equal to the greatest elongation of its orbit, from the same colure in the adverse part, and to the distance of the poles of the orbit from the equinoctial points.

Of the various Genera and Species of Music among the Ancients, with some Observations concerning their Scale. By John Chrtstoph. Pepusch, Music. D., and F.R.S. N° 481, p. 266.

In compliance with your request, I here send you some of my thoughts on the various genera and species of the Greek music. What were these, and how far the doctrine of the ancients in this respect is reconcileable with the true nature of musical sounds, are questions which have not a little perplexed the learned. That musical intervals are founded on certain ratios expressible in numbers, is an old discovery. It is well known that all musical ratios may be analysed into the prime numbers 2, 3, and 5; and that all intervals may be found from the octave, 5th and 3d major; which respectively correspond to those numbers. These are the musician's elements, from the various combinations of which, all the agreeable variety of relations of sounds result. This system is so well founded on experience, that we may look upon it as the standard of truth. Every interval that occurs in music is good or bad, as it approaches to, or deviates from, what it ought to be on these principles.

The doctrine of some of the ancients seems different. Whoever looks into the numbers given by Ptolemy, will not only find th primes 2, 3, and 5, but 7, 11, &c. introduced. Nay he seems to think all 4ths good, provided their component intervals may be expressed by superparticular ratios. But these are justly exploded conceits; and it seems not improbable that the contradictions of different numerical hypotheses, even in the age of Aristoxenus, and their inconsistency with experience, might lead him to reject numbers altogether. It is pity he did: had he made a proper use of them, we should have had a clearer insight into the music of his times. However, what remains of the writings of this great musician, joined to observation and experience, has enabled Dr. P. to throw some light on the obscure subject of the ancient species of music.

By the manner in which Euclid and others find the notes of their scale, it

* Dr. Pepusch was one of the greatest theoretic or scientific musicians among the moderns. He was a Prussian by birth; and in 1680, when not quite 15 years of age, he was chosen to teach music to the Prince Royal of Prussia. He afterwards came to England, and was engaged at Drury-lane theatre; though the popularity of Handel kept Pepusch in the 2d rank; yet his talents and judgment were so much respected, that he taught music to professors of music themselves. The university of Oxford honoured Dr. P. with the degree of Dr. of music, and the R. S. elected him one of their members. He married a Tuscan lady, an eminent opera singer, who had acquired by her profession a fortune of £10,000. Dr. P. died in 1752, being 85 years of age, and was buried in the Charterhouse.

Hence the 7 intervals

256

256

4, 4, 4, 244, f, f.

must have been composed of tones major, and limmas. of one octave would be thus expressed in numbers, 4, Some modern authors have from this inferred the imperfection of the Greek music. They allege that we here find the ditonus, or an interval equal to 2 tones major, expressed by, instead of the true 3d major expressed by 4. As there can be no question of the beauty and elegance of the latter, the former therefore must be out of tune, and out of tune by a whole comma, which is very shocking to the ear. In like manner the trihemitone of the ancients falls short of the 3d minor by a comma; which is also the deficiency of their hemitone or limma, from the true semitone major, so essential to good melody. These errors would make their scale appear much out of tune to us; and indeed it appeared out of tune to them; since they expressly tell us that the intervals less than the diatessaron or 4th, as also the intervals between the 5th and octave, were dissonant and disagreeable to the ear. Their scale, which has been called by some the scala maxima, was not intended to form the voice to sing accurately, but was designed to represent the system of their modes and tones, and to give the true 4ths and 5ths of every key a composer might choose. Now if, instead of tones major and limmas, we take the tones major and minor, with the semitone major, as the moderns contend we should, we shall have a good scale indeed, but a scale adapted only to the concinnous constitution of one key; and whenever we proceed from that into another, we find some 4th or 5th erroneous by a comma. This the ancients did not admit of. If, to diminish such errors, we introduce a temperature, we shall have nothing in tune but the octave. We see then that the scale of the ancients was not destitute of reason; and that no good argument against the accuracy of their practice can from thence be formed.

It was usual among the Greeks to consider a descending, as well as an ascending scale, the former proceeding from acute to grave, precisely by the same intervals as the latter did from grave to acute. The first sound in each was the proslambanomenos. The not distinguishing these two scales has led several learned moderns to suppose, that the Greeks, in some centuries, took the proslambanomenos to be the lowest note in their system, and in other centuries to be the highest. But the truth is, that the proslambanomenos was the lowest, or highest note, according as they considered the ascending or descending scale. The distinction of these is conducive to the variety and perfection of melody; but Dr. P. never yet met with above one piece of music, where the composer appeared to have any intelligence of this kind. The composition is about 150, or more, years old, for 4 voices; and the words are, Vobis datum est noscere mysterium regni Dei, cæteris autem in parabolis; ut videntes non videant, et audientes non intelligant. By the choice of the words, the author seems to allude to his having performed something not commonly understood.

The following is an octave only of the ascending and descending scales of the diatonic genus of the ancients, with the names of their several sounds, as also the corresponding modern letters.

Where it appears that the same Greek names serve for the sounds in the ascending and descending scales.

In the octave here given, 4 sounds, viz. the proslambanomenos, hypate hypaton, hypate meson, and mese, were called stabiles, from their remaining fixed throughout all the genera and species. The other 4 sounds being the parhypate hypaton, lychanos hypaton, parhypate meson, and the lychanos meson, were called mobiles, because they varied according to the different species and varieties of music.

By genus and species was understood a division of the diatessaron, containing 4 sounds, into 3 intervals. The Greeks constituted 3 genera, known by the names of enharmonic, chromatic, and diatonic. The chromatic was subdivided into 3 species, and the diatonic into 2. The 3 chromatic species were the chromaticum molle, the sesquialterum, and the toniæum. The 2 diatonic species were the diatonicum molle, and the intensum; so that they had 6 species in all. Some of these are in use among the moderns, but others are as yet unknown in theory or practice.

The diatonicum intensum was composed of 2 tones, and a semitone: but, to speak exactly, it consists of a semitone major, a tone minor, and a tone major. This is in daily practice; and we find it accurately defined by Didymus, in Ptolemy's Harmonics published by Dr. Wallis. The next species is the diatonicum molle, as yet undiscovered by any modern author. Its component intervals are, the semitone major, an interval composed of 2 semitones minor, and the complement of these 2 to the 4th, being an interval equal to a tone major, and an enharmonic diesis. The 3d species is the chromaticum toniæum. Its component

intervals are, a semitone major, succeeded by another semitone major; and lastly the complement of these 2 to the 4th, commonly called a superfluous tone. The 4th species is the chromaticum sesquialterum, which is constituted by the progression of a semitone major, a semitone minor, and a third minor. This is mentioned by Ptolemy, as the chromatic of Didymus. Examples among the moderns are frequent. The 5th species is the chromaticum molle. Its intervals are two subsequent semitones minor, and the complements of these 2 to the 4th; that is, an interval compounded of a 3d minor, and an enharmonic diesis. This species is never met with among the moderns. The 6th and last species is the enharmonic. Salinas and others have determined this accurately. Its intervals are, the semitone minor, the enharmonica, diesis and the third major.

Examples of 4 of these species may be found in modern practice. But he `does not know of any theorist who ever yet determined what the chromaticum toniæum of the ancients was: nor have any of them perceived the analogy between the chromaticum sesquialterum and our modern chromatic. The enharmonic, so much admired by the ancients, has been little in use among our musicians as yet. As to the diatonicum intensum, it is too obvious to be mistaken.

Aristoxenus and others often mention the tone is divided into 4 parts, and the semitone into 2; thus making 10 divisions or dieses in the 4th. And this is true, if we consider these sounds in one tension; that is, either ascending or descending; but, accurately speaking, when we consider all the dieses or divisions of the 4th, both ascending and descending, we shall find 13; 5 to each tone, and 3 to the semitone major. But then it is to be observed, that some of these divisions will be less than the enharmonic diesis; for if we divide the semitone major into the semitone minor, and enharmonic diesis, ascending, for instance, E, E, F, and then divide in like manner descending, F, F, E, we shall have the semitone major divided into 3 parts thus, E, F, XE, F; where the interval between F and E is less than the enharmonic diesis between E and F, and between E and F, as is easily proved.

Now, if we suppose these small intervals equai, by increasing the least division, and diminishing the true enharmonic diesis, we shall then have a 4th divided into 13 equal parts; and consequently the octave divided into 3 such equal parts; which gives us the celebrated temperature of Huygens, the most perfect of all.

From this it appears, that the division of the octave into 31 parts, was necessarily implied in the doctrine of the ancients. The first of the moderns who mentioned such a division was Don Vincentino, in his book L'Antica Musica ridotta alla moderna Prattica, printed at Rome, 1555, folio. An instrument had been made according to his notion; which was condemned by Zarlino and Salinas,

without sufficient reason. But Mr. Huygens, having more accurately examined the matter, found it to be the best temperature that could be contrived. Though neither this great mathematician, nor Zarlino, Salinas, nor even Don Vincentino, seems to have had a distinct notion of all these 31 intervals, nor of their names, nor of their necessity to the perfection of music.

In Huygens's temperature the tones are all equal; but in a true and accurate practice of singing they are not so. And the tone divided in every species must be the tone minor; for the division of the tone major is harsh and inelegant. So that, in the division of the 4th, it is to be observed, that in every species, the tone major must either be an undivided interval, or make part of one.

It may perhaps be wondered how the foregoing doctrine can be found in the writings of the ancients, since the distinction of tones into major and minor is no where mentioned in them. But it is to be observed, that though the terms do not occur, yet the thing itself was not unknown to them. They have not indeed expressed themselves fully; yet, from the whole of their writings come to our hands, the loctrine before laid down may be well supported.

Observations on the Precipices or Cliffs on the North-east Sea Coast of the County of Norfolk. By Mr. Wm. Arderon, F. R. S. N° 481, p. 275. These dreadful heights are equally dangerous to come near above or below; as they are so frequently tumbling down, and as often washed away by the billows; and though they are 20, 30, and in some places 40 yards, or more, in perpendicular altitude, yet the sea has gained on the land at least 110 yards in less than 20 years time for some miles on this coast.

The various strata, which make up this long chain of mountainous cliffs, must be very entertaining to every one, who takes a pleasure in looking into the many changes which the earth undoubtedly has undergone, since its first creation. Vegetable mould, oaz, sands of various kinds and colours, clays, loams, flints, marls, chalk, pebbles, &c. are here to be seen at one view beautifully interspered; and frequently the same kind many times repeated; as if at one time dry land had been the surface; then the sea; after morassy ground; then the sea, and so on, till these cliffs were raised to the height they are now found.

This is demonstrated by the roots and trunks of trees, which are to be seen at low water in several places on this coast near Hasborough and Walket; bones of animals are often found here also.

Among the many strata found in these cliffs, there is one of a dark grey colour, that sweats out a yellow sulphureous matter; it seems to be that sort of

* Dr. Hook, in his posthumous works says, the like are to be seen on the coasts of Cumberland and Pembrokeshire.-Orig.