SHOSYS ACADEMY 8 LESSON: Conventions Of Tone Labeling
Kelvin Sholar
1 Introduction To The Blog Series
This series of lessons and tests incorporates an easy music appreciation curriculum for adult beginners who are remote learning, or are self-taught. Lessons are posted on Mondays while Tests are posted on Saturdays. For more in depth and private guidance, I offer personal instruction by Zoom (Personal Meeting ID 8522954569) – for 1 dollar a minute. Time schedules range from a minimum of 30 minutes to a maximum of 60 minutes. Email me at [email protected] to set up personal instruction. I accept payments and cash gifts by Cash App ($KelvinSholar), Zelle ([email protected]) or Paypal (paypal.me/kelvinsholar).
2 Revisiting The Tree Of Knowledge
In Lesson 7, we learned about conventions of Italian navigation markings. In this Lesson, we will learn about conventions of pitch labeling. This knowledge resides in the Ways branch (1.20) of the Tree of Knowledge (1.00), at the third leaf from the left (1.21) – Conventions.
2.1 Conventions Of Tone Labeling
In western music there are the twelve tones from which harmonies are made. In England and America, tones are traditionally named relative to the first seven letters of the Roman (i.e. Latin) alphabet: A B C D E F G. In ancient Italy, Guido D’Arezzo created word names or Solfeggio for tones; they are based on the first syllable of each line of the first verse of the Latin hymn “Ut Queant Laxis”: “Ut queant laxīs, resonāre fibrīs, Mīra gestōrum, famulī tuōrum, Solve pollūtī, labiī reātum, Sāncte Iōhannēs”
(Loy 292). For this reason, continental Europeans use seven basic Solfeggio syllables for the tones of a given major scale (here the A Major scale tones are shown):
- A=Do (instead of Ut),
- B=Re,
- C#=Mi,
- D=Fa,
- E=So,
- F#=La,
- G#=Si (or Ti in England and America – via the changes made by English teacher Sara Glover).
Solfeggio must be altered to define the twelve tones of equal temperament. Likewise, “Accidentals” like sharps, naturals and flats need to be adjoined to the seven Roman letters in order to define the twelve tones of equal temperament tuning: A, A# or Bb, B or Cb, C# or Db, D, D# or Eb, E, F, F# or Gb, G, G# or Ab. Note that in cases where there are two choices of name then they are called enharmonic; like A# and Bb or F# and Gb (Miller 18).
Instead of naming twelve tones relative to seven Roman letters and three accidentals (sharps and flats), of texts of a Latin Hymn, we could use the first twelve Roman letters to represent the twelve tones of equal temperament if necessary:
- A=A,
- A#=Bb=H,
- B=B,
- C=C,
- C#=Db=I,
- D=D,
- D#=Eb=J,
- E=E,
- F=F,
- F#=Gb=K,
- G=G,
- G#=Ab=L.
The twelve tones used in Western music can be labeled by twelve nonnegative numbers, or integers modulo twelve (Loy 301):
- 0=A=A,
- 1=A#=Bb=H,
- 2=B=B,
- 3=C=C,
- 4=C#=Db=I,
- 5=D=D,
- 6=D#=Eb=J,
- 7=E=E,
- 8=F=F,
- 9=F#=Gb=K,
- A=G=G,
- B=G#=Ab=L.
The main advantage of designating twelve tones with integers modulo twelve is that each tone is numbered by its ordinal position within the chromatic scale.
3 Bibliography
Bloom, B. S.; Engelhart, M. D.; Furst, E. J.; Hill, W. H.; Krathwohl, D. R. Taxonomy Of Educational Objectives: The Classification Of Educational Goals. Handbook I: Cognitive Domain. New York: David McKay Company, 1956
Loy, Gareth. Musimathics The Mathematical Foundations of Music: Volume 1. Cambridge, Massachusetts: The MIT Press, 2006
Miller, Michael. The Complete Idiots Gude To Music Theory. New York: Alpha Books, 2005