ON TEMPERAMENT. 165 



how the comma of Pythagoras is got without unnecessary 

 computation. 



Twelve 5ths = 31 X 12 = 372 

 Seven octaves =53 X 7 = 371 



Therefore the comma = 1 



On the larger scale the comma rises to 539, and the 

 schisma to 49 or ^yth of the comma. 



Having now established our standard, we are in a position 

 to compare the various systems ; but before doing so, without 

 intending disrespect to anybody, I must remark on the 

 complex nomenclature with which we have here to deal. It 

 is perfectly astounding. I do not propose to go into all of it, 

 but I may simply mention it to show you what names exist. 

 Amongst them I find, Commatic, Pythagorean or Quintal, 

 Mean or Meso-tonic, Commato-Skhismatic, Hemitonic, Skhis- 

 matic, Skhismic, Skhistic, Cyclic, and Skhismo-cyclic. 

 These words of course are of value for investigation, but 

 there are too many, and they are too near to one another in 

 sound for ordinary use. 



The difficulty, of course, which all these systems were 

 made to meet, is that the advance of music requires free 

 power of modulation from every key into every other, both 

 of the major and minor forms. We can obtain this in 

 two ways ; either by a slight falsifying of the intervals, 

 or by increased mechanism and an increased number 

 of notes in the octave. These two views are very well 

 represented by the two quotations I gave you, from 

 Perronet Thompson and from Dr. Stainer. Dr. Stainer at 

 the time took, and in a great measure still takes the view, 

 that the organ at present built is as complicated as it will 

 bear being. Indeed, in speaking about it the other day he 

 said that he should be very glad to adapt true temperament 

 to the St. Paul's organ : but imagine the St. Paul's organ, 

 which is now very large, with eighty-four keys in each 

 octave ! St. Paul's itself would not hold the .organ, much 

 less the congregation. There is great truth in that. Mr. 

 Bosanquet's harmonium has eighty-four keys to each octave, 

 and if you multiply that by the number of stops it would 

 become so utterly unwieldy that practically no one could play 

 upon it. In the equal temperament, as .1 have said before, 



