Lecture 06 Part II a little more history of science October 1, 2004

This famous drawing of Pythagoras engaged in testing the relationships of music and numbers dates from a 1492 book of Gaffurius: Theorica Musices, Milan, From the Anvil flowed an idea (?)

Pythagoras

Pythagoras Observed ….. The heavier the bell, the “lower” the tone. The water inside a glass was directly related to the tone. He probably NEVER made any of these observations. But he did look at STRINGS and he did some very interesting “science”.But he did look at STRINGS and he did some very interesting “science”.

The Monochord

Closer to us. A SCIENTIFIC INSTRUMENT

Modern Design

L0L0 L1L1 L2L2

FIRST OBSERVATION The shorter the plucked length of the string, the “higher” the tone. With TWO strings, some lengths sounded well together and some did not. Pythagoras studied this carefully and developed the “mathematics” of the musical scale.

CLARIFICATION The musical scale was NOT invented by Pythagoras or by anyone else that we know of. But he STUDIED IT. The scale was developed naturally based upon which tones sounded well together. The scale probably goes back to the Neanderthal times (bone flute).

Pythagoras Looked for “Consonance” What length of string will be consonant with the open string? What is consonance??

Consonance Two tones are consonant when they sound pleasing together. They are dissonant if they do not. BUT whether or not a harmony is pleasing is a matter of personal taste, as there are consonant and dissonant harmonies, both of which are pleasing to the ears of some and not others. Pythagoras did not subscribe to the last statement. Pythagoras tried to define the right string lengths for harmony.

MOST INPORTANT Most harmonious sound (according to Pythagoras was (L 1 /L 0) = (1/2) This is called the OCTAVE L0L0 L1L1

Properties of the Octave The two tones almost sound like the same tone! –Whatever that means. When men and women sing together in “unison”, they will sing an octave apart and think they are singing the same tone! The octave defines an INTERVAL between two closely related tones.

Octave Having defined the interval of the octave, we can proceed to put more tones between them to establish a scale of notes that may be easily played together. Some combinations will not be a consonant as others but they are still considered harmonious.

Notation – A practical necessity FIRST TONE OCTAVE Notes between 5 pentatonic 7 diatonic What about higher? What about lower? HIGH LOW

A look at the musical scale ~500BC Length = L Unstopped string produces the primary tone of the scale. We will start our scale with an A. A

The Octave Length = L A L/2 Also A but HIGHER

The octave Is a higher pitch Sounds higher There is “a sameness” about the two tones when they are played together.

Move it! Length = L LOWER PITCH HIGHER PITCH We can therefore create a wide range of tones by changing the position of the “fret” along the string.

Play them together Length = L Tone 1 Tone 2

Look at the Piano Structure First Note Octive ????? How many notes to an octave???

Notes & Notation