however, from the following specimens of 95 Arabic melodies given by Eli Smith, that one or more of the notes were frequently sharpened or flattened by a Quartertone of 50 cents, giving intervals with different characters. He has engraved 11 of these so-called melodies, without any indication of time or rhythm, in a peculiar notation for which we may substitute a simple modification of ordinary notation, using q (or in music notation the inverted sign for flat) read quarter, to signify sharpened by a quarter of an equally tempered tone. Taking the first note of the scale as A, the normal scale throughout two octaves, with the name of each note in Arabic (as Eli Smith writes them, omitting diacritical signs) will be — A yegah, B osheiran, Cq araq, D rest, E dugah, Fq sigah, G jehargah, a nawa, b huseiny, cq auj, d mahur, e muhhaigar, fq buzrek, g mahuran, á remel-tuty.

Each Quartertone has also its peculiar name throughout two octaves, and by means of them the following melodies were written in the original Arabic treatise, here translated as above.

The scales subjoined have been collected from the melodies, and give every note in each melody independent of octave. Of course every note in a scale does not occur in every melody. There is no notion of a tonic, but Eli Smith calls the final (to use a medieval term for the last note of a melody) the keynote, and hence I have arranged the scale from and to the final in each case. Though the melodies are free, that is, not fixed in rhythm or length, some notes in some melodies are marked as distinct (to these I have added an acute accent), and others as glanced at, obscure, highly touched (to these I have added the mark of degree °), of which Eli Smith says he does not fully understand the technical meaning. However, it cannot be far from forte and piano, or accented and unaccented, or long and very short.


[Capitals indicate the lower, small letters the upper octave.]
  1. Shed Araban.a bfl a d dfl bfl a e f e d dfl bfl a G F E D Dfl B A.
    [Scale, A 100 Bfl 100 B 200 Dfl 100 D 200 E 100 F 200 G 200 a, in which there is no note not in our equally tempered scale.]
  2. Araq.a G Fq E D Cq. [This is a portion of the normal scale descending from a to Cq.]
  3. Araq Zemzemy.Cq D E a G Fq E D Cq Fq′ e c° a G Fq E Fq E D Cq B A D Fq a G Fq E. [Scale, A 200 B 100 C 50 Cq 150 D 200 E 150 Fq 150 G 200 a′. This lightly touched is possibly mere grace note.]
  4. Rahhat el Arwahh.a afl afl E F E D F E D Cq. [Scale, A 350 Cq 150 D 200 E 100 F 300 Afl 100 a′.]
  5. Remel.a G G a afl b° a G G Gflq G a° Fq′ F E D Cq.
    [Scale, A 200 B 150 Cq 150 D 200 E 150 Fq 100 Gflq 50 G 100 Afl 100 a. The G fl q is a mere grace note, and probably G fl would do as well.]
  6. Nikriz.a afl Fq′ b a′ afl Fq E D. [Scale, A 200 B 300 D 200 E 150 Fq 250 Afl 100 a.]
  7. Nishawerk.a′ afl Gfl E D. [Scale A 500 D 200 E 200 Gfl 200 Afl 100 a.]
  8. Penjgah.a′ afl Gfl′ afl a cq′ b′ a′ afl Gfl′ G′ Fq E D.
    [Scale, A 200 B 150 Cq 150 D 200 E 150 Fq 50 Gfl 100 G 100 Afl 100 a.]
  9. Sadhkar el muta'arif.D E Gfl′ E D a′ b′ a G Gfl E′ B Cq D. [Scale, A 200 B 150 Cq 150 D 200 E 200 Gfl 100 G 200 a.]
  10. Hhejaskar. E b c b a afl Fq E B E. [Scale, A 200 B 100 C 400 E 150 Fq 250 Afl 100 a.]
  11. Shawerk of the Egyptians.a′ G° Fq′ E′ D C. [Scale, A 300 C 200 D 200 E 150 Fq 150 G 200 a.]

In these 11 melodies there is only one, No. 2, which contains the notes of the normal scale, A B Cq D E Fq G a, unaltered. On looking through the whole of the 95 melodies I find only 6 others with unvaried notes. These are

  1. Mukhalif arak.Cq D E G Fq E D Cq.
  2. Rest.D E Fq G a G E D A D.
  3. Ssuba called Rekb.G′ b° G Fq E.
  4. Sigah.Fq D Fq a d cq b a G Fq.
  5. Bestniker.cq d cq b a′ d cq b a G Fq.
  6. Nejdy-Sigah.Fq G a b cq b a b cq d cq b a G Fq.

These scales and melodies introduce two entirely new points, unknown in European and common in Oriental music. First, the series of neutral intervals, intermediate in position and character between the European, and hence bearing a neutral stamp, so that the European ear does not know how to appreciate them. They have consequently led musicians into many errors in attempting to record them. Thus, 250 cents is neutral between a Tone 200 (just 204) and a minor Third 300 (just 316). Again, 350 cents (more accurately Zalzal's 355) lies on the boundary between the appreciation of a minor Third 300 (just 316), and a major Third 400 (just 386). The experiment is easily tried on the Dichord. At 355 cents Mr. Hipkins could not say to which Third the character of the interval approached. It was purely neutral. Observe that 350 cents is half a Fifth 700 (just 702), and the succession of 0 350 700 rapidly becomes pleasing to the ear. The interval 450 cents lies between a major Third 400 and a Fourth 500 (just 386 and 498), and is rather appreciated as a very flat Fourth. All these ambiguities are repeated a Fourth higher. Thus, 850 cents (between a minor Sixth 800, and a major Sixth 900) is precisely analogous to 350 cents, and (as 853 cents) forms part of Zalzal's scale. Observe that these intervals have no harmonic value or meaning. They could not exist in any system of music which recognised chords. Chords were an entirely European medieval discovery, of which Greece and Asia are still totally ignorant. Observe also that a solo player on a stringed instrument without frets, who is absolutely unchecked by harmony, is able to amuse himself by taking all manner of strange intervals, or occasional variations of established intervals. And this leads to the second point, the constant alteration of the normal notes in the scale, nominally by a Quartertone, really most probably by some indefinite but small interval at the pleasure of the performer, who consulted only his own ear at the moment, and could scarcely be checked by the ears of an audience. But these variations were reduced to a system, at least on paper, and Meshaqah is strong on the principles and details of his science of music.

(2.) The Highland Bagpipe. — It will seem strange to introduce this instrument among the Arabian. But the bagpipe is found sculptured at Nineveh. It was possibly brought to Europe during the Crusades, long after the deaths of Zalzal and Al Farabi, but before the introduction of the Arabic scale of 17 (or 19) notes to the octave. And it seems originally to have had that Zalzal scale already noted, viz. :—

I204II151III143IV204V151VI143 VII 204 I′

Of which the tempered representative is the principal scale of Meshaqah just discussed. Of course, there must have been some alterations, but this Damascus scale of Meshaqah would represent the scale sufficiently well for all purposes. The Highland bagpipe has at present only nine notes, written g′ a′ b′ c″ d″ e f″ g″ a″ (g′ being on the second line of the treble staff), and also two drones or deep notes which are always sounding (being the first and second octave below a′, that is, on the top line and bottom space of the bass staff). Now it is generally said that g′ to a′ is not quite a tone, and that c″ f″ are not exactly c″ and f″, or c″sh and f″sh of the ordinary notation, but in each case some intermediate sound, the consequence being that the bagpipe cannot play with any other instrument in a band, and two or more bagpipes can only play in unison. The instrument is a kind of oboe played with a bellows instead of the mouth. To determine what this scale really was, Mr. C. Keene, the well-known artist of Punch, who is a performer on the bagpipe, kindly brought his instrument to my house and played through the scale, while Mr. Hipkins determined the pitch by my forks. The following was the result. The first line gives the number of vibrations, the second line gives the names of the notes and the interval in cents between them, the third line gives the intervals in cents from the lowest a′, omitting the low g′ which is repeated in the octave as g″.

Obs. vib.395441494537587662722790882
Notes.g′191a′197b′144c″154d″208e″150f″156g″191 a″

This scale took us quite by surprise, and we immediately wrote to Mr. Glen, the great bagpipe seller, to make an inquiry. He informed us that the scale as regards intervals has never been altered. If the chaunter [the oboe played on] you had is one of McDonald's [it was so] or our own, it was no doubt correct. Our opinion is that if a chaunter was made perfect in any one scale it would not go well with the drones. Also there could not be nearly so much music produced (if you take into consideration that it has only 9 invariable notes), as at present it adapts itself to the keys of A [major], D [major], B minor, G major, E minor, and A minor. Of course we do not mean that is has all the intervals necessary to form scales in all those keys, but that we find it playing tunes that are in one or other of them.

Now the equal temperament of the scale just deduced would be clearly 0 200 350 500 700 850 1000 1200, or precisely the normal Damascus lute scale, just considered. For comparison, I determined the number of vibrations in such a scale, and also for Zalzal's taking the a&prime, with the result —

Notes.a′b′c″d″e″f″g″ a″
Observed vib.441494537587662722790882
Damascus vib.441495540587661721786882
Zalzal's vib.441496541587661722783882

Mr. Keene's chaunter was not perfect (none is), and the blowing (which was difficult, as wind had to be got up in the bag for each separate note), could not be absolutely relied on. Clearly c″ was a little flat, and g″ a little sharp, the latter designedly, because the custom is to make the interval g″:a″ less than 8:9 or a whole tone, which is an accommodation to the major scale of A, and is evidently a modernism. Mr. Colin Brown (Euing Lecturer on the Science, Theory and History of Music at Anderson's College, Glasgow), informs me, after diligent inquiry, that there is no scientific principle adopted in boring the holes of the chaunters, and that only about one in six made turns out to be useful. He himself thinks the bagpipe ought to play the major scale A. I should recommend reverting to Zalzal's scale, either in the pure or tempered form. In the pure form the ratios are a′:b′ = d″:e″ = g″:a″ = 8:9, b&prime:c″ = e″:f″ = 11:12, a′:d″ = 3:4, a′:e″ = 2:3. There is, therefore, only one unfamiliar interval 11:12 = 151 cents, and that occurs on the trumpet. From these ratios Zalzal's vibrations were calculated above. Of course in this case c q and f q should in theoretical writing take the place of c and f.

(3.) Northern Tambour, or that of Khorassan. — A guitar with a circular or oval body, and a very long neck on which (formerly) the frets extending to a Ninth were placed. Of these 5 were fixed, representing the Second 204, Fourth 498, Fifth 702, Octave 1200 and Ninth 1404 cents, of the open string. The other 13 were movable, so that they could be adjusted for the different scales or maqamat, following the plan of the 12 scales already given. Referring to the table of the later 17 division, the notes of the tambour and lute coincided as far as 588 cents, then in place of the lute's 678 cents (our A ffl), the tambour had 612 cents or 498+114 cents (our F sh). Then tambour and lute again coincided till the lute's 882 B ffl which the tambour replaced by 816 or 702+114 cents our G sh, and then again the two coincided up to 996 B fl, but the remaining intervals, 1020 A sh, 1110 B and 1224 B sh, were different. The scale was then as follows, (*) marking the fixed, and (†) auxiliary tones :—


Instead, therefore, of taking Fourths up from B to D ffl, this scale formed the series from B sh to E ffl, with the exception of four, marked by being inclosed in ( ) in the following list, where the subscribed numbers give the cents from C, subtracting 1200 where needed.

Bsh Esh Ash (Dsh) Gsh Csh Fsh B E A D G C F Bfl Efl Afl Dfl Gfl (Cfl) Ffl (Bffl) Effl
1224 522 1020 (318) 816 114 612 1110 408 906 204 702 0 498 996 294 792 90 588 (1086) 384 (882) 180

Al Farabi gives the means of tuning two strings out of the three occasionally used: first, with the strings in unison; secondly, with an interval of 228 cents, or two apotomes of 114 cents between them; thirdly, with the interval of a major Tone, 204 cents; fourthly, with the interval of a Pythagorean minor Third, 294 cents; and fifthly, with the interval of a Fourth, 498 cents.

(4.) Al Farabi's Flutes or Oboes. — Professor Land calls them flutes, but his figures show that they were played with a double reed like the oboe. These were intended to play in Zalzal's scale —

0 204 355 498 702 853 996 1200 cents,
a b cq d e fq g a′
but the Third and Sixth varied. A double flute, figured by Professor Land from a Madrid MS. gives 9 notes, just as on the bagpipe, but having the Persian 303 and 801 cents, which are 52 cents lower than Zalzal's, thus (giving the nearly equally tempered notes written below, -204 means an interval of 204 cents downwards) —
-204 0 204 304 498 702 801 996 1200
G a b c d e f g a′
This gives the tempered form of our descending A minor played upwards.

(5.) The Rabab. — This was a two-stringed viol played with a bow. The one Professor Land figures has a finger board, the one I saw had none. It was supposed to be the custom to stop at 89, 56, 6481, 3245, the lengths of the string, that is, 0 204 316 408 590 cents, or at a major Tone, minor Third, Pythagorean major Third, and Tritone, but player was really guided by ear only. It is believed, but not certain, that the two strings were stopped in the same way. Usually the interval between the strings was a minor Third 316 cents; but it was sometimes a (Pythagorean) major Third 408 cents, and sometimes a Tritone 590 cents.

This gives three scales which may be written thus, I being the open string :—

First string0204316408590
Second string316520632724906
Or else408612724816998
Or else5907949069981180
Or say &mdash
First stringCDEflEFsh
Second stringEflFGflGA
Or elseEFshGGshAsh
Or elseFshGshAAshBsh

This gave the sharp Tetrachord C to F 520 cents, and the exact Tetrachord E to A 498 cents. But the consequent scales are not clear.

(6.) The Southern Tambour or that of Bagdad. — This was long-necked and two-stringed, and was used in Bagdad and to the west and south of that city. We may consider that the string was divided into 40 parts, of which only 5 were used for stopping or fretting, and the higher string was tuned in unison with the highest note on the lower string. This gave the following arrangement :—

Vib. lengths403938373635parts.
Lower string04489135182231cents.
Second string231275320366413462''

This is a scale entirely without parallel; but Prof Land conjectures that a process of this kind may have led to the first scale of the Persian lute before Pythagorean intonation was invented. The principle is that equal divisions of the difference of two lengths of a string will give nearly equal intervals extending from one to the other. In the present case, these intervals are 44, 45, 46, 47 and 49 cents, of which the three first at least do not differ perceptibly. Then he supposes that the string may have been divided into 20 parts, and 5 of them taken; this would give —

Vib. lengths201918171615Parts.
or sayCDflDEflEF
Where D fl is properly 90 cents, E fl 281 is half a comma less than the Pythagorean E fl 294, and the others are exact. The alteration into Al Farabi's intervals
does not, in any case, amount to more than a comma (22 cents).

The mode in which the Persian and afterwards Zalzal's middle finger was obtained, by halving the distance between the frets, shows that this plan is in accordance with the habits of the people. Compare also the 9 and 13 division in the modern Bengali string in the next section.

a Recherches sur l'histoire de la Gamme Arate. Tiré du Vol II. des Travaux de la 6e session du Congrès international des Orientalistes à Leide, par J. P. N. Land. Mr. Land is a D.D., Professor of Mental Philosophy at Leyden, an Orientalist and a musician, and as his researches are most recent, while he has had access to all previous accounts, I follow him implicitly.

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