August 2021 Tonalibus update

This August 2021 Tonalibus update first touches briefly on the new album Tonalibus A, B, & C. Then it presents a new personal and two new cooperation sound samples. Further it highlights the current expansion of the tonalities catalogue. This is a work in progress and linked to ongoing research and experimentation with harmonics or overtones, including reciprocals, inverse and nested relations.

Tonalibus A, B, & C — the album released

Tonalibus A, B, & C - album

The album Tonalibus A, B, & C with its thirty-one personal sound samples by Ulrico is available globally on many music platforms, e.g., Spotify, YouTube Music, Apple Music, Deezer, and more. You can find links to the main platforms and a detailed listing of the tracks in the Fidibus Shop entry for the album Tonalibus A, B, & C. May you enjoy these sounds — heart to heart, soul to soul!

New personal and cooperation sound samples

“Natural harmonics gateway” — first step in a Na tonality

PentaPro / PentaNa — triple 8-string guitar — July 2021 — 4:36 — as loop on a separate tab

“Christina’s theme” — a work in progress

Melodic theme in D minor / Aeolian and voice by Christina Braun, 6 and 8-string guitar by Ulrico — August 2021 — 8:49

“Hallo Stille [Hello silence]” — a booklet by Nicole Keller

Text by Nicole Keller, voice by Karin Gsöllpointner, 8-string guitar in C# Mixolydian by Ulrico — August 2021 — 5:09

Tonalities catalogue expansion

The Tonalibus catalogue of anchored tonalities is in the process of being significantly expanded. As a result of further researching the natural harmonic or overtone series a new group of tonalities became evident. Tonalibus chose its name to be Na tonalities, with Na for natural harmonics.

Harmonics or overtones and resonance are fundamental to harmony. Therefore, Na tonalities are uniquely harmonious. Ideally, they span over multiple octaves, at least three or four. They follow the sequence of natural harmonics or overtones and form an arch with secondary harmonics turning into tertiary ones (or reciprocals). Thus they lead to more commonly known tonalities. Na(tural harmonics) tonalities and other additions will soon appear in the Tonalibus catalogue.

Finding these tonalities was like mining ore. New tonalities kept leading to others like in a main strand of ore. Plus there were also side strands leading to further tonalities outside the Na group qualifying to be added to the catalogue. Eventually though they all led to already existing tonalities, which strengthens the validity of the catalogue as it is.

In total, so far this brought forth close to twenty additional tonalities qualifying for the Tonalibus catalogue, including a few existing tonality name adjustments. Thus, PentaPro or PentaNa, the tonality of the current month of August, received its second name, PentaNa. And the group of clustered or melodic tonalities expands to include also two super-clustered tonalities with a step pattern of five consecutive whole steps and two consecutive half steps.

The following two visuals present the group of Na tonalities and their main modulation path that fully follows the natural harmonics series.

Tonalibus 1e-3 tonalities – 2023-11 – 82
Tonalibus 1e-3 tonalities – 2023-11 – 81
Tonalibus 1e-3 tonalities – 2023-11 – 83x
Tonalibus 1e-3 tonalities – 2021-08 – 75y
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Tonalibus 1e-3 tonalities - 2023-11 - 82
Tonalibus 1e-3 tonalities - 2023-11 - 81
Tonalibus 1e-3 tonalities - 2023-11 - 83x
Tonalibus 1e-3 tonalities - 2021-08 - 75y
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The numbers in the above visuals represent the halftone positions of a tonality’s pitches within their vertically, top-down depicted octave.

Reciprocal harmonics — fascinating relationships

Current Tonalibus research focuses among other things on reciprocal harmonics. These are mirror image or inverse harmonic relationships.

The most significant example of this is the quart (perfect fourth). It carries its fundamental octave as primary harmonic, its quint (perfect fifth). However, the quart itself is but the second last pitch of the occidental twelve-tone system to appear approximately in the harmonic or overtone series as the twenty-first harmonic or overtone and one of the four most deviating ones. Nevertheless, besides the quint, the quart is one of the two primary anchors of a tonality, as the tonality’s fundamental is its reciprocal quint. Tonalibus calls the quart the regressive tonality anchor, because it shows where a tonality comes from. The quart in a way creates the fundamental. But then it has to contend with being one of the least harmonious pitches in the resulting tonality’s harmonic series. This can be called the generational interplay of harmony, the theme of a previous blog post.

The above may lead one to look for and recognize corresponding relationships of harmony in life in other contexts beyond music. But this goes beyond the current scope of Tonalibus and you may contemplate this as you see fit.

Similarly fascinating harmonic relationships can be observed between the major sixth and major third, between the minor third and minor seventh, as well as between other pitches. Relationships of this kind go beyond mere concepts. They are based on physically measurable observations that can be reproduced. More about this may come out in future Tonalibus posts.

Best wishes to conclude this August 2021 Tonalibus update

„Schläft ein Lied in allen Dingen, [Sleeps a song in things abounding,]
Die da träumen fort und fort, [that keep dreaming to be heard,]
Und die Welt hebt an zu singen, [Earth’s tunes will start resounding,]
Triffst du nur das Zauberwort. [if you but find the magic word.]“

— Joseph Freiherr von Eichendorff, Wünschelrute, 1835

August 2021 Tonalibus Update
Forests, fields, a horizon of mountains, and the silhouette of a lonely birch — Grächwil/Meikirch, Switzerland