Sound Examples for
Tuning Timbre Spectrum Scale

1. The Octave is Dead... Long Live the Octave

[S: 1] Challenging the octave (challoct.mp3 0:24). The spectrum of a sound is constructed so that the octave between f and 2f is dissonant while the nonoctave f to 2.1f is consonant. See video [1].

[S: 2] A simple tune (simptun1.mp3 0:47). Harmonic timbres in the 12-tet scale set the stage for the next three examples. Chord pattern is taken from Plastic City , sound example [S: 38].

[S: 3] The "same" tune (simptun2.mp3 0:47). Harmonic timbres in the 2.1-stretched scale appear uniformly dissonant.

[S: 4] The "same" tune (simptun3.mp3 0:47). 2.1-stretched timbres are matched to the 2.1-stretched scale.

[S: 5] The "same" tune (simptun4.mp3 0:47). 2.1-stretched timbres in 12-tet appear uniformly dissonant.

2. The Science of Sound

[S: 6] Virtual pitch ascending (virtpitchup.mp3 0:22) Harmonic and inharmonic timbres alternate with sine waves at the appropriate virtual pitch. See Table 2.2 for a listing of all frequencies in this example.

[S: 7] Virtual pitch descending (virtpitchdown.mp3 0:22) Harmonic and inharmonic timbres alternate with sine waves at the appropriate virtual pitch. Comparing this example with shows how virtual pitch may be influenced by context. See Table 2.2 for a listing of all frequencies in this example.

3. Sound on Sound

[S: 8] Beating of sine waves I (beats1.mp3 0:24). See video [V: 5].

(a) A sine wave of 220 Hz (4 seconds),
(b) A sine wave of 221 Hz (4 seconds), and
(c) Sine waves (a) and (b) together (8 seconds).

[S: 9] Beating of sine waves II (beats2.mp3 0:24). See video [V: 5].

(a) A sine wave of 220 Hz (4 seconds),
(b) A sine wave of 225 Hz (4 seconds), and
(c) Sine waves (a) and (b) together (8 seconds).

[S: 10] Beating of sine waves III (beats3.mp 3 0:24). See video [V: 5].

(a) A sine wave of 220 Hz (4 seconds),
(b) A sine wave of 270 Hz (4 seconds), and
(c) Sine waves (a) and (b) together (8 seconds).

[S: 11] Dissonance between two sine waves (sinediss.mp3 1:06). A sine wave of fixed frequency 220 Hz is played along with a "sine wave" with frequency that begins at 220 Hz and slowly increases to 470 Hz. See video [V: 8]. Figure 3.6 provides a visual representation.

[S: 12] Dissonance between two sine waves: Binaural Presentation (sinedissbin.mp3 1:06). The same as [S: 11], except the sine wave of fixed frequency is panned completely to the right and the variable sine wave is panned completely to the left. Using headphones will ensure that only one channel is audible to each ear. The dissonance percept is still present, though diminished.

4. Musical Scales

[S: 13] Dream to the Beat (dreambeat.mp3 5:28). A 19-tet pop tune with a bass that beats like the heart. A microtonal love song.

[S: 14] Incidence and Coincidence (incidence.mp3 5:23). What happens when you play simultaneously in different tunings? Each note in this 19-tet melody is "harmonized" by a note from 12-tet, resulting in some unusual inharmonic sound textures. The distinction between "timbre" and "harmony" becomes confused, although the piece is by no means confusing.

[S: 15] Haroun in 88 (haroun88.mp3 3:36). In all 12-tet instruments (like the piano), there are 100 cents between adjacent steps. Haroun in 88 uses a tuning in which there are 88 cents between adjacent steps, a scale first explored by Gary Morrison. One feature of this scale is that it does not repeat at the octave - instead, it has 14 equal steps in a stretched "pseudo-octave" of 1232 cents. One way to exploit such "strange" tunings is to carefully match the tonal qualities of the sounds to the particular scale.

[S: 16] 88 Vibes (vibes88.mp3 3:47). Also in the 88 cent per tone tuning, 88 Vibes features a spectrally mapped "vibraphone."

[S: 17] Sonata K380 by Scarlatti (k380tet12.mp3 1:29). Performed in 12-tet in the key of C.

[S: 18] Sonata K380 by Scarlatti (K380JImajC.mp3 1:29). Performed in just intonation centered in the key of C.

[S: 19] Sonata K380 by Scarlatti (K380JIC+12.mp3 1:29). Performed in just intonation centered in the key of C and 12-tet simultaneously. The notes where the differences are greatest stand out clearly.

[S: 20] Sonata K380 by Scarlatti (K380JImajC+.mp3 1:29). Performed in just intonation centered in the key of C#.

[S: 21] Sonata K380 by Scarlatti (K380JImeanC.mp3 1:29). Performed in the quarter comma meantone tuning centered in the key of C.

[S: 22] Sonata K380 by Scarlatti (K380JImeanC+.mp3 1:29). Performed in the quarter comma meantone tuning centered in the key of C#.

[S: 23] Imaginary Horses (imaghorses.mp3 3:58). This sequence contains the harmonic spectra of a piano and a "perc flute" which are matched to the simple integer ratios

1/1 6/5 4/3 3/2 8/5 9/5 2/1

to form a Just Intonation scale that was called "solemn procession" by Lou Harrison. The consequence is a piano and synth duet with galloping piano riff and bucking synth lines that does not sound solemn to me.

[S: 24] Joyous Day (joyous.mp3 4:35). This uses the just intonation

1/1 9/8 5/4 3/2 5/3 15/8 2/1

created by Lou Harrison. To my ears, it is a majestic, extra-major sounding tuning.

[S: 25] What is a Dream? (whatdream.mp3 3:51). Although the ancient Greeks didn't record their music, they did write about it. They noticed the relationships between musical pitches and mathematical ratios. Some of the ancient scales fell into disuse, among them the "aeolic" scale, which uses the justly tempered pitches

1/1 9/8 32/27 4/3 3/2 128/81 16/9 2/1.

Lyrics expertly crafted by a non-ancient Greek, George Sethares.

[S: 26] Just Playing (justplay.mp3 2:52). In this piece, the 12 notes of the keyboard are mapped

 

cents:

0

19

205

267

386

498

583

702

766

884

969

1088

mapped to:

C

C#

D

D#

E

F

F#

G

G#

A

A#

B

interval:

1.0

1.011

1.125

1.167

1.25

1.33

1.4

1.5

1.56

1.67

1.75

1.87

ratio:

1/1

x/x

9/8

7/6

5/4

4/3

7/5

3/2

11/7

5/3

7/4

15/8

This includes all the ratios of the JI major scale, along with a few extras. The small interval between C and C#, for which there is no (small integer) just ratio, was used primarily for trills.

[S: 27] Signs (signs.mp3 3:41). One of the more prolific ancient Greeks (from the point of view of discovering and codifying musical scales) was Archytas, who lived about 400 B.C. Though his music has been lost, his tunings have survived. This song is played in one of Archytas' chromatic scales that is based on equal "tetrachords" (a set of four descending notes) with the intervals

28/27 243/224 32/27.

It is rather amazing that the sonorous beauty of scales such as this were surrendered by the European musical tradition for centuries in exchange for a keyboard that could be played equally in all keys.

[S: 28] Immanent Sphere (imsphere.mp3 4:17). Each note is an overtone of a single underlying fundamental.

[S: 29] Free from Gravity (freegrav.mp3 3:28). The melodic and harmonic motion conform to a simple additive scale, a regular lattice that organizes pitch space additively in frequency.

[S: 30] Intersecting Spheres (intersphere.mp3 3:33). The basic timbre is harmonic and all partials of all tones are integer multiples of 50 Hz. The tuning is similarly a spectral scale consisting of all multiples of 50 Hz (though only a small subset are actually used.) The timbres were created using additive-style synthesis with the program Metasynth, and the results were passed through various nonlinearities in Matlab. This causes many new overtones at ever higher frequencies which eventually hit the fold over frequency (22050 for normal CD recording) and begin descending. Because 22050 is divisible by 50, when the partials fold back, they still lie on the same 50 Hz lattice - they just augment (or decrease) the amplitude of the partials. So no matter how many nonlinearities are used, the sound remains within the same harmonic template. Much of the character (the "hair-raising on end") of the timbres is due to this unorthodox method of creating the sounds.

[S: 31] Over Venus (overvenus.mp3 4:25). This melody floats above a single low tone, playing on the multidimensional harmonics.

[S: 32] Pulsating Silences (pulsilence.mp3 3:33). A single living note that changes without moving, that grows while remaining still. Even if there were only one note, there would still be music.

[S: 33] Overtune (overtune.mp3 3:54). Additive synthesis can create very precise and clean sounds. All partials are from the same harmonic series.

[S: 34] Fourier's Song (fouriersong.mp3 3:54). Also known as Table 4.1: Properties of the Fourier Transform, this song was written by Bob Williamson and Bill Sethares "because we love Fourier Transforms, and we know you will too." Perhaps you've never taken a course where everything is laid out in a single song. Well, here it is... a song containing 17% of the theoretical rests, 25% of the practical insights, and 100% of the humor of ECE330: Signals and Systems. The music is played in an additive (overtone) scale that consists of all harmonics of 100 Hz. Lyrics appear in Appendix K.

7. Related Spectra and Scales

[S: 35] Tritone dissonance curve (tridiss.mp3 1:06). This is the auditory version of Fig. 6.2. See video [V: 9].

[S: 36] Tritone chime (trichime.mp3 0:37). First, you hear a single note of the "tritone chime." Next, the chime plays the three chords from Fig. 6.3. The chords are then repeated using a more "organ-like" tritone timbre. See video [V: 10].

[S: 37] Tritone chord patterns (trichord.mp3 0:52). This sound example presents two chord patterns, each repeated once. Which passage appears more consonant, the major or the diminished?

(a) F major, C major, G major, C major
(b) C dim, D dim, D# dim, C dim

Which of the next two patterns feels more resolved?

(c) C dim, C major, C dim, C major, or
(d) C major, C dim, C major, C dim

Musical scores for these four segments are given in Fig. 6.4.

[S: 38] Plastic City: A Stretched Journey (plasticity.mp3 6:00). The "same" piece is played with harmonic sounds in 12-tet, with 2.2-stretched sounds, with 1.87-compressed sounds, and finally with 2.1-stretched sounds, all in their respective stretched or compressed tunings.

[S: 39] October 21st (october21.mp3 1:42). There are no real octaves (defined as a frequency ratio of 2 to 1) anywhere in this piece. The sounds in October 21st are constructed so that the octave between f and 2f is dissonant, while the nonoctave between f and 2.1f is consonant. Thus the unit of repetition is a "stretched pseudo-octave" with a frequency ratio of 2.1 to 1. Since the structure of the timbres are matched to the structure of the scale, these nonoctave intervals can be consonant, even as the (real) octave is dissonant. The same 2.1-stretched tones were demonstrated in [S: 1]-[S: 5].

[S: 40] A note with partials at 4:5:6:7 (4567.mp3 0:08). This note/chord is built from four sine wave partials with frequencies 400, 500, 600, and 700 Hz.

[S: 41] A note with partials at 1/7:1/6:1/5:1/4 (7654.mp3 0:08). This note/chord is built from four sine wave partials with frequencies 400, 467, 560, and 700 Hz.

[S: 42] 4:5:6:7 vs. 1/7:1/6:1/5:1/4 (4567_7654.mp3 0:16). The two notes from sound examples and alternate. Which is more consonant?

8. A Bell, A Rock, A Crystal

[S: 43] Tingshaw (tingshaw.mp3 4:03). The tingshaw is a small handbell with a bright and cheerful ring, and it is played in a scale determined by the spectrum of the bell itself. Tingshaw is discussed extensively in Chap. 7.

[S: 44] Chaco Canyon Rock (chacorock.mp3 3:38). Piece based on the rock described at length in Chap. 7.

[S: 45] Duet for Morphine and Cymbal (morphine.mp3 3:21). Each angle in an x-ray diffraction pattern can be mapped to an audible frequency, transforming a crystalline structure into sound. In this piece, complex clusters of tones derived from morphine crystal resonances are juxtaposed over a rhythmic bed supplied by the more percussive timbre of the cymbal. The mapping technique is described at length in Chap.7.

9. Adaptive Tunings

[S: 46] Adaptation of stretched timbres: minor chord (streminoradapt.mp3 0:06) Stretched timbres play a 12-tet minor chord. After adaptation this converges to the stretched minor chord detailed in Table 8.2.

[S: 47] Adaptation of stretched timbres: major chord (stremajoradapt.mp3 0:06) Stretched timbres play a 12-tet major chord. After adaptation this converges to the stretched major chord detailed in Table 8.2.

[S: 48] Circle of fifths in 12-tet (circle12tet.mp3 0:38) The circle of fifths moves through all twelve keys, demonstrating one of the great strengths of 12-tet: reasonable consonance in all keys.

[S: 49] Circle of fifths in C major just intonation (circleJICmaj.mp3 0:38) The circle of fifths demonstrates one of the liabilities of JI: keys which are distant from the tonal center are unusable.

[S: 50] Circle of fifths in adaptive tuning (circleadapt.mp3 0:38) Applying adaptation to the circle of fifths allows all chords to maintain the simple integer ratios, combining the best of 12-tet (modulation to all keys) with the consonance of JI.

[S: 51] Syntonic comma example: JI (syntonJIdrift.mp3 0:43) Each repeat of the phrase in Fig. 8.7 the tuning drifts lower.

[S: 52] Syntonic comma example: 12-tet (synton12tet.mp3 0:21) The phrase of Fig. 8.7 is performed in 12-tet.

[S: 53] Syntonic comma example: adaptive tuning (syntonadapt.mp3 0:21) The phrase of Fig. 8.7 does not drift yet maintains fidelity to the simple integer ratios when played in adaptive tuning with harmonic sounds.

[S: 54] Listening to adaptation (listenadapt.mp3 0:32). Each note has a spectrum containing four inharmonic partials at f,  1.414f,  1.7f,  2f. Three notes are initialized at the ratios 1, 1.335, and 1.587 (the 12-tet scale steps C, F, and Gb) and allowed to adapt. The final adapted ratios are 1, 1.414, and 1.703. The adaptation is done three times:

(a) with extremely slow adaptation (very small stepsize), (b) slow adaptation, and (c) medium adaptation.

[S: 55] Scarlatti's K1 Sonata in 12-tet . (k001tet12.mp3 0:32) The first phrase of the sonata. See Fig. 8.10.

[S: 56] Scarlatti's K1 Sonata in adaptive tuning (k001adaptX.mp3 0:32) Poor choice of stepsizes can lead to wavering pitches in the adaptive tuning. See Fig. 8.10.

[S: 57] Scarlatti's K1 Sonata in adaptive tuning . (k001adapt.mp3 0:32) Better choices of stepsizes can ameliorate the wavering pitches. See Fig. 8.10.

[S: 58] Wavering pitches (waverpitch.mp3 0:21). The second measure of Domenico Scarlatti's harpsichord sonata K1 is played three ways:

(a) Scarlatti's K1 sonata in 12-tet. (b) Scarlatti's K1 sonata with adaptation. Observe the wavering pitch underneath the trill at the end of the second measure. (c) Scarlatti's K1 sonata with adaptation, modified so that "new" notes are adapted 10 times as fast as held notes. The wavering pitch is imperceptible.

[S: 59] Sliding pitches (slidepitch.mp3 0:45). The kinds of pitch changes caused by the adaptive tuning algorithm are often musically intelligent responses to the context of the piece.

(a) A simple chord sequence from F major to G major is transformed by the adaptive tuning algorithm. The sliding pitch of one note stands out. Each measure is played separately, then in together. (b) The adaptive tuning algorithm "changes" the chord on the fourth beat.

[S: 60] Three Ears (three_ears.mp3 4:24). As each new note sounds, its pitch (and that of all currently sounding notes) is adjusted microtonally (based on its spectrum) to maximize consonance. The adaptation causes interesting glides and microtonal pitch adjustments in a perceptually sensible fashion. Listen for the two previous segments from [S: 59]. Many similar effects occur throughout.

10. A Wing, An Anomaly, A Recollection

[S: 61] Adaptive Study No. 1 (adapt_study1.mp3 2:36) Example of the pitch glides and wavering pitches using Adaptun.

[S: 62] Adaptive Study No. 2 (adapt_study2.mp3 2:28) Using Adaptun's context feature, the wandering of the pitch is reduced.

[S: 63] Compositional technique: example 1 (breakdrums1.mp3 0:10) A standard MIDI drum file from the Keyfax Software 'Breakbeat' collection is performed using drum sounds. See Fig. 9.3.

[S: 64] Compositional Technique: Example 2 (breakdrums2.mp3 0:10) The same MIDI file as in is reochestrated with guitar and bass guitar.

[S: 65] Compositional technique: example 3 (breakmap1.mp3 0:20) Editing the MIDI data in Fig. 9.3 leads to the sequence in Fig. 9.4. The original cymbal part is time stretched and offset in pitch.

[S: 66] Compositional technique: example 4 (breakmap2.mp3 0:20) A variant of [S: 65].

[S: 67] Compositional technique: example 5 (breakmap3.mp3 0:20) Another variant of [S: 65].

[S: 68] Compositional technique: example 6 (breakadapt1.mp3 0:23) Adaptation the standard MIDI file of Fig. 9.4 using no context and default settings in Adaptun.

[S: 69] Compositional technique: example 7 (breakrand1.mp3 0:20) The sequence in Fig. 9.4 and sound example is transformed by randomizing the bass line over an octave.

[S: 70] Compositional technique: example 8 (breakrand2.mp3 0:20) Randomization of the 'fast' line in Fig. 9.4 leads to this arpeggiated guitar.

[S: 71] Compositional technique: example 9 (breakrand3.mp3 0:20) Randomization of the 'slow' line in Fig. 9.4 leads to this synthesized melody.

[S: 72] Compositional technique: example 10 (breakadapt2.mp3 0:21) After adaptation, example [S: 9] sounds very different.

[S: 73] Compositional technique: example 11 (breakadapt3.mp3 0:47) Sound example is adapted with full convergence of the algorithm. The sound example is played twice: first without the melody, and then with.

[S: 74] Adventiles in a Distorium (adventiles.mp3 4:46) An adaptively tuned composition featuring frenetically distorted guitars.

[S: 75] Aerophonious Intent (aerophonious.mp3 3:24) An adaptively tuned composition orchestrated using an extreme form of hocketing.

[S: 76] Story of Earlight (earlight.mp3 3:53) An adaptively tuned recitation of whispers and flutes.

[S: 77] Excitalking Very Much (excitalking.mp3 3:32) An adaptively tuned conversation between a synthetic bass and a synthetic clarinet.

[S: 78] Inspective Liquency (inspective.mp3 3:46) An adaptively tuned piece where no note remains fixed.

[S: 79] Local Anomaly (localanomaly.mp3 3:27) This piece was created from a standard MIDI drum track, which was randomized and orchestrated using various percussive stringed sounds such as sampled guitars and basses. The extremely dissonant but highly rhythmic soundscape was input into Adaptun, and the notes adapted towards consonance. No context was used.

[S: 80] Maximum Dissonance (maxdiss.mp3 3:24). Instead of minimizing the dissonance, this piece maximizes the dissonance at every time instant.

[S: 81] Persistence of Time (persistence.mp3 4:54) Polyrhythms beat three against two, a paleo-futuristic audio conundrum where all intervals adapt to maximize instantaneous consonance.

[S: 82] Recalled Opus (recalledopus.mp3 3:45) At each instant in time, these "violins" strive to minimize dissonance.

[S: 83] Saint Vitus Dance (saintvitus.mp3 3:32). Begin with a MIDI drum pattern. Use the pattern to trigger a sampled guitar sound - it is wildly dissonant since the pitches are essentially random. At each time instant, perturb the pitches of all currently sounding notes to the nearest intervals that maximize consonance. Thus is born an adaptively tuned dance.

[S: 84] Simpossible Taker (simpossible.mp3 3:20) An adaptively tuned composition that began as a hip hop drum pattern.

[S: 85] Wing Donevier (wing.mp3 3:17) An adaptively tuned composition in seven beats per measure.

13. Spectral Mappings

[S: 86] 11-tet spectral mappings: before and after (tim11tet.mp3 1:20). Several different instrumental sounds alternate with their 11-tet spectrally mapped versions:

(a) harmonic trumpet compared to 11-tet trumpet. (b) harmonic bass compared to 11-tet bass. (c) harmonic guitar compared to 11-tet guitar. (d) harmonic pan flute compared to 11-tet pan flute. (e) harmonic oboe compared to 11-tet oboe. (f) harmonic 'moog' synth compared to 11-tet 'moog' synth. (g) harmonic 'phase' synth compared to 11-tet 'phase' synth.

[S: 87] 12-tet vs. 11-tet (tim11vs12.mp3 0:37). A short sequence of major chords are played:

(h) harmonic oboe in 12-tet (i) spectrally mapped 11-tet oboe in 12-tet

The next segments contain 11-tet dyads formed from scale steps 0-6 and 0-7, and culminate in a chord composed of scale steps 0-4-6.

(j) harmonic oboe in 11-tet. (k) spectrally mapped 11-tet oboe in 11-tet.

[S: 88] The Turquoise Dabo Girl (dabogirl.mp3 4:16). Many of the kinds of effects normally associated with (harmonic) tonal music can occur, even in such strange settings as 11-tet (which is often considered among the hardest tunings in which to play tonal music). Consider, for instance, the harmonization of the 11-tet pan flute melody that occurs in the 'chorus.' Does this have the feeling of some kind of (perhaps unfamiliar) 'cadence' as the melody resolves back to its 'tonic'? Spectral mapping of the instrumental sounds allows such xentonal motion.

[S: 89] The Turquoise Dabo Girl (first 16 bars) (dabogirlX.mp3 0:29). In 11-tet, but using unmapped harmonic sounds. The 'out-of-timbre' percept is unmistakable.

[S: 90] Tom Tom Spectral Mappings: Before and After (tomspec.mp3 0:37 ). Several different instrumental sounds alternate with versions mapped into the spectrum of a tom tom:

(a) harmonic flute compared to tom tom flute. (b) harmonic trumpet compared to tom tom trumpet. (c) harmonic bass compared to tom tom bass. (d) harmonic guitar compared to tom tom guitar.

[S: 91] Glass Lake (glasslake.mp3 3:08). Instruments which are spectrally mapped "too far" can lose their tonal integrity. When guitars, basses and flutes are transformed into the partial structure of a drum (a tom tom), they are almost unrecognizable. But this does not mean that they are useless. All sounds in this piece (except for the percussion) were demonstrated in [S: 90]. The "tom tom" scale supports perceptible "chords," though the chords are not necessarily composed of familiar intervals. Tom Staley played a key role in writing and performing Glass Lake.

[S: 92] A harmonic cymbal (harmcym.mp3 0:23). A cymbal is spectrally mapped into a harmonic spectrum. The resting sound is pitched and capable of supporting melodies and chords.

(a) the original cymbal contrasted with the spectrally mapped version. (b) a simple 'chord' pattern played with the original, and then with the spectrally mapped version.

[S: 93] Sonork (sonork.mp3 3:15). The origin of each sound is a cymbal, spectrally mapped to nearby harmonic templates to create the bass, synth, and other instrumental sounds.

[S: 94] Inharmonic drum (inharmdrum.mp3 0:59). This drum sound is incapable of supporting melody or harmony.

[S: 95] Harmonic drum (harmdrum.mp3 1:29). The drum sound from [S: 94] is spectrally mapped to the nearest harmonic template. It can now support both melody and harmony.

[S: 96] Harmonic and inharmonic drum (harm+inharm.mp3 1:29). The sounds from (the original inharmonic drum) and (the spectrally mapped version) are combined.

[S: 97] Hexavamp (hexavamp.mp3 3:22). A "classical" guitar is spectrally mapped into 16-tet and overdubbed with itself.

[S: 98] Seventeen Strings (17strings.mp3 3:22). A sampled Celtic harp is transformed for compatibility with 17-tet.

[S: 99] Unlucky Flutes (13flutes.mp3 3:51). Flutes, guitars, bass, and keyboards are spectrally mapped into 13-tet. All instruments clearly retain their tonal identity, yet sound harmonious even on sustained passages. Compare to the 13-tet demonstration on Carlos' Secrets of Synthesis which is introduced, "But the worst way to tune is probably this temperament of 13 equal steps."

[S: 100] Truth on a Bus (truthbus.mp3 3:22). A 19-tet guitar piece that is unabashedly diatonic. If you weren't listening carefully, you might imagine that this was a real guitar, tuned normally, and played skillfully. You would be very wrong.

[S: 101] Sympathetic Metaphor (sympathetic.mp3 3:59). This guitar has 19 tones in each octave, the melody dances pensively on a delicately balanced timbre. Peter Kidd plays the excellent fretless bass.

14. A "Music Theory" for 10-tet

[S: 102] Ten Fingers (tenfingers.mp3 3:18). Demonstrates the kind of consonance effects achievable in 10-tet. The guitar-like 10-tet timbre is created by spectrally mapping a sampled guitar into an induced spectrum. The full title of this piece is "If God Had Intended Us To Play In Ten Tones Per Octave, Then He Would Have Given Us Ten Fingers."

[S: 103] Ten Fingers: harmonic guitar (tenfingersX.mp3 0:28). The first 16 bars of Ten Fingers are played with a harmonic (sampled) guitar. The out-of-spectrum effect is unmistakable.

[S: 104] Circle of Thirds (circlethirds.mp3 3:41). There is an interesting and beautiful chord pattern in 10-tet that is analogous to (but very different from) the traditional circle of fifths. This piece cycles around the Circle of Thirds over and over: first fast, then slow, and then fast again.

[S: 105] Isochronism (isochronism.mp3 3:55). When there are ten equal tones in each octave, special tone colors are needed to align the partials into consonant patterns..

[S: 106] Anima (anima.mp3 4:03). Uses modified timbres to effect a balance between coherence and chaos, between the obvious and the obscure. Exploits the 10-tet tritone chords.

[S: 107] Swish (swish.mp3 3:20). Timbres constructed in Metasynth swirl and mutate as the piece evolves in 5-tet, which is analogous to a wholetone scale inside 10-tet.

15. Classical Music of Thailand and 7-tet

[S: 108] Tuning of a classical Thai piece (thai7tet.mp3 0:28). Demonstrates the procedure whereby the tuning of a piece can be found from the recording. Begins with the first 10 seconds of "Sudsaboun" and then separates the melody into individual notes, each of which is compared to a sine wave to determine its pitch. See Sect. 15.2.

[S: 109] Comparison of harmonic sounds and their spectrally mapped 7-tet versions. (7tetcompare.mp3 0:25). Three instruments are demonstrated:

(a) three different notes of a bouzouki,
(b) three different notes of a harp, and
(c) a pan flute.

[S: 110] Comparison between 7-tet and a 12-tet major scale (7vs12.mp3 1:19 ). The theme of the simple tune from sound example [S: 2]-[S: 5] is played first in 12-tet and then in 7-tet, using the 'naive' mapping between 7-tet and the diatonic (major) scale defined in (15.2) and using harmonic timbres.

[S: 111] Comparison between 7-tet and a 12-tet major scale (7vs12bar.mp3 1:19). The theme of the simple tune from sound example is played first in 12-tet and then in 7-tet, using the 'naive' mapping between 7-tet and the diatonic (major) scale defined in (15.2) with timbres have been mapped to the spectrum of an ideal bar.

[S: 112] Scarlatti's K380 in 7-tet (K380tet7.mp3 1:29). Using the 'naive' mapping between 7-tet and the diatonic (major) scale of (15.2), Scarlatti's theme looses its harmonic meaning. The timbres are harmonic.

[S: 113] Scarlatti's K380 in 7-tet (K380tet7bar.mp3 1:29). Using the 'naive' mapping between 7-tet and the diatonic (major) scale of (15.2), Scarlatti's theme looses its harmonic meaning. The timbres have been mapped to the spectrum of an ideal bar.

[S: 114] Scarlatti's K380 in 12-tet (K380tet12bar.mp3 1:29). This performance of K380 uses timbres that have been mapped to the spectrum of an ideal bar.

[S: 115] March of the Wheels (marwheel.mp3 3:38). The notes of a standard MIDI drum track are mapped into the 7-tet scale, creating the rhythmic foundation for this piece. The notes are randomized, creating a variety of serendipitous melodies.

[S: 116] Pagan's Revenge (pagan.mp3 3:55). The notes of a standard MIDI file (Paganini's Caprice No.24 performed by D. Lovell) are mapped into 7-tet, creating the foundation for this piece. At the half way point, the MIDI data in the file was time reversed so that the theme proceeds forwards and then backwards - finally ending on the first note.

[S: 117] Nothing Broken in Seven (broken.mp3 3:29). A single six note isorhythmic melody is repeated over and over, played simultaneously at five different speeds.

[S: 118] Phase Seven (phase7.mp3 3:41). A single eight note isorhythmic melody is repeated over and over, played simultaneously at five different speeds.