4 A remarkable numeration system
This unit looks at Babylonian mathematics. You will learn how a series of discoveries have enabled historians to decipher stone tablets and study the various techniques the Babylonians used for problem-solving and teaching. The Babylonian problem-solving skills have been described as remarkable and scribes of the time received a trainng far in advance of anything available in medieval Christian Europe 3000 years later.
Learning outcomes
This unit looks at Babylonian mathematics. You will learn how a series of discoveries have enabled historians to decipher stone tablets and study the various techniques the Babylonians used for problem-solving and teaching. The Babylonian problem-solving skills have been described as remarkable and scribes of the time received a trainng far in advance of anything available in medieval Christian Europe 3000 years later.
Acknowledgements
This unit continues our examination of ‘voice-leading’ or ‘Schenkerian’ analysis, perhaps the most widely-used and discussed method of analysing tonal music. In this unit, this method is explained through the analysis of piano sonatas by Mozart. The unit is the second in the AA314 series of three units on this form of harmonic analysis, and concentrates on the ‘middleground level’ of voice leading. As you work through this unit, you will become familiar with the deeper levels of harm
References
This unit continues our examination of ‘voice-leading’ or ‘Schenkerian’ analysis, perhaps the most widely-used and discussed method of analysing tonal music. In this unit, this method is explained through the analysis of piano sonatas by Mozart. The unit is the second in the AA314 series of three units on this form of harmonic analysis, and concentrates on the ‘middleground level’ of voice leading. As you work through this unit, you will become familiar with the deeper levels of harm
6.2 The idea of the background, and unit summary
This unit continues our examination of ‘voice-leading’ or ‘Schenkerian’ analysis, perhaps the most widely-used and discussed method of analysing tonal music. In this unit, this method is explained through the analysis of piano sonatas by Mozart. The unit is the second in the AA314 series of three units on this form of harmonic analysis, and concentrates on the ‘middleground level’ of voice leading. As you work through this unit, you will become familiar with the deeper levels of harm
6.1 Considering patterns on a larger scale
This unit continues our examination of ‘voice-leading’ or ‘Schenkerian’ analysis, perhaps the most widely-used and discussed method of analysing tonal music. In this unit, this method is explained through the analysis of piano sonatas by Mozart. The unit is the second in the AA314 series of three units on this form of harmonic analysis, and concentrates on the ‘middleground level’ of voice leading. As you work through this unit, you will become familiar with the deeper levels of harm
5.5 Interruption: a summary
This unit continues our examination of ‘voice-leading’ or ‘Schenkerian’ analysis, perhaps the most widely-used and discussed method of analysing tonal music. In this unit, this method is explained through the analysis of piano sonatas by Mozart. The unit is the second in the AA314 series of three units on this form of harmonic analysis, and concentrates on the ‘middleground level’ of voice leading. As you work through this unit, you will become familiar with the deeper levels of harm
5.4 Different analyses of a single theme
This unit continues our examination of ‘voice-leading’ or ‘Schenkerian’ analysis, perhaps the most widely-used and discussed method of analysing tonal music. In this unit, this method is explained through the analysis of piano sonatas by Mozart. The unit is the second in the AA314 series of three units on this form of harmonic analysis, and concentrates on the ‘middleground level’ of voice leading. As you work through this unit, you will become familiar with the deeper levels of harm
5.3 Interrupted structure and typical features of the style
This unit continues our examination of ‘voice-leading’ or ‘Schenkerian’ analysis, perhaps the most widely-used and discussed method of analysing tonal music. In this unit, this method is explained through the analysis of piano sonatas by Mozart. The unit is the second in the AA314 series of three units on this form of harmonic analysis, and concentrates on the ‘middleground level’ of voice leading. As you work through this unit, you will become familiar with the deeper levels of harm
5.2 Identifying an interrupted structure
This unit continues our examination of ‘voice-leading’ or ‘Schenkerian’ analysis, perhaps the most widely-used and discussed method of analysing tonal music. In this unit, this method is explained through the analysis of piano sonatas by Mozart. The unit is the second in the AA314 series of three units on this form of harmonic analysis, and concentrates on the ‘middleground level’ of voice leading. As you work through this unit, you will become familiar with the deeper levels of harm
5.1 Interruption as a structural device
This unit continues our examination of ‘voice-leading’ or ‘Schenkerian’ analysis, perhaps the most widely-used and discussed method of analysing tonal music. In this unit, this method is explained through the analysis of piano sonatas by Mozart. The unit is the second in the AA314 series of three units on this form of harmonic analysis, and concentrates on the ‘middleground level’ of voice leading. As you work through this unit, you will become familiar with the deeper levels of harm
4 Self-contained musical structures
This unit continues our examination of ‘voice-leading’ or ‘Schenkerian’ analysis, perhaps the most widely-used and discussed method of analysing tonal music. In this unit, this method is explained through the analysis of piano sonatas by Mozart. The unit is the second in the AA314 series of three units on this form of harmonic analysis, and concentrates on the ‘middleground level’ of voice leading. As you work through this unit, you will become familiar with the deeper levels of harm
3.3 Unfolding: a summary
This unit continues our examination of ‘voice-leading’ or ‘Schenkerian’ analysis, perhaps the most widely-used and discussed method of analysing tonal music. In this unit, this method is explained through the analysis of piano sonatas by Mozart. The unit is the second in the AA314 series of three units on this form of harmonic analysis, and concentrates on the ‘middleground level’ of voice leading. As you work through this unit, you will become familiar with the deeper levels of harm
3.2 Identifying unfoldings
This unit continues our examination of ‘voice-leading’ or ‘Schenkerian’ analysis, perhaps the most widely-used and discussed method of analysing tonal music. In this unit, this method is explained through the analysis of piano sonatas by Mozart. The unit is the second in the AA314 series of three units on this form of harmonic analysis, and concentrates on the ‘middleground level’ of voice leading. As you work through this unit, you will become familiar with the deeper levels of harm
3.1 Unfolding in Mozart
This unit continues our examination of ‘voice-leading’ or ‘Schenkerian’ analysis, perhaps the most widely-used and discussed method of analysing tonal music. In this unit, this method is explained through the analysis of piano sonatas by Mozart. The unit is the second in the AA314 series of three units on this form of harmonic analysis, and concentrates on the ‘middleground level’ of voice leading. As you work through this unit, you will become familiar with the deeper levels of harm
2 Melodies within melodies
This unit continues our examination of ‘voice-leading’ or ‘Schenkerian’ analysis, perhaps the most widely-used and discussed method of analysing tonal music. In this unit, this method is explained through the analysis of piano sonatas by Mozart. The unit is the second in the AA314 series of three units on this form of harmonic analysis, and concentrates on the ‘middleground level’ of voice leading. As you work through this unit, you will become familiar with the deeper levels of harm
1.2 Moving beyond the foreground
This unit continues our examination of ‘voice-leading’ or ‘Schenkerian’ analysis, perhaps the most widely-used and discussed method of analysing tonal music. In this unit, this method is explained through the analysis of piano sonatas by Mozart. The unit is the second in the AA314 series of three units on this form of harmonic analysis, and concentrates on the ‘middleground level’ of voice leading. As you work through this unit, you will become familiar with the deeper levels of harm
1.1 Voice-leading concepts
This unit continues our examination of ‘voice-leading’ or ‘Schenkerian’ analysis, perhaps the most widely-used and discussed method of analysing tonal music. In this unit, this method is explained through the analysis of piano sonatas by Mozart. The unit is the second in the AA314 series of three units on this form of harmonic analysis, and concentrates on the ‘middleground level’ of voice leading. As you work through this unit, you will become familiar with the deeper levels of harm
Learning outcomes
This unit continues our examination of ‘voice-leading’ or ‘Schenkerian’ analysis, perhaps the most widely-used and discussed method of analysing tonal music. In this unit, this method is explained through the analysis of piano sonatas by Mozart. The unit is the second in the AA314 series of three units on this form of harmonic analysis, and concentrates on the ‘middleground level’ of voice leading. As you work through this unit, you will become familiar with the deeper levels of harm
Introduction
This unit continues our examination of ‘voice-leading’ or ‘Schenkerian’ analysis, perhaps the most widely-used and discussed method of analysing tonal music. In this unit, this method is explained through the analysis of piano sonatas by Mozart. The unit is the second in the AA314 series of three units on this form of harmonic analysis, and concentrates on the ‘middleground level’ of voice leading. As you work through this unit, you will become familiar with the deeper levels of harm
