# Harmonograph

Music is one of the oldest and most universal of the ancient Arts, yet few people understand what the elements of harmony really are and how they actually fit together, or sometimes dont quite. In this charming little book Anthony Ashton uses a Victorian device called a Harmonograph to tell the story of Harmony and the intervals in the scale. With useful appendices and exquisite line drawings this is a unique and original introduction to this magical subject.- Unison 11 a spiral, a spiral drawn the same way over a spiral, and a spiral drawn the opposite way
- 100 recycled papers throughout. All rights reserved. For permission to reproduce any part of this bo
- Dedicated to John, Antonia and Imogen. Grateful acknowledgements to Harmonic Vibrations and Vibratio
- 1 Harmonic patterns from Sir Thomas Bazleys Index to the Geometric Chuck 1875, showing concurrent
- 3 2 Wigmore Street I went one day to see if they were still there. They were, though reduced merely
- 5 4 The Discovery of harmony on passing a blacksmith To understand what the harmonograph does we nee
- 7 6 The monochorD of creaTion a singular string theory There are seven octaves in the keyboard of a
- 9 8 overTones anD inTervals harmonic ratios in and outside the octave How are musical scales constru
- 11 10 WholeTones anD halfTones the fourth and fifth get their names Pythagoras hammers hide a set of
- 13 12 arranging The harmonies the power of silence The simple ratios of the primary overtones and un
- 15 14 lissajous figures sound made shape In the mid nineteenth century a French mathematician, Jules
- 16 17 Diatonic Ratio 21 158 95 53 85 32 43 54 65 98 1615 11 The PenDulum keeping time A fundamenta
- 19 18 TWo harmonograPhs lateral and rotary Two harmonographs and some of the simple patterns they dr
- 21 20 simPle unison 11 and the arrow of time The simplest harmonograph drawing is produced when both
- 22 near unison lateral phases and beat frequencies A source of pleasing variety in harmonograph draw
- 24 roTary unison 11 eggs and shells At first this is disappointing Unison in contrary motion produc
- 27 26 The laTeral ocTave 21 figures of eight and wings After Unison the next harmony to try is the O
- 28 The roTary ocTave 21 hearts and triangles From rotary motion with a 21 ratio come some of the mos
- 31 30 The laTeral fifTh 32 and the second overtone 31 The next interval to be tried is the dominant
- 32 The roTary fifTh 32 encircled hearts and fives The loudness of musical tones is represented on th
- 34 The fourTh 43 with thirds, sixths and sevenths By now it will be evident that each harmony displa
- 37 36 furTher harmonics seven limit and higher number ratios As the numbers in the ratios increase i
- 38 amPliTuDe circles, polygons, flowers and another circle Much variation can be obtained from a rot
- 41 40 Tuning Troubles the Pythagorean comma Leaving the harmonograph drawings and returning to the p
- 43 42 equal TemPeramenT changing keys made easy Although early tunings enabled many pure harmonic ra
- 45 44 The KaleiDoPhone squiggles from a vibrating rod Despite the invention of equal temperament, sc
- 46 chlaDni PaTTerns vibrating surfaces So far we have only considered vibrating strings and other si
- 48 resonance PicTures and how to sing a daisy A more complete set of Chladni figures is shown opposi
- 51 50 some feaTureD Tunings selecTeD musical inTervals Interval Cents Name 11 0 Unison 3280532768
- 53 52 The ratios and intervals in this book concern frequencies, normally expressed as cycles per se
- 54 Tables of PaTTerns Overtone and simple ratio harmonics are shown below and opposite, arranged in
- builDing a harmonograPh builDing a harmonograPh Pen Lever Table Clamp Gimbals Clamps can be obtai
- just the two singleaxis pendulums. This can be done by mounting two brackets on the table near the